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"cells": [
{
"cell_type": "markdown",
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"source": [
"## Lesson 07 - GLMs, Linear Optimization and Clustering\n",
"\n",
"Welcome to lesson 8! We will continue on with our application of what we have learned so far to statistical analysis of our data.\n",
"\n",
"Today we will cover Generalised Linear Models (in the form of logistic regression), Linear Optimization using NumPy, and clustering using UPGMA and Kmeans in scikit-learn.\n",
"\n",
"Download the [notebook here](/pythoncourse/assets/notebooks/applied/lesson 07.ipynb).\n",
"\n",
"### Generalised Linear Models\n",
"\n",
"Linear models can be extended to fit certain non-linear data, using GLMs.\n",
"\n",
"To do this, we need a 'link' function, which gives us a linear response. For today we will use a logistic regression, but we have a [wide array of link functions available](http://statsmodels.sourceforge.net/devel/glm.html#families).\n",
"\n",
"We use logistic regression where we have a binomial output - 0 or 1. For example whether a patient is sick (1) or not (0) relates to their temperature (continuous), but not in a linear fashion.\n",
"\n",
"Let's do some imports:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pandas import Series, DataFrame\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"import statsmodels.formula.api as smf\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import seaborn as sns\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will read in some college admissions data. This data shows whether an applicant was admitted to a college or not, their gre and gpa, and a categorical ranking of the college by 'prestige'.\n",
"\n",
"We are interested in the relationship between admission, gpa, gre and prestige."
]
},
{
"cell_type": "code",
"execution_count": 167,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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" admit gre gpa prestige\n",
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"source": [
"df = pd.read_csv(\"http://www.ats.ucla.edu/stat/data/binary.csv\")\n",
"df.columns = [\"admit\", \"gre\", \"gpa\", \"prestige\"]\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pandas has a crosstab function, which is useful for tabulating data based on categorical variables. Here we tabulate admit and prestige, before plotting out our data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"pd.crosstab(df['admit'], df['prestige'], rownames=['admit'])"
]
},
{
"cell_type": "code",
"execution_count": 168,
"metadata": {
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TswhL2ITIHaXJVsxsMkHh8VIz+zKwBDgqRnmeSkjG0Qec5SWpDIVoJ1I5/CjJ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\nKbA+4Xt4Pss6GkEljR0zexW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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df.hist();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can carry out our regression - we will model admission as a response of gre, prestige (as a categorical variable) and gpa.\n",
"\n",
"To do this we can use the formula interface, similar to last week, and using the glm function with the family specified as Bionomial:"
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: admit No. Observations: 400\n",
"Model: GLM Df Residuals: 394\n",
"Model Family: Binomial Df Model: 5\n",
"Link Function: logit Scale: 1.0\n",
"Method: IRLS Log-Likelihood: -229.26\n",
"Date: Fri, 25 Mar 2016 Deviance: 458.52\n",
"Time: 09:57:37 Pearson chi2: 397.\n",
"No. Iterations: 6 \n",
"====================================================================================\n",
" coef std err z P>|z| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------------\n",
"Intercept -3.9900 1.140 -3.500 0.000 -6.224 -1.756\n",
"C(prestige)[T.2] -0.6754 0.316 -2.134 0.033 -1.296 -0.055\n",
"C(prestige)[T.3] -1.3402 0.345 -3.881 0.000 -2.017 -0.663\n",
"C(prestige)[T.4] -1.5515 0.418 -3.713 0.000 -2.370 -0.733\n",
"gre 0.0023 0.001 2.070 0.038 0.000 0.004\n",
"gpa 0.8040 0.332 2.423 0.015 0.154 1.454\n",
"====================================================================================\n"
]
}
],
"source": [
"#using smf\n",
"logit = smf.glm('admit ~ gre + C(prestige) + gpa', family=sm.families.Binomial(), data = df)\n",
"print(logit.fit().summary())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is difficult to plot two continuous variables against each other: here we will use seaborn to plot the effects of gre and gpa seperately:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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V4jhO3Fq74qAhiikyZIz5uUtuenPJut+V9Lv9rQhAv1hrNT2XUiN0mW+5A2ut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yYX4AHQgu1Wx87MrbgNLBbJo94nbUXys1PV2O+3b8/M1eG4Xmy7VbVuxwrQ1bod23/87BwmZ6rR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\nIiIiIiIiIiIi6sj/BxzZV3lnbKj1AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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wcRPjvW6OiIiIiIiIiEjfqNZqZPMlGpGN445veAJYCWYRGRjGGFLpLNUGuO44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\nT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33A9X1fPyQRkV2imCsi0h+KtyIi/aF4K0edWjCLbM0y8ITneS97\nnvdNYBr4k+Zz1v4VS0TkSFLMFRHpD8VbEZH+ULyVI00tmEVERERERERERERkR9SCWURERERERERE\nRER2RAlmEREREREREREREdkRJZhFREREREREREREZEeUYBYRERERERERERGRHVGCWURERERERERE\nRER25P8HqcMe+t7oyCwAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plot\n",
"g = sns.lmplot(x=\"gre\", y=\"admit\", col=\"prestige\", data=df, y_jitter=.02, logistic=True)\n",
"f = sns.lmplot(x=\"gpa\", y=\"admit\", col=\"prestige\", data=df, y_jitter=.02, logistic=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To use the non-formula interface, we need to create dumm variables. Dummy variables allow us to treat categorical variables as 1s and 0s by adding on more factors:"
]
},
{
"cell_type": "code",
"execution_count": 170,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" prestige_1 | \n",
" prestige_2 | \n",
" prestige_3 | \n",
" prestige_4 | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" 1 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" 2 | \n",
" 1.0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 0.0 | \n",
"
\n",
" \n",
" 3 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
" 4 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" prestige_1 prestige_2 prestige_3 prestige_4\n",
"0 0.0 0.0 1.0 0.0\n",
"1 0.0 0.0 1.0 0.0\n",
"2 1.0 0.0 0.0 0.0\n",
"3 0.0 0.0 0.0 1.0\n",
"4 0.0 0.0 0.0 1.0"
]
},
"execution_count": 170,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#we can also do it using the non-formula interface:\n",
"dummy_ranks = pd.get_dummies(df['prestige'], prefix='prestige')\n",
"dummy_ranks.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To avoid multi-colinearity, we must remove one of the dummy variables.\n",
"\n",
"We also need to manually add an intercept column if we wish to allow for an intercept term in our model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" admit | \n",
" gre | \n",
" gpa | \n",
" prestige_2 | \n",
" prestige_3 | \n",
" prestige_4 | \n",
" intercept | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 0 | \n",
" 380 | \n",
" 3.61 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
" 1 | \n",
" 1 | \n",
" 660 | \n",
" 3.67 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
" 2 | \n",
" 1 | \n",
" 800 | \n",
" 4.00 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
" 3 | \n",
" 1 | \n",
" 640 | \n",
" 3.19 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
" 4 | \n",
" 0 | \n",
" 520 | \n",
" 2.93 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 1.0 | \n",
" 1.0 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" admit gre gpa prestige_2 prestige_3 prestige_4 intercept\n",
"0 0 380 3.61 0.0 1.0 0.0 1.0\n",
"1 1 660 3.67 0.0 1.0 0.0 1.0\n",
"2 1 800 4.00 0.0 0.0 0.0 1.0\n",
"3 1 640 3.19 0.0 0.0 1.0 1.0\n",
"4 0 520 2.93 0.0 0.0 1.0 1.0"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#remove the first dummy variable\n",
"df2 = df[['admit', 'gre', 'gpa']].join(dummy_ranks.ix[:, 'prestige_2':])\n",
"#manually add an intercept:\n",
"df2['intercept'] = 1.0\n",
"df2.head()"
]
},
{
"cell_type": "code",
"execution_count": 187,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: admit No. Observations: 400\n",
"Model: GLM Df Residuals: 394\n",
"Model Family: Binomial Df Model: 5\n",
"Link Function: logit Scale: 1.0\n",
"Method: IRLS Log-Likelihood: -229.26\n",
"Date: Fri, 25 Mar 2016 Deviance: 458.52\n",
"Time: 10:16:29 Pearson chi2: 397.\n",
"No. Iterations: 6 \n",
"==============================================================================\n",
" coef std err z P>|z| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"gre 0.0023 0.001 2.070 0.038 0.000 0.004\n",
"gpa 0.8040 0.332 2.423 0.015 0.154 1.454\n",
"prestige_2 -0.6754 0.316 -2.134 0.033 -1.296 -0.055\n",
"prestige_3 -1.3402 0.345 -3.881 0.000 -2.017 -0.663\n",
"prestige_4 -1.5515 0.418 -3.713 0.000 -2.370 -0.733\n",
"intercept -3.9900 1.140 -3.500 0.000 -6.224 -1.756\n",
"==============================================================================\n"
]
}
],
"source": [
"logit = sm.GLM(df2['admit'], df2[df2.columns[1:]], family=sm.families.Binomial())\n",
"print(logit.fit().summary())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the results are the same. The choice of formula or non formula interface is up to you - use whichever you feel most comfortable with.\n",
"\n",
"We can get our odds ratios out by calling .params and taking the exp:"
]
},
{
"cell_type": "code",
"execution_count": 198,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"gre 1.002267\n",
"gpa 2.234545\n",
"prestige_2 0.508931\n",
"prestige_3 0.261792\n",
"prestige_4 0.211938\n",
"intercept 0.018500\n",
"dtype: float64"
]
},
"execution_count": 198,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#odds ratios\n",
"np.exp(logit.fit().params)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Linear Optimization\n",
"\n",
"Python has a variety of ways of carrying out linear optimization. We can either use the built in NumPy solver, or interface with a commercial or open source solver through Python.\n",
"\n",
"[Gurobi](https://www.gurobi.com/documentation/6.5/refman/py_python_api_overview.html) and AMPL both offer Python apis, as well as [PuLP](http://www.coin-or.org/PuLP/) and [pyomo](http://www.pyomo.org/) which offer integration into a wide range of solvers. For use of these packages, see their help pages, as they have their own idiosyncracies. \n",
"\n",
"The main purpose of these interfaces is to get the data in from our equations and then run the solvers - We will use the built in solver in scipy, available in the scipy.optimize library:\n",
"\n",
"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.optimize import linprog"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Imagine we are working for French's and we want to take advantage of the goodwill we have recently got from Canadian consumers.\n",
"\n",
"We want to maxmise our profit on mustard and ketchup: We have 650 units of Canadian tomatoes, 1800 units of vinegar and 600 units of mustard seed available. We need 2 units of tomatoes and 4 of vinegar per pallet of ketchup, and 3 units of mustard seed and 7 units of vinegar per palette of mustard.\n",
"\n",
"We can sell ketchup at \\$400 per palette, and mustard at \\$300 per palette.\n",
"\n",
"We also have a limit on our new Canadian ketchup factory - we can produce at most 400 palettes of both products.\n",
"\n",
"We also have to produce at lease 100 units of each product to protect our brand.\n",
"\n",
"First let's state our constraints mathematically:\n",
"\n",
"maximize:\n",
"\n",
"* profit = 400 \\* ketchup + 300 \\* mustard\n",
" \n",
"subject to: \n",
"\n",
"* ketchup \\* 2 <= 650\n",
" \n",
"* ketchup \\* 4 + mustard \\* 7 <= 1800\n",
" \n",
"* mustard \\* 3 <= 600 \n",
" \n",
"* ketchup + mustard <= 400\n",
"\n",
"* ketchup >= 100\n",
"\n",
"* mustard >= 100\n",
"\n",
"Let's plot out our system using our knowledge of matplotlib from last lesson:"
]
},
{
"cell_type": "code",
"execution_count": 201,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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KFSvh5+d32bSomzdvZPr0qaSknGfo0KdYs+ZPFi36lcjISpw7dy7f2ubMmYWvry/R0bV5\n+ulnGTZsECNGjKJmzVpMmzaNgweP0rRpc6ZN+xYfH1+OHTtKx46d6Nv3MYYNG0TduvXYsWM7aWlp\nvPLKWMCW6f7jj7M5ceI4/fs/AcDTTw9h2LCnqVUr+rI6nEHNvACKehURd3dqwTxO/vwT2akpDlun\nxa8M4d17ENalW4HLHDp0kE8+mcR//vMjU6d+y9dfT2Pu3J9ZuHAB9933QL5Tkc6ePZNhw56mUaMm\nLFv2O9nZWXTrdichIaG0bdueJUsWXjYtqr+/P3v37mH69DmkpKTw44/PMn36HNLS0ujV667L6vr+\n+2m8++6HRERUYN68X0hNTb388+UUZJo7+Pe/f8ZisdKnz332DPbg4BA++uhzZs+ewcyZ39Gu3c1Y\nLBY6dbqdoUMH0L//E5w9m8yZM2eKrZGDDrMXKqpWOLXrVbA/Xr5gJ+lpGYW8QkSk5Ej4dYFDGzlA\ndmoKCb8uKHSZOnXqAhAeXp4bbojGYrEQFhZOcnLy5evLOb+4Y8fOvPPOWKZM+YbatWMIDQ27aLmC\npkWNjq6Nt7c3Bw8eoGbNG/D29iYgIADDqHPZe912WxfGjHmGmTOnc9NNbfHz8yvwM9SrVx8/vzL4\n+vpSq1YtDh2yXarcokUrAOrXb8SBA/vtywcGBlKtWhS7dpmsWvVHsWe2q5lfgaJeRcRdhd7eBYtf\nGYeu0+JXhtDbC58f3MvLK9/7tiuDLp6KNHcmtC5d7uDjjycSHBzM6NEj2L8/7qJ1FjQtqre3T+7a\nL9rjz8q6/Cqkhx56lLFj3yE7O4vhw5/gzJnEi37vTk9Pz/P6C6FhtqlRrTn3c8dtnyWvrl3/xuLF\nC1m5ckWxz3Guw+xXkBv1umTuDsAW9Vq7XgUqVApycWUiIoUL69Kt0MPhrlDQVKTffDOZe+7pRffu\nd5OQcIq4uDisVqt9DvT8pkXNq3Llquzbt4+MjAxSU1PYuXP7Rc9nZ2czadJn9Os3kF69+hAXF8ex\nY0cpW7YcJ0+eoGbNWsTGxlK1ag0Adu407Yfh4+L2Uq1aNQA2blxPnTr12LJl02Uzqd10U1umTfs/\nAgMDqVixomM33BWomReB0SCSXVuPcTAugexsWDpvJz0faYaXlw5siIhcjcDAQFq0uPGyqUgjIyvy\n1FP/IDAwkKCgYHr3fgh/f3/Gjn2FkJCQfKdFHTTowkQnQUFBdOv2N554oh+VK1ehbt36F72vxWIh\nICCAJ57oR7ly5ahcuQq1axt0734X48e/SbVq1YmOvtCca9Soybhxr3LgwH7uuute+3zpx44dZeTI\nJzl7NjnnxL199td4e3tTo0ZNDKOuMzdhvjQFahElJpxn5pdryMiwHWK56ZZaNL0pqtje39E0Bapj\naNpJx/Ck7agpUEuu3G24fv065syZxWuvvXnR83nPfM9PamoqQ4cO5MMPPyUgoKwz6tMUqNdLUa8i\nIp6tsOvJt27dwqBBj3H//Q84pZFfiQ6zX4XGN1Zl97Z4TsQn26Ne/967cYkIDBAREcdo2rQ5TZs2\nv2z8o48+L/A19es34JtvvnNmWYXSnvlVUNSriIiURGrmV0lRryIiUtKomV+Dlu1rEhhkCxvIjXoV\nERFxFTXza5Ab9Zpr17Z49u056cKKRETEk6mZX6P8o14zXViRiIjrZWRkMHDgo4wd+8pVvW7FimX2\nNDh3cerUSd59dxxgC5M5ffq0y2pRM78Ol0a9rlm+18UViYi41okTJ8jISOe55166qtfNmDHtojhV\ndxAWFs4zz4wBYO7cn+3Jdq6gS9Ouw6VRr5vWHiRaUa8i4sEmTHiPQ4cOMm7cq/Tv/wSvvfYvLBYL\nGRkZPP/8y1SuXIX58+cye/YMrFYv7r//QTIy0tm6dQv//OdwPvjgU+bMmcXixb9hsUD79rfw4IMP\nM3bsK3h7e3PmTCLHjx/npZdep3LlKhw/Hs/o0SP58ssp9hqOHj3KG2+8RHZ2NpGRFXnhhVfYs2c3\n7733Fj4+PlgsFl577S3Onk3mxRdHUa1adQ4c2EezZk0ZPPhpdu/eddmygYGBTJv2Lb//vhgvLy8G\nDRpCpUqVeeGFUQwaNIRly35n796/aNu2PRkZGcU+Faqa+XVS1KuIlFQb/jzA2j/iHPoToI+vFy3a\n1qBJq2r5Pj906NO8+OIoxoz5Fzt2bOOxxwbQtGlz5s79mR9++DePPTaAb775kilTZpCamsobb7zM\nuHHvMnny54wf/xHHj8czf/5cvvxyCllZWQwc+Cg333wrYJt+9Nlnn2fOnFksWvQrffs+xooVy7jt\ntosnfpk06RMeeKAvbdq047PPPmbHjm2cPXuWp59+ltq1Y/jyyy/49dd5tG3bnj17djNu3HjKl49g\n8ODH2LNnNwkJpy5btlWr1ixduoRJk77l0KGDTJ36LY880g+LBVq2bEXt2jGMHDmasLBwhg0bWOxT\noarjXCeLxUKHLjF4e9s25Yn4ZDatOejiqkREYOOaAw4/lyc9LZONaw4UadmwsHBmzfqeoUMHMnPm\ndBITT7Nv315q1KiBj48P5cqVY9y4d3OWts2mtnOnSf36DbFYLHh5edGwYWN277bFT+fmrXfufDvL\nli0BYOXK5ZfNUGaaJg0aNAJg8OBh1K1bn9DQML74YgJDhw5k4cIFnDmTCEC1alGULx8BQOPGjdm/\nP46wsPDLlt2506RevQYAVKlSlVGjnr/s82ZnZxMUFOSSqVCdumduGIY/8A0QCfgBrwMbgSnYvkgc\nAfqappluGEYfYDiQCUwyTfMrZ9bmSLlRr//7/S/AFvVay4ggONTfxZWJiCdr3LKaU/bMG7fMf6/8\nUpMnf06rVq3p0aMnv/++iJUrV+Dl5XXR9KKXslgseaYZhfT0NPuRTh8fW8sKCgomIiKSHTu2kZ2d\nTfny5S9ah5eX10XrAPjww3fp2/dRWra8ienTp5KSYovjzsy8eKrTgpa11V207Zg7FeqxY0cZOHDI\nlV/gAM4+zP53YI1pmu8ahhEF/Ab8AUwwTXO2YRhvAP0Mw5gCvAi0ADKANYZhzDFN03WnBl4lRb2K\nSEnTpFW1Ag+HF4fExNNUqWIL2Vq+fCnZ2dlERdVg//79pKSkYLFYGD16BO+//wkWC2RmZhATY/D1\n1xPJysoiKyuL7du38vDD/Vi27PeL1t2lSzfGj3+LHj16Xva+devWY926tdx6a2e+/PILGjduSmJi\nIpUrVyUtLY3//e8P6tdvCMDhwwc5deokISGhbNy4kW7d7sp3WcOow7ffTiYrK4vTpxN49903efLJ\nEfb3tFqt9rPxXTEVqlMPs5umOdM0zdxjKFHAAeBm4Oecsf8AtwGtgNWmaSabppkCrADaOrM2R1PU\nq4jIxXr0uIf333+bZ555ks6du7BhQyybN2+kf/9BDB8+mOHDB9O9+92ALQ/9H//oT0BAAN2792TI\nkAEMGzaQv//9biIjL2+Ibdt24PDhg/kexu7XbyA//zyHYcMGceTIYZo3b8k999zP6NEjeOmlMdx7\nby/mz5/L2bNnqVatOl988QlPPNGP5s2bU6NGzQKX7dLlDoYM6c/zz/+T++9/4KL3bNKkGS++OJq4\nuL32qVDbtGnvnA2bj2KZAtUwjD+AKtj21H8zTbNizngtbIfcPwZamqY5Mmf8VWC/aZqTC1ltsU6B\nWlQrF+1mY85v5n5lvOk94EYCyvq6uKrLaQpUx9C0k47hSdtRU6A6RmzsWubPn3vVl8DldfToEV54\nYRSTJ/8f4Lht6KypUAubArVYzmY3TbOtYRiNgGlA3mIKKqxIx6YjIgKvtzSH63Z3Q+J2nyQx4Typ\nKRmsW7GPng81c3VZhSqJ29GdaPs5hiduR0d/Zk/Zhh9//DF//PEHH3300XV95rS0M/j4eF20juvd\nhhs3buRf//oXAwYMoHr14jnEDs4/Aa4ZEG+a5kHTNDcZhuEFJBmG4WeaZiq2vfVDwGGgUp6XVgFW\nXWn9JfVbaLvbopk7czMAW9YfonrtMKJqhbu4qoKV1O3oDjxtb8hZPHU7OvIze9I27N37UXr3fhS4\nvm3o6xvEZ599bV+HI7Zh5cq1mDx56nXXlp/Cvmg4+9K0DkDuofNIoBywELg35/l7gPnAaqCFYRhB\nhmGUA9oAy51cm9NcGvW6bMEuRb2KiIjTOLuZfw5UMAxjGbaT3QYDLwGPGIaxFAgFvs056W008GvO\n7WXTNN36K+ZFUa+JKYp6FRERp3HqYfacJt0nn6duz2fZOcAcZ9ZTnBT1KiIixUUJcE5kNIikao1Q\nAHvUa96AAhEREUdQM3ciRb2KiFy7Y8eOsn371mt67QsvjGLDhtires0PP/zA8uW/F/j8xx+/x9Gj\nR66pHmdTM3ey3KjXXGtWxJGYcN51BYmIuInY2LVs23Ztzfxa3H333bRvf0uBzw8bNoKKFSsV+Lwr\nada0YqCoVxHxFPPm/cL69etITDxNXNxeBgwYzMKFC4iLi+Oll14jNDTsoqCW/v0f5vXX3+bAgTgm\nTvyMMmXKEBYWxtNPj+Krrybi7e1NxYqV8PPzY/Lkz/Hx8SEwMIhXXx3H5s0b7dnpQ4c+xZo1f7Jo\n0a9ERlbi3Llzl9U2bNggmjVrwZo1f2K1Wuna9W/Mm/cLXl5efPjhZ0yYMAFvb39q1bqB2bNnYrFY\n2L8/jo4dO/Poo/0ZNmwQI0aMYsmShSQmnubgwYMcOXKI/v0HM3fuzxw7doR33vmQo0ePMHv2TF5/\n/S0A7ryzM7/8svCK7389PUHNvBjkRr3O/nYd2dkXol7rNCy+QAER8Txnjq0i8ehSsrPSHLZOi9WX\n4Io3ExTZusBlDh06yCefTOI///mRqVO/5euvpzF37s8sXLiA++57gLw9K/f+7NkzGTbsaRo1asKy\nZb+TnZ1Ft253EhISStu27VmyZCEvv/wGFStW4vXXX2L16v/h7+/P3r17mD59DikpKfz447NMnz6H\ntLQ0evW6K9/aypeP4NNPJzN48OMkJSXxySeTGDp0IHv27M6px1bQjh3b+O672WRmZnLffd159NH+\nF60nKSmJ8eM/YuLET5k/fy7jx3/E5Mmfs2LFMqKja1/SmC/cz+/9hwwZwJ49u4mOvvY0Th1mLyYR\nFQNp1KKq/fHKRbs5d9Zx/wcTEblUUvwqhzZygOysNJLiC8/0qlOnLgDh4eW54YZoLBYLYWHhJCcn\nX76+nETxjh078847Y5ky5Rtq144hNDTsouVCQkIZN+41hg4daN/zB4iOro23tzcHDx6gZs0b8Pb2\nJiAgAMOok29tudOohoeXJybGsK/77NmLa4uJqYOvry/+/vnPfpnfekJDwy5bj6NedyVq5sWoZfsa\nBAb5AZCaksHKRbtdXJGIlGaBFVpjsTp2bgiL1ZfACgXvlYNtCtL87tvmArGQd0qQ3JnGunS5g48/\nnkhwcDCjR49g//64i9Y5btyrjBw5igkTJtKuXQf7uLe3T+7aL9rjz8rKf96RwmvLf7mrXc+lh8tz\nP+PVvP/V0mH2YuTj602HrjH2qNdd2+KJaRBZoqNeRcR9BUW2LvRwuCuULVuWU6dOAnDy5AkOHz4E\nwDffTOaee3rRvfvdJCScIi4uDqvVSmamLT3z3LmzREZGkpSURGzsWqKjYy5ab+XKVdm3bx8ZGRmk\npqawc+f24v1geZQtW5YTJ44DsHv3Ls6fv/z3e0dTMy9muVGvu7bFA7ao116Ph+DjW/i3QBGR0iAw\nMJAWLW5kwICHiY6OsR9qjoysyFNP/YPAwECCgoLp3fsh/P39GTv2FUJCQrj77vt44ol+REVVp0+f\nR/jqq4kMGjTEvt6goCC6dfsbTzzRj8qVq9gPZ+eVd4+5oPuFyV3uSstHR8fg7+/P4MGP07BhIypV\nquyQ9y+0tuKYAtVJSuQUqEVx7mwa309aTWqK7dBL45ZVadMpulhr0BSojuFJk1s4kydtR02BWnKV\n9G1Y2BSo+s3cBXKjXnNtWnuQ+CNnXFiRiIi4MzVzF1HUq4iIOIqauYso6lVERBxFzdyFFPUqIiKO\noGbuYo1vrEr5CuUA7FGvbnxSooiIuICauYvlRr3mXpmQG/UqIiJSVGrmJYCiXkWktJg37xc++eTD\nIi27Z89exRojAAAgAElEQVRuDh48UODzw4YNYu/evxxVWqF27drJhAkTCnx+3rxfCp0e1dXUzEsI\nRb2KSGlR1AyUpUsXs3//PucWU0S1a8cwdOjQAp/v1u3OQqdHdTUlwJUQinoVkdLmiy8+wd/fn4ce\nepS3336DI0cOk5GRweOPDyIkJISffprN0qVLCAsLIykpiYkTP8HLy5tOnW7nvvt6A7B48W9s2rSR\npKRE3nzzPQ4dOljg9KJ169Zjx47tpKWl8corY4mMvDAz5VdfTbzitKW//DKHF198g969bfOab968\nkcDAQN5++wO+/noSwcEh1Kp1A7NmfY+Xlxe7dpn07fsYf/65il27TIYMGU67djfbawJ44YVR3Htv\nL2Jj1xb6/rkpcddKzbwEUdSriDjS8qMJLDp0krQCJh25Fr5WC52qhNO+Ymihyy1ZspD4+GO8+OKr\nLFjwX8qXj2D06BdJTDzNk08O5ttvp9OqVRs6duxMnTr16N27JxMnfk25coGMGTOS7t3vBmwzin34\n4ad88cUnLF26pNDpRYODQ/joo8+ZPXsGM2d+x7BhIy6qqajTlh4+fIhu3e5kyJDhPPFEv8umR929\neyfffTeb9evX8dpr/2LWrJ/ZsmUTs2fPpF27my+qqajvn/vl5VqpmZcwbTpFs/+vU6SmZJCUmMKa\n5XuLPepVREqHFUcTHNrIAdKysllxNKHQZv7XX3tYunQJU6fOAmDz5k1s3ryBTZs2kJ2dTXp6Wp6Z\nxLJJSEjAz8+PoKBgAN566337uho1agLY5gFPSio8KbNFi1YA1K/fiD//vHya1rzTj1qttl+ZQ0PD\nLltvQEBZatW6wf6+l05PGh0dg7e3N+Hh5alWLQo/P79LpjHNf5sX9f2vhZp5CZMb9bpk7g7AFvUa\nXa8CFSoFubgyEXE37SqGOmXPvN0V9sqPHj1CzZq1WLJkIbff3g0fHx8efrgfnTrdnu/yXl5WsrIy\nC3iu6NOLZmfnpmjaplotbF2FTT/q7X3x0dDCpke90jSmmZnOn/4U1MxLJKNBJLu2HuNgXII96rXn\nI83w8tL5iiJSdO0rhl7xcLgztGnTjj59HuEf/+hPy5atqFevPsuW/U6nTreTkHCKmTOnM2jQECwW\nC5mZmQQFBZOdnc2JEycIDw9n1KgR/Otfr+W77sKmF924cT116tRjy5ZN1KhRs1g+a34sFiupqalk\nZ2ezc6dZLO+pZl4C5Ua9zvxyDRkZWfao16Y3Rbm6NBGRIgkODqFfv4GMH/8mr776JrGxaxk8uB9Z\nWdn06zcQgMaNm/LBB+8SEFCWESNG8cILz2KxwK233k65cuXynRq0oOlFAY4dO8rIkU9y9mwyr79+\nPTPSXT496dVMU3rXXfcwcOCj1KhRkzp16l7166+FpkAtwdb/bz//+912jaWXt5Vej7ckONTfIevW\nFKiOUdKnTHQXnrQdNQWqcwwbNogRI0ZRs2ata15HSd+GmgLVTSnqVUSkaJy951vSqZmXYIp6FREp\nmo8++vy69srdnZp5CaeoVxERuRI1czfQsn1NRb2KiEiB1MzdgI+vFx26xtgf79oWz749J11YkYiI\nlCRq5m4iN+o11/IFO0lPyyjkFSIi4inUzN1Im07R+JWxRQMknUllzfI41xYkIiIlgpq5G8mNes21\nae1B4o9cf6aviIi4NzVzN2M0iKRqDVs8Y27Ua2Zm1hVeJSIipZmauZvJjXr19rb9p8uNehUREc+l\nZu6GgkP9adGuhv3xmhVxJCacd11BIiLiUmrmbkpRryIikkvN3E0p6lVERHKpmbsxRb2KiAiombu9\nlu1rEhhcBlDUq4iIp1Izd3M+vl506HJhPnJFvYqIeB4181JAUa8iIp5NzbyUUNSriIjnUjMvJRT1\nKiLiudTMSxFFvYqIeCY181JEUa8iIp5JzbyUUdSriIjnUTMvhRT1KiLiWdy2mU//1ST5fLqryyiR\nFPUqIuJZ3LaZf7dgB+OmruNkYoqrSymRFPUqIuI53LaZAxw5eY43pqzlYHyyq0spkRT1KiLiGdy2\nmXt72Y4hn05OY9y0WMz9CS6uqORR1KuIiGdw22b+8oDWlPH1AuB8agbjZ2xk7Y54F1dV8ijqVUSk\n9HPbZt64dgSj+zQjuKwvABmZWXz24xYWrdN11ZdS1KuISOnmts0cICoykOf6Nicy1B+AbGDabzuZ\nvXSPLsXKI7+oVxERKT28nf0GhmG8DbQDvIA3ge5Ac+BEziLvmKY5zzCMPsBwIBOYZJrmV0VZf0SI\nP2P6NufDWZvYm5NFPnfVPhKT03i4q4G3l1t/X3EYo0Eku7Ye42BcAvqeIyJSuji10xmGcQtQzzTN\nNkA34ANsO9CjTdO8Nec2zzCMAOBF4FagI/C0YRghRX2foABfnn2gKY1uCLePrdh8hAlzNpOalunA\nT+S+Lo16FRGR0sPZ/7IvBe7LuX8aKIttD91yyXKtgNWmaSabppkCrADaXs0b+fl6MbRnQ9o2rGgf\n27TnJG9PX0/SOV1fDZdHvYqISOng1GZumma2aZq5weD9gbnYDqMPNQxjkWEY3xmGEQ5UBI7neelx\noNLVvp+3l5V+d9TlzjbV7WN7j5xh7NRYjp9WPjlcHPWaS+cXiIi4N6f/Zg5gGEYP4DHgdqAFcNI0\nzU2GYTwLvAysvOQll+655ysiIjDf8UH3NKFqZBBf/LiZ7Gw4duocb06L5eUBralVJfiaP0dpcdeD\nTVm/+S/74yP7EmncspoLK3JvBf0dytXxxO3o6M/sidvQ0dx1GxbHCXBdgDFAF9M0k4AleZ7+D/Ap\nMAv4e57xKsCqK637+PGkAp+70YjA2qMBE/+zlYzMbBKSUhk1YTnDejakbo2wa/kopYZPGa+LHs//\ncQshEQEE5FzmJ0UXERFY6N+hFI2nbkdHfmZP3YaOVNK3YWFfNJx9AlwQ8DZwp2maiTlj/zYMo2bO\nIrcAW4DVQAvDMIIMwygHtAGWX+/7t6hTgZG9muDvZ/vOkpKWyXszN7J6uyYdyUtRryIi7s3ZJ8D1\nAsKBmYZhLDEMYzHwEzDDMIwlwB3AKzknvY0Gfs25vZyzF3/djKhQxvRpRkg5215nZlY2n/+0ld/W\nHHDE6ksNRb2KiLgvpx5mN01zEjApn6em5LPsHGCOM+qoWqEcz/dtwXszN3Dk5DkApi/aRUJyKvfe\ncgNWS5F+oi/1li/YSeX+LfHxLZZTKURExEE85qLj8OAyjHmoOdF5ToCb/+d+vvxlGxmZWS6szPXy\nRr2uVtSriIjb8ZhmDlDO34dnejehSXR5+9iqrcf48N+bOJ/quZOP5I163bz2IPE5SXoiIuIePKqZ\nA/j6eDGkZwNublLZPrZ17ynenr6exLOeGS5jNIikao1QALKzYem8nWR6+NEKERF34nHNHMDLauXh\nLgY92tW0j+07msS4KeuITzjnwspc49Ko1xPxyWxao8lYRETchUc2c7A1sB7tavJwV4Pc89/iT59n\n7JR1xB31vMPMl0a9rlkRR2KCUvNERNyBxzbzXLc0qcLQuxvik7NXeuZcOm9NW8+WvZ53mVbeqNfM\njCyWzjcV9Soi4gY8vpkDNI2J4JneTSibc1Z3anomH87axKotR11cWfGyWq3ccseFIxWH9p3G3KKA\nHRGRkk7NPEftqiGMfqg5YUF+gC1cZtIv25j/536P2juNqBhIoxZV7Y9XLtrNOQ89MVBExF2omedR\npXxZnnuoOVUiytrHZi7ZzYzFu8nyoIbesn1NAoPLAIp6FRFxB2rmlwgLKsOYPs2IqRZiH/t1zQEm\n/ryV9AzPuFzLx9eLDl1q2x8r6lVEpGRTM89HQBkfRvZqTHMjwj62ens8H8za6DHhMlG1wqldr4L9\n8fIFO0lP84zPLiLibtTMC+Dj7cXgHg24tVkV+9j2fQm8OS2W08mpLqys+LTpFK2oVxERN6BmXgir\n1UKf22Lo2aGWfexAfDJjp6zjyMmzLqyseASU9VXUq4iIG1AzvwKLxcKdbWrw2B117LOrnUhMYdzU\nWPYcTnRxdc6nqFcRkZJPzbyI2jeqzLB7GuKbEy6TfD6dd6avZ+PuEy6uzLkU9SoiUvKpmV+FxtHl\n+eeDTSnn7wNAWnoWH8/ezPJNh11cmXMp6lVEpGRTM79KN1QOZsxDzSifcx12VnY2X/93B7+sjCvV\n4TKKehURKbnUzK9BpfCyPNe3OdVymhvAnGV/Me23nWRllc4Gp6hXEZGSS838GoWU82PUg82oWz3U\nPrY49hCf/bSF9IxMF1bmPIp6FREpmdTMr0NAGW+euq8xN9a9EK6yzjzO+BkbOZeS7sLKnEdRryIi\nJY+a+XXy8bYysHt9bmtRzT6288Bpxk2LJSGp9IXL2KJeY+yPFfUqIuJ6auYOYLVY6N0pmvs7XghY\nOXT8LG9MWcvhE6UvXCaqVhi16yvqVUSkpFAzdxCLxULXVlEMuLMeXlbbWWKnzqQybuo6dh8sfeEy\nbRX1KiJSYqiZO1jrBhUZfl8j/Hy8ADibksE7369n/a7jLq7MsfwDFPUqIlJSqJk7QYOa4Tz7YFMC\nA2zhMukZWUyYs5mlGw65uDLHujTq9fd5pqJeRURcQM3cSWpWCuK5vs2pEOIP2Jrdt/NNflqxt9SE\nrVwa9Xoy/qyiXkVEXEDN3IkiQwMY07c51SsG2sd+WrGX/1tgkplVOvZgFfUqIuJ6auZOFlzWl2cf\naEr9mmH2saUbDvPpD1tISy8d4TKKehURcS0182Lg7+fN8Hsb0bp+pH1s/a4TvPv9BpLPu3+4jKJe\nRURcS828mHh7WXn8znp0axVlH9t9KJFxU9dxMjHFhZU5hqJeRURcR828GFktFu7rGE3vTrXtY0dO\nnmPs1HUcPJ7swsocQ1GvIiKuoWbuAre3rMag7vXt4TIJSamMmxqLuT/BxZVdH0W9ioi4hpq5i7Sq\nF8mI+xtTxtcWLnM+NYPxMzaydke8iyu7Pop6FREpfmrmLlS3Rhij+zQjuKwvABmZWXz24xYWx7r3\ntdqKehURKV5q5i4WFRnIc32bExmaEy4DTP11J3OW7XHby7sU9SoiUrzUzEuAiBB/xvRtTs1KQfax\nX1bu4+t5O9w2XEZRryIixUfNvIQICrCFyzS6Idw+tmLTET6evZnUNPcLl1HUq4hI8VEzL0H8fL0Y\n2rMhbRtWtI9t2nOSt6evJ+mc+12zrahXEZHioWZewnh7Wel3R13ubFPdPrb3yBnGTo3l+Gn3a4SK\nehURcT418xLIYrHQs8MN9LkthpyEVI6dOsfYKevYfyzJpbVdLUW9iog4n5p5CdapeVUG39UAby9b\nJ0w8m8ab02LZHnfKxZVdHUW9iog4l5p5CdeiTgVG9mqCv5/tuu2UtEzem7mR1dvda+9WUa8iIs6j\nZu4GjKhQxvRpRkg5W7hMZlY2n/+0ld/WHHBxZUWnqFcREedRM3cTVSuU4/m+LagUHmAfm75oF7OW\n7CbLTU4oU9SriIhzqJm7kfDgMox5qDnRVYLtY/P+3M+Xv2wjw00CWRT1KiLieGrmbqacvw/P9G5C\nk+jy9rFVW4/x4b83cT615O/lKupVRMTx1MzdkK+PF0N6NqBD48r2sa17T/H29PUkusFZ4op6FRFx\nLDVzN+VltfJIV4Me7Wrax/YdTWLclHXEJ5xzYWVXpqhXERHHUjN3YxaLhR7tavJw1wuhLPGnzzN2\nyjrijpbsQ9eKehURcRw181LgliZVGHp3Q3xy9nTPnEvnrWnr2bK3ZF/6pahXERHHUDMvJZrGRPBM\n7yaUzTlTPDU9kw9nbWLVlqMurqxginoVEXEMNfNSpHbVEEY/1JywID/AFi4z6ZdtzP9zf4nd41XU\nq4jI9VMzL2WqlC/L831bUCWirH1s5pLdzFhccsNlFPUqInJ91MxLodBAP8b0aUZMtRD72K9rDjDx\n562kZ5S8S8AU9Soicn3UzEupgDI+jOzVmOZGhH1s9fZ4Ppi1sUSGyyjqVUTk2nk7+w0Mw3gbaAd4\nAW8Ca4Ap2L5IHAH6mqaZbhhGH2A4kAlMMk3zK2fXVtr5eHsxuEcDvlu4k8WxhwDYvi+BN6fFQsNQ\nF1d3uTa3RrN/zylSUzLsUa9t86TFiYhI/py6Z24Yxi1APdM02wDdgA+AV4EJpmneDOwB+hmGEQC8\nCNwKdASeNgwjJP+1ytWwWi30uS2Gnh1q2ccOxCe7sKKCBZRV1KuIyLVw9mH2pcB9OfdPA2WBm4Gf\nc8b+A9wGtAJWm6aZbJpmCrACaOvk2jyGxWLhzjY16HdHXay514GVUJdGvS6dt1NRryIiV+DUw+ym\naWYDubFejwNzgS6maabnjMUDlYBI4Hielx7PGS/Qql59yEpJcWzBpVwF4Nmc+990et4+vrP/o64o\np0DVvAM5HNWDLKs3J+KTWTzqPaqf3uLqsvK109UFlBKetB2H57m/87tHHbZeT9qGzlLSt2HET7ML\nfK5YToAzDKMH0A8YCuTdNSxoN/GKu49q5KVXQEYStU5tsD/+K6wJ57wDXViRiEjJ5vRmbhhGF2AM\n0NU0zSQgyTAMv5ynqwCHgMNcvCdeJWesQNYyZZxQrZQU1U5vpVyq7fK0LKs3Oyq0pmReJS8i4npO\nPcxuGEYQ8DbQyTTNxJzhhcA9wHc5/zsfWA1Mzlk+C2jDxUejLtN6xjSOH09yVuml35pd9rtvRj9s\nv39rsyo82DkGq9X1v62HH01i9rfryM6GhIDKZA9/E6NhRVeXdZGIiED9HTqAJ23HIYuftd//5Na3\nHbZeT9qGzuLO29DZe+a9gHBgpmEYSwzDWAy8ATxqGMZSIBT4Nuekt9HArzm3l3P24qUY1K1+4TK1\nxbGH+OynLaRnZLqwIhtFvYqIFI2zT4CbBEzK56nb81l2DjDHmfVI/p66rzFfzt3G6u3xAKwzjzP+\n3EaevKchAWV8XFpby/Y1+cs8TtKZVHvUa+fu9Vxak4hISaMEOMHH28rA7vW5rUU1+9jOA6cZNy2W\nhKRUF1aWE/XaVVGvIiKFUTMXAKwWC707RXN/xwuhLYeOn+WNKWs5fOKsCyuDqFrh1K6nqFcRkYKo\nmYudxWKha6soBvy9Hl45J8CdOpPKuKnr2H0w8Qqvdq42naLxy5mrPTfqVUREbNTM5TKt61dk+H2N\n8PP1AuBsSgbvfL+e9buOX+GVzqOoVxGRgqmZS74a1Axn1INNCQqwnQCXnpHFhDmbWbrhkMtqUtSr\niEj+1MylQDUqBvFc3+ZUCPEHbA302/kmP6/YS3Z28Ue4WCwWOnSJwdvb9md7Ij6ZTWsOFnsdIiIl\njZq5FKpCaADP9W1O9YoX4lR/XLGX/1tgkplV/HvFwaH+tGhXw/54zYo4EhPOF/wCEREPoGYuVxRU\n1pdRDzalfs0w+9jSDYf59IctpKUXf7hM4xurUr5COQAyM7JYOt90yZECEZGSQs1ciqSMrzfD721E\n6/qR9rH1u07w7vcbSD6fXsgrHc9qtXJztxhyZ3M9tO805pZjxVqDiEhJUmgCnGEYHQp73jTNZY4t\nR0oyby8rj99Zj5Byfsz7cz8Auw8lMm7qOkbc34Tw4OKb/KZCpSAatqhq/8185aLdRNUKI6Csb7HV\nICJSUlxpz/yNnNu7wALgQ2AC8BvwunNLk5LIarFwX8doeneqbR87cvIcY6eu4+Dx5GKt5cb2NQgM\nsk3Alxv1KiLiiQpt5qZptjdNsz2wHahpmmZT0zQbAdHAX8VRoJRMt7esxqDu9e3hMglJqYybGou5\nP6HYavDx9VbUq4gIRf/NPNo0zaO5D0zTPADUdE5J4i5a1YtkxP2NKZMTLnM+NYPxMzaydkd8sdWg\nqFcRkaI38xOGYUw3DGOIYRiDDcP4P+CcMwsT91C3Rhij+zQjOOe36ozMLD77cQuLY4vv+m9FvYqI\npytqM+8NLAYMoB6wCrjPWUWJe4mKDOS5vs2JDM0JlwGm/rqTOcv2FMslY4p6FRFPV9T5zIebpvmm\nUysRtxYR4s+Yvs35cNYm9uY00l9W7uN0chqPdDXwsjr3KkijQSS7th7jYFyCPeq15yPN8PLS1Zci\nUvoV9V+6BoZhRF95MfFkQQG+PPtAUxrdEG4fW7HpCB/P3kxqmnPDZXKjXr0U9SoiHqiozbwRsM0w\njKOGYew3DOOAYRj7nVmYuCc/Xy+G9mxI24YV7WOb9pzkne/Xk3QuzanvHRzqT0tFvYqIBypqM/87\nUBtoBbQH2gHdnVWUuDdvLyv97qjLnW2q28f+OnyGsVNjOX7auc21UcuqhFcoCyjqVUQ8R5GauWma\n+4CyQPWcWwww3Yl1iZuzWCz07HADfW6LISd1lWOnzjF2yjr2H0ty2vt6eVm5pZuhqFcR8ShFauaG\nYXwIzAZ+AsYDM4ApTqxLSolOzasy+K4GeHvZumvi2TTenBbL9rhTTnvP3KjXXCsX7ebcWece4hcR\ncaWiHma/0TTNusAG0zRbArcBAc4rS0qTFnUqMLJXE/z9bBdPpKRl8t7Mjaze7rw9ZkW9iognKWoz\nT835Xz/DMCymaa4D2jqpJimFjKhQxvRpRkg5W7hMZlY2n/+0ld/WHHDK+ynqVUQ8SVGbuWkYxj+A\nZcBvhmF8AoQ4rywpjapWKMfzfVtQKfzCQZ3pi3Yxa8luspxwkpqiXkXEUxS1mT8BfA88B3wN7Abu\ndFZRUnqFB5dhzEPNuaFKkH1s3p/7+fKXbWRkZjn8/RT1KiKeoKjN/GvTNE+ZppllmuY00zTfB75y\nZmFSepXz9+GZ3k1pEl3ePrZq6zE++vcmUhy856yoVxHxBIU2c8Mw+hiGsRzoYRjGsjy3VdguTxO5\nJn4+Xgzp2YCbm1S2j23Ze4q3vltPooPPPDcaRFK1RigA2dnw+zyTTCccBRARcZUrzWc+DdskKxuB\nF/PcngWaO706KdW8rFYe7mLQvW0N+9i+o0mMm7KO+ATHTcqXG/XqnRP1ejL+rKJeRaRUueJhdtM0\nDwG3A3tM01wKJAA1gBTnliaewGKxcFf7Wjzc9ULQS/zp84ydso64o447HB4c6k8LRb2KSClV1N/M\nvwFuMgyjCjAHaJgzJuIQtzSpwtC7G+KTs/d85lw6b01bz5a9jrucrPGNVSlfoRygqFcRKV2K2syr\nmKb5b6AX8Klpms8CYc4rSzxR05gInundhLI5Z5+npmfy4axNrNpy1CHrt1qt3HKHol5FpPQpajP3\nMwzDAtwN/JIzVs45JYknq101hNEPNScsJ70tMyubSb9sY/6f+x2yFx1RMZBGinoVkVKmqM38dyAR\nOGKa5k7DMJ4CTKdVJR6tSvmyPPdQc6pElLWPzVyymxmLHRMu07J9TQKDywCKehWR0qGos6aNBqJM\n07w/Z+hH4HGnVSUeLyyoDGP6NCOm2oWgwV/XHGDiz1tJz7i+y8p8fL3o0KW2/bGiXkXE3XkXZSHD\nMKYA2YZhXPrUww6vSCRHQBkfRvZqzMT/bGOdeRyA1dvjSTqXztCeDe0Tt1yL3KjXXdviAVvUa+X+\nLfHxvfZ1ioi4SlEPsy8EFuXclmP7EuCcGTJE8vDx9mJwjwbc2qyKfWz7vgTemhbL6eTUQl55ZYp6\nFZHSoki7IaZpfnvJ0CTDMH7Jd2ERB7NaLfS5LYaQcn7MWfYXAPvjkxk7ZR1P39+YSuFlr7CG/OVG\nvS6ZuwOwRb3WrleBCpWCrvBKEZGSpUh75oZhWC+5VUdxrlKMLBYLd7apwWN31MGac23ZicQUxk2N\nZc/hxGter6JeRaQ0KOph9gwgPc9tA/Cls4oSKUj7RpV58t6G+PrY/nSTz6fzzvT1bNx94prWp6hX\nESkNitrMqwEjgFeAV4EPAD9nFSVSmEY3lOefDzSlnL8PAGnpWXw8ezPLNx2+pvUp6lVE3F1Rm/l/\ngcaAD7bf2b1z7ou4xA2Vg3mub3PK51wvnpWdzdf/3cEvK+OuKVxGUa8i4s6Keh3OSdM0+zm1EpGr\nVDEsgOf6NueDmRvZH58MwJxlf3E6OZUHO8dgtVqKvK7cqNfZ364jO/tC1GudhhWdVb6IiMMUdc/8\nh5y5zWsZhhGVe3NqZSJFEFLOj1F9mlG3eqh9bHHsIT77aQvpGZlXtS5FvYqIuypqM28ETAKWAn/k\n3FY4qyiRq+Hv581T9zXmxroV7GPrzOOMn7GRcynpV7UuRb2KiDsqajO/CQg1TbNanpv2zKXE8PG2\nMrB7fW5rUc0+tvPAacZNiyUhqejhMrao1wtXXSrqVUTcQVGb+RqgjDMLEbleVouF3p2iub9jtH3s\n0PGzvDFlLYdPnC3yeqJqhVG7/oW9/OULdpKeluHQWkVEHKmozbwqEGcYxkrDMJbl3pxZmMi1sFgs\ndG0VxYA76+GVcwLcqTOpjJu6jt0Hix4u01ZRryLiRop6NvsbTq1CxMFaN6hIYFkfPvlhC6lpmZxN\nyeCd79fzRI/6NK0dccXX+wco6lVE3EdRs9mXOrsQEUdrUDOcUQ825YOZGzlzLp30jCwmzNnMw10M\nbm5S5YqvNxpEsmvrMQ7GJdijXu95pDleXkU9oCUiUjz0r5KUajUqBvFc3+ZUCPEHbPnr3843+XnF\n3iuGwijqVUTchZq5lHoVQm3hMtUrBtrHflyxlykLTLKyCm/oinoVEXegZi4eIaisL6MebEr9mmH2\nsd83HOaTHzaTll54uIyiXkWkpFMzF49Rxteb4fc2onX9SPvY+l0nePf7DSSfLzhcJjfqNWfmVXvU\nq4hISaFmLh7F28vK43fWo1urC5lHuw8lMm7qOk4mphT4OkW9ikhJ5vRmbhhGA8MwdhuG8Y+cx18b\nhrHJMIzFObduOeN9DMNYbRjGKsMwNKmLOI3VYuG+jtH07lTbPnbk5DnGTl3HwePJBb5OUa8iUlI5\ntZkbhhEAfAQsvOSp0aZp3ppzm5ez3IvArUBH4GnDMEKcWZvI7S2rMah7fXu4TEJSKuOmxmLuT8h3\neaiPaMsAACAASURBVFvU64UvALu2xbNruw63i4jrOXvPPAXoBhy5wnKtgNWmaSabppmCbRKXtk6u\nTYRW9SIZcX9jyvh6AXA+NYPxMzaydkd8vstH1Qqndr0LUa//nb1ZUa8i4nJObeamaWaZppnfLBdD\nDcNYZBjGd4ZhhAMVgeN5nj8OVHJmbSK56tYIY3SfZgSX9QUgIzOLz37cwuLY/K8pb5Mn6jUx4byi\nXkXE5Yoa5+pI/wecNE1zk2EYzwIvAysvWcZSlBVFRAReeSG5Im1H2zZ4t1IwL01cxeETZ8kGpv66\nk7QseKhrHSyWPH+SEdD1rgb89P0GwBb12rJNTapE6Zeh6+GJf4eO/syeuA0dzV23YbE3c9M0l+R5\n+B/gU2AW8Pc841WAVVda1/HjSY4tzkNpO9p4Ac8+2JQPZ21i75EzAMxcuJPD8Uk83MXAO0+Ma6Xq\nwVStEWqPev1xeqyiXq9DRESgR/4dOvIze+o2dKSSvg0L+6JR7P/yGIbxb8MwauY8vAXYAqwGWhiG\nEWQYRjmgDbC8uGsTCQrw5dkHmtLohnD72IpNR5gwZzOpaRfCZexRrz6KehUR13P22ezNDMNYAjwC\nDDcMYzEwDZiRM34H8ErOSW+jgV9zbi+bpllyvx5Jqebn68XQng1p27CifWzTnpO8PX09SecuXFse\nHOrPzbcb9seKehURV3HqYXbTNGOxXWp2qR/yWXYOMMeZ9YgUlbeXlX531CU00I9fVu4DYO+RM4yd\nGsuI+xsTkTNxS+uba7FxzQFOxCfbo17/3rvxxb+xi4g4mX7gEymAxWKhZ4cb6HNbjP2MzGOnzjF2\nyjr2H7MdOLJ6Wbm5W4yiXkXEpdTMRa6gU/OqDL6rAd5eto6deDaNN6fFsj3uFAAVKgXRUFGvIuJC\nauYiRdCiTgVG9mqCv5/tl6mUtEzem7mRZettJ73d2L4GgUF+gKJeRaT4qZmLFJERFcqYPs0IKWcL\nl8nMyuadqev4dc0BfHy96dA1xr7srm3x7Ntz0lWlioiHUTMXuQpVK5Tj+b4tqBQeYB/7ftEuZi7Z\nTdWaYRdFvS5fsFNRryJSLNTMRa5SeHAZxjzUnBuqBNnH5v9/e3ceHmV97338PZONJCQh7JtAIPCT\nnSQqFREEWkUfHmlxQwGtnnrO5dFzaOtSoafPafu04P606qk9bT2eFlCUloriXlSEwqMQAiEIv7Aj\na8IWAtmX88eMQwgTSEJm7lk+r+vycuaXycyX+wp85r5z35/5fB8vL/+S0RP6+6peS09VqupVRIJC\nYS7SCu0T43hkehajh569Fn3tliP87t1tXDkuw7e2ef1+irxtciIigaIwF2mlhLgY5txzJeNG9vSt\nbdl9nKWbDtD9sjQA6uvh0/cstbV1To0pIlFAYS5yCWJi3Nwz2XDzNf18a3uPnCb3ZDkxsap6FZHg\nUJiLXCKXy8W3r+3P3ZONrzzmYGkFh1z1vseo6lVEAklhLtJGrhvVi4e+M5w47x753upavo7vr6te\n6+vrm34CEZFWUpiLtKGsQV14ZPookr1ntO+ijno8Aa6qVxEJFIW5SBsb2LsDj8/MoWNqAmVAw/hW\n1auIBILCXCQAenVOZu7MHHp1SeYA9VR6984rK2r4u6peRaSNKcxFAqRjajsen5FNZu809nD2d+U7\nvixiV+FRBycTkUijMBcJoOR2cTw8fRQDB3XhWINAf2/ZFk6drnRwMhGJJApzkQCLi43hgW8P47Lh\n3ajxBrq7tp7fvbyOkwp0EWkDCnORIHC7Xdx902C6DOriW0sqr+aZV9Zx6NgZBycTkUigMBcJEpfL\nxR3fGUqy9xPXXLjocKaa+Qty2XmwxOHpRCScKcxFgsjlcjH11uG4YzxVccm4aF9Rw9Ov5bFph06K\nE5HWUZiLBFlaeiJXXXv2k9V64cJVXccLf9nMqvyDDk4mIuFKYS7igJFX9aZz1/YAuHHRFxd19fW8\n8u42lq/Zo9pXEWkRhbmIA9xuN9fddPaDWdJw0cn7taWf7WLRR4XU1SnQRaR5FOYiDunSPYURV/T2\n3c9wxxDrvf3xhgO8tKyA6ppaZ4YTkbCiMBdx0JXXZpCS1g4AV109WamJvq/l2mKefX0TZRXVTo0n\nImFCYS7ioLj4GMbdMOjswqlKxg/s7Ltb+NVJ5i/awIlSlcuISNMU5iIO69O/IwOHdvXdjykq45Zx\nZ892P1B8hl8uWM/BoyqXERH/FOYiIeCaSZm0S/T8xry0pIL08lrunzKEGLfnDLnjpyqZvzCXHftV\nLiMi51OYi4SAxKR4xkzM9N3PX7+fAZ2SmH3bCBLiYgA4U1HD04vzyNte7NSYIhKiFOYiIWLQsG70\n7pcOQH09rHyvkMF90nnsrixSkuIAqK6p48Wlm1m58YCTo4pIiFGYi4QIl8vF+MmDiI31/LU8WnSa\n/HX7yeiRytxZOXTt4DnTvb4e/vi+5a3Vu1UuIyKAwlwkpKR2SOSKsf1899et3kPJiXK6pScxZ1YO\nfbun+L725urdLPjAqlxGRBTmIqGmYdVrbU0dK9+31NfXk5Ycz2N3ZjE0o6PvsZ9uPMh//HUzVdUq\nlxGJZgpzkRDTuOr1wN6T2IIjACQmxDL71hF8Y2g33+Pzth/lmdc3crpc5TIi0UphLhKCGle9rlmx\ng/KyKgBiY9x8b8oQJo/u4/v6jv0lzF+Yy7GSiqDPKiLOU5iLhKiGVa+VFTX8fcUO39fcLhe3T8hk\n+qSBvrVDx8qYtzCX/cWngz6riDhLYS4SohpXvW7fUsS+XcfPecz1V17GP9081Fcuc6K0kvkLN2D3\nnQjqrCLiLIW5SAhrXPX62QeFVFede7Lb6CHd+OHtI2kX7ymXKa+s4dnXN7F+W1FQZxUR5yjMRUJc\n46rXdat2n/eYwf068viMbNKS4wGoqa3jpTcL+HjD/qDOKiLOUJiLhDh/Va9Fh06d97g+3VKYOyuH\nbunechlg4YeFLP1sp8plRCKcwlwkDPireq2trTvvcV06JDJnVg4ZPVJ9a8vX7OWV97ZRW3f+40Uk\nMijMRcKAy+Vi3A3nV736k5rkKZcZMaCTb211/iFe+MtmKqtULiMSiRTmImEiLd1/1as/CfExPDRt\nONcM7+5by995jKdey6PUe726iEQOhblIGGmq6tWf2Bg39900mClj+vrWdh86xbyFGyg+6f9NgIiE\nJ4W5SBi5UNWrPy6Xi2njBjDz+kF4v4Ujx8uYtyCXfUdKAz+wiASFwlwkzPirei07c+FD5xOze/PA\nt4cRG+P5K19ypoonFm1g657jF/w+EQkPCnORMNS46nVNg6rXplxxeVcevmMkiQmea9Yrqmp57o1N\nfP5l03v2IhIeFOYiYchT9Xq2l337l0Xs3Xnsot9n+qQzZ0Y26SkJANTW1fOfb23hw3VfBWxWEQk8\nhblImOrTvxMDh5ytel31QSHVVTUX/b7eXdszd2YOPTol+dYWr9jOG5/soE7lMiJhSWEuEsbGTMok\noZ236vVUJV+s2tOs7+uU1o45M3PI7JXmW3v/8328vPxLavyU0YhIaFOYi4SxpOR4xkw6W/W6uYmq\nV3/aJ8bxyPRRjMrs7Ftbu+UIv/5zPuWVF9/DF5HQoTAXCXOmUdXrp+9Zv1Wv/sTHxfDgtGGMH9XT\nt7Zl93Geei2PkoucIS8ioUNhLhLmGle9His602TVqz8xbjd332CYOjbDt7b3cCnzF+RSdKKszecV\nkbanMBeJAC2pevXH5XIxdWwG90w+W0hTdLKceQty2XO4eYftRcQ5CnORCNGSqtemjB/Vi4emDSfO\nu5d/qqyaJxflUbDr4pe9iYhzAh7mxphhxpgdxph/9t7vbYz5xBiz0hiz2BgT512fYYz5whiz1hhz\nX6DnEok0La16bUrWwC48Oj2LZO9Z8pXVtfz6z/msKTjUluOKSBsKaJgbY5KA54G/NVj+OfCCtXY8\nsBO4z/u4nwATgQnAD4wxHQI5m0gkak3Vqz+ZvdOYMzOHjqlny2X+sHwr732+t8V7+yISeIHeM68A\nbgQavqW/Dnjbe/tt4FvAaOALa+1pa20FsBq4JsCziUSkK6/NIMUbws2tevWnZ+dkfjzrCnp1Sfat\nLflkJ4tXqFxGJNTEBvLJrbV1QKUxpuFysrW22nu7COgBdAOKGzym2LvepLwV/0ZdbWUbThtt7vTd\n2pf3cwfnCG/7nB6gCeOuPvf+vrzWP9f92eev7d/Y+ufzJ1S3YyD8KL2973Zb/t2Lpm0YKKG+Dbtc\n/3STX3P6BDhXC9d9FOQiIiIeToR5qTEmwXu7F3AAOMi5e+K9vGtNcsckXOjLIiIiUSOgh9mb8Dfg\nFuBV7//fB74A/mCMSQXqgDHA7As9SdakX1BcXBrgUSPYuu2+m32y/o+Dg4S3Ll1SQvrncNvmw3zy\nzjYAXC6Ydnc2XXuktvr56uvreWftXpZ+tsu31jmtHT+4fSQ9OiVf4DsvLNS3Y1t68OPHfLf/Y+JT\nbfa80bQNAyWct2Ggz2bPNsZ8AtwDzDbGfAz8DPiuMWYlkA780XvS2+PAh97/fmqtDc8tKhJCLqXq\n1R+Xy8WUMf2496bLcXuvgTtaUsH8hRvYebCkTWYWkZYL9AlwG/BcatbY9X4euxRYGsh5RKLN11Wv\nb7y8jpqaOl/Va9Y3+lzS8147oiepSfG89GYBVTV1nC6v5unX8nhg6jBGNvjgFhEJDqdPgBORALvU\nqtemjMzszKN3ZdE+MQ6Aquo6XvjLZlblX/B0FxEJAIW5SBRoi6pXfwb0TGPOzGw6p7UDoK6+nlfe\n3cbyNXtULiMSRApzkSjgdrsZf+OgS6569adHp2Tmzsrhsq5nr59e+tkuFn1USF2dAl0kGBTmIlGi\na49UhrdB1as/Hdon8KO7shncN9239vGGA7y0rIDqmto2eQ0RaZrCXCSKXHVtvzapevUnqV0s379t\nJFcN7upby7XFPPv6Jsoqqi/wnSJyqRTmIlEkLj6WcZMH+e5v/7KIvTvb7uNN42Ld/OPNQ/lmgyMA\nhV+dZP6iDZwoVWujSKAozEWiTJ/+nRg45Oze86oPCqmuqmmz53e7XNw5aSC3TRjgWztQfIZfLljP\nwaNn2ux1ROQshblIFBozKZME7+eVl56qZN2qPW36/C6XixtH9+X+KUOIcXvOujt+qpL5C3PZvv9k\nm76WiCjMRaJSUnI8YyZl+u7nr99P0aFTbf46Vw/rzuzbRpAQFwPAmYoanlm8kbzC4ot8p4i0hMJc\nJEo1rnpd+V7hJVW9NmVYRiceuyuLlCRPuUx1TR0v/nUzn2480OavJRKtFOYiUerrqtfYWM8/A0eL\nTpO/bn9AXiujRypzZ+XQtUMi4Hnz8Kf3LctW71a5jEgbUJiLRLFAVb360y09iTmzcujbPcW3tmz1\nbv70waV9+IuIKMxFol6gql79SUuO57E7sxia0dG3tnLjQeb/cR1V1SqXEWkthblIlAtk1as/iQmx\nzL51BN8Y2s239vmWwzyzeCOny1UuI9IaCnMRCWjVqz+xMW6+N2UIk0ef/SjWHQdKmL8wl2MlFQF7\nXZFIpTAXEcBP1evHbVf16o/b5eL2CZlMnzTQt3boWBnzFuayv+h0QF9bJNIozEUE8FP1uqWIfbuO\nB/x1r7/yMh6dmeMrlzlRWsn8RRuw+04E/LVFIoXCXER8Gle9fva+pboq8CemjcvqzQ9vH0m7eE+5\nTHllDc++von124oC/toikUBhLiLnOL/qdXdQXndwv448PiObtOR4AGpq63jpzQJW5Abm2neRSKIw\nF5FzBKvq1Z8+3VKYOyuHbh2TAKgHFn1UyF9W7lS5jMgFKMxF5DzBqnr1p0uHRObMzCajR6pv7Z21\ne3nl3W3UqFxGxC+FuYicJ5hVr/6kJnnKZUYM6ORbW735EC8u3UxlEH6HLxJuFOYi4lcwq179SYiP\n4aFpw7lmeHffWv7OYzz1Wh6lZYG7Bl4kHCnMRaRJwax69Sc2xs19Nw1mypi+vrXdh04xb+EGik8G\n742FSKhTmItIk4Jd9eqPy+Vi2rgBzPjWILxjcOR4GfMW5LLvSGlQZxEJVQpzEbmgYFe9NmVSTm8e\n+PYwYmM8/2yVnKniiUUb2Lon8MU2IqFOYS4iF3Ve1euKwFa9NuWKy7vy8B0jSUzwXAdfUVXLc29s\n4outwT1aIBJqFOYiclHnVb1+WcTencccmcX0SWfOjGzSUzxvLmrr6vntsi18tO4rR+YRCQUKcxFp\nlsZVr6s+KKS6qsaRWXp3bc/cmTn06JTkW3ttxXaWfLKDOpXLSBRSmItIszWuev1i1R7HZumU1o45\nM3PI7JXmW3vv8328vHyrymUk6ijMRaTZGle9bg5i1as/7RPjeGT6KEZldvatrd1ymOf/nE+FQ0cN\nRJygMBeRFmlc9frpezZoVa/+xMfF8OC0YYwf1dO3VrD7OE++mscpB866F3GCwlxEWqRx1euxojNB\nrXr1J8bt5u4bDFPHZvjW9h4uZd6CXIpOlDk4mUhwKMxFpMWcrnr1x+VyMXVsBndPNr6Sm6KT5cxb\nkMuew879KkAkGBTmItIqTle9NuW6Ub14aNpw4rxHDk6VVfPkq3kU7HbmUjqRYFCYi0iruN1urrvJ\nOFr12pSsgV14dHoWyd4z7yuravn1knzWFhx2eDKRwFCYi0irdemewogQqHr1J7N3GnNm5tAx9Wy5\nzO+Xf8n7n+8LiSMIIm1JYS4il+TKazNCourVn56dk/nxrCvo1SXZt/bGJzt4/WOVy0hkUZiLyCWJ\ni48JmapXf9JTEpgzI5tBl3XwrX247it+99YWqmtULiORQWEuIpcslKpe/UlqF8fDd4wkx3TxrX2x\ntYhfLdlEeWXozCnSWgpzEWkToVT16k9cbAwPTB3GxOxevrWte0/w5KINnDxd6eBkIpdOYS4ibSLU\nql79cbtdzPjWIKaN6+9b21d0mnkLcjl8XOUyEr4U5iLSZkKt6tUfl8vFlDH9uPemy3F7r6s7WlLB\nvAW57DxY4vB0Iq2jMBeRNhOKVa9NuXZET/7lluHEe2c9XV7N06/lsWnHUYcnE2k5hbmItCn/Va+h\neQh7ZGZnHr0ri/aJcQBUVdfxwl82syr/oMOTibSMwlxE2tz5Va+FIVvUMqBnGnNmZtM5rR0AdfX1\nvPLuNpav2ROyM4s0pjAXkTYXylWv/vTolMzcWTlc5n0DArD0s10s+qiQujoFuoQ+hbmIBEQoV736\n06F9Aj+6K5vBfdN9ax9vOMBLywqorql1cDKRi1OYi0jAhHLVqz9J7WL5/m0juWrw2QKcXFvMs69v\noqyi2sHJRC5MYS4iARPqVa/+xMW6+cebh/LNBkcVCr86yfxFGzhRqnIZCU0KcxEJqFCvevXH7XJx\n56SB3DZhgG/tQPEZfrlgPQePnnFwMhH/FOYiEnChXvXqj8vl4sbRfbl/yhBi3J4z+Y6fqmT+wlx2\n7Fe5jIQWhbmIBFw4VL025eph3Zl92wgS4mIAOFNRw9OL88grLHZ4MpGzFOYiEhThUPXalGEZnXjs\nrixSkjzlMtU1dbz41818uvGAw5OJeCjMRSQowqnq1Z+MHqnMnZVD1w6JgOcNyZ/etyxbvVvlMuK4\n2GC/oDFmPLAEKABcQD7wNLAAz5uLQ8Asa62uAxGJMF9Xvf7/T3cBnqrX/qYLXbqkODxZ83RLT2LO\nrBx+tWQTew+XArBs9W5Onq5k5vWDiHFr/0ic4dRP3qfW2onW2gnW2tnAz4EXrLXjgZ3AfQ7NJSIB\ndn7Vqw2rPdu05HgeuzOLoRkdfWsrNx7kN38toKpa5TLiDKfC3NXo/nXA297bbwPfDOo0IhI0/qpe\n89eHz+F2gMSEWGbfOoKrh3bzreVtP8ozizdyulwHFSX4nArzIcaYN40xnxljvgkkNTisXgT0cGgu\nEQmCxlWvH761JaSrXv2JjXHzD1OGcOPoPr61HQdKmL8wl2MlFQ5OJtEo6L8zB7YDP7XWLjHG9Ac+\naTRH4732JoXL79lCnbbjpdH2a50bvzOcPTuOUXKinPKyanJX72XazGynx2qxf749i17dU/nDsgIA\nDh0r44lXN/Cz+6+mb4/UC35vW//s6Gfx0oXrNgx6mFtrD+I5AQ5r7S5jzGHgCmNMgrW2EugFNOvD\nhIuLSwM3aBTRdmy9Ll1StP0uwdhvZfLOG5sBKMg7QJ/MjvQd0MnhqVpuzOCuxNQP5Q/Lv6S2rp5j\nJRU8+sIq/vWW4Zg+6U1+X1v+7Ohn8dKF+ja80BuNoB9mN8bcZYx52Hu7O9ANeAW41fuQW4D3gz2X\niARfOFa9NmX0kG788PaRtIv3lMuUV9bw7OubWL+tyOHJJBo48Tvzt4DxxpjPgL8C/wT8G3CPMWYl\nkA780YG5RMQBYyZlkugtYwmXqtemDO7XkcdnZJOWHA9ATW0dL71ZwIrc8DrBT8KPE4fZTwM3+/nS\n9cGeRUScl5Qcz/U3D2XZ4o2Ap+p14JCudL3I75tDVZ9uKfx4Vg7PvrGJI8fLqAcWfVTIydOVTBvX\n3+nxJEKp4UBEHDfiit7nVL2ufK8wbKpe/encIZG5M7Pp3/PsG5J31u7llXe3OTiVRDKFuYg4rnHV\n69Gi02FV9epPSlI8j07PYkSDE/pWbz7k4EQSyRTmIhISvq56/dq61XsoOVHu3EBtICE+hoemDWfs\ncFVnSGApzEUkZIR71as/sTFu7r3pcqaM6Xve14pPhvebFQkdCnMRCRn+ql5twRFnh2oDLpeLaeMG\nMPP6Qeesz1uQy74joXtds4QPhbmIhJTGVa9rVuwIu6rXpkzM7n3O/ZIzVTyxaANb9xx3aCKJFApz\nEQk5V16bQUpqAgCVFTWsWbHD4YkCp6Kqlufe2MQXW8P/CIQ4R2EuIiEnLj6GcZPPHpLe/mUR+3Yd\nc3CiwEhP8bxhqa2r57fLtvDRuq8cnkjClcJcREJS46rXzz7YTnVVZH1e+NyZOfTolOS7/9qK7Sz5\nZAd1YX7SnwSfwlxEQtaYSZkktPMUVZaWVLBu1W6HJ2pbndLaMWdmDpm90nxr732+j5eXb6UmjEtz\nJPgU5iISspKS4xkzKdN3P3/9fooOnXJworbXPjGOR6aPYlRmZ9/a2i2Hef7P+VSE6YfOSPApzEUk\npJlh3SKq6tWf+LgYHpw2jPGjevrWCnYf56lX8zgVIWfyS2ApzEUkpEVi1as/MW43d99gmDo2w7e2\n53Ap8xbkUnSizMHJJBwozEUk5EVi1as/LpeLqWMzuHvy2eKcopPlzFuQy57DkfXrBWlbCnMRCQuR\nWPXalOtG9eKh7wwnzns04lRZNU++mkfB7si7PE/ahsJcRMJCpFa9NiVrUBcenZ5Fsvds/sqqWn69\nJJ+1BYcdnkxCkcJcRMJGJFe9+pPZO405M3PomHq2XOb3y7/k/c/3RexRCWkdhbmIhJUrr+0XNVWv\nAD07J/PjWVfQq0uyb+2NT3bw+scql5GzFOYiElbi4mOjouq1ofSUBObMyGbQZR18ax+u+4rfvbWF\n6prIukxPWkdhLiJhJxqqXhtLahfHw3eMJMd08a19sbWIXy3ZRHmlymWincJcRMJSpFe9+hMXG8MD\nU4cxMbuXb23r3hM8uWgDx09VODiZOE1hLiJhKRqqXv1xu13M+NYgpo3r71vbV3SaR19YxeHjKpeJ\nVgpzEQlb0VD16o/L5WLKmH7ce9PluL3X6hUdL2Peglx2HixxeDpxgsJcRMJWtFS9NuXaET35l1uG\nE+/9858ur+bp1/LI33nU4ckk2BTmIhLWoqXqtSkjMzvz6F1ZpCTFA1BVXcfzf97MqvyDDk8mwaQw\nF5GwF01Vr/4M6JnGU/8yls5p7QCoq6/nlXe3sXzNnqjaDtFMYS4iYS/aql796d01hbmzcrjM+6YG\nYOlnu1j0USF1dQr0SKcwF5GIEG1Vr/50aJ/Aj+7KZnDfdN/axxsO8NKyAqprIvs6/GinMBeRiBFt\nVa/+JLWL5fu3jeSqwWdLdXJtMc++vomyimoHJ5NAUpiLSMSIxqpXf+Ji3fzjzUP5ZoMjFYVfnWT+\nog2cKK10cDIJFIW5iESUaKx69cftcnHnpIHcNmGAb+1A8Rl+uWA9B4+ecXAyCQSFuYhEnGisevXH\n5XJx4+i+fG/KYGLcnrMDj5+qZP7CXHbsV7lMJFGYi0jEidaq16aMGdaD2beNICEuBoAzFTU8vTiP\nvO3FDk8mbUVhLiIRKVqrXpsyLKMTj92VRUpSHADVNXW8uHQzn2484PBk0hYU5iISkaK96tWfjB6p\nzJ2VQ9cOiYDnTc6f3rcsW71b5TJhTmEuIhEr2qte/emWnsScWTn07Z7iW1u2ejd/+sBSWxe9Ry7C\nncJcRCJatFe9+pOWHM9jd2YxNKOjb23lxoP85q8FVFVH35n/kUBhLiIRze12M/7GQVFd9epPYkIs\ns28dwdVDu/nW8rYf5ZnFGzldrnKZcKMwF5GI17VHKsOjvOrVn9gYN/8wZQg3ju7jW9txoIT5C3M5\nVlLh4GTSUgpzEYkKV6nq1S+3y8VtEzKZPmmgb+3QsTLmLcxlf/FpByeTllCYi0hU8Ff1undn9FW9\nNuX6Ky/jn24e6iuXOVFayfyFG7D7Tjg8mTSHwlxEokbjqtdVHxRGZdVrU0YP6cYPbx9Ju3hPuUx5\nZQ3Pvr6J9duKHJ5MLkZhLiJR5Zyq11OVUVv12pTB/Try+Ixs0pLjAaipreOlNwtYkRvd1+iHOoW5\niEQVVb1eXJ9uKfx4Vg7dOiYBUA8s+qiQv6zcGfWX9YUqhbmIRB1VvV5c5w6JzJ2ZTf+eqb61d9bu\n5ZV3t1GjbRVyFOYiEnVU9do8KUnxPDo9ixEDOvnWVm8+xItLN1Opcw1CisJcRKKSql6bJyE+hoem\nDWfs8B6+tfydx3jqtTxKy3StfqhQmItI1FLVa/PExri596bLmTKmr29t96FTzFu4geKTegMUobOH\n8gAAB6ZJREFUChTmIhK1VPXafC6Xi2njBjDz+kF4NxdHjpcxb0Eu+46UOjqbKMxFJMqp6rVlJmb3\n5oFvDyM2xhMfJWeqeGLRBrbuOe7wZNFNYS4iUU9Vry1zxeVdefiOkSQmeK7Xr6iq5bk3NvHFVh3V\ncIrCXESinqpeW870SWfOjGzSUzxvgmrr6vntsi18tO4rhyeLTgpzERGaqnqtcXCi0Ne7a3vmzsyh\nR6ck39prK7az5JMd1OlEwqBSmIuIeJ1f9brH2YHCQKe0dsyZmUNmrzTf2nuf7+Pl5VtVLhNECnMR\nES9VvbZO+8Q4Hpk+ilGZnX1ra7cc5vk/51OhoxtBEVJhbox5zhizxhiz2hhzhdPziEj0UdVr68TH\nxfDgtGGMH9XTt1aw+zhPvZrHKV0dEHAhE+bGmHFAprV2DPA94HmHRxKRKKSq19aLcbu5+wbD1LEZ\nvrU9h0uZtyCXohNlDk4W+UImzIFJwJsA1tptQAdjTHtnRxKRaKSq19ZzuVxMHZvB3ZONr4yn6GQ5\n8xbksuewfmURKKEU5t2B4gb3j3rXRESCrnHVqy047PBE4eW6Ub146DvDifMe4ThVVs2Tr+ZRsFuX\n/AWCK1R6iI0x/wkst9a+7b2/CrjXWqv2BhERkQsIpT3zg5y7J94TOOTQLCIiImEjlML8Q+BWAGNM\nNnDAWnvG2ZFERERCX8gcZgcwxswDxgO1wIPW2s0OjyQiIhLyQirMRUREpOVC6TC7iIiItILCXERE\nJMwpzEVERMJcrNMDtIYx5jngG0Ad8H1r7XqHRwppxphheNr1nrPW/sYY0xtYgOfN3CFglrW22hgz\nA5iN5wTE31tr/8uxoUOMMeYpYCwQAzwBrEPbsFmMMYnAfwPdgATgF8AmtP1axRjTDigAfg58jLZj\nsxljxgNL8Gw/F5APPE0EbMOw2zNXh3vLGGOS8GyjvzVY/jnwgrV2PLATuM/7uJ8AE4EJwA+MMR2C\nPW8oMsZcBwzx/szdCPwKzzZ8UduwWf43sM5aex1wB/Ac2n6X4ifA1zVq+rvccp9aaydaaydYa2cT\nIdsw7MIcdbi3VAWeAGpYwHMd8Lb39tvAt4DRwBfW2tPW2gpgNXBNEOcMZSuB27y3TwLJeC6hfMu7\npm14AdbaN6y1z3jv9gG+QtuvVYwxBrgceAfPnuV49He5pVyN7l9HBGz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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 8))\n",
"k = np.linspace(0, 1000)\n",
"m = np.linspace(0, 1000)\n",
"#vinegar supply\n",
"plt.plot(k, (1800 - k*4)/7, lw=3, label='vinegar')\n",
"#tomato supply\n",
"plt.plot(375 * np.ones_like(k), k, lw=3, label='tomato supply')\n",
"#mustard supply\n",
"plt.plot(m, 200 * np.ones_like(m), lw=3, label='mustard supply')\n",
"#factory limit\n",
"plt.plot((350 - k), k, lw=3, label='factory capacity')\n",
"#minimum mustard\n",
"plt.plot(m, 100 * np.ones_like(m), lw=3, label='mustard minimum')\n",
"#minimum ketchup\n",
"plt.plot(100 * np.ones_like(k), k, lw=3, label='ketchup minimum')\n",
"#set axis limits\n",
"ax.set(xlim=[0, 550], ylim = [0,350], ylabel = 'mustard', xlabel = 'ketchup')\n",
"#legend\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we need to specify our system to solve it.\n",
"\n",
"To do this, we give an array, c, to be minimized, a 2D array (A) which gives the coefficients to be satisfied, and a 1D array with the upper bounds.\n",
"\n",
"We can also optionally use equalities rather than upper bounds."
]
},
{
"cell_type": "code",
"execution_count": 202,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: -130000.000000\n",
" Iterations: 3\n"
]
}
],
"source": [
"#optimize minimizes, so we take the negative of our values\n",
"c = [-400, -300]\n",
"#our input formula\n",
"A = [[2,0], [4,7], [0,3], [1,1], [-1,0], [0,-1]]\n",
"#our values\n",
"b = [650, 1800, 600, 350, -100, -100]\n",
"#bounds as a tuple\n",
"k_bounds = (0, 400)\n",
"#secondary bounds\n",
"m_bounds = (0, 400)\n",
"#linprog:\n",
"res = linprog(c, A_ub=A, b_ub=b, bounds=(k_bounds, m_bounds), options={\"disp\": True})"
]
},
{
"cell_type": "code",
"execution_count": 203,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
" fun: -130000.0\n",
" message: 'Optimization terminated successfully.'\n",
" nit: 3\n",
" slack: array([ 150., 100., 300., 0., 150., 300., 0., 0.])\n",
" status: 0\n",
" success: True\n",
" x: array([ 250., 100.])"
]
},
"execution_count": 203,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res"
]
},
{
"cell_type": "code",
"execution_count": 165,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"130000"
]
},
"execution_count": 165,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"250 * 400 + 100 * 300"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can generalize this to multiple dimensions and variables! In scipy, we only have a simplex solver available, so to find faster and other solvers, try playing with pyomo and pulp. In general, these packages produce the same arrays to pass into the solvers from nicer inputs - the solvers and algorithms are the differences here."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Clustering\n",
"\n",
"Clustering allows us to put multidimensional data into bins by similarity.\n",
"\n",
"Clustering is one of the major methods used, and be both supervised or unsupervised - where we know a priori the ;number of clusters or not.\n",
"\n",
"Today we will use two supervised clustering examples, before we move on to more sophisticated methods of clustering in the next lessons.\n",
"\n",
"First, let's load in some libraries and data:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iris Plants Database\n",
"\n",
"Notes\n",
"-----\n",
"Data Set Characteristics:\n",
" :Number of Instances: 150 (50 in each of three classes)\n",
" :Number of Attributes: 4 numeric, predictive attributes and the class\n",
" :Attribute Information:\n",
" - sepal length in cm\n",
" - sepal width in cm\n",
" - petal length in cm\n",
" - petal width in cm\n",
" - class:\n",
" - Iris-Setosa\n",
" - Iris-Versicolour\n",
" - Iris-Virginica\n",
" :Summary Statistics:\n",
"\n",
" ============== ==== ==== ======= ===== ====================\n",
" Min Max Mean SD Class Correlation\n",
" ============== ==== ==== ======= ===== ====================\n",
" sepal length: 4.3 7.9 5.84 0.83 0.7826\n",
" sepal width: 2.0 4.4 3.05 0.43 -0.4194\n",
" petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)\n",
" petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)\n",
" ============== ==== ==== ======= ===== ====================\n",
"\n",
" :Missing Attribute Values: None\n",
" :Class Distribution: 33.3% for each of 3 classes.\n",
" :Creator: R.A. Fisher\n",
" :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
" :Date: July, 1988\n",
"\n",
"This is a copy of UCI ML iris datasets.\n",
"http://archive.ics.uci.edu/ml/datasets/Iris\n",
"\n",
"The famous Iris database, first used by Sir R.A Fisher\n",
"\n",
"This is perhaps the best known database to be found in the\n",
"pattern recognition literature. Fisher's paper is a classic in the field and\n",
"is referenced frequently to this day. (See Duda & Hart, for example.) The\n",
"data set contains 3 classes of 50 instances each, where each class refers to a\n",
"type of iris plant. One class is linearly separable from the other 2; the\n",
"latter are NOT linearly separable from each other.\n",
"\n",
"References\n",
"----------\n",
" - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
" Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
" Mathematical Statistics\" (John Wiley, NY, 1950).\n",
" - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
" (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.\n",
" - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
" Structure and Classification Rule for Recognition in Partially Exposed\n",
" Environments\". IEEE Transactions on Pattern Analysis and Machine\n",
" Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
" - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\". IEEE Transactions\n",
" on Information Theory, May 1972, 431-433.\n",
" - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al\"s AUTOCLASS II\n",
" conceptual clustering system finds 3 classes in the data.\n",
" - Many, many more ...\n",
"\n"
]
}
],
"source": [
"from sklearn import datasets\n",
"from scipy.cluster.hierarchy import dendrogram, linkage, fcluster\n",
"\n",
"iris = datasets.load_iris()\n",
"\n",
"dat = iris.data\n",
"target = iris.target\n",
"print(iris.DESCR)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's plot the first two dimensions:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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8PIKnnnqG++//g0MyDR7ch0OHDlJWVkZcXBxr1ybbjKCpTnFxMZ07t7UOt42L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\nWCphYRXH0YOCAsnNde/bxxmNRdYCDxA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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(dat[:, 0], dat[:, 1], c = target);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can plot these using seaborn. We will use the same dataset, but in a slightly different format:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" sepal_length sepal_width petal_length petal_width species\n",
"0 5.1 3.5 1.4 0.2 setosa\n",
"1 4.9 3.0 1.4 0.2 setosa\n",
"2 4.7 3.2 1.3 0.2 setosa\n",
"3 4.6 3.1 1.5 0.2 setosa\n",
"4 5.0 3.6 1.4 0.2 setosa\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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uJXUDfzPwr6SWA2uBUVKIasnQVEJTK0rArI0upz9vgJIkCYAzgOOBDwKbgetJ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\nUNAkIiIiksH/A/Aw2i29uotPAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"iris = sns.load_dataset(\"iris\")\n",
"print(iris.head())\n",
"sns.clustermap(iris[['sepal_length', 'sepal_width', 'petal_length', 'petal_width']], col_cluster=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, we quickly run into the same problem as last lesson - how do we get the values out?\n",
"\n",
"Under the hood, seaborn is using [scipy.cluster.hierarchy](https://docs.scipy.org/doc/scipy/reference/cluster.hierarchy.html)\n",
"\n",
"To recapitulate the results, we can use the function linkage:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(149, 4)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"linkagemat = linkage(dat, 'average')\n",
"linkagemat.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here I am using straight pairwise differences, we can use a [wide range of distance metrics](https://docs.scipy.org/doc/scipy/reference/spatial.distance.html). You should also correct your data for outliers and different scales - here we have data all in a similar scale, so the differences are simple to use as is.\n",
"\n",
"The method for clustering used is 'average', also known as the UPGMA method, common in ecology (and many other fields).\n",
"\n",
"This works by finding the two most similar items, clustering them and meaning their values. The branch length is then the distance between these objects. The method works recursively until there is only one group left. We have a [wide range of methods to use here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html#scipy.cluster.hierarchy.linkage).\n",
"\n",
"Now we can plot using dendrogram:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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37xT4AwAAANCsN8EyAAAAAOw6s3o5uXpl9DUIJnldhD0185t3tgZ94B1Cjcd5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\nFhEREREREREREZG+/H/8HlyxYbL3sgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(25, 10))\n",
"dendrogram(\n",
" linkagemat,\n",
" leaf_rotation=90., # rotates the x axis labels\n",
" leaf_font_size=8. # font size for the x axis labels\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From here we can cluster [using a variety of methods](https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.fcluster.html#scipy.cluster.hierarchy.fcluster), with the function fclust.\n",
"\n",
"We can specify a number of clusters, which works by descending a line until we hit the given distance or specifying a distance. Let's specify three clusters:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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AAABQGKEzAAAAAACFae7tBaVSaWiSHyTZOklbkq+Vy+Xr3/H8nCQvJ6kkqSb5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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"out = fcluster(linkagemat, 3, criterion='maxclust')\n",
"#and plot\n",
"fig = plt.figure(figsize=(25, 10))\n",
"ax1 = fig.add_subplot(1,2,1)\n",
"ax2 = fig.add_subplot(1,2,2)\n",
"ax1.scatter(dat[:, 0], dat[:, 1], c = target, cmap=plt.cm.Paired)\n",
"ax2.scatter(dat[:, 0], dat[:, 1], c = out, cmap=plt.cm.Paired)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also use kmeans, another clustering algorithm. This works by putting k random centroids on a graph, finding the closest centroid to each point, then moving centroids to minimize the error within each group.\n",
"\n",
"Let's do this in scikit-learn, the machine learning library.\n",
"\n",
"We will cover sci kit learn exclusively in the next lesson, but for now we can do a brief overview.\n",
"\n",
"We have already imported the dataset, iris from it. Datasets are generally used or made into numpy matrices, with data and targets as seperate arrays. The data are stored as np.float64 by default, and we need to convert categorical variables into dummy variables, but targets are ok as categorical variables.\n",
"\n",
"There is a [wide range of clustering algorithms available](http://scikit-learn.org/stable/modules/clustering.html#clustering). For now we will run a [simple kmeans](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html).\n",
"\n",
"Scikit-learn is set up to allow validation, pipelining etc etc. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
" 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
" 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
" 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
" 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1,\n",
" 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
" 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1], dtype=int32)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.cluster import KMeans\n",
"\n",
"#describe the model note, no data yet\n",
"k_means = KMeans(n_clusters=3)\n",
"k_means.fit(dat) \n",
"k_means.labels_"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
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yB52lj7SUL+bd2nrd+S/bbCNFNXWERHYFQK1W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rZM2mJE3nfCCc2OBDTZupzp/JUkn0nStsLt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\niH33ySO3XJOeBQsy69kZ2aq9J8OGDVtuzQlHHJ4Hrrsk3V3z8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WRlZbRqJiGE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UdujJtL8863YcG2Pzmp9YN/sZ/LFQjh93vvxfuvd0nSOF+XnM//cTUJqFNjyG8b9/ik5de7jU\nFBcX8c79NxDqrMCsaOl/20NMue23Tc7jTc/cdzPq7P0YtCqyrEb+s2Q3Go3GpWb/LxvIXPxfDDYT\nFVFduf6vL7jNtTU/zmXr56/ih40yVSD3vT2XjrFxLjWnMtP58T9Po6rIRQmN4YY/v0hMrOvvo7co\nisKcfz2L6dhWnBoDvabczejJN7nVzf/43xTsWgEqNfGjpjPlV/c2S57GOnnsMMs/eBFVZQFKWBy3\n/PVVIttFu9ScOdeUoHZc+8BzbnNNXN58sV8risLXCxZQbFPA6SSxQzsmjh3jVvfj8uWkl1SCCmIC\n/bj5uqktH/YMO/fsZu7KtQRFRFFRXMCvJ45nQP8BLjXl5WXMWbQYp94fbBYmDR9Cj27dXGqsViuf\nfjcXq84PDXaGJSVyRb/+LflS3GxZs5S9Cz9EZTWj7zyAux/7p0c9dNPqn1g580kC1TbKFCO/feUL\neiSdu4dezHnNarXyzIwJhFkLsShqEsbczl3/9w+XGkVR+HbWPylP2YhGr6Pz2NsZP/0Ot7Fe++vd\nOE7uRAU4YnrzVAPXGS1p7ZIFHPr0VeICdWRV2eh17z8Ye63rNVR5WSnfvPEYFJ1ECYjk6t8/SY/k\nvi41VVVVzLpvGt00NZTZFSKu+RXTfvugS403r9caozHXa4d3byNt3gcYrVVUhMcz+eEX8fPza7ZM\nF+JwOFj09vME5R7BqjXS4do7GTh6gkuNoij89OFb6NN24lBpCBp5PVdef1srJRZtkS/2a2jafaii\nM6Cxmlr9PtTpdPL3V14hqH0c1hozMf56HrjnHre673/8kdxqCyjQOSKY6yZOdKtZsW4dR3IK0eq1\nhGng1zfe2BIv4ZyKCvLZOPsFgioLMfmHMfC3fyOuS/cmj2O1Wpl133S6UkW1XUE3fCo3//Exlxpv\nnte+ev1ptCkb8NOoOKGL4KH357md+0/fh/o7LZSGd2rwPnTD4nmcnDuTcK1Cpk3Lja9+RsxZ96Et\nyeFw8OCUAcTrLVgcCs74/rzw3ly3uhWfz0KVsglFABDyLwAAIABJREFUpUY/aAJjb73breadpx6k\n+uB61CoFc3g3nv94kVuNt67XGqMx12smk4k5r/4NJf8Yil8Io2Y8Su+BQ5slT2OtX/o9h3/6ApXD\nQkDPEdz5f8+iUqlcanZuXsuO72aislSiie3N3X9/3W2uiYvT6FmZmJi4GfgS+MsZX24PFJ6xXQB0\n8E40z/2wajWJY68jeeR4ksZNZemmzW413y9ZSrfRU0geOZ5eY6eweudeFEVphbS19u/fhyUoitE3\n3M7wSdMYOu0O3po9y6XGarWy+XAayWOuJXnkeOJHXMP8pUvdxlqxZQdJY6eQOHwc3cdMZd6y5S31\nMhq0fsFXXFO0k6lhTqaHWHCu+pzCwsILf+NZNq5eRv+iA9yRGM1tPdpxZ0g1n73xrEtNRUU5FYs/\n5sZgM1PDnEytOMCabz7xKPe6957l6lg1w2P9mNhR4Zvn/+hW8+P7L9PXlEI/YwW9TEdY8eHLbjWz\nH5nBhPZWhsf6MS5Ox95v38bpdHqUyRvWrl1N+9JDTOwWyphOIdwQr+Hxu693qbFareT88B43BVUz\nNVzhRksqa76Y7TbWls9eZVystvYYxdj55An3i7ifPnyZ/tZU+hkr6F9zhKXvv9Jsr23Z95/T4fgy\n+hnKGKDN5/gP77jNtS3rV6Df+S399SX01xVhWv9fDuzZ0WyZGmPlR6/Q35ZGP2MF/Uwp/PiB+zw6\nc671t6U1ONeEAN/q12s3bsTYtS/JI68h+aqJZFnhZPpJl5o9+/dRGRhF8lUTSB41AUd0Alt3bG+l\nxLXmrlzDhDvuZfikaUy84w98s2K1W828ZcvrrkWSx05h+Rb3zPOXLiXhygkkjxxP4shJbDpwBLvd\n3hIvoUEVFeUc+O4t+qtz6Wcso1PWWn788n2Pxlo56ykmJ+i5Ki6A6+LUfPHcH9xqvHVee/2R3zIx\nooqr4gK4Jt6Pgo1fk5eX61Kzbul8Qg/+QD9DCb1V+eQtm83JE2kuNfPmfEynkj2MjfdnTLw/yeYj\nfDb7TY8yecuBT1/jkUEJ3NozhkcGJbD/I/ce+sP7r9C3cm/tcXScYM1H7sfxg0d/x+OJIfy6Zwf+\n2DuGqtXfUFNT41Ljreu1xmjM9ZqiKBz7diY3B1YyNVzhVudJ1vz3nWbJ01hrvvmY66sO1F4bBZsp\nXfwRVVWVLjVbli9iRPZmpoY5uCHUStDP35JxMu0cI4rLmS/166behyaPHN8m7kNfn/kfRky/k+GT\npjF62q8wBYRz5Mhhl5pftm3F2aEryaMmkHzVBMr8wjhwMMWlJu1EGtk2Db1GTyRx+NXoO/dm7aaN\nLflS3Gz+9C1u1+UzNULhVr8Sdn/xtkfjfPTEA/y5k55burfj7qRo/HYsdeuh3jqvpezfS8Lxzczo\nGc0t3dtxb7SDT174m0vNmfeh14bYz3kfevK7/3BfUhS3dG/Hw0lhLHjW/V69JT06YzLTO2kZ0zmE\nid1CaVeUwpYtrutQOzasot/R1VwX5uD6UBvxe37k0N6dLjXrVy4l+OQGxsb7MzougMGqLGb/80mX\nGm9erzVGY67XFrz/Kr1Kd9DPWE5/JZMNn77SqutreXm5nPzhXfpr8+lnKCP66FJWLPjSpcZqtbJ9\nzuv0V2XTz1hOj/xNLPzUs98jcW4XfNL5tNTU1CsTExP7AV8B/c5RpjrH111ERQU1drce0fn7u7yD\nofHzc9un1t8P9RlPduoDgwkJMWAwGM45bnPmPnYilfju9U9JBYWGUeNwuuwzNzeXwMj6px/1BiNq\ng96lRlEU1EZj3bZarUbr59/sx/x8tKZiwgz1U62H3kZVeR5RyV3O+T0N5T2+byt3nfH1DoFGbAWZ\nLrVFhVl0VZsAfwCC9BoMljKPXn+Aykrtx6yBSqUikBq3cfS2Mpe5prOUutUEOE1o1PU1IVoHfn4q\ngoNb52ey95dV9AytnyPBRi1KQYHbXItVqoHaOqNWg7+90qXG6XQSoLZx+jSiVqkIVExur19nKXXZ\n1ts8+3mcraExHFUFhOnqj3U7KqksyyX5jLlWUZhJpKG+AXY02CjKPU7UhHEXnelCzvW6tTWldWdP\nlUqF3lru0VxrLq15/hBN581+Dc378zfbzIREtqvbbt+5B0WlmQwZXP+UZnFpIe26DKrbjoiJp/zY\ntvPmau45GxgacdZ2uPu5zz/A5XdWbXS/FlEb9Oj09dcd/hHt0GrtREWFNUPqCysqzCLMXgrUPuHh\np1VRYSr26FgHntEfVCoVAVia7bymMRVjDKx/jiIuUENeXgZ9+tQ/hWMpzyFUX7+vGK2FkrwTDBla\nf+2VfmQXI4L1ddsdgvQcO3mwVc+BHfxdL9Xb+2ndj6O13PW6t8b9OIY4qzBo/eu2e4QYqKoqIi4u\nqe5rnlyvNUZDx68x12smk4lIRxWn55FWrSbIUdWqvc9oLSdAV3+MOmPCbq8mKiqm7muOijza+9XX\nJPnDobx0Bg1x/WuI5iD92rf4Ur9urvvQ5p6zNgUCQ+p7alz3nqSdOMKoUUPqvlZRXUFEj/pzYfvO\nPShM30VU1PC6r23ZnkeHLvU9JTQqGnPJyVb9nQtxVruc+4PPuldrSEP/P+Cs81rPMD/yz+qh3jqv\nnTy0i1GRgXXb4X56NIX5Ht2HRp7xMKpapSJCbWvVn4equpigyPpj1CnUwO4ta7j++kl1X7OUnCIh\n4IzjGKhmfV46UVFj6752aO8vJIfWXxtG+GtJyT3htubR1Ou1xjjX9zfmek1nK3dZ8zDUlF5wfc1b\nGsp99NAOotXVnL6GCNKpKK7Ic5trwbaS00s+6DXqBq+hmsvl0rMb8w8JDgQKUlNTs1NTU/clJiZq\nExMTI1NTU4uAHFzfee34v6+dV2Fh5YVKLorKUoPNakGnN+B0OFBM1W77NDgVqivLCQgKQVEUbOWl\nVFRYAWuDY0ZFBTVr7mGDh/Px0tVcObn2z3SyTxwlLirKZZ8qlR+VuZnQq/ZPb8uLCgjQ6txzmapQ\nFAWVSkWNqRqt3dbsx/x8/OJ6knZ4A90Caxf5d9kDGR6dcM5M5zrWQydOZ/XbG7muSyQAe/Mr6DB4\nokttYFAUW1VhdMcCQEa1HV1Md49efymBOBUrapUKq8NJlaGd2zhKaAK2ssPoNGocTgVHRJxbjS2k\nI1XWIwTqNSiKQqHdiMWiarWfyeSb72LBYwsZ27n2T92yyi1EdBvqNteOaSK4gmoA8sx2nJGd3DKX\nKn51c81sc1LjH+1W4wiNx5GXgUatwu5UcIS4H6OmOtcciUjoTd72H2hvcACQrW3P6PauueMTB7Fn\nzRw6G2qf8DpmDWRs8uBm/3mc7xxiD43DWZZfN9eUMPffj8bMtZbO3VZdLg38bM3Rr6F5e3aHyGgO\nHj9CTNfaj6vMOLCToVcNd9lnt07dWLV/J537DQYg89BeRnRyPx+d1hJztqIgF4fdjkarxW6zUVmY\n57ZPjc1KjdmE0c+/9kkPc5VbTYBWS3lxISERUQBU5WXjdOpb7XcuMCiKAr9YYskHoMiiIjQuyaNj\nXUIATsVR30P1Ec12XgtM6EVBxlraBdbefB0pczK5S7LLWNFd+nN803fEGmwAnFDCuKFbf5ea4dfc\nyP73f6ZfdO3HNxwuMtP/tmtb9Rx4rNKO3elEq1ZjczhJq3a45VGFd6ImfzdGrRpFUXCEuh9HS3g8\neVXZtA+svYnfUVzDwND2LnVNvV5rjHPNkcZer+UaI1GUUlQqFaUWO9b41u192uiuZJ7YQvz/3gxI\nUYcz0S/MpTa0U29S9q6id1DtGyG/mPT06ta3Va8z2rLLsWf7Yr9ujvvQlpizMRHh5KQfJ6ZTVwAO\n7/iFe69zvX9MiIln66F9xCXXrvuf3Ledif16utR0SejO/M3b6THkKgBOHTtMv6j2rfo7Vx7YAUtZ\nHgZtbQ8tDXC/DzvTuY63KqY7GWX7SQipfRNwS4GJ68/qod46rw0cNYH1y7/gth61DxwcKakiqMfV\nHt2HplvVdXOtymqnUB/aqj+PsM59yC7bTWxw7QrmvnwTtzx6m0umdt36sWvbYq4Irj2OP1eoie85\n0KVm9LU3s/L5RQzrWPvzSCupoduEsW5rHk25XmuM8/0+NuZ6TRfVhaqMzQTqan8ultC4866vecu5\ncreP7cFaTTvCKAEg16IhpnNft7lWFhALZANQZlXw6+DZ2pG3crdlnvZr1YUeeU9MTPwLkJCamvpw\nYmJiNLAtNTW10xn//wAwhdpm+Avw69TU1PP9rYXS3AfXarXy7aJFWFVaVHYLt02dQmCg6wFyOp3M\nXfwjVTYFxWbh+qvHEd2u3TlGbJlJsWzlSn4+cAitwUiw2skjf3T/E5GsU9ks3/QLKq2OcD890ydP\ndvtcmpKSYhasWIU+IACN3cbtN9zg9nm9LW3jwm+wHNqGVa0h8boZdOt1rjfzz3+sl33zKXmrvkOv\nUnAkDmPGYy+41aQfO8zBBf9F77Cg7TGQsTff5VHm3JxTfPjYXQQ6qqn2i+BvM+fi7+/vUmO1Wpk7\n+xXsRZn4RcUw5XePu801u93OG3/+NfqyLKpVBm558l2Sert+1mJL+/Td1zi87DP8NGCJ6MJrn7v/\neVxOZjq7v30fg80MnXox/tf3us21E8dS+fK5BwhwmrEEtedvM79Dr9e71JjNZr6f9RLOslzUYTHc\n+qenMJ7xFIQnzjdHVsz/gty9G3FqdIy4+T569nb/fNTNq5dwbMMiFJWKvpN+xRUjxjYwknedL3Nl\nZQXzZ70EVUVoIxO47U9Pun2W1JlzTRUUxU1/esptrrV07rYqKiqo0U8FXUqaoV9DC/TsNRs3ciK/\nCMXpYGivnvTr3cetZvvu3exLOwkqSI6P5cqh5/6MuJaYs6WlJbz23vsYQ8Ixl5XwxJ/+SGhoqEuN\nw+Hg24ULMStqsFm4adIEwsLCXWoURWHB0p8orbGi1zi5eugwOsZ0bNbsF3Li6GE2fDMTla2GqN4j\nmHL7785Ze75jnZNzipmP3EGAsxqzMZIn35t/3h56see11/92D7asFCyKlmvue5pRV1/rVrN2yfdk\nbluBzs9Anwm/oe+gYW41X3/4L9JWf4dKBbHDp/LbvzztUR5vyc3N4dM/3kycH2Sa4d73FxAd3d6l\nxuFwMPe9V7HkHUfxD2fa/U8SFu4615xOJ+/+7R5CSjKpcGq46sEXGDBkOGdryvVaY5xvjjTmeq0g\nL4dtc2ZitFZjj+nGpLsfdLsWaQ7ny7127mc40vZgURvoc/PvSOiW6Fbzy7IfqNqzAZtKQ+eJt5Lc\nAp9r6Yv9Gi7Pnu2r/bop96HoDPiplfPeh7bUnH1z1kwqFS3WGjOj+/dm0vhr3Go2bd3KkaxToMCA\n7p0ZNGCgW82+lANsP5iKwU9PbFgo40Zd1ezZz8dqtbLio7cwluVi8g/n6nsfOW8PPd/x/vDJPxKU\nn0alQ02fGQ8zfJz7Z1p767y2ZtFcMhZ+gp9awZzQh3ueecut5vR9aKDahq1DYoP3oSePHWXpKw8T\nobZRZAznvn9/4XYf2tIe+81kDKUnqXFCryn3cPefHnWr2bF2OcVbl6Oo1HQcM42+w93n0cKvPmbf\njx+jUZxE9B/LA0++5lbTlOu1xjjf/GjM9ZrT6WT+x/+mOvMgijGYKfc+Trvo5v9koPPlPrx/D1vn\nf4hKsRHTfwwTbrzTrSY74ySrPv8XKms1od0HcsOMP7X6dUZb5Wm/bsyisxH4BIij9m8cngcigbLU\n1NRFiYmJI4HXAQWYl5qa+u8L7LPZG2Jz8NFJ4XOZQXK3JF/MDL6Z2xczg2/mvhxvYKFZ+jX4YM/2\nxTkLvpnbFzODb+b2xcwguVuSL2aGy7NnS7+u5cNzVnK3EF/MDL6Z2xczg+RuSZ726wt+vEZqamoN\n4P7Pe9f//5+BEZ7sXAghhBDeIf1aCCGEaPukXwshhLhcqC9cIoQQQgghhBBCCCGEEEI0jiw6CyGE\nEEIIIYQQQgghhPAaWXQWQgghhBBCCCGEEEII4TWy6CyEEEIIIYQQQgghhBDCa2TRWQghhBBCCCGE\nEEIIIYTXyKKzEEIIIYQQQgghhBBCCK+RRWchhBBCCCGEEEIIIYQQXqNt7QCtaV/KAVJPphNoNHDt\n+GtQqVStHUlcQFVVFT/P/wKcDgZMnEZ0TJxbjdVqZf28L1BqTPS48ho6JyY1a6bdm9ZQdCyFjknJ\n9Bp+TYM1h3ZtJXvfNnRhUYyZ9qsG59qJIwdJ27IGjAGMvXkGOp3OreZUVgZbls9DpdEy6bbfExAQ\n4FZTXlbCloXfAAqDp9xKRFQ7j16Xw+Fg7bw5OKvL6TJkNN179/doHF9VVVXFirmf4LTbGTnlVjp0\ndJ9rQoiWUVZWysqNmwCFcSOuJDIysrUjiUZYt3Q+xdnHiUsawNCrGu6PWzesJPvIPiLjuzHm2unN\nmud0Dw0MDmDU1N802EPLSktYPf9zUBTGTLuTyAZ6aE1NDT99+zFOaw2Dr5lGQudubjWN6aGKorBq\n0TdU5GfTpe9QBg4f7fFr2/XLek4e2EFIdBzjb7jtsrum/WX5Iipz0mnXow8DRo5r7ThCXLYURWHF\n2rWUV1fTLT6OK/oPaO1IohEacx+am5XB/jWLUdQaRt00o8Ee6i2ne6hRqaF972Hn7KGbFn+PuSiX\nmF4D6TN0VINjbVvzE+UZxwjtlMiQcZMarGlMDz26fw/pOzeiDgpl7I13otFoPHptRQX57PxpLgpq\nrpx+B8EhoR6N46uOHTnAvo0r0PoFMuX23zU418SlRfPcc8+19D6fM5msLb1PN5u3bSOlxET7PkOo\nMQaxaeVSrujb95z1AQEG2kLupvDFzHDu3DU1NSx+/kFurjlCUnUm69atIbjPMAKDgutqnE4n8178\nK9eX7aKXKYsDW9ZjielBeLv2zZJ1w4Kv6Ljxc4Zbs1EOb2NDRiHdBwx1qdm5fgW6H//DaFsWEadS\nWLznMMnDx7rUHN2/h8LPX2SiPZP4olTmbdpGr9GTXBpeTnYGP75yPz2Kd+Cfu58lazcyYNz1aLX1\n7x1VVVaw6uWHuNl6jMTKdJavWUP0oNH4+fk3mP9cx1pRFL7/52NMLthCH3M2ads3UhIaR7s2svDa\n3HO7pqaGD5+4mx65GwktOsi6dWuIGzjGZa411aX2+9iWBQQYnm/tDJeQVu/ZlZUVfDx/IZ2unIhf\nh06sWvkTifEdm3xea+t8Mff5Ms99/3VUGz8iuvQQOXs3kGnR0y25n0vNsu8/o2zRm8SUplBxaDP7\ncirodcWIZsl6Zg/VZexusIdWVlbw2T9+S8+CzQQVpLBy7Vq6D5uIn3/9XLPb7bz/xD10zV5DaNEh\nftmwhoikoYSGR9TVNLaHfvn28wRs/4KoksOk71xPoTqUTj2SG8x/vmO9dsn35Mx9mdjSFGqO/sLW\n43n0Heb5ArY3tcS8XvbJO/Q7sJBBlmz+n707j4vivP8A/pm92eXGFQTxRgQPwCse8YrGmHjnMjaX\nsU3SpkfatL/80qRp0zZJtb8mzdW0uY/mNKfGaOJ934qCoosiKCCX3LDsPb8/MOCKyrLs7uzA5/16\n5fXK6MMznxkf5jvz7OyM+dgeZNWL6DtkeKf67Gq/j8GMNdtnJK/XAPDeihVQ9huGyAEpOH2uFJWF\np9G/b9/LtpXxmO1SuT25Di0tOouslx7DPEc+kmpO4/MNm5E0aZZbDfWVi2vokLozV6yhq/71N0w4\n+T0yLEWozNqFXIcWiYOGuLVZ/9EbGLzvU4y1FcFl2o+95Q0YMHykWxtPamj2vh2wrvgHptvPIr40\nB1/uzcTQSZf/MB248r6uOl+BnX//DRba85BcX4CV6zegz/jrodFoOrqbfC4Q4/p41kHsevkRDKjK\nhPrsQazdnYkx183p1AflXe33MZh5W6+77eM1covOIfHCCakhLAJNGgPsdrvEqehqDmzfiAW6aigV\nzQelBVEOHF63yq3NmTP5GNWYB52q+ZPHaZEiTm1b67dM1qM7kRTavK74EBVUufvbtKk8sBkZ4c2/\nalFaFaKLstuMtdM71mLqhQ85Q1RKpNefQlFRoVub3d99iXRNJQBAqRAw1HYK+3dudmuzZ91q3B7e\nCEEQIAgCbou0YN/3X3d4u6qqqjCoMhcGdfOJxIQIAcW7v+9wP3K1e+t6DLfntYy1DE0ldq39XOJU\nRN3T1p07Mey6uS3HteHXzcGWXbukjkXtqD66DdHa5v/vpXWi+MCGNm1KDm5AnM4JAIjWiKjO3uq3\nPJ7U0G3frcQooahlrI1SlWLbms/c2mQfOYR+tcegulAfhmtrsH/dl25tPKmhoiii4fgOhGua+0nU\n2XFmr3d19uy+deitcwAAwjUC6nO2e9WPXKlO7kd8SPO+HhyqgiV7h8SJiLonURRR61IiLCoaABA/\nKAWny85LnIra48l16JEN32BeVHOdUSoEzNNUInOXf2q2pzVUn5+JHrrmNsPDlKjL3NamL/H4HvQ1\nNLfpb1DBdXxvmzae1NBzu9Zj3IV7j0I1KvQrP4Ha2poOb9v+71fi1kgrBEGAQhBwe1gj9m5Y3eF+\n5Orwpq8xRNsAANCqFIguPdRmrFHX020nneFyui/abV5/RYICI8QQhjp767+b3emCoHb/VDAkRI9G\nsXVYi6IIl+C/Ye4U3MeMQ9H2095L29igbDPWXIISoii2LDe6lNBqdW5tBJUGTldrG7OjeZ9cTB2i\nR6O9tY3F6YJKG+Lh1rTSajVoEt33m1PoPk/jMYSGwexs/cTV4RKh0GglTETUfWk1WlgtTS3LdqsF\nWn4VL/gpLvk3Urb9NxMvaSNepo2veFJDtSF6WC9qY3OKUOvcvz6s1xtgcbXWR6dLbLNtntRQQRDa\nbK+32y9eeu6hlP6OqUC69NzrcudiROR/giAALpf7n12yTMHHk+tQqNRwXPRvWWd3QWcI9UseT2uo\n85JjvVN5metwhfKqy4BnNfTSn2uCEmp1x2utUquD1dm6HxvsLmj1/tmPQUmhdhtrNqjajjXqcrrt\npPOkURnI2b4OjfW1OJNzBIN6REKh6La7QxZGjp+ELRHDUFBnQYXZio8sPTD55rvc2sTF9UJR0mQc\nr7GiymLDJ3UGjL9tqd8y9Z55OzZUC6i12rGrVkTM1LbPo0yZexe+qVGjxmLHwWo7tOPntBlr19x6\nHz6t1aPKYkNOrRVlKVPRs6f7cyRvXLQUB9WDUWtxoMzsREW/qRg51v1ryJNmzcPXqr4oqreitNGK\nFc54TJl3e4e3KzQ0DI1pM5BVY0O1xY7Pa7QYefM9He5HrsZMmIKS3pNQZnaixuLAIU0yZt12n9Sx\niLql6VOn4syu9agsK0F1RRlyt6zBDdNnSB2L2jFk1l3INWvRaHPimDUcI+cuadMmY84SHLOGodHm\nhKlJh5RZd/stj1sNbXJdtoZed9NCmKLG4HyTA1VNDmSHpeGGhYvd2iSnDIU55QaUNLpQZ3XgoGIA\nZi2+362NpzV00IwfIc+sRoPNiWxbFK5Z+BOvtm3sgqXItkWiwebEKbMaSdff6VU/chU9ZSF2VjtR\na7VjfY2APjMXSR2JqNsaEm9EwdFDaKyvxYldmzAhrXOPuiH/8+Q6dPItd+NDcwzOm23Ir7diR9Rw\npI0Z75c8ntbQ0GvnY1+NAzUWO9bUKJF004/atOl53S3YWiOi1mrHlhogbvptbdp4UkMzFt6LL2q0\nqLbYcaTGCtvImdDrL/+Yt6uZMn8RPnH0QlmjFYUNFnyjHYgJM27qcD9ydf0dD+KgKwH1VicKG0Xo\nRs9vM9ao6xEu/qQhQMSKivpAr/OyamqqkXX0KBITEtC//4CrtjUawxAsuT0lx8zA1XOLoojsQ/tg\nbWpC+jUTr/jgedOxLFSfL8eIMRO8KggdUVFehpPZmRg14RpoQ6Iu26a2pho5h/ahV78B6Dcg6bJt\nzGYzsvbtRFTPOCSnXv4EzWaz4cCe7dAbQpE2cuxln3/kcrlwZP9uuFwupI+dcNU7+NsbI6dO5OB8\nSRGGjZmA0NDg+RQ2EGNbFEUcPrgX1qYmjBp3badfctAVfx+DldEY1r3eoOVfQVGzXS4XDmUeglMU\nMTpjZKeOa8FKjrnby1xceAanThxFatoYGK9wUVFeVobjWQeQlDIc8b37+CsqgNYaGp/QE30HDLti\nDT20fxdcDidGjbv2imMt+/AB1NdWY9S4ydBqL/9NGE9qaEHBaZw5eRzDR41D9EXPhb5Ue/u6srIS\nRw/tQb+kVPTt1/+K7QItUOP6XNFZFJhyMHjEyMu+/LGjuuLvY7BizfaZoKjXAFBwpgAFZ89ixNCh\nnTquBauumNvT69DDe3cgxBCKYRlj/P7C2lMncmAzV6LP4Iwr1tCzBadRlJeLlIwxiLrCWCsrKUZe\nThYGDk1DbFz8Zdt4UkMbGupxdP9uGOMTMTA55arZr7avnU4nMvfuhEqlRtqYcUHz4t9AjWuz2YzM\nvTsQ3TMOKUOv/E41T3XF38dg5W297taTzh0h00Ehu8wAcweSHDMD8swtx8yAPHPzAtanZFez5Thm\nAXnmlmNmQJ655ZgZYO5AkmNmgDXbh1ivA4S5A0eOmQF55pZjZoC5A8nbes3nSRARERERERERERGR\nz3DSmYiIiIiIiIiIiIh8hpPOREREREREREREROQznHQmIiIiIiIiIiIiIp/hpDMRERERERERERER\n+QwnnYmIiIiIiIiIiIjIZzjpTEREREREREREREQ+w0lnIiIiIiIiIiIiIvIZldQBiDriuxXv4vTm\nTyG4HIgcPg2Lf/F4mzafvvg0xAProFcJOCmG4pevfwWNRuPW5sj+ndj1wXNAUy2E2CTc8/vnodfr\n/ZK5oqICH/16MfprbKixA7Fz7sMNd9zn1sbhcOC95Y/BduYwRI0eGQsfxPjps93aiKKIj195BrVH\nt0JUqjBw+mLccMs9bda37Nd3QzyTCUCEo9f8TW0VAAAgAElEQVRQPPnqijZtdq/5AjVbvoBWcKG+\n93DM+8XjEATBp9v9g3NnC7DvjWUwmM+j0dAD19z/e/RK7OuXdQXajnWrkLXqDSjsTVD3y8CSR5dB\nqVT6ZV1lZSX48vnHgKpCiOGxuPGnf0T/pBS/rIuIqLNOm3Lw/et/AerKgehE3PrIchhj49zaHDt6\nGB8+uRSRghV1LjVu+MWzmDTjJrc2jY2N+O+y30IsOwkxJBKT7v4dho8e77fcntTQTd98ihPfvQ+F\nwwb94PG4+5E/t6mh+7dtwP7PXoFgbYCq91Dc+9j/tTkX2bLyU5z57FVEq0UU2FS4edk7SLikPhad\nyceqV56Eqr4UzrBemPerp9u08RVRFPH+c0+i6eReuJQapM5egqmzb/PLugKtoqwE21/9K8IaymEO\niUL6kt+i76AhflmXKIr49rV/QHvqAJyCEoaJczBpwY/8si4ios5yOBxY+cJTCC8xwa7SIfbGuzBq\n6g1ubVwuF17++SL0ayqH3SWifsAo3PfUP9v0teGjN+E8tAECAHHYJNyw5Od+y+1JDfXkOrS2pgob\nXvoTwmtLYNZGYNhdD2Ng6gi3NnV1dXhm6SzEuGrR5FJg8E1LsfiB37i1EUURK196GobCbLjUWkRM\nuQXjZi3wz8YDOLBxDcrXfQy1w4q6+GQs+PVTfrsODSRP5zx8xZPzNeoc3ulMsnHKlIOq9a8jQ1OJ\ndF0tIo99hc1rvnRrU1xciIgj63FvSixuS+qJX/XT4I3Hf+bWRhRFbH93GdJRhPSQegyrOYgvX1vu\nt9wfP/EAfpsSiduSYnF/aizKVr8Nl8vl1mbV+69i4LktSA+pQ4ayFFmfPo+Ghnq3NhtXf4bonJVI\n19UiQ12Jiu9eQ37eSbc2K957HQNqsjC1jx5T+xgwzJKLd15237ay0hIoN32ABZF23BjhxPXnD2DL\nVx/5ZdsBYP97z2NRSCXmxAhYpKvEvvfanqDIUV1dLXI++ycylGVI09Whf+FmrPrvf/y2vtX/fhpp\nTTlI1zcgw5GHdW/8zW/rIiLqrHVvPot0x2mk6xuQ1pSDVa8926bNR3/+GeYkKjEp0YDZfTX4/l9/\naNPmq9eWYVjNQaSH1CMDhdj6zt8giqJfMntSQ0tLS3Bm1cvIUFUgTVeLXnlrsfbz993a2Gw27P/o\n/5ChOIf0kDokl+/E12+/0GZ9BZ+9igdSe+LWpFg8khqNL//U9uJ8zevPIMOWi+HaOqTbTFjz2jO+\n3eiL17XiXcSf/h5pulpkqCuQ99VLKC8v99v6AmnXO//EHZpyzIkRcLu+Boc/eMlv69q55itMOrcL\nc6JdmB9lR8TOz1Bw+mT7P0hEJIGNH72JBY05mBMDLIywoOabN9pch76z7A9YEm3B7YN74s4hsUg/\nn42dWza4tcnevxtJR7/FvGgn5kY7MeLURuzf5t7GlzypoZ5ch255659YrCxprg+hdTj64Ytt2jz3\nyF2YHWfHpEQDZvYNQd6aN2GxWNzabP7iA8ysOoQ50SLmhVkgrn/PbzW0rq4W9WvewsIIC+bEiJhX\nfxQbP3nLL+sKNE/mPHzF0/M16hxOOpNs5OceR7zG1rIcqRFQea7Arc2J48eQEt16x3KoRgWtucat\nTVNTE7RNVS3LSoUAsbEK/hIlWqBUtN4B1UunRENDg1sba00ZtKrWX8coe1WbIlVz7gwiNK39xKut\nKDiZ49YmN3sfeoe3fjIXF6ZB0cmjbm2KC/KQrHW2rkurgq2y1Ist84zeWn/VZbkqKy1FlLN1bIWo\nFbDW+G8/CuZqtzvpBLP/xiwRUWcJF9VVQRAue8wywOp2XAtV2Nu0cTVUudVQjaUaNputTTtf8KSG\nFuafQpxgblkOVQtoKC92a1NdXY0wW3XLslqpgL22wq2Ny+VCjLp18lwhCIgR2m6X4pLzE38e+xsq\nihGqbt3XsUIDis6c9tv6AklvqXMba3pLnd/W1VhWhJ661i+TphiAwpMmv62PiKhT6s9Dr269Q7af\n0NTmOtRWehY9DbqW5WE9wnBs3063NiX5uUgyXNSPXomqwny/RPa0hnpyHepJfVBb6qBWtraJ0ws4\ne/aMWxt7ZSmitK3H/sFaB0rO+mf7y8tKMUDR1LIcqlFBrD3vl3UFmidzHr7iyfkadR4nnUk20sZO\nxClnZMvyWasWSWnj3NqMGj0OO0pbJ3TzaxoRMnCYWxu9Xg9bVN+WO6XqbC6EJ/rnK5YA0BDRC9VN\nzUVQFEWcMosIDw93axM3OAPnra0H14rQPkhI6O3WZlDGeBRa1C3Lp8VoDB81wa3N9PmLcaS89VPX\nnPMWjJu50K1N0tAR2Gc3tCybGpzomZLu5da1ryEyAXZn853ddqcLjVEJfltXICX26YtyfWLLcrlV\nQHzySL+tTx03CLYL+9HpEqEw9vfbuoiIOksw9ofT1VxnrQ4XNHGD2rRp1Bndjmu1irA2bcL6pKDB\n3tyPKIqwR/WFVqv1S2ZPauiQYWk4q4ptWT5nVaLvsDFubYxGI2pCW+tDtVVEzMDhbm0UCgXO2lQt\n5yL1Ngeq9cY2mRQ9B8BxYT86XCKUPQd4uXXt6ztsDEqtrRMGhepeGJwy1G/rC6SmHomwOJo/cHe6\nRDRExvttXQnDxyC7vvXD/Z1mLVJHXeO39RERdUb4wGE40+hoWT6mjGlzHZo4diqOlLdOxm4srMZ1\nC253a5My9lrsqG+dXtpfJ2LQSP88DsvTGurJdai9Z1802Jq33yWKqItoWx9CEpJRZW79YDy/QYFB\ng5Lc2hhTMnCysfXYf8ARhoFDUr3Yuvb1TuyLbCG6NU+jA5GDhl3lJ+TDkzkPX/HkfI06T/nUU08F\nep1Pmc3+uUPFnwwGLeSWW46ZgSvnNoSGQt0rGVlny1GpjUWf6+/FNVOud2uj0+nQGJmA1Vu24Vh1\nE3Kik7HkibaPzuifPhG7c4tQqYyEkDoDC5b8stPPNL5S7lEz5uKNb76HqfQ8Nlc6MfOJlxDdw70o\n9h+cirxGJQrrbKgI7YeZDz6JHsaebm3iEvrgvCoKpyoaUKnvjbF3PoJ+Awe7tUnsOwB5NXbsyzqG\n/AYgauLtuPmu+93aaLVaIGEwtp88i0JtFBrTZ2HsjDmd2var6T9yAtYcL8BpqwLHIpNww4OPQqXq\n3OPkg2Fsq1QqGJMycCDvHKo0MQi/5mbMWLD4iu07mzl19LXYnV+BcocW1bEjsOjhvwTkeVPBsK87\nymDQ/lnqDF2I7Gq2HMcsIM/cV8ucPGYKduYW4zxCYe47Drc/9HibZw2On3UL3v/6WxRWm3HcFo7f\nvPwFDAaDW5shaWNwuLQR5ywKnI8cjJsf/iv0l7TxVW5Pa2hYv+HIzC9FlaYnjJMXY/IN893aCIKA\n3sPGYd/JIlSqo6FNn43Zi3/SZn29Rk/Cu199g9xqM7bbI/DA8++22UcpYyZj96kS1KnDUN0zA4t+\n+cdO19Ar6d1vEIrsISiotqDc0AdTlz6GXgl9OtVnsIzrARnjsfZEIU5bgOzQ/rj+Z7+/ag3tTO6e\nCYk46QxBVmk1cpTRSLz5AfQZkNT+D3ZSsOzrjmLN9hnW6wDparkTBw3BgWobTlSZka3qgfR7H0F0\nD/fr0MEjRuK77DxknszDviobwm9agrGTpru1iYiMRmVoLPafKYUJ4QiZvhhDR7vfIOarzIBnNdST\n69AB6WOxPq8Up8wuHNH1xvSHfg+tLsStzbjps/HFxp3IL6tETqMGt/7+JcRfUh979R2AbLOAYxX1\nOKmPxaDbHkJsfCL8QaVSQdt/KLaaCpAnGlA7fAYmzuncOxiCZVx7Mudxsc7k9vR8zR+CZX93hLf1\nWvDXc/GuQqyokN/X643GMMgttxwzA8wdSHLMDMgztxwzA/LMbTSG+eetmN2T7Gq2HMcsIM/ccswM\nyDO3HDMDzB1IcswMsGb7EOt1gDB34MgxMyDP3HLMDDB3IHlbr/l4DSIiIiIiIiIiIiLyGU46ExER\nEREREREREZHPcNKZiIiIiIiIiIiIiHyGk85ERERERERERERE5DOcdCYiIiIiIiIiIiIin+GkMxER\nERERERERERH5DCediYiIiIiIiIiIiMhnOOlMRERERERERERERD6jkjoABbcju7agNCcTuh69MHn+\nIgiCIGmehvo6bP/iPQguF9KuX4BeiX296sdiseBXCydB4zAjdug1ePKFt73OdGDLOlSeOoZeQ4Zg\nxLU3et2PJ4rO5GP3d58BCjVuXHw/QkND27SpqqzExi/eBUQXpi64G8bYOL9mIiIi6ZWVnsO2lR9A\nhAIzb1+KyKhoSfOIoohNqz9DVdFpJA7JwLhpN3jd1x9/cTfKju+HXR2KV7/eAZ1O51U/P9RQQ5gB\nk+fde9ka6isOhwPffvIWbPXVGDphBlLTRrdpI4oitq38BJbzpeg1dBRGjJ/stzxERBQcXC4XNn/x\nARy1leidPh5DR4+TOhLycrJwavdGQGfAtNuWQKPReNXPti3rsebvj0MBEVMf+gNmzlngVT8OhwOb\nP38POtGK2KHjMHjESK/68ZQncx7HDu9Dzu5N0IbHYPYdS6FUKv2aiair4KQzXdGuNV8ibscHGBuq\nxPmzDnxTXIB5P39MsjxNTU1Y8/TDuDO8HgpBwKqX9kDxm78jNj6xw3398oZhWJQaDoPGAFPFfjx2\n71wse++bDvez5fP/YlDml5hoUKH0zHasNeXixh8/3OF+PFFceAbfLn8II9SVcLpEvHV0Dx5c/p7b\nxXddXS0++ONSjFaeAwB8cmQr7vzru4iO6eGXTEREJL3zFeX4/C8PIENVBgB478md+PGy9xEaGiZZ\nphX/Xo7w7C/QWyOg5MhKrD1fghtvW9Lhfh658yakCYW4cVg4GqwO/GzmULyzLa/D/bSpoXu3tamh\nviKKIt74y8NIqdwLrUqBQ0e+g3XJX5Axzn1SedUrz2LG+QOI1qqQc3oHdtdWYfws7y7QiYhIHr58\n/o+YU5+DCK0SmZ/vwMHGBzFqykzJ8piOHETNR8swLwKwOJz49JmjuP1PL0Ch6NiX4jP378Pxlx/H\n8xObbwp7/f1nsU0fgsnXdexDZ1EU8cXyx3Cr4zT0aiX2HNmMbMvDGD722g714ylP5jwO7dqKnPf+\niIG6JlgcLrxxMgs/feplv+Qh6mr4eA26ovoj25ES2vwJXg+dCiEFmZLmObhjE+braqC48MnjvCgH\nDq/v+ERxcXERUnuoYdA0f+aS3CMEQlmuV5lsObsx0NDcT1yIEqq8g17144k933+BEepKAIBSISDV\ndgoHdm1xa7P9+1UYqTgHQRAgCAJGqcqwfe0XfstERETS2772C2SoylqO/SOFImz7fpWkmWpydiBS\n01yv47ROlGZu9qof5fmTGBwTAgAI1aowLEaN8+fPd7gfT2qor1RVVUFfdBBaVfNp9kCtGce3f+vW\nRhRF6AuOIFrbfA6RGqpA/eHtfslDRETBwWq1omfxMURom6+xM8IVqDywRdJM+Tu+x+SI5v/XqZTI\naDyN4uKiDvfz1l8fwUMZfVrORR5I64Ovnnuqw/1UVVUhqSoXenXzPhoXDpTs3djhfjzlyZzH8R2r\nMVDXBADQqRTQnj2A2toav2Ui6ko46UxX5BCUV10ONH1YBGrtzpZlm9MFQaPtcD8REZGw2F1uf2Zx\nil5lcijc94ndj/tIodbB4WrNaXYA+tBwtzY6Q6jbtticItQ6g98yERGR9DS6ENguOvY3OUSESHiX\nMwCISvev5roE775cZ3W412eLQ/TqsRie1FBf0Wo1sF6yvS6F+7IgCJc5h+BpORFRV6ZSqWARAnf9\n6AmnoIQottbHepcAnS6kw/0odXo02Bwty00OFxzKjtd+rVaDRpd7PbTDf/vIkzkP8ZIabhXUUKu9\newQJUXfDs1u6oqSb7sS31UpUNtmwq8qBiMk3S5on45qJ2BY5HHm1FpQ0WPCx1YgpN9/V4X5CQ0NR\n5AxDToUZdVYH1p+qwbB5P/YqU58b7sC6agFVTTbsqBVhnHarV/144sZFS3FIk4yqJgdKGhyo6H8d\nMsaMd2szbdZ85Pa4BmWNDlSYHTgano6ZC+7wWyYiIpLezIV3Iis0DefNdpQ1OpDXcxymXD9H0kyp\nN96DE0061FmdOGoNx+gFS73rZ9a9WJ9XgzqrAznlZpx1hXr1SAy3GtrovGwN9ZXQ0DD0mHAr8huA\nWosDBx1xmL74Z23ahU9egN3VDlQ22bC6WoXkOR0/pyEiIvlQKpVQj5uD/VU2VDbZ8HW1GsMX3CNp\npvG3L8UndQZUmK3IqragIvU6GI3GDvez/P1VeHZPPgpqzSisa8LTu0/hr+93/FvJoaFhaMqYicxq\nK86bbVhRo8PoW5Z0uB9PeTLncd0dP8MhRxxqLQ6cbhQQN+k26PV6v2Ui6kqEiz/VChCxoqI+0Ovs\nNKMxDHLL7YvMNTXVMGVlInHAIMT37uOjZFd3tdyiKCInKxPWJjNGjB4Hlcr7x5K/+Z+XkLVnC+57\n+AlkZIzyup/K8+dxKucIRo4bA7XGP3dN/cBut+PwwT3Q6fQYljbysi85EEURRw7th9PpQPqoa676\nkgM5jmtAnrnlmBmQZ26jMUzaN552LbKr2XIcs0DnczudThw+sAdKtQZpGaMD8uLf9jKXnCtGfm4O\nkoePRExMjNfrycw8iLf++TTSJkzD/T/9ldf9/FBDe8UbkZCY7Pd9lHcqF+UlRRgx8hoYDJf/1lFx\n4RkU5edhSNpIREREXrGv7jqupSLH3HLMDLBm+xDrdYD4IvfZgnyUFuYjJX00wsL8e/34g6vlbmpq\nwrFD+xBl7ImBg1O8XofD4cBfH/0l7DYbHl/2Yqde2Hv6VC6cTdWIHzDsijXUVzyZ82hoaEB25j7E\nxidiwMCkq/Ynx7Etx8wAcweSt/Wak84ekumgkF1mgLkDSY6ZAXnmlmNmQJ65eQHrU7Kr2XIcs4A8\nc8sxMyDP3HLMDDB3IMkxM8Ca7UOs1wHC3IEjx8yAPHPLMTPA3IHkbb3m4zWIiIiIiIiIiIiIyGc4\n6UxEREREREREREREPsNJZyIiIiIiIiIiIiLyGU46ExEREREREREREZHPcNKZiIiIiIiIiIiIiHyG\nk85ERERERERERERE5DOcdCYiIiIiIiIiIiIin+GkMwUVURQhiqLP+vJFG18J5Lqo6+I4IqJg0ZXr\nNY+11FkcR0QULHxZr9vrK9DHPh5nyRc4jvxHJXUAoh+sfesFqHJ2QVApgbTrMONH93vVz/4Nq1Hx\n/cfQuGyoiRuMhY/8BUql0q3Nsf27kPfFa9DbGlAd1Qc3PfI0DAaDLzajjYaGBvz3b48A5afgConA\ntXf/DmljJvplXdR1lZWew+fP/S8U1UUQw3ti1oN/woDkVKljEVE3dHjvduz84Hmo7XVwxgzCPY8/\n71UN9eS4Fugauv6D1yAe3gQBgCN1Im5c+iu/rYu6JlEU8c2ryxFy+hCcCgX04+dg8s13SR2LiLqh\nhoYGfPf8E4isKYJdH4G+Cx5A6uhxHe7H0+NaIGtozpH92Pz2MigaqwBjfyx+9B+IjIr22/qoa9q7\n9Xsc+OxfUFoboUhIxZLHn4NGo5E6VpfCO50pKOzd/D1G5W/FnBgRsyMcGJi9BkcP7etwP3V1tWhc\n8w4WRtkwOwZYYM7Bxo/fdGsjiiJOr/gXbgs3Y3YPBRYLhdj0zou+2pQ2vnp9GYbXZSJd34CRQjG2\nv7ucn6RRh61+7VmMtJmQbmhEhjMf69/6m9SRiKgbEkURO95fjpGKYgzX1mN43SF89dpyr/ry5LgW\nyBqatW8XknO+x9xoF+ZEu5CRtxn7t23wy7qo69q55ktMLduLOTEi5kc5EbX7c+SfypU6FhF1Q5vf\neQF3KIoxu4cCC/T1OLniFa9qqCfHtUDX0K3vLMdIFCLd0Ii0xmx8/RqvjahjbDYbDn70HEYqS5Gm\nr8eQ87vx5ZvPSx2ry+GkMwWFmuICJOpbb7wfHKpEyemOn6CXl5Wiv7KpZdmgVkGsq3RrY7FYEO1o\naFlWKgRoLXVepPaM2FANpUJoWdZYqmGz2fy2PuqahMYq92VztURJiKg7s1gs0Da1Hn+UCgGil8cj\nT45rgayhpQUnMcjQemrc16BCVWG+X9ZFXVdjeTGMutZz2iEGAUV5nHQmosDTWurcamiUvcGrGurJ\ncS2QNVQUReCicwhBEHhtRB1WXV2NMHtNy7JaqYCzvvIqP0He4KQzBYWBI8djX13rp67b6hQYOvba\nDvfTO7EvjggxLcv5jQ5EDhru1iYkJAQlhriWT3nPWxxQJAzyMnn7wvqmoM7mAtBcIO1RfaHVav22\nPuqa1HGDYHU0jyOnS4Rg7C9xIiLqjkJCQmCN6tdSQ+tsIiL6eveoH0+Oa4GsoaljJ2F7XevF+d46\nIGnUBL+si7qu3sPH4ki9q2V5u1mD1FHXSJiIiLoroddAVFrsAJpraHlonFc11JPjWiBrqCAIQI/+\ncF04FzE7XNAnDPHLuqjrMhqNqA5NbFmusgLGQSMkTNQ1KZ966qlAr/Mps1l+d3kaDFrILbecMkcb\nY3FOE43Mc+dxWmdE9KwlGJg6vP0fvIRKpYJ+0AhsMZ3BKYSiLu16TJx9S5t2scOvwbpjechz6VHc\nfxxm/Oj+5uLVCVfa30PSxiCr3IISixKVUcm45eG/Qq/3z/OjO0pOY+Ricszd2cypo6/FvjNVKHfq\nUBuXhkUP/wVqtdqHCS9Ppvv6z1Jn6EJkV7PlOGYBeeUeMHISducWo8FghJgyA/PvecirGurJcc0f\nNfRK+zo8MgrVEfHYf7YMJiEChhk/QurI4JgslNP4uFh3zN0zvjfyYEBWaQ1ylNHod/PPkNh/oI8T\ntiXjfc2a7Rus1wEip9wDho/C1uIa5NY7kBvRFxN//ChCvKihnhzX/FFDr7avB4+ejF25RahURMAx\neBpuuf+RTl/P+4qcxsgP5JgZ6FxuQRDQZ8QE7D1ZjCp1DEJGzcGNi5b6OOHlyXF/e1uvBQmeLStW\nVNQHep2dZjSGQW655ZgZYO5AkmNmQJ655ZgZkGduozEsOM44uwbZ1Ww5jllAnrnlmBmQZ245ZgaY\nO5DkmBlgzfYh1usAYe7AkWNmQJ655ZgZYO5A8rZe8/EaREREREREREREROQznHQmIiIiIiIiIiIi\nIp/hpDMRERERERERERER+QwnnYmIiIiIiIiIiIjIZzjpTEREREREREREREQ+w0lnIiIiIiIiIiIi\nIvIZlSeNkpOT/w7gWgBKAMtMJtNXF/1dPoCzAFwARAB3mkymEj9kJSIioqtgvSYiIgp+rNdERNQd\ntDvpnJycPBVAqslkmpCcnBwNIBPAVxc1EQHMMplMTf6JSERERO1hvSYiIgp+rNdERNRdeHKn81YA\ney/8fw0AfXJysmAymcQLfyZc+I8CwOFwYPVHr8PeWIuUcddhWMY1Xve1+7uVqCs8hYi+gzFu5lwf\npvROWUkRMr/9DDqDDmkzb0NUTI82berrarHj8/cguJwYMXMh4vv0a9PGarVi9YevwWU1Y8TkG5E8\nNC0A6QNj347N2PTBK3AKSix98p/oFZ8gaR5RFLH28/fRUFGMfsPHYuykGZLmIermWK+DzN6t63Hm\n2H6E9eyNWbfcDUHwbvfnmXJwaNMqCGotZt/5U4SEhPg4ace4XC58+8nbUNhqkZAyFunXTGrTRhRF\nbFj5MarPFSBhcBomzph92b52bFiNc7lZiE4YgOnzFnm9j4KNxWLBc/97P1zmOqTPWIi5i5ZIHQnH\nM/fh7MEdUBgiMO22e6FSefSFRyLyPdbrIPPDdagoKDBuwZ2XvQ71hNVqxeZP34Zgs2DQhOkYmDrC\nx0k7LnvfDpzL2oeI+HiMnXU7FIq2T1g9dewI8nZvhKjR47o7lkKj0bRpU1SQh6MbVsGlUGLybUsQ\nGhYeiPgB8cVr/8T57H0QYnrhJ3/6x2X3USDV1dXi+0/eBJx2jL9pEXr37S9pHqLOaPds80Lx++FT\n1p8AWHNRQfzBf5KTk/sD2G4ymR73cUa6QBRFvP7UL5FavR9alQKHD38H271/wcgJUzrc17r//hsZ\npnXorVeh8MwOrC8/h+vvetAPqT1zvrwMB55/FDdH2SGKIj5Ztgsz//gvt2LW1NSE7555GD8Kb4BC\nELD65X0QfrUMvRL7trRxuVx4/cmfIs18FGqlgN1HvofroX8gZcQoKTbLpw7t2Y6dLzyMKQk6uEQR\nr/50Nn77/hZERkZKlun95/+I+LzvkKgWcDbrW9TXVGL63EWS5SHqzlivg8uGlZ+gdu2LSNQ6UX9U\nxAeFebj7N3/ucD95J45h8wsPY6i2Dk6XiNePH8DPl78n6YThW8/+DwaUbIVepYBp91dorH8ME2fM\ncWvzyavLEHX0SyRqBJRlfYO1leW4cdF9bm2+/fhNOLa+iUStCzXZwIriAix66LFAbopfuFwuPHHH\nFMxNcEKrV+DYyufxaX09Fv3kl5Jlytq9DVj5EuaFCzDbnfh8+XEseuIfkuUh6s5Yr4NL2+vQA22u\nQz3hcrnw1TOPYLG6FBqlAtve2wXnnY9j8IgMPyVv376NaxCx4S3MC1OgrsiJL3OO4tbfPe3W5sTh\nA6j/eDnmRQBWhwufPHMUt//pJbeJ13NnC3Di1ScwP9IJlyjiw6czMe/P/4ZOpwv0Jvncu8/8LyZX\nZSElPhRVTXl48cFb8Js3vmr/B/2kqakJ7/zhxxiNM81zHllbMPfx15Bw0ZwHkZx4/BFOcnLyfAD3\nAfjFJX/1JIBHAEwBMDw5Oflm38Wji1VWVsJw7hC0quZ/toG6JpzYuca7zkz70VvffMGaqFcBuQd8\nFdMrB9evwsJIGwBAEATcGm7G3o3u23Zw+0bMD6mF4sJdUHOiHMja9K1bm4L80+h5/gjUyuY2ydpG\nZG1eFYAt8L/1H/wL4xKaC7tCEDA5QflnLuwAACAASURBVInP33lVsjyiKMJs2oVQdfO+TtDaUXxg\no2R5iKgZ63VwKDqwAfFaJwAgTC2g8cRur/o5uGklhmrrAABKhYB+dcdx/OgRn+XsKKvVCjF/H/QX\nzkX66GzI37u+Tbu64zsRoWmuD7FaJ0qPbGnTpuzIFvTUugAAkRqg7sQu/wUPoFOnTmJISGPL+dpQ\now6526S7gAWAkr0bMCa8+d9Dr1ZiQOVJ1NRUS5qJqLtjvQ4OnlyHeqKg4DRGmwugUTYf+ydHAPk7\nv/dp1o6qPrQVI8Ka84RrlIg5lwO73e7WpmDnOlwb0fz/WpUCGY0FKCo869Yme9NqzI5sPqdRCALm\naquRuWur/zcgANSnM5ESEwoAiA7RYKCjStI8e7atxzBHfsucR5qmCnvWSXsOQdQZnr5I8AYAvwdw\ng8lkqr/470wm0wcXtVsDYDiAL6/Wn9EY1vGkQUDq3CEhAuxKLQALgOZJP61Bf9VcV/o7hU4HoPWf\nUtBpJd2+SGM0LHkuhKiUAIB6uws9e/V0yxSf2As1NhfCLnzbx+Z0ITQq3K2NwxGH7YIGze/daN5H\nulBDwLbNn+vRGgxwmEWoFM0FqNHmRO/+fTu9zs78vFIbgovHkVp/9fHoS1L/PnpDjpkB+ebujnxd\nrwF5/vsHQ2aNXg/UtS4rdLp2c13u7w3hYXC6RCgvHPubXEr06Rcv2TY6nXqIai0Aa8ufaS5z7Fdq\ndYCjdVl9me1X60Ja7/UDoNC2v498xZ/rcTp7Y6299aZFURQhKtWS1mu1PgQwty43CUokJPSAXq/v\nVCZPBMPvozfkmFuOmbsr1utmwZDZk+vQS13u7xyOOBwVlS3LoihCYwiRdBtVISHARXPMDqUacXGR\nbncxa0JDINaILY+3ahCVGNwn1i13aFQ47IUuqC9MqNc4RCT06RWQbfP3OuyC0m3Z4vTNOr3to3di\nPE44BejVzct2p4iIqIgusa/9hbmDmycvEgwH8HcA000mU+1l/m4FgLkmk8mO5k9jP2uvz4qK+vaa\nBB2jMSwocveYeBvytn+AaKUdpzV9cNvN918x19Uy95h6Czau/A9GaK04YtXCuPBWSbdv1HXzsWLX\nVkyty4dDFLErcihuGzvNLVP/ISPxRfQIjCnPhF4JbFQlYuENt7m1UalCoRu9EAUHPke40onTIQNw\n980/Cci2+XuMLPn9c1h+7wxM6OmAxeHCEZsRf5m3uFPr7GzmgTPugmn1K4gVzDij7Ilpc+/rEvva\nH+SYGZBn7u5SwC/lj3oNyK9mB8uYHTnnPmz9dy76OMpRJuqRNO+uq+a6Uu4pC+7D2wd3YkCDCQ0u\nJZwj5iEispek29hn2mKcXP8WjAoL8tXxuGn+0jZ5kmfejeNfPIdeQgOKFD0wbnbb+jBi9hLsfetP\nSBSrUCKGYcjce7pEDVEqDWiMT8OJ89mINaixp8yORX/9m6T1euicu7DihRxMUdei0ArYRs1FY6MT\njY3+3d/B8vvYUXLMLcfMQPes2azXzYJlzHpyHXqxK+VWqUJRkjINR05sQqxWwCZnDGbMu1vSbUy6\n6U58/Z8/YYK6AQU2JbTjb0VlZaNbm4y59+Dj5UdwnaoKpTYRFUOvhyCEuOUedcPt+Gj/bsxwFqHB\nKeJg3CjcPHC437ctEGOk7/wfY8WXL2NqfARyKhtgS7220+vsTO5BKaOwtd80WE9tgkZw4UzUCDww\n+0ddYl/7A3MHjrf1WhDFSx8f5S45Ofl+AH8CkIvmFxqIADYByDaZTCuTk5N/CWAJmu+fyDSZTL9q\nZ52i3HYuEFyDoiA/DxWl5zA0bdRV71BpL/P5igoU5Oagf/JQxPTw7mUJvuRyuXDsyEHExESgV2LS\nZV8mJIoiTDlHYW0yY2j6qCs+0zLvVC6qK8sxLG10wJ41FYgxYrFYsOqzDxEaEYlZcxZ2+iUHvsh8\nrrgIhfmnkDIiA+HhEZ3qy1PB9PvoKTlmBuSZ22gM65Yv3/FDvQZkWLODaczW1dXieFYm+gxIavfF\nr1fLbbPZkJ25H2ERURg8JNUfUTus8GwBmuorEN83BaGhoZdtU1ZWioKTx5E8LB2RkVGXbVNdXYXc\nY0fQLykVsbGx/ozcIlBjZOf2zThtysFNCxchxsuXUv3AF5kbGxthys5Ej7gE9OkXmJcSBdPvY0fI\nMbccMwPds2azXjcLpjH7w3WoQqlC6vD0q77Utr3cp0/lorayAilpo4LimccNDfUwZR9GaloqQvQx\nl21jsVhw/MhBRPToiQEDky7bxuFw4NjhA9CGGJCcOiwgL/4N1BgpLi7E1jWrMGzMOIxI7/y7oDqb\nWxRFHM/JhsVsxoiM0QF5j0cw/T52BHMHjrf1ut1JZz+QXUEEZDsoZJcZYO5AkmNmQJ655ZgZkGfu\n7ngB60eyq9lyHLOAPHPLMTMgz9xyzAwwdyDJMTPAmu1DrNcBwtyBI8fMgDxzyzEzwNyB5G297txt\nkkREREREREREREREF+GkMxERERERERERERH5DCediYiIiIiIiIiIiMhnOOlMRERERERERERERD7D\nSWciIiIiIiIiIiIi8hlOOhMRERERERERERGRz3DSmYiIiIiIiIiIiIh8hpPOMuVyuaSO4BcOh6PL\nbhsREXU/XbmmORwOqSMQERH5hMvlgiiKUsfwC9ZrIpKKSuoA1DGZ29bj3Op3oXM0oSqmP+b97llo\ntVqpY/nEK79YjD4NxXABKOmRhJ/94y2pIxEREXmlqvI8Pln+WwiVBXAZYjDtx79HatoYqWP5xGdv\nv4ycVa/DoHSi3GXA/7y+BkajUepYREREXln75j+hytkJUVBAyJiO6+96UOpIPlF6rhif/c/dGKhx\notohIvKGuzD7rgekjkVE3QjvdJYRq9WK8pVv4OZIG27qocTtrgJsfP9fUsfyifdf/BvuCKvHbYNj\nsWhwLGbhHFZ+9I7UsYiIiLyy6rW/Id2Sg/TQJowUirD1nb9LHcknXC4Xjq/8D2b2DcHE3qGY1xt4\n8bd3Sh2LiIjIK3s2fYcxBdswp4eAuTEiBh/7DtkH90odyyc++9PP8UhqNBYm9cTSlFjUfPffLv0N\nLCIKPpx0lpGamhrEo6llWaNUQGWulTCR79SePYWEsJCW5cFRBpw5milhIiIiok4wV0MQBLflrqC2\ntgaRmtZlpUKAztEoXSAiIqJOqD13Bgn61i+ADwpVojT/pISJfCcSViguOhfpqVOioaFBwkRE1N1w\n0llGjEYjTKoeLc+aKmx0QN8/VeJUvjFi+hzsKK5pWV53pgqTFy6WMBEREZH39L2HwOxovpvIJYqA\ncYDEiXwjKioaxTZ1y7lITZMdythBEqciIiLyzqBRE7C3rnV5a50Sw8ZNki6QDzVE9cZ5sxUAIIoi\ncs0iwsPDJU5FRN0Jn+ksIwqFApN+/Vd8+dF/oHFYoE4fjmnzFkkdyyem3LQQXxafxet7vgMUAnpe\ndxfSx4yXOhYREZFXbn3gd/jyLSWKi3MhGqJx109/L3Ukn7n//z7Gu0/9DAZY4eqRhN8/x8dhERGR\nPA1MGY7Dcx/Cyp1rIEKBvrcvRK/efaWO5RMPLnsNrz36E4SXnkOtoMZNf31T6khE1M1w0llmYnv1\nxpzfPi11DL+4+f6HgfsfhtEYhoqKeqnjEBEReU2hUODW+38rdQy/GDQ4BU9/tIX1moiIuoT0idOA\nidOkjuFzCoUCP/vH2wDAmk1EkuDjNYiIiIiIiIiIiIjIZzjpTEREREREREREREQ+w0lnIiIiIiIi\nIiIiIvIZTjoTERERERERERERkc9w0pmIiIiIiIiIiIiIfIaTzkRERERERERERETkM5x0JiIiIiIi\nIiIiIiKf4aQzEREREREREREREfmMSuoAwS7nxHFk5Z5EuEGD6ddOg1arlTpSu1wuF7Z8+SHUlioY\n+gzFyMkzpI7kkdLiszi89gvo9BqMmHk7onsYpY4UdArzTyFn4zdwCQpMvPVehEdESh2JiCgoNDQ0\n4NuNGxCi1yF1YBIGDRgodSSPHNm/E7n7tyKiZyymzb8HarVa6kjtcjqd+PbjN6Gw1SF+yFiMnDBF\n6khBx26345sPX4OjsQ5DrpmGEaPHSx2JiChobNy6FQ02C0K1IZg+ebLUcTxSW1OF3V/8F3qdEgMm\n3oje/eRxnpG1extKj+5HWK9eGHvjIiiVSqkjBZ2DW9ejMjcLqqhYTLvlTgiCIHUkoi6Dk85XkXXs\nKPYWlKD/yClw2G149b8f4OGl90GhCO4bxFe+/DRuqMpElFaFE8e2YGddDSbOuVXqWFdVUVaCzBce\nw4IoO0RRxKfLd2PGk/9CWHiE1NGCRvGZfOT++w+YF+mESxTx4TOZmPvnfyMkJETqaEREkrLZbHjt\nkxUYfv0CKJRKrNu3HQCCfuJ53/YNOPXhX9Bfa4H1mAtvHD6Ah57+t9Sx2vXWs7/DoJLtCFErkLv3\na5gbH8O118+VOlbQEEURrz/1CwyrPQiNUoHsrO9gt/0ZoyZMkzoaEZHkVqxaCSFxCKKMcagqK8Hn\nq77BrfOCu4aYzWase/Y3+FFEIxSCgNWHd0Dxy2WI79NP6mhXtXfDakRtfBtzw5SoP+fEVzlHceuj\nz0odK6js+GYFEnd/jAmhKlQXObDyXAEW/OoPUsci6jKCe/ZUYtkn89A/bSwAQKXWIHLAUBQVFUqc\n6upEUUTo2WxEaZs/TxgSpkLj0d0Sp2rfoQ2rMT/SBgAQBAG3RjRh36a1EqcKLkc3f4ubIp0AAIUg\nYK6uBod3b5M4FRGR9I4eO4reGROguHD3zuCxk3Ag+5jEqdp3ctf36K+1AAC0KgX0546gpqZa4lRX\nZ7VagYIDCFE3n0L21dlRsG+DxKmCS2VlJUJLDkOjbN5HA3QWmHZ+J3EqIqLgUGlxIsoYBwCIiu2F\nCqtd4kTtO7h9E+br66C4cAfsnCgnsjevkThV+2oP78DwsOZzozC1Ej1KT8BuD/79HUhNR3djcGjz\n3EmUVgVDYbbEiYi6Fk46X4XodEAUxZZlS0Mt9HqDhInaJwgCHAr3r+baFcF/Q7sqxIAmh6tlucbm\nREgY73K+mKDRweZs3UfVNhdCI6IkTEREFBzCwsJgrqtpWXY6HFBAvMpPBAdRqXY/zxBU0Gp1EiZq\nn0qlgl2hcfszlzL4HwkSSDqdDlahdR+JogiR+4iICEDzNbbbssNxhZbBIzQyClW21uswq8MFhTb4\nv2166TyARVDy8RqXsAnu++jSuRQi6hxOOl/F7OumIXv916gsK8HZ41mIgRU9evSQOla7Iqfdgm1V\nDpQ0WLCqRo2UefdKHaldU+bdjs+QiPzaJpysacJ3hhSMv26W1LGCypRb7sbHtlicqbMgp9qCvXGj\nMGzkGKljERFJLmlQEpTnC1GYm4PzJcU4tmEl5lx/vdSx2jXjzp/jkJiASrMdeY1KJExbHPSPTFIq\nlRh4/V3IbVSh0mxHpjMO0+54SOpYQSU0NBSxk+/AqQYFKs12HBJ74/o7fy51LCKioDA6eRBMe7eh\nuqIMpj1bMTYlSepI7UofOwE7e6TjeE0TztQ14RNHHKbcfKfUsdo1YuESfFWrRUmDBbur7QiddHPQ\nPyo00IbMuxura1QoabBga6UDUdOC+7GkRHIjXHyHTYCIFRX1gV6n16xWK3KO52DgwN4ID5PPi+3K\nykphrimFMWEgQkPDpI7jEZfLheNHj8BojIAxrr/sHuBvNIbB32Pb6XQiJysTIXoDBiWndLq/QGT2\nBznmlmNmQJ65jcYweR08gpusanbe6VNQqlxI6NVfFi/kA4CmpiYcP3oYKUOTEaKPljqOx86dK0ZT\nQwXiEpJgMAT3t8AuFajjWuHZM6goO4eUYemd/jBBjsdigLkDSY6ZAdZsH5JVva6qqkRVdRliouMQ\nFSWf2nfyRA70IQrE9U6SzR3DjY2NOHksC6npQ6HRhEsdp0MCdVyrr6/DqZyjSOg3ED1jYzvdnxyP\nx3LMDDB3IHlbr4P/uQsS02q1yEjPkN2giI2Ng3FYkqwyKxQKDB0hv30dSEqlEsMzRksdg4goKA0c\nMEh2NSQkJAQjx4yXXe74+AQYjUNklTnQEvv0RWKfvlLHICIKOtHRMUhO7ie7GpI0JFV29dpgMCB9\nrPzOMwIpLCwcGddMkDoGUZfE71YQERERERERERERkc9w0pmIiIiIiIiIiIiIfIaTzkRERERERERE\nRETkM5x0JiIiIiIiIiIiIiKf4aQzEREREREREREREfkMJ52JiIiIiIiIiIiIyGc46UxERERERERE\nREREPsNJZyIfsFgsPunH4XBAFEWf9EVERETubDYbXC5Xp/sRRRFOp9MHiYiIiOhSLpfLp9fYRCQN\nldQBiOTsyP7d+Ppvv0Ckwop6UY1rf/xHTL1pYYf7sdvtWPmPJxBdfhIWpQ49Zi7G2Jnz/JCYiIio\n+3G5XHjinhsQ01QMh0uActA4/M//veVVX+u++C9OrfsACqcV6oFjcd//LoNCwfs4iIiIfOGzfy2H\nc8+3iFQLOG5V475/fY7IyMgO93M2LxeH3l6OcHMV6vQxGPWTx5DYf5AfEhPRlfAMmagTvnnuUcxM\nVGJsgh7Te6ux4+1nvOpn44dv4Bb7KdxoVGFhtAPm799DfX2dj9MSERF1Ty8+9QimGCoxsXcopvQx\noGfJfmxZ922H+zlXXISStf9Bhq4aaQYz+hVtwpoV7/ghMRERUfdTV1cH5b5vcW9KLOYP6onfDonA\nfx9/0Ku+jnz0ChYZ6nCjUYVFhlpkfviyj9MSUXs46UzUCSGi+1d+9IJ3X90RGqugUylblhMFCyoq\nyjuVjYiIiJo1lBciQtf6Bb/e4WpkH9rT4X6KC/NhVDS1LOtVCpirynySkYiIqLsrLDyL/mGalmW1\nUoEwZ9NVfuLKdNYGt+WQS5aJyP846UzUCY2GWFgczc+GdLhE1KoivOoncnAa8hpbJ6yzlT3Qu3cf\nn2QkIiLq7kZMng1TZesHxQdLrbjp1ns63E/KsHQUqHq1LBdZ1RiYPt4nGYmIiLq75OQh2FtpbXnP\n0ZlaM9Anxau+GqITYb1wrW5xONEYw+trokDjM52JOuHRVz/H8w/fBU1NGRyGKPzm3+971c8118/F\njiYzck4chE2pwTW/uB8ajab9HyQiIqJ2zf/RUrxTXowNe9cCChXGLX0UAwcldbif0NAwzPr1P7D9\ns9cguOzoN2YGRk2Y5ofERERE3Y9KpcLUJ17Bi/98AhFKF8xxSfjJE8u96mv2L57At2+/AHVtOezR\ncZj944d9nJaI2sNJZ6JO0Ol0ePy1zwEARmMYKirqve7r2nmLgHmLfBWNiIiILnLfr58E8GSn6/WA\nwSkY8MQLvgtGRERELYYMS8OQt1Z3ul5rNBrM/umjPkxGRB3Fx2sQERERERERERERkc9w0pmIiIiI\niIiIiIiIfIaTzkRERERERERERETkM5x0JiIiIiIiIiIiIiKf4aQzEREREREREREREfkMJ52JiIiI\niIiIiIiIyGc46UxEREREREREREREPsNJZyIiIiIiIiIiIiLyGU46ExEREREREREREZHPcNKZiIiI\niIiIiIiIiHyGk85ERERERERERERE5DOcdCYiIiIiIiIiIiIin+GkMxERERERERERERH5DCediYiI\niIiIiIiIiMhnOOlMRERERERERERERD7DSWciIiIiIiIiIiIi8hlOOhMRERERERERERGRz3DSmYiI\niIiIiIiIiIh8hpPOREREREREREREROQznHQmIiIiIiIiIiIiIp/hpDMRERERERERERER+YzKk0bJ\nycl/B3AtACWAZSaT6auL/m4GgGcAOACsNZlMT/sjKBEREV0d6zUREVHwY70mIqLuoN07nZOTk6cC\nSDWZTBMA3AjghUuavAhgIZqL5szk5OQhvg5JHSeKImw2m9QxiIgoQFiv5ctms0EURaljEBFRALBe\ny5fL5YLD4ZA6BhGRbHhyp/NWAHsv/H8NAH1ycrJgMpnE5OTk/gAqTSbTOQBITk5eA2A6gBN+SUse\nyTmwBydXvIJopxll+p7/397dxVpW1mcAfw4wI5aZqeKMgdLASNK+1IjWwkU/okxEkQYsaqxtmRjQ\nmEYukNTYi0bA2qIXJjSlSVsbLRBjigWMoPJR21Isxpp+YayJvIGUQBQqjNRKOkhhzu7F3kc2A+ec\nPeQ9e693zu+XTHL2WitnnvznZJ7Jf+9ZK2+45A9z7M5di44FwMbS153Zv39/rr3ikhz1vZrlF+/I\na952UX7pzHMWHQuAjaWvO/T3130qB/7l9rzoiFH++8TX5ryLP5SlpaVFxwIYtHWXzrXWUZInJi/f\nm+TWybEkOS7Jo1OXP5Lk5KYJOWT33fjneedLnkxyZEajfbnx2qvyax/0v7IADmf6uj83f+rKvPrx\nb+TIbUtJfpS7r78qp7/+rGzZsmXR0QDYIPq6P/d++1v56W98Ka/euSXJUvbt+7d89ZbP5XXnvmPR\n0QAGbaZ7OidJKeW8JO9OctYal830Vt+uXdtn/W0HpYfco9Eo2w7s//HrpaWl7Fh6sovs03rLu6LH\n3D1mTvrM3WPmpN/cm1XLvk76/PPvJfPW5f/NkUc880ex7cAPs3Xrcnbu7CN/0s+sD9Zj7h4zJ3LP\nU4+ZNzN93U/mf7/rO/n5Y565M+nOo4/K0hOPdZN/RW95kz4zJ33m7jFzIvfQzfogwTcn+b0kb661\nPj516qEkx0+9PmFybE2PPvr4epcMzq5d27vJ/diOE3Jg+Ts58oilPPbkU3nyhFd0kz3pa9bTeszd\nY+akz9w9Zk76zL1ZCvz5tO7rpL/O7ulndsdJp2bfPf+QnS8aZTQa5Qfbd2d5eWs3+Xua9bQec/eY\nOZF7nnrMnGzeztbXff3M7n7l6bnji9fmnJccSJL86w9H2fWzp3WTP+lr3it6zJz0mbvHzInc8/RC\n+3rdpXMpZUeSjyc5s9b6P9Pnaq0PlFK2l1JOzLgMz01y/gtKQjNn/84V+fw1f5wdy0/k/048MWft\n/e1FRwJgg+nr/rzpbXtz+4Gnc++3/zlH/+RLc/5vvd/9IQEOc/q6P8e+bGdOfs+luemW6/LirUdk\nx+v25NTXnLboWACDN8snnX8jycuSXF9KWUoySnJHkv+otd6c5KIkn50cv67Wet9GhWU227Zty1su\nvrTLd08AeMH0dYfOfscFSS7Q2QCbh77u0MmnvConn/JRfQ1wCGZ5kOAnk3xyjfNfTfLLLUMBAIdG\nXwPA8OlrADaLI9a/BAAAAAAAZmPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwA\nAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOW\nzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAA\nNGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAA\nAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bO\nAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0\nY+kMAAAAAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAA\nAEAzls4AAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4A\nAAAAADRj6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0Y+kMAAAAAEAzls4AAAAAADRj\n6QwAAAAAQDOWzgAAAAAANGPpDAAAAABAM5bOAAAAAAA0c9QsF5VSXpXkpiR/VGv9s4PO3Z/kwSTL\nSUZJ9tZaH24dFABYm74GgD7obAAOd+sunUspP5HkT5L83SqXjJKcXWt9omUwAGB2+hoA+qCzAdgM\nZrm9xo+S/GqS1d5ZXZr8AgAWR18DQB90NgCHvXWXzrXW5Vrrk+tc9olSyl2llI81ygUAHAJ9DQB9\n0NkAbAYtHiR4WZIPJDkjyamllLc3+J4AQFv6GgD6oLMB6N7SaDSa6cJSyoeTPHrwQw4OuuaiJC+v\ntX6kUT4A4BDoawDog84G4HB2qJ90ftZ9pUopO0opt5dStkwOnZHkW02SAQAvlL4GgD7obAAOS+t+\n0rmU8gtJrkxyUpKnknw3yReS3F9rvbmUcnGSC5PsT3J3rfX9G5oYAHgOfQ0AfdDZAGwGM99eAwAA\nAAAA1tPiQYIAAAAAAJDE0hkAAAAAgIYsnQEAAAAAaOaojfzmpZSjM37S7h/UWj89dfyNST6a5Okk\nt9Var9jIHIdqjdz3J3kwyXKSUZK9tdaHF5PyGaWUM5LckHHmpSTfrLVeMnV+cPOeIfMgZ50kpZS9\nSX4344d+XF5rvW3q3OBmvWKd3IObdynlPUneNcmzlOS0WuuOqfODnPUMuYc462OSfDrJS5Nszfjv\nvi9PnR/qrNfLPbhZD1mPna2v56PXztbX89NjZ/fY10mfna2v2+qxrxOdPQ+99nXSZ2fr6/npsbN7\n7OukfWdv6NI5yWVJvv88x69K8qYkDyf5SinlxlrrPRuc5VCslnuU5Oxa6xNzzjOLO2ut71zl3FDn\nvVbmQc66lHJsksuTvDbJ9iQfSXLb1CWDnPUMuQc371rr1UmuTpJSyuuT/PpBlwxy1jPkHtysM346\n+j211g+VUo5PckeSn5s6P8hZZ/3cQ5z1kPXY2fp6frrqbH09Xz12dqd9nfTZ2RdGX7fUY18nOnte\nuurrpM/O1tfz1WlnX5j++jppERa4+gAABJlJREFU3NkbtnQupZQkpyS55aDjr0jy/VrrQ5PXtyY5\nM8kQhrtq7omlya8het5cA5/3WrMc6qzfmORva637k+xP8r6VEwOf9aq5J4Y67xWXJzl/5cXAZz3t\nWbknhjjrfUlOnXx9bJJHV04MfNar5p4Y4qwHqcfO1tdz11tn6+vF6bGze+n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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn import decomposition\n",
"#PCA\n",
"pca = decomposition.PCA(n_components=3)\n",
"pca.fit(dat)\n",
"X = pca.transform(dat)\n",
"\n",
"#rerun kmeans\n",
"k_meanspca = KMeans(n_clusters=3)\n",
"k_meanspca.fit(X) \n",
"\n",
"#rerurn UPGMA\n",
"linkagematpca = linkage(X, 'average')\n",
"outpca = fcluster(linkagemat, 3, criterion='maxclust')\n",
"\n",
"#plot\n",
"fig = plt.figure(figsize=(25, 20))\n",
"ax1 = fig.add_subplot(2,3,1)\n",
"ax2 = fig.add_subplot(2,3,2)\n",
"ax3 = fig.add_subplot(2,3,3)\n",
"ax4 = fig.add_subplot(2,3,4)\n",
"ax5 = fig.add_subplot(2,3,5)\n",
"ax6 = fig.add_subplot(2,3,6)\n",
"ax1.scatter(dat[:, 0], dat[:, 1], c = target, cmap=plt.cm.Paired)\n",
"ax2.scatter(dat[:, 0], dat[:, 1], c = out, cmap=plt.cm.Paired)\n",
"ax3.scatter(dat[:, 0], dat[:, 1], c = k_means.labels_, cmap=plt.cm.Paired)\n",
"ax4.scatter(dat[:, 0], dat[:, 1], c = target, cmap=plt.cm.Paired)\n",
"ax5.scatter(dat[:, 0], dat[:, 1], c = outpca, cmap=plt.cm.Paired)\n",
"ax6.scatter(dat[:, 0], dat[:, 1], c = k_meanspca.labels_, cmap=plt.cm.Paired)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's it for today, we have had a brief tour of GLMs, linear optimisation and clustering. Nect week we will focus on scikit-learn and some applied pipelines and examples."
]
}
],
"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": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}