Morten Hjorth-Jensen
3809 lines
719 KiB
Plaintext
3809 lines
719 KiB
Plaintext
{
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"cell_type": "markdown",
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"<!-- dom:TITLE: Data Analysis and Machine Learning: Logistic Regression -->\n",
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"# Data Analysis and Machine Learning: Logistic Regression\n",
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"<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
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"<!-- Author: --> \n",
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"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
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"\n",
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"Date: **Oct 26, 2021**\n",
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"\n",
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"Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"## Plans for week 38\n",
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"\n",
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"* Thursday: Summary of regression methods and discussion of project 1. Start Logistic Regression\n",
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"\n",
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"* [Video of Lecture September 23](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureSeptember23.mp4?vrtx=view-as-webpage)\n",
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"\n",
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"* Friday: Logistic Regression and Optimization methods\n",
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"\n",
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"* [Video of Lecture September 24](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember24.mp4?vrtx=view-as-webpage)\n",
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"\n",
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"## Thursday September 23\n",
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"\n",
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"\n",
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"## Ridge and LASSO Regression, reminder\n",
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"\n",
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"The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is \n",
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"our optimization problem is"
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]
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},
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"cell_type": "markdown",
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"source": [
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"$$\n",
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"{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p}}}\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"or we can state it as"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n",
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"{\\mathbb{R}}^{p}}}\\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2,\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"where we have used the definition of a norm-2 vector, that is"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"\\vert\\vert \\boldsymbol{x}\\vert\\vert_2 = \\sqrt{\\sum_i x_i^2}.\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"By minimizing the above equation with respect to the parameters\n",
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"$\\boldsymbol{\\beta}$ we could then obtain an analytical expression for the\n",
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"parameters $\\boldsymbol{\\beta}$. We can add a regularization parameter $\\lambda$ by\n",
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"defining a new cost function to be optimized, that is"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n",
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"{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"which leads to the Ridge regression minimization problem where we\n",
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"require that $\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\\le t$, where $t$ is\n",
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"a finite number larger than zero. By defining"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1,\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"we have a new optimization equation"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n",
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"{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"which leads to Lasso regression. Lasso stands for least absolute shrinkage and selection operator. \n",
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"\n",
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"Here we have defined the norm-1 as"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"\\vert\\vert \\boldsymbol{x}\\vert\\vert_1 = \\sum_i \\vert x_i\\vert.\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- !split -->\n",
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"## Various steps in cross-validation\n",
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"\n",
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"When the repetitive splitting of the data set is done randomly,\n",
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"samples may accidently end up in a fast majority of the splits in\n",
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"either training or test set. Such samples may have an unbalanced\n",
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"influence on either model building or prediction evaluation. To avoid\n",
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"this $k$-fold cross-validation structures the data splitting. The\n",
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"samples are divided into $k$ more or less equally sized exhaustive and\n",
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"mutually exclusive subsets. In turn (at each split) one of these\n",
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"subsets plays the role of the test set while the union of the\n",
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"remaining subsets constitutes the training set. Such a splitting\n",
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"warrants a balanced representation of each sample in both training and\n",
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"test set over the splits. Still the division into the $k$ subsets\n",
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"involves a degree of randomness. This may be fully excluded when\n",
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"choosing $k=n$. This particular case is referred to as leave-one-out\n",
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"cross-validation (LOOCV). \n",
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"\n",
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"<!-- !split -->\n",
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"## How to set up the cross-validation for Ridge and/or Lasso\n",
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"\n",
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"* Define a range of interest for the penalty parameter.\n",
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"\n",
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"* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n",
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"\n",
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"* Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\boldsymbol{\\sigma}_{-i}^2(\\lambda)$, as"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$$\n",
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"\\begin{align*}\n",
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"\\boldsymbol{\\beta}_{-i}(\\lambda) & = ( \\boldsymbol{X}_{-i, \\ast}^{T}\n",
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"\\boldsymbol{X}_{-i, \\ast} + \\lambda \\boldsymbol{I}_{pp})^{-1}\n",
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"\\boldsymbol{X}_{-i, \\ast}^{T} \\boldsymbol{y}_{-i}\n",
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"\\end{align*}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Evaluate the prediction performance of these models on the test set by $C[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]$. Or, by the prediction error $|y_i - \\boldsymbol{X}_{i, \\ast} \\boldsymbol{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n",
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"\n",
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"* Repeat the first three steps such that each sample plays the role of the test set once.\n",
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"\n",
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"* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. \n",
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"\n",
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"## Cross-validation in brief\n",
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"\n",
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"For the various values of $k$\n",
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"\n",
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"1. shuffle the dataset randomly.\n",
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"\n",
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"2. Split the dataset into $k$ groups.\n",
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"\n",
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"3. For each unique group:\n",
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"\n",
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"a. Decide which group to use as set for test data\n",
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"\n",
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"b. Take the remaining groups as a training data set\n",
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"\n",
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"c. Fit a model on the training set and evaluate it on the test set\n",
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"\n",
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"d. Retain the evaluation score and discard the model\n",
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"\n",
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"\n",
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"5. Summarize the model using the sample of model evaluation scores\n",
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"\n",
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"## Code Example for Cross-validation and $k$-fold Cross-validation\n",
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"\n",
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"The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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"data": {
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\n",
|
||
"text/plain": [
|
||
"<Figure size 432x288 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import KFold\n",
|
||
"from sklearn.linear_model import Ridge\n",
|
||
"from sklearn.model_selection import cross_val_score\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(3155)\n",
|
||
"\n",
|
||
"# Generate the data.\n",
|
||
"nsamples = 100\n",
|
||
"x = np.random.randn(nsamples)\n",
|
||
"y = 3*x**2 + np.random.randn(nsamples)\n",
|
||
"\n",
|
||
"## Cross-validation on Ridge regression using KFold only\n",
|
||
"\n",
|
||
"# Decide degree on polynomial to fit\n",
|
||
"poly = PolynomialFeatures(degree = 6)\n",
|
||
"\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 500\n",
|
||
"lambdas = np.logspace(-3, 5, nlambdas)\n",
|
||
"\n",
|
||
"# Initialize a KFold instance\n",
|
||
"k = 5\n",
|
||
"kfold = KFold(n_splits = k)\n",
|
||
"\n",
|
||
"# Perform the cross-validation to estimate MSE\n",
|
||
"scores_KFold = np.zeros((nlambdas, k))\n",
|
||
"\n",
|
||
"i = 0\n",
|
||
"for lmb in lambdas:\n",
|
||
" ridge = Ridge(alpha = lmb)\n",
|
||
" j = 0\n",
|
||
" for train_inds, test_inds in kfold.split(x):\n",
|
||
" xtrain = x[train_inds]\n",
|
||
" ytrain = y[train_inds]\n",
|
||
"\n",
|
||
" xtest = x[test_inds]\n",
|
||
" ytest = y[test_inds]\n",
|
||
"\n",
|
||
" Xtrain = poly.fit_transform(xtrain[:, np.newaxis])\n",
|
||
" ridge.fit(Xtrain, ytrain[:, np.newaxis])\n",
|
||
"\n",
|
||
" Xtest = poly.fit_transform(xtest[:, np.newaxis])\n",
|
||
" ypred = ridge.predict(Xtest)\n",
|
||
"\n",
|
||
" scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)\n",
|
||
"\n",
|
||
" j += 1\n",
|
||
" i += 1\n",
|
||
"\n",
|
||
"\n",
|
||
"estimated_mse_KFold = np.mean(scores_KFold, axis = 1)\n",
|
||
"\n",
|
||
"## Cross-validation using cross_val_score from sklearn along with KFold\n",
|
||
"\n",
|
||
"# kfold is an instance initialized above as:\n",
|
||
"# kfold = KFold(n_splits = k)\n",
|
||
"\n",
|
||
"estimated_mse_sklearn = np.zeros(nlambdas)\n",
|
||
"i = 0\n",
|
||
"for lmb in lambdas:\n",
|
||
" ridge = Ridge(alpha = lmb)\n",
|
||
"\n",
|
||
" X = poly.fit_transform(x[:, np.newaxis])\n",
|
||
" estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)\n",
|
||
"\n",
|
||
" # cross_val_score return an array containing the estimated negative mse for every fold.\n",
|
||
" # we have to the the mean of every array in order to get an estimate of the mse of the model\n",
|
||
" estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n",
|
||
"\n",
|
||
" i += 1\n",
|
||
"\n",
|
||
"## Plot and compare the slightly different ways to perform cross-validation\n",
|
||
"\n",
|
||
"plt.figure()\n",
|
||
"\n",
|
||
"plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n",
|
||
"plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')\n",
|
||
"\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('mse')\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## To think about, first part\n",
|
||
"\n",
|
||
"When you are comparing your own code with for example **Scikit-Learn**'s\n",
|
||
"library, there are some technicalities to keep in mind. The examples\n",
|
||
"here demonstrate some of these aspects with potential pitfalls.\n",
|
||
"\n",
|
||
"The discussion here focuses on the role of the intercept, how we can\n",
|
||
"set up the design matrix, what scaling we should use and other topics\n",
|
||
"which tend confuse us.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The intercept can be interpreted as the expected value of our\n",
|
||
"target/output variables when all other predictors are set to zero.\n",
|
||
"Thus, if we cannot assume that the expected outputs/targets are zero\n",
|
||
"when all predictors are zero (the columns in the design matrix), it\n",
|
||
"may be a bad idea to implement a model which penalizes the intercept.\n",
|
||
"Furthermore, in for example Ridge and Lasso regression, the default solutions\n",
|
||
"from the library **Scikit-Learn** (when not shrinking $\\beta_0$) for the unknown parameters\n",
|
||
"$\\boldsymbol{\\beta}$, are derived under the assumption that both $\\boldsymbol{y}$ and\n",
|
||
"$\\boldsymbol{X}$ are zero centered, that is we subtract the mean values.\n",
|
||
"\n",
|
||
"\n",
|
||
"## More thinking\n",
|
||
"\n",
|
||
"\n",
|
||
"If our predictors represent different scales, then it is important to\n",
|
||
"standardize the design matrix $\\boldsymbol{X}$ by subtracting the mean of each\n",
|
||
"column from the corresponding column and dividing the column with its\n",
|
||
"standard deviation. Most machine learning libraries do this as a default. This means that if you compare your code with the results from a given library,\n",
|
||
"the results may differ. \n",
|
||
"\n",
|
||
"The\n",
|
||
"[Standadscaler](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html)\n",
|
||
"function in **Scikit-Learn** does this for us. For the data sets we\n",
|
||
"have been studying in our various examples, the data are in many cases\n",
|
||
"already scaled and there is no need to scale them. You as a user of different machine learning algorithms, should always perform a\n",
|
||
"survey of your data, with a critical assessment of them in case you need to scale the data.\n",
|
||
"\n",
|
||
"If you need to scale the data, not doing so will give an *unfair*\n",
|
||
"penalization of the parameters since their magnitude depends on the\n",
|
||
"scale of their corresponding predictor.\n",
|
||
"\n",
|
||
"Suppose as an example that you \n",
|
||
"you have an input variable given by the heights of different persons.\n",
|
||
"Human height might be measured in inches or meters or\n",
|
||
"kilometers. If measured in kilometers, a standard linear regression\n",
|
||
"model with this predictor would probably give a much bigger\n",
|
||
"coefficient term, than if measured in millimeters.\n",
|
||
"This can clearly lead to problems in evaluating the cost/loss functions.\n",
|
||
"\n",
|
||
"\n",
|
||
"## Still thinking\n",
|
||
"\n",
|
||
"Keep in mind that when you transform your data set before training a model, the same transformation needs to be done\n",
|
||
"on your eventual new data set before making a prediction. If we translate this into a Python code, it would could be implemented as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"ename": "NameError",
|
||
"evalue": "name 'y_train' is not defined",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||
"\u001b[0;32m/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_42372/1132315548.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m#Model training, we compute the mean value of y and X\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0my_train_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0mX_train_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mX_train\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX_train\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mX_train_mean\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0my_train\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my_train\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0my_train_mean\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
"\u001b[0;31mNameError\u001b[0m: name 'y_train' is not defined"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"#Model training, we compute the mean value of y and X\n",
|
||
"y_train_mean = np.mean(y_train)\n",
|
||
"X_train_mean = np.mean(X_train,axis=0)\n",
|
||
"X_train = X_train - X_train_mean\n",
|
||
"y_train = y_train - y_train_mean\n",
|
||
"\n",
|
||
"# The we fit our model with the training data\n",
|
||
"trained_model = some_model.fit(X_train,y_train)\n",
|
||
"\n",
|
||
"\n",
|
||
"#Model prediction, we need also to transform our data set used for the prediction.\n",
|
||
"X_test = X_test - X_train_mean #Use mean from training data\n",
|
||
"y_pred = trained_model(X_test)\n",
|
||
"y_pred = y_pred + y_train_mean"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## What does centering (subtracting the mean values) mean mathematically?\n",
|
||
"\n",
|
||
"\n",
|
||
"Let us try to understand what this may imply mathematically when we\n",
|
||
"subtract the mean values, also known as *zero centering*. For\n",
|
||
"simplicity, we will focus on ordinary regression, as done in the above example.\n",
|
||
"\n",
|
||
"The cost/loss function for regression is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\beta_0, \\beta_1, ... , \\beta_{p-1}) = \\frac{1}{n}\\sum_{i=0}^{n} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij}\\beta_j\\right)^2,.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Recall also that we use the squared value since this leads to an increase of the penalty for higher differences between predicted and output/target values.\n",
|
||
"\n",
|
||
"What we have done is to single out the $\\beta_0$ term in the definition of the mean squared error (MSE).\n",
|
||
"The design matrix\n",
|
||
"$X$ does in this case not contain any intercept column.\n",
|
||
"When we take the derivative with respect to $\\beta_0$, we want the derivative to obey"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial \\beta_j} = 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"for all $j$. For $\\beta_0$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial \\beta_0} = -\\frac{2}{n}\\sum_{i=0}^{n-1} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij} \\beta_j\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Multiplying away the constant $2/n$, we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i=0}^{n-1} \\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} \\sum_{j=1}^{p-1} X_{ij} \\beta_j.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Further Manipulations\n",
|
||
"\n",
|
||
"\n",
|
||
"Let us special first to the case where we have only two parameters $\\beta_0$ and $\\beta_1$.\n",
|
||
"Our result for $\\beta_0$ simplifies then to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"n\\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} X_{i1} \\beta_1.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We obtain then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\beta_1\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we define"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mu_1=\\frac{1}{n}\\sum_{i=0}^{n-1} (X_{i1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and if we define the mean value of the outputs as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mu_y=\\frac{1}{n}\\sum_{i=0}^{n-1}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\mu_y - \\beta_1\\mu_{1}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"In the general case, that is we have more parameters than $\\beta_0$ and $\\beta_1$, we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\frac{1}{n}\\sum_{i=0}^{n-1}\\sum_{j=1}^{p-1} X_{ij}\\beta_j.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Replacing $y_i$ with $y_i - y_i - \\overline{\\boldsymbol{y}}$ and centering also our design matrix results in a cost function (in vector-matrix disguise)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{\\beta}) = (\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta})^T(\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Wrapping it up\n",
|
||
"\n",
|
||
"If we minimize with respect to $\\boldsymbol{\\beta}$ we have then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\boldsymbol{\\tilde{y}} = \\boldsymbol{y} - \\overline{\\boldsymbol{y}}$\n",
|
||
"and $\\tilde{X}_{ij} = X_{ij} - \\frac{1}{n}\\sum_{k=0}^{n-1}X_{kj}$.\n",
|
||
"\n",
|
||
"For Ridge regression we need to add $\\lambda \\boldsymbol{\\beta}^T\\boldsymbol{\\beta}$ to the cost function and get then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X} + \\lambda I)^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"What does this mean? And why do we insist on all this? Let us look at some examples.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Linear Regression code, Intercept handling first\n",
|
||
"\n",
|
||
"This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (*code example thanks to Øyvind Sigmundson Schøyen*). Here our scaling of the data is done by subtracting the mean values only.\n",
|
||
"Note also that we do not split the data into training and test."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"True beta: [2, 0.5, 3.7]\n",
|
||
"Fitted beta: [2.08376632 0.19569961 3.97898392]\n",
|
||
"Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n",
|
||
"MSE with intercept column\n",
|
||
"0.004113634617443142\n",
|
||
"MSE with intercept column from SKL\n",
|
||
"0.004113634617443129\n",
|
||
"Manual intercept: 2.0837663229239056\n",
|
||
"Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n",
|
||
"Sklearn intercept: 2.0837663229239043\n",
|
||
"Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n",
|
||
"MSE with Manual intercept\n",
|
||
"0.004113634617443132\n",
|
||
"MSE with Sklearn intercept\n",
|
||
"0.00411363461744314\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 432x288 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"\n",
|
||
"np.random.seed(2021)\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"\n",
|
||
"\n",
|
||
"def fit_beta(X, y):\n",
|
||
" return np.linalg.pinv(X.T @ X) @ X.T @ y\n",
|
||
"\n",
|
||
"\n",
|
||
"true_beta = [2, 0.5, 3.7]\n",
|
||
"\n",
|
||
"x = np.linspace(0, 1, 11)\n",
|
||
"y = np.sum(\n",
|
||
" np.asarray([x ** p * b for p, b in enumerate(true_beta)]), axis=0\n",
|
||
") + 0.1 * np.random.normal(size=len(x))\n",
|
||
"\n",
|
||
"degree = 3\n",
|
||
"X = np.zeros((len(x), degree))\n",
|
||
"\n",
|
||
"# Include the intercept in the design matrix\n",
|
||
"for p in range(degree):\n",
|
||
" X[:, p] = x ** p\n",
|
||
"\n",
|
||
"beta = fit_beta(X, y)\n",
|
||
"\n",
|
||
"# Intercept is included in the design matrix\n",
|
||
"skl = LinearRegression(fit_intercept=False).fit(X, y)\n",
|
||
"\n",
|
||
"print(f\"True beta: {true_beta}\")\n",
|
||
"print(f\"Fitted beta: {beta}\")\n",
|
||
"print(f\"Sklearn fitted beta: {skl.coef_}\")\n",
|
||
"ypredictOwn = X @ beta\n",
|
||
"ypredictSKL = skl.predict(X)\n",
|
||
"print(f\"MSE with intercept column\")\n",
|
||
"print(MSE(y,ypredictOwn))\n",
|
||
"print(f\"MSE with intercept column from SKL\")\n",
|
||
"print(MSE(y,ypredictSKL))\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(x, y, label=\"Data\")\n",
|
||
"plt.plot(x, X @ beta, label=\"Fit\")\n",
|
||
"plt.plot(x, skl.predict(X), label=\"Sklearn (fit_intercept=False)\")\n",
|
||
"\n",
|
||
"\n",
|
||
"# Do not include the intercept in the design matrix\n",
|
||
"X = np.zeros((len(x), degree - 1))\n",
|
||
"\n",
|
||
"for p in range(degree - 1):\n",
|
||
" X[:, p] = x ** (p + 1)\n",
|
||
"\n",
|
||
"# Intercept is not included in the design matrix\n",
|
||
"skl = LinearRegression(fit_intercept=True).fit(X, y)\n",
|
||
"\n",
|
||
"# Use centered values for X and y when computing coefficients\n",
|
||
"y_offset = np.average(y, axis=0)\n",
|
||
"X_offset = np.average(X, axis=0)\n",
|
||
"\n",
|
||
"beta = fit_beta(X - X_offset, y - y_offset)\n",
|
||
"intercept = np.mean(y_offset - X_offset @ beta)\n",
|
||
"\n",
|
||
"print(f\"Manual intercept: {intercept}\")\n",
|
||
"print(f\"Fitted beta (wiothout intercept): {beta}\")\n",
|
||
"print(f\"Sklearn intercept: {skl.intercept_}\")\n",
|
||
"print(f\"Sklearn fitted beta (without intercept): {skl.coef_}\")\n",
|
||
"ypredictOwn = X @ beta\n",
|
||
"ypredictSKL = skl.predict(X)\n",
|
||
"print(f\"MSE with Manual intercept\")\n",
|
||
"print(MSE(y,ypredictOwn+intercept))\n",
|
||
"print(f\"MSE with Sklearn intercept\")\n",
|
||
"print(MSE(y,ypredictSKL))\n",
|
||
"\n",
|
||
"plt.plot(x, X @ beta + intercept, \"--\", label=\"Fit (manual intercept)\")\n",
|
||
"plt.plot(x, skl.predict(X), \"--\", label=\"Sklearn (fit_intercept=True)\")\n",
|
||
"plt.grid()\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The intercept is the value of our output/target variable\n",
|
||
"when all our features are zero and our function crosses the $y$-axis (for a one-dimensional case). \n",
|
||
"\n",
|
||
"Printing the MSE, we see first that both methods give the same MSE, as\n",
|
||
"they should. However, when we move to for example Ridge regression,\n",
|
||
"the way we treat the intercept may give a larger or smaller MSE,\n",
|
||
"meaning that the MSE can be penalized by the value of the\n",
|
||
"intercept. Not including the intercept in the fit, means that the\n",
|
||
"regularization term does not include $\\beta_0$. For different values\n",
|
||
"of $\\lambda$, this may lead to differeing MSE values. \n",
|
||
"\n",
|
||
"To remind the reader, the regularization term, with the intercept in Ridge regression is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=0}^{p-1}\\beta_j^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"but when we take out the intercept, this equation becomes"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=1}^{p-1}\\beta_j^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"For Lasso regression we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_1 = \\lambda \\sum_{j=1}^{p-1}\\vert\\beta_j\\vert.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. \n",
|
||
"\n",
|
||
"## Code Examples\n",
|
||
"\n",
|
||
"Armed with this wisdom, we attempt first to simply set the intercept equal to **False** in our implementation of Ridge regression for our well-known vanilla data set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
|
||
" 2.80847477e-01 2.12552073e-01 8.13220609e-02 -1.69634578e-02\n",
|
||
" -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
|
||
" -9.80609615e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
|
||
" 2.64742912e-02 1.63249532e-02 -5.01831224e-05 -2.15098090e-02]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
|
||
" 2.80847477e-01 2.12552073e-01 8.13220609e-02 -1.69634577e-02\n",
|
||
" -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
|
||
" -9.80609615e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
|
||
" 2.64742912e-02 1.63249532e-02 -5.01831185e-05 -2.15098090e-02]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"4.3632959128006053e-07\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"4.363295916429748e-07\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
|
||
" 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
|
||
" -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
|
||
" 0.02976145 0.04543942]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
|
||
" 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
|
||
" -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
|
||
" 0.02976145 0.04543942]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"5.1940428269262024e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.194042826836048e-06\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
|
||
" 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
|
||
" 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
|
||
" -0.01708852 -0.01708781]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
|
||
" 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
|
||
" 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
|
||
" -0.01708852 -0.01708781]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"2.0940821989672366e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"2.0940821989628246e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
|
||
" 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
|
||
" 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
|
||
" 0.00249435 0.00105081]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
|
||
" 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
|
||
" 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
|
||
" 0.00249435 0.00105081]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.0003153514830958068\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.00031535148309580843\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
|
||
" -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
|
||
" -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
|
||
" -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
|
||
" 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
|
||
" -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
|
||
" -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
|
||
" -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
|
||
" 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.015072388895177166\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.015072388895177053\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
|
||
" 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
|
||
" 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
|
||
" 0.0036237 0.003301 ]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
|
||
" 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
|
||
" 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
|
||
" 0.0036237 0.003301 ]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.26409315307910025\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.26409315307910025\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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gw31LYpg+fTr33XcfZWVltG3blr/+9a9BRxKRCPmrXqF1gxT6nH9lnV9bBaKeGzNmDGPGjKl+RxGpczs2f83Mo77il2WZpKTW/a/rpC8Q7n5E02xKckqWR6uS3GZMup+SNMjrfVUg10/qTur09HQ2bdqkXwayH3dn06ZNpKenBx1F5KDyV+Tzo11GvwuuDuT6Sd2CaNOmDcXFxWgyIakqPT19vyFOROLNrm0bmdG4mJ+VdSY1rWEgGZK6QKSlpR30m78iIvHq9ckPsLMh5PW4PLAMSV0gREQSVcGHL9MizThr2PWBZUjqPggRkUS0Z+d3TG20jpHlHWjQMLi+MrUgRETizKzJD7K9EeR2uzTQHCoQIiJxpmDxCzRLg3NH3hRoDj1iEhGJI6Ulu5iS9gkjSk+hYeOMQLOoBSEiEkfmTH2YLelObuexQUdRgRARiSf5RX8jIw3OHzUh6Ch6xCQiEi/K9pYwOWUVQ0tOJj2jedBx1IIQEYkXb0//LzY2dvI6/kvQUQAVCBGRuJH/3rM0aQAX5N4adBRAj5hEROJCRXkZk3wFF+xuTZNmLYOOA6gFISISF+a/9hRfH1VB3gmjg45SSS0IEZE4kP/OX2hUBkNyfxd0lEpqQYiIBKyivIyCsg8ZVHI8TVucGHScSmpBiIgErPDN/6E4o5y8DiOCjrKfmBYIMxtsZqvMbI2Z/aDdZGY3mdkKM1tqZm+ZWduIbZeZ2erwn8timVNEJEgF854krRyG5d4WdJT9xKxAmFkq8BhwAdAZuNjMOlfZ7QMgx90zgXzgD+FjjwXuBPoAvYE7zeyYWGUVEQmKV1SQv+cDztveiubHta3+gDoUyxZEb2CNu691973Ai8B+7Sd3n+Puu8KL7wH75oAcBMxy983uvgWYBQyOYVYRkUB8MPcFPm1aRm77C4OO8gOxLBCtgS8ilovD6w7kF8Brh3OsmY03syIzK9K80yKSiArm/hepFTBiVHw9XoI46aQ2s3FADvDA4Rzn7k+5e46757Rq1So24UREYsQrKsjfWcg5246l5Umdgo7zA7EsEOuBkyKW24TX7cfMzgNuB4a7+57DOVZEJJEtf3cKHx9dSu7Jg4KOElUsC0Qh0MHM2ptZQ2AsMDVyBzPrDjxJqDh8G7HpdeB8Mzsm3Dl9fnidiEjSyJ/1MOYwatS/BR0lqph9Uc7dy8zsOkK/2FOBZ9x9uZndDRS5+1RCj5QygH+YGcDn7j7c3Teb2T2EigzA3e6+OVZZRUSCkP/de/SvaMZx7bsGHSWqmH6T2t1nADOqrLsj4vV5Bzn2GeCZ2KUTEQnORwtnsLzZHh5pMjToKAcUF53UIiL1TcHrfwJg9Ij4GXupKo3FJCISgILN79DXM2jdMSfoKAekFoSISB37ZPFsPmi+m7zjfxp0lINSgRARqWMF0x8EIHfYbwNOcnB6xCQiUscKNs4jhya07dIv6CgHpRaEiEgd+nzFuyxsvpO8lgOCjlItFQgRkTo0adofAMi98JaAk1RPj5hEROpQ/ldvkWXp/Lj7uUFHqZZaECIideTL1e/zzjHbyTsmvvse9lGBEBGpI5OnTAQgd9CNwQY5RHrEJCJSR/KLZ9E5pRGn94nf4TUiqQUhIlIHvl23nHnNtpLbtHfQUQ6ZWhAiInXglVfuoyIF8n56Q9BRDpkKhIhIHchf9xodUtPo1m900FEOmR4xiYjE2Kbi1cxutpncJj2xlMT5tasWhIhIjE2dfB/lKZA34NdBRzksKhAiIjGWv/ZV2qU2oMc5lwQd5bAkTltHRCQBbfv2c2Y13UBuo6yEerwEakGIiMTUtIL7KE2FvDOuCTrKYVOBEBGJoYKPp9C6QQq9B14edJTDlljtHRGRBLJ905e8lvEVuQ26kZKaeO/HEy+xiEiCmDHpfvY0gNxevwg6So2oQIiIxEjBykkcl5ZCvwuuDjpKjegRk4hIDOzatpHpjYsZzemkpjUMOk6NqAUhIhIDr09+gF0NIbfHZUFHqTEVCBGRGMj/8CVapBlnDbs+6Cg1pkdMIiK1bM/O75jW6DNGlnegQcP0oOPUmFoQIiK1bNbkB9neCPIyfxZ0lCMS0xaEmQ02s1VmtsbMfhdl+wAze9/Myswsr8q2cjNbHP4zNZY5RURqU/7iv9O8xPjpiBuDjnJEYtaCMLNU4DFgIFAMFJrZVHdfEbHb58DlwC1RTrHb3bNjlU9EJBb27t7BlLS1DC9tT8PGGUHHOSKxfMTUG1jj7msBzOxFYARQWSDcfV14W0UMc4iI1Jk5Ux9ma7qT1zmxRm6NJpaPmFoDX0QsF4fXHap0Mysys/fMbGStJhMRiZH8oufI2AsDR90cdJQjFs+d1G3dfb2ZnQLMNrMP3f2TyB3MbDwwHuDkk08OIqOISKWyvSW8kvoxw0rakp7RPOg4RyyWLYj1wEkRy23C6w6Ju68P/3ctMBfoHmWfp9w9x91zWrVqdWRpRUSO0LxXH2NjYyev678EHaVWxLJAFAIdzKy9mTUExgKH9GkkMzvGzBqFX7cE+hHRdyEiEo8KFvyVJnth8OjfBh2lVsSsQLh7GXAd8DqwEnjZ3Zeb2d1mNhzAzHqZWTFwEfCkmS0PH346UGRmS4A5wMQqn34SEYkr5aV7meQruHB3a5o0axl0nFoR0z4Id58BzKiy7o6I14WEHj1VPW4+0C2W2UREatP8mU/x9VEV5J4wOugoteagLQgzGxfxul+VbdfFKpSISKIpmP80jcpgSO4PvhOcsKp7xHRTxOtHq2y7spaziIgkpIryMgrKPmTwjuNp2uLEoOPUmuoKhB3gdbRlEZF6qfDN/6E4o5zcDiOCjlKrqisQfoDX0ZZFROql/HlPkFYOw3JvCzpKraquk/o0M1tKqLVwavg14eVTYppMRCQBeEUF+XsWM7C8Fc2Paxt0nFpVXYE4vU5SiIgkqA/mvsC6pmX8n2OGBB2l1h20QLj7Z5HLZtYCGAB87u6LYhlMRCQR5M95jNQUGDH634KOUuuq+5jrq2bWNfz6BGAZoU8vPWdmN8Y+nohI/PKKCvJ3FXHOtmNp0aZD0HFqXXWd1O3dfVn49RXALHcfBvRBH3MVkXpu2fzJrD66lLy2g4OOEhPVFYjSiNfnEv5WtLtvBzSHg4jUa/lvPkJKBYwcmVyfXtqnuk7qL8zsekJzOfQAZgKYWWMgLcbZRETiWsF3C+hf0Yzj2ncNOkpMVNeC+AXQhdC0oGPcfWt4/U+AZ2MXS0Qkvn20cAbLm+0hr/XAoKPETHWfYvoWuCbK+jmERlkVEamXCl7/EwCjRtwacJLYOWiBMLODzt/g7sNrN46ISGLI3/wOZ3hTWnfMCTpKzFTXB9GX0LzSLwAL0PhLIiJ8sng2i5vv5o+NkmvspaqqKxDHAwOBi4FLgOnAC+6+/KBHiYgksYLpDwIwetiEgJPE1kE7qd293N1nuvtlhDqm1wBzNReEiNRn+Rvn0WvrUbTt0q/6nRNYtTPKheeGHkKoFdEOeASYHNtYIiLx6bPl71DYfCcTGyTnl+MiVddJ/TegK6EvyP0+4lvVIiL10qRpDwCQe+EtASeJvepaEOOAncBvgBvMKvuoDXB3PzqG2URE4k7+17PJtsb8uPu5QUeJueq+B1HdF+lEROqN9R8XMf+Y7dxjyV8coPpvUouISNjkKfcDkDf4poCT1I1qO6lFRCSkYP2bdE5pxGm9Lww6Sp1QC0JE5BB88+ky5jXbSt7RfYKOUmfUghAROQSvvHIfFSmQd+4NQUepMyoQIiKHoOCzmXRITaPrGaOCjlJn9IhJRKQam4pXM7vZZvKa5GAp9efXploQIiLVmDr5PspTIHfAtUFHqVMqECIi1chf+yrtUhvQ45xLgo5Sp2LaVjKzwWa2yszWmNnvomwfYGbvm1mZmeVV2XaZma0O/7ksljlFRA5k6zefMavpBvIaZderx0sQwxaEmaUCjxEaLrwYKDSzqe6+ImK3zwlNZ3pLlWOPBe4EcgAHFoWP3RKrvCIi0bw6aSKlqZB7xtVBR6lzsSyHvYE17r7W3fcCLwL7za7h7uvcfSlQUeXYQcAsd98cLgqzgOQfOlFE4k7+x6/QZkcqvQdeHnSUOhfLAtGa0Gx0+xSH19XasWY23syKzKxow4YNNQ4qIhLN9k1fMjPja0Y36EpKav3rsk3oB2ru/pS757h7TqtWrYKOIyJJZsak+9nTAPLOuCroKIGIZYFYD5wUsdwmvC7Wx4qI1Ir8lQUcvzOFMwaPDzpKIGJZIAqBDmbW3swaAmOBqYd47OvA+WZ2jJkdA5wfXiciUid2bdvIjMbrGWWnk5rWMOg4gYhZgXD3MuA6Qr/YVwIvu/tyM7vbzIYDmFkvMysGLgKeNLPl4WM3A/cQKjKFwN3hdSIidWLmpD+wqyHk9bki6CiBMXcPOkOtyMnJ8aKioqBjiEiSuPTmdrye9jlf372LBg3Tg44TM2a2yN1zom1L6E5qEZFYKNmxlWmNPmNUecekLg7VqX+f2xIRqcasyf+X7Y0gL+tnQUcJlAqEiEgVBUteoHmacc7w3wQdJVB6xCQiEmHv7h1MSVvLiNJTaNg4I+g4gVILQkQkwpypD7M13cnrUr9Gbo1GBUJEJEJ+0XM0TYOBo26pfuckp0dMIiJhZXtLmJz6McP2tKXRUUcHHSdwakGIiITNe/UxNjV2cjv9S9BR4oIKhIhIWP6CZ2nSAAaP/m3QUeKCHjGJiADlpXuZxEqG7G5Dk2Ytg44TF9SCEBEB5s98im+aVJB74uigo8QNFQgRESB//n+TngoXjr416ChxQwVCROq9ivIyJpUtY1DJ8TRtcWLQceKG+iBEpN5bOOuvFGeUk9dxZNBR4ooKhIjUe/lvP0FaOQzLvS3oKHFFj5hEpF7zigoK9ixhYHkrmv3o5KDjxBW1IESkXnt/zt9Z17SMvFOGBh0l7qhAiEi9VjD3v0itgOGj9HipKj1iEpF6yysq+MeuIn5afiwt2nQIOk7cUQtCROqtD9+ZxJqjS8lrd0HQUeKSWhAiUm8VvPUoKQ4jR+rxUjQqECJSb+V/t4ABFc35UbsuQUeJS3rEJCL10soFr7Ki2R5yW58XdJS4pQIhIvVSwesPATBaj5cOSI+YRKReyt/yDv28KSd26BF0lLilFoSI1DtrPniLJc1LyD3+p0FHiWsqECJS7xTMeBCA3OEa2vtg9IhJROqdgo1v04ujOLlz36CjxLWYtiDMbLCZrTKzNWb2uyjbG5nZS+HtC8ysXXh9OzPbbWaLw3+eiGVOEak/Plv+DoXNd5LXckDQUeJezFoQZpYKPAYMBIqBQjOb6u4rInb7BbDF3X9sZmOB+4Ex4W2fuHt2rPKJSP1UMO0PAOQOuSXgJPEvli2I3sAad1/r7nuBF4ERVfYZAfxP+HU+cK6ZWQwziUg9V/D1HLK3NubUbHVQVyeWBaI18EXEcnF4XdR93L0M2Aa0CG9rb2YfmNk/zax/tAuY2XgzKzKzog0bNtRuehFJOus/LmL+MdvJO7Zf0FESQrx+iukr4GR37w7cBPzdzI6uupO7P+XuOe6e06pVqzoPKSKJZfKU+wHIHfSvASdJDLEsEOuBkyKW24TXRd3HzBoAzYBN7r7H3TcBuPsi4BOgYwyzikg9kL9+Fl22NeK03hcGHSUhxLJAFAIdzKy9mTUExgJTq+wzFbgs/DoPmO3ubmatwp3cmNkpQAdgbQyzikiS++bTZcxrvo28o38SdJSEEbNPMbl7mZldB7wOpALPuPtyM7sbKHL3qcDTwHNmtgbYTKiIAAwA7jazUqACuMbdN8cqq4gkv1deuQ83yD33+qCjJAxz96Az1IqcnBwvKioKOoaIxKmBN7bg89TtfPRACZYSr92vdc/MFrl7TrRt+imJSNLbVLyaOc02k9skR8XhMGioDRFJelMm/SflKZB31q+DjpJQVCBEJOnlfzqd9qkN6H72xUFHSShqa4lIUtv6zWe82XQDuY2y9XjpMKkFISJJbVrBfZSmQl6/a4KOknBUIEQkqRWsnsJJDVLpPfCKoKMkHLW3RCRpbd/0JTMzvmZ0g256vFQDakGISNKaXjCRPQ0gr88vg46SkFQgRCRpFXw0ieMbpHDGBeODjpKQ1OYSkaS0a9tGZjRez2jrTEqq3gvXhH5qIpKUZk76A7saQl6OOqdrSgVCRJJS/rKXaZlm9B9ybdBREpYeMYlI0inZsZVp6Z8xqqITDRqmBx0nYakFISJJZ9bk/8uOhpCbOS7oKAlNBUJEkk7+kr9zTJrx0xGaWvRI6BGTiCSVvbt3MDXtU0aUnkpaepOg4yQ0tSBEJKnMnvIQW9Od3C4aufVIqUCISFLJX/QcTdNg4Khbgo6S8PSISUSSRtneEl5JXc2wPW1pdNTRQcdJeGpBiEjS+Oe0R9nU2Mk7bUzQUZKCCoSIJByvqODLNe+zdNEMlq59lyWbV7LUv+ajpnvIKINBoyYEHTEpqECISFwr2bGVFQuns2T5Wyz9cjFLdn/K0vRtbGrslfu0tVQyK1oy0n/M6HN/RZNmLQNMnDxUIEQkLnhFBetXL/q+VbBlJUv9G1Y13UN5uLe0cSp0s6MYXdGJzCZdyTrtLLr1Hkbz49oGGz5JqUCISJ3b/d1mVhTOCLUKvlrMkt3rWJq+jc0RrYJ21oDMipaM5sdktelNZtb5nJp1DqlpDQNMXr+oQIhIzHhFBcWrCln6/mssWTufpVs+YinfsKrpXirCrYImKaFWQV5FJzKP6kbWaWfTrfdQmv3o5GDDiwqEiNSO3d9tZvnCV1myYvb3rYLG37ElPaJVkNKArPKW5NGBrJP6hFoF2edovoY4pb8VETksXlHBFx8tCLUKPn2XpVtWscS+YXXG962Co1Kgm2XwL+WnkZmRSdZpZ9G11xC1ChKMCoSIHNCubRtZtmAaS1fODbUKSj5jaePv2BrRKmif0oCs8laMsQ5kndyHzOxBnJJ5lloFSUB/gyKCV1Tw+cp3Wfr+zFCrYGu4VdC0FLfQPhmp0I0MxlacTmZGJpmnDaBb72Ec3apNsOElZmJaIMxsMPAwkAr8t7tPrLK9EfA3oCewCRjj7uvC224DfgGUAze4++uxzCpSX+zc8i3LFk5j6cp/suTrxSwNtwq2Rcyrc0q4VXAxHclqG2oVtO82QK2CeiZmf9tmlgo8BgwEioFCM5vq7isidvsFsMXdf2xmY4H7gTFm1hkYC3QBTgTeNLOO7l4eq7wi8cIrKnCvOPT/RrwGcPfK5W0b1/PhktdZ8ul74VbBt6yp0irIpCmXVHQhs2kmWaefTdfeQ2na4sQAfwISL2L5dqA3sMbd1wKY2YvACCCyQIwA7gq/zgf+bGYWXv+iu+8BPjWzNeHzvVvbITd/+QlnPti5tk8b97z6XQ7vfFbLJwS8llN65R/HLfoyB9rHwusqX1PltVf+DA64z8H+G4OfX1WnWgOy/Edcah3JavcTMrMH0a7rmWoVyAHF8l9Ga+CLiOVioM+B9nH3MjPbBrQIr3+vyrGtq17AzMYD4wFOPrlmn45okNaIrvyoRscmOqMWfys5tXm2SqH3C7V4vvBdm4demf1wObRflX2ciNcHX//9dQyziPMc7H++L4tV3vf3+ar5b+XrlO+vHV7fpGEGXTudSbc+w8k49vha/VlK8kvotw7u/hTwFEBOTk6N3m4e3aoNL//xi+p3FBGpZ2I5H8R64KSI5TbhdVH3MbMGQDNCndWHcqyIiMRQLAtEIdDBzNqbWUNCnc5Tq+wzFbgs/DoPmO3uHl4/1swamVl7oAOwMIZZRUSkipg9Ygr3KVwHvE7oY67PuPtyM7sbKHL3qcDTwHPhTujNhIoI4f1eJtShXQb8Wp9gEhGpWxZ6w574cnJyvKioKOgYIiIJxcwWuXtOtG2ak1pERKJSgRARkahUIEREJCoVCBERiSppOqnNbAPw2RGcoiWwsZbiBClZ7gN0L/EqWe4lWe4Djuxe2rp7q2gbkqZAHCkzKzpQT34iSZb7AN1LvEqWe0mW+4DY3YseMYmISFQqECIiEpUKxPeeCjpALUmW+wDdS7xKlntJlvuAGN2L+iBERCQqtSBERCQqFQgREYlKBaIKM7vZzNzMWgadpabM7B4zW2pmi83sDTNL2AmGzewBM/sofD+Tzax50JlqyswuMrPlZlZhZgn38UozG2xmq8xsjZn9Lug8NWVmz5jZt2a2LOgsR8rMTjKzOWa2Ivxv6ze1eX4ViAhmdhJwPvB50FmO0APununu2cCrwB0B5zkSs4Cu7p4JfAzcFnCeI7EMGA3MCzrI4TKzVOAx4AKgM3CxmSXqZO5/BQYHHaKWlAE3u3tn4CfAr2vz70UFYn9/An7L9/PXJyR3/y5i8SgS+H7c/Q13LwsvvkdodsGE5O4r3X1V0DlqqDewxt3Xuvte4EVgRMCZasTd5xGafybhuftX7v5++PV2YCXQurbOn9BzUtcmMxsBrHf3Jfsmrk9kZnYv8HNgG3BOwHFqy5XAS0GHqKdaA5GTtxcDfQLKIlGYWTugO7Cgts5ZrwqEmb0JHB9l0+3AvxF6vJQQDnYv7j7F3W8Hbjez24DrgDvrNOBhqO5ewvvcTqg5/XxdZjtch3IvIrXNzDKAAuDGKk8Qjki9KhDufl609WbWDWgP7Gs9tAHeN7Pe7v51HUY8ZAe6lyieB2YQxwWiunsxs8uBocC5Hudf3DmMv5dEsx44KWK5TXidBMzM0ggVh+fdfVJtnrteFYgDcfcPgR/tWzazdUCOuyfkSI9m1sHdV4cXRwAfBZnnSJjZYEL9Qme5+66g89RjhUAHM2tPqDCMBS4JNpJY6B3t08BKd/9jbZ9fndTJaaKZLTOzpYQem9XqR9/q2J+BpsCs8Md2nwg6UE2Z2SgzKwb6AtPN7PWgMx2q8AcFrgNeJ9QR+rK7Lw82Vc2Y2QvAu0AnMys2s18EnekI9AN+Bvw0/P+PxWZ2YW2dXENtiIhIVGpBiIhIVCoQIiISlQqEiIhEpQIhIiJRqUCIiEhUKhCSlMxsxxEce114xNL9RvW1kEfC25aaWY+IbSeY2avh12fve32kzGzuoYz8ambrqhuB2MzeNLNjaiOX1A8qECI/9A5wHvBZlfUXAB3Cf8YDj0dsuwn4S52kq7nngGuDDiGJQwVCklr4Xf8D4S8OfmhmY8LrU8zsv8JzTcwysxlmlgfg7h+4+7oopxsB/M1D3gOam9kJ4W25wMwo1+9tZu+a2QdmNt/MOoXXX25mr4SvvS7carkpvN97ZnZsxGl+Fv4C1DIz6x0+vkV4ro/lZvbfgEVc8xUzWxTeNj7iPFOBi2v6s5T6RwVCkt1oIBvIItQqeCD8S3000I7Q3AY/I/Tt5upEG9G0dXj4iS3uvifKMR8B/d29O6F5Of4zYlvXcI5ewL3ArvB+7xIaiXefJuG5Pa4FngmvuxP4f+7eBZgMnByx/5Xu3hPIAW4wsxYA7r4FaLRvWaQ6GotJkt2ZwAvuXg58Y2b/JPQL+UzgH+5eAXxtZnOO4BonABsOsK0Z8D9m1oHQvBxpEdvmhMfw325m24Bp4fUfApkR+70AoXkMzOxoC82qN4BQccHdp5vZloj9bzCzUeHXJxF6JLYpvPwtcGLEssgBqQUhcugONKLpbiD9AMfcQ6gQdAWGVdkvssVREbFcwf5v3qqOh3PA8XHM7GxCLaW+7p4FfFDlmunhvCLVUoGQZPc2MMbMUs2sFaF33gsJdUTnhvsijgPOPoRzTQV+Hu7X+Amwzd2/IjQVarsDHNOM74fFvryG97Cv3+TM8DW3EZq29JLw+guAfZ9OakbocdcuMzuN0DSUhPczQnNVrKthDqlnVCAk2U0GlgJLgNnAb8NzfBQQ6kNYAfwv8D6h2fcwsxvCo662AZaGO4EhNK/GWmANoU8sXQvg7juBT8zsx1Gu/wfgPjP7gJo/0i0JH/8EsG/k0d8DA8xsOaFHTfvmUZ8JNDCzlcBEQtO07tMTeC9iCleRg9JorlJvmVmGu+8Id9ouBPrVdIKo8DP/nu7+77UashaZ2cPAVHd/K+gskhjUSS312avhDt+GwD1HMnugu09OgE8HLVNxkMOhFoSIiESlPggREYlKBUJERKJSgRARkahUIEREJCoVCBERier/A5PsezvJwAMMAAAAAElFTkSuQmCC\n",
|
||
"text/plain": [
|
||
"<Figure size 432x288 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn import linear_model\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"\n",
|
||
"\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(3155)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = np.random.rand(n)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
|
||
"\n",
|
||
"Maxpolydegree = 20\n",
|
||
"X = np.zeros((n,Maxpolydegree))\n",
|
||
"#We include explicitely the intercept column\n",
|
||
"for degree in range(Maxpolydegree):\n",
|
||
" X[:,degree] = x**degree\n",
|
||
"# We split the data in test and training data\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
|
||
"\n",
|
||
"p = Maxpolydegree\n",
|
||
"I = np.eye(p,p)\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 6\n",
|
||
"MSEOwnRidgePredict = np.zeros(nlambdas)\n",
|
||
"MSERidgePredict = np.zeros(nlambdas)\n",
|
||
"lambdas = np.logspace(-4, 2, nlambdas)\n",
|
||
"for i in range(nlambdas):\n",
|
||
" lmb = lambdas[i]\n",
|
||
" OwnRidgeBeta = np.linalg.pinv(X_train.T @ X_train+lmb*I) @ X_train.T @ y_train\n",
|
||
" # Note: we include the intercept column and no scaling\n",
|
||
" RegRidge = linear_model.Ridge(lmb,fit_intercept=False)\n",
|
||
" RegRidge.fit(X_train,y_train)\n",
|
||
" # and then make the prediction\n",
|
||
" ytildeOwnRidge = X_train @ OwnRidgeBeta\n",
|
||
" ypredictOwnRidge = X_test @ OwnRidgeBeta\n",
|
||
" ytildeRidge = RegRidge.predict(X_train)\n",
|
||
" ypredictRidge = RegRidge.predict(X_test)\n",
|
||
" MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
|
||
" MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
|
||
" print(\"Beta values for own Ridge implementation\")\n",
|
||
" print(OwnRidgeBeta)\n",
|
||
" print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(RegRidge.coef_)\n",
|
||
" print(\"MSE values for own Ridge implementation\")\n",
|
||
" print(MSEOwnRidgePredict[i])\n",
|
||
" print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(MSERidgePredict[i])\n",
|
||
"\n",
|
||
"# Now plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'r', label = 'MSE own Ridge Test')\n",
|
||
"plt.plot(np.log10(lambdas), MSERidgePredict, 'g', label = 'MSE Ridge Test')\n",
|
||
"\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('MSE')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The results here agree when we force **Scikit-Learn**'s Ridge function to include the first column in our design matrix.\n",
|
||
"We see that the results agree very well. Here we have thus explicitely included the intercept column in the design matrix.\n",
|
||
"What happens if we do not include the intercept in our fit?\n",
|
||
"Let us see how we can change this code by zero centering (thanks to Stian Bilek for inpouts here).\n",
|
||
"\n",
|
||
"## Taking out the mean"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 3.43579948e-02 -5.43330971e-01 -3.10141414e-03 2.47116868e-01\n",
|
||
" 2.18613217e-01 1.02054837e-01 -4.25617659e-04 -5.90475506e-02\n",
|
||
" -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
|
||
" 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n",
|
||
" 2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03 2.47116868e-01\n",
|
||
" 2.18613217e-01 1.02054837e-01 -4.25617657e-04 -5.90475506e-02\n",
|
||
" -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
|
||
" 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n",
|
||
" 2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.033030804518907\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.03303080451838\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"3.139255959141931e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"3.1392559585690806e-06\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n",
|
||
" 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
|
||
" -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n",
|
||
" 0.04423486]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n",
|
||
" 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
|
||
" -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n",
|
||
" 0.04423486]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.0411487294305777\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0411487294305242\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"1.9601304850224855e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"1.9601304850078175e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n",
|
||
" 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n",
|
||
" -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n",
|
||
" -0.01290947]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n",
|
||
" 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n",
|
||
" -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n",
|
||
" -0.01290947]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.04955699662783\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0495569966278266\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"5.495916150937975e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.495916150936546e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n",
|
||
" 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n",
|
||
" 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
|
||
" -0.00905423]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n",
|
||
" 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n",
|
||
" 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
|
||
" -0.00905423]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.0399676689527961\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0399676689527975\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"7.571105947979378e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"7.571105947979412e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n",
|
||
" -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n",
|
||
" 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n",
|
||
" 0.00683964]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n",
|
||
" -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n",
|
||
" 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n",
|
||
" 0.00683964]\n",
|
||
"Intercept from own implementation:\n",
|
||
"0.999955585168597\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"0.999955585168597\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.0007698473260556331\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.0007698473260556325\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
|
||
" -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n",
|
||
" -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
|
||
" -0.00058016]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
|
||
" -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n",
|
||
" -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
|
||
" -0.00058016]\n",
|
||
"Intercept from own implementation:\n",
|
||
"0.9637117593816477\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"0.9637117593816477\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.0023813163025848865\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.002381316302584886\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 432x288 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn import linear_model\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(315)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = np.random.rand(n)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
|
||
"\n",
|
||
"Maxpolydegree = 20\n",
|
||
"X = np.zeros((n,Maxpolydegree-1))\n",
|
||
"\n",
|
||
"for degree in range(1,Maxpolydegree): #No intercept column\n",
|
||
" X[:,degree-1] = x**(degree)\n",
|
||
"\n",
|
||
"# We split the data in test and training data\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
|
||
"\n",
|
||
"#For our own implementation, we will need to deal with the intercept by centering the design matrix and the target variable\n",
|
||
"X_train_mean = np.mean(X_train,axis=0)\n",
|
||
"#Center by removing mean from each feature\n",
|
||
"X_train_scaled = X_train - X_train_mean \n",
|
||
"X_test_scaled = X_test - X_train_mean\n",
|
||
"#The model intercept (called y_scaler) is given by the mean of the target variable (IF X is centered)\n",
|
||
"#Remove the intercept from the training data.\n",
|
||
"y_scaler = np.mean(y_train) \n",
|
||
"y_train_scaled = y_train - y_scaler \n",
|
||
"\n",
|
||
"p = Maxpolydegree-1\n",
|
||
"I = np.eye(p,p)\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 6\n",
|
||
"MSEOwnRidgePredict = np.zeros(nlambdas)\n",
|
||
"MSERidgePredict = np.zeros(nlambdas)\n",
|
||
"\n",
|
||
"lambdas = np.logspace(-4, 2, nlambdas)\n",
|
||
"for i in range(nlambdas):\n",
|
||
" lmb = lambdas[i]\n",
|
||
" OwnRidgeBeta = np.linalg.pinv(X_train_scaled.T @ X_train_scaled+lmb*I) @ X_train_scaled.T @ (y_train_scaled)\n",
|
||
" intercept_ = y_scaler - X_train_mean@OwnRidgeBeta #The intercept can be shifted so the model can predict on uncentered data\n",
|
||
" #Add intercept to prediction\n",
|
||
" ypredictOwnRidge = X_test_scaled @ OwnRidgeBeta + y_scaler \n",
|
||
" RegRidge = linear_model.Ridge(lmb)\n",
|
||
" RegRidge.fit(X_train,y_train)\n",
|
||
" ypredictRidge = RegRidge.predict(X_test)\n",
|
||
" MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
|
||
" MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
|
||
" print(\"Beta values for own Ridge implementation\")\n",
|
||
" print(OwnRidgeBeta) #Intercept is given by mean of target variable\n",
|
||
" print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(RegRidge.coef_)\n",
|
||
" print('Intercept from own implementation:')\n",
|
||
" print(intercept_)\n",
|
||
" print('Intercept from Scikit-Learn Ridge implementation')\n",
|
||
" print(RegRidge.intercept_)\n",
|
||
" print(\"MSE values for own Ridge implementation\")\n",
|
||
" print(MSEOwnRidgePredict[i])\n",
|
||
" print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(MSERidgePredict[i])\n",
|
||
"\n",
|
||
"\n",
|
||
"# Now plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'b--', label = 'MSE own Ridge Test')\n",
|
||
"plt.plot(np.log10(lambdas), MSERidgePredict, 'g--', label = 'MSE SL Ridge Test')\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('MSE')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We see here, when compared to the code which includes explicitely the\n",
|
||
"intercept column, that our MSE value is actually smaller. This is\n",
|
||
"because the regularization term does not include the intercept value\n",
|
||
"$\\beta_0$ in the fitting. This applies to Lasso regularization as\n",
|
||
"well. It means that our optimization is now done only with the\n",
|
||
"centered matrix and/or vector that enter the fitting procedure. Note\n",
|
||
"also that the problem with the intercept occurs mainly in these type\n",
|
||
"of polynomial fitting problem.\n",
|
||
"\n",
|
||
"The next example is indeed an example where all these discussions about the role of intercept are not present.\n",
|
||
"\n",
|
||
"\n",
|
||
"## More complicated Example: The Ising model\n",
|
||
"\n",
|
||
"The one-dimensional Ising model with nearest neighbor interaction, no\n",
|
||
"external field and a constant coupling constant $J$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto1\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = -J \\sum_{k}^L s_k s_{k + 1},\n",
|
||
"\\label{_auto1} \\tag{1}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins\n",
|
||
"in the system is determined by $L$. For the one-dimensional system\n",
|
||
"there is no phase transition.\n",
|
||
"\n",
|
||
"We will look at a system of $L = 40$ spins with a coupling constant of\n",
|
||
"$J = 1$. To get enough training data we will generate 10000 states\n",
|
||
"with their respective energies."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
|
||
"import seaborn as sns\n",
|
||
"import scipy.linalg as scl\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"import tqdm\n",
|
||
"sns.set(color_codes=True)\n",
|
||
"cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
|
||
"\n",
|
||
"L = 40\n",
|
||
"n = int(1e4)\n",
|
||
"\n",
|
||
"spins = np.random.choice([-1, 1], size=(n, L))\n",
|
||
"J = 1.0\n",
|
||
"\n",
|
||
"energies = np.zeros(n)\n",
|
||
"\n",
|
||
"for i in range(n):\n",
|
||
" energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here we use ordinary least squares\n",
|
||
"regression to predict the energy for the nearest neighbor\n",
|
||
"one-dimensional Ising model on a ring, i.e., the endpoints wrap\n",
|
||
"around. We will use linear regression to fit a value for\n",
|
||
"the coupling constant to achieve this.\n",
|
||
"\n",
|
||
"## Reformulating the problem to suit regression\n",
|
||
"\n",
|
||
"A more general form for the one-dimensional Ising model is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto2\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
|
||
"\\label{_auto2} \\tag{2}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here we allow for interactions beyond the nearest neighbors and a state dependent\n",
|
||
"coupling constant. This latter expression can be formulated as\n",
|
||
"a matrix-product"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto3\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{H} = \\boldsymbol{X} J,\n",
|
||
"\\label{_auto3} \\tag{3}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the\n",
|
||
"elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
|
||
"with the form utilized in linear regression, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto4\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
|
||
"\\label{_auto4} \\tag{4}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We split the data in training and test data as discussed in the previous example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"X = np.zeros((n, L ** 2))\n",
|
||
"for i in range(n):\n",
|
||
" X[i] = np.outer(spins[i], spins[i]).ravel()\n",
|
||
"y = energies\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Linear regression\n",
|
||
"\n",
|
||
"In the ordinary least squares method we choose the cost function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto5\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" C(\\boldsymbol{X}, \\boldsymbol{\\beta})= \\frac{1}{n}\\left\\{(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})\\right\\}.\n",
|
||
"\\label{_auto5} \\tag{5}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We then find the extremal point of $C$ by taking the derivative with respect to $\\boldsymbol{\\beta}$ as discussed above.\n",
|
||
"This yields the expression for $\\boldsymbol{\\beta}$ to be"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta} = \\frac{\\boldsymbol{X}^T \\boldsymbol{y}}{\\boldsymbol{X}^T \\boldsymbol{X}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which immediately imposes some requirements on $\\boldsymbol{X}$ as there must exist\n",
|
||
"an inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. If the expression we are modeling contains an\n",
|
||
"intercept, i.e., a constant term, we must make sure that the\n",
|
||
"first column of $\\boldsymbol{X}$ consists of $1$. We do this here"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"X_train_own = np.concatenate(\n",
|
||
" (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
|
||
" axis=1\n",
|
||
")\n",
|
||
"X_test_own = np.concatenate(\n",
|
||
" (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
|
||
" axis=1\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
|
||
" return scl.inv(x.T @ x) @ (x.T @ y)\n",
|
||
"beta = ols_inv(X_train_own, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Singular Value decomposition\n",
|
||
"\n",
|
||
"Doing the inversion directly turns out to be a bad idea since the matrix\n",
|
||
"$\\boldsymbol{X}^T\\boldsymbol{X}$ is singular. An alternative approach is to use the **singular\n",
|
||
"value decomposition**. Using the definition of the Moore-Penrose\n",
|
||
"pseudoinverse we can write the equation for $\\boldsymbol{\\beta}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta} = \\boldsymbol{X}^{+}\\boldsymbol{y},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where the pseudoinverse of $\\boldsymbol{X}$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{X}^{+} = \\frac{\\boldsymbol{X}^T}{\\boldsymbol{X}^T\\boldsymbol{X}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Using singular value decomposition we can decompose the matrix $\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma} \\boldsymbol{V}^T$,\n",
|
||
"where $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are orthogonal(unitary) matrices and $\\boldsymbol{\\Sigma}$ contains the singular values (more details below).\n",
|
||
"where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for\n",
|
||
"$\\omega$ to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto6\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{\\beta} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^{+} \\boldsymbol{U}^T \\boldsymbol{y}.\n",
|
||
"\\label{_auto6} \\tag{6}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Note that solving this equation by actually doing the pseudoinverse\n",
|
||
"(which is what we will do) is not a good idea as this operation scales\n",
|
||
"as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a\n",
|
||
"general matrix. Instead, doing $QR$-factorization and solving the\n",
|
||
"linear system as an equation would reduce this down to\n",
|
||
"$\\mathcal{O}(n^2)$ operations."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
|
||
" u, s, v = scl.svd(x)\n",
|
||
" return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"beta = ols_svd(X_train_own,y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"When extracting the $J$-matrix we need to make sure that we remove the intercept, as is done here"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"J = beta[1:].reshape(L, L)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"A way of looking at the coefficients in $J$ is to plot the matrices as images."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J, **cmap_args)\n",
|
||
"plt.title(\"OLS\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It is interesting to note that OLS\n",
|
||
"considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as\n",
|
||
"valid matrix elements for $J$.\n",
|
||
"In our discussion below on hyperparameters and Ridge and Lasso regression we will see that\n",
|
||
"this problem can be removed, partly and only with Lasso regression. \n",
|
||
"\n",
|
||
"In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD?\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## The one-dimensional Ising model\n",
|
||
"\n",
|
||
"Let us bring back the Ising model again, but now with an additional\n",
|
||
"focus on Ridge and Lasso regression as well. We repeat some of the\n",
|
||
"basic parts of the Ising model and the setup of the training and test\n",
|
||
"data. The one-dimensional Ising model with nearest neighbor\n",
|
||
"interaction, no external field and a constant coupling constant $J$ is\n",
|
||
"given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto7\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = -J \\sum_{k}^L s_k s_{k + 1},\n",
|
||
"\\label{_auto7} \\tag{7}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition.\n",
|
||
"\n",
|
||
"We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
|
||
"import seaborn as sns\n",
|
||
"import scipy.linalg as scl\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"import sklearn.linear_model as skl\n",
|
||
"import tqdm\n",
|
||
"sns.set(color_codes=True)\n",
|
||
"cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
|
||
"\n",
|
||
"L = 40\n",
|
||
"n = int(1e4)\n",
|
||
"\n",
|
||
"spins = np.random.choice([-1, 1], size=(n, L))\n",
|
||
"J = 1.0\n",
|
||
"\n",
|
||
"energies = np.zeros(n)\n",
|
||
"\n",
|
||
"for i in range(n):\n",
|
||
" energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"A more general form for the one-dimensional Ising model is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto8\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
|
||
"\\label{_auto8} \\tag{8}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here we allow for interactions beyond the nearest neighbors and a more\n",
|
||
"adaptive coupling matrix. This latter expression can be formulated as\n",
|
||
"a matrix-product on the form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto9\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = X J,\n",
|
||
"\\label{_auto9} \\tag{9}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the\n",
|
||
"elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
|
||
"with the form utilized in linear regression, viz."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto10\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}.\n",
|
||
"\\label{_auto10} \\tag{10}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We organize the data as we did above"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"X = np.zeros((n, L ** 2))\n",
|
||
"for i in range(n):\n",
|
||
" X[i] = np.outer(spins[i], spins[i]).ravel()\n",
|
||
"y = energies\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n",
|
||
"\n",
|
||
"X_train_own = np.concatenate(\n",
|
||
" (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
|
||
" axis=1\n",
|
||
")\n",
|
||
"\n",
|
||
"X_test_own = np.concatenate(\n",
|
||
" (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
|
||
" axis=1\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We will do all fitting with **Scikit-Learn**,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"clf = skl.LinearRegression().fit(X_train, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"When extracting the $J$-matrix we make sure to remove the intercept"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"J_sk = clf.coef_.reshape(L, L)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"And then we plot the results"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_sk, **cmap_args)\n",
|
||
"plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The results perfectly with our previous discussion where we used our own code.\n",
|
||
"\n",
|
||
"## Ridge regression\n",
|
||
"\n",
|
||
"Having explored the ordinary least squares we move on to ridge\n",
|
||
"regression. In ridge regression we include a **regularizer**. This\n",
|
||
"involves a new cost function which leads to a new estimate for the\n",
|
||
"weights $\\boldsymbol{\\beta}$. This results in a penalized regression problem. The\n",
|
||
"cost function is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"3\n",
|
||
"7\n",
|
||
" \n",
|
||
"<\n",
|
||
"<\n",
|
||
"<\n",
|
||
"!\n",
|
||
"!\n",
|
||
"M\n",
|
||
"A\n",
|
||
"T\n",
|
||
"H\n",
|
||
"_\n",
|
||
"B\n",
|
||
"L\n",
|
||
"O\n",
|
||
"C\n",
|
||
"K"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"_lambda = 0.1\n",
|
||
"clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n",
|
||
"J_ridge_sk = clf_ridge.coef_.reshape(L, L)\n",
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_ridge_sk, **cmap_args)\n",
|
||
"plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## LASSO regression\n",
|
||
"\n",
|
||
"In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto12\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\sqrt{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta}}.\n",
|
||
"\\label{_auto12} \\tag{12}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
|
||
"J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_lasso_sk, **cmap_args)\n",
|
||
"plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It is quite striking how LASSO breaks the symmetry of the coupling\n",
|
||
"constant as opposed to ridge and OLS. We get a sparse solution with\n",
|
||
"$J_{j, j + 1} = -1$.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Performance as function of the regularization parameter\n",
|
||
"\n",
|
||
"We see how the different models perform for a different set of values for $\\lambda$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"lambdas = np.logspace(-4, 5, 10)\n",
|
||
"\n",
|
||
"train_errors = {\n",
|
||
" \"ols_sk\": np.zeros(lambdas.size),\n",
|
||
" \"ridge_sk\": np.zeros(lambdas.size),\n",
|
||
" \"lasso_sk\": np.zeros(lambdas.size)\n",
|
||
"}\n",
|
||
"\n",
|
||
"test_errors = {\n",
|
||
" \"ols_sk\": np.zeros(lambdas.size),\n",
|
||
" \"ridge_sk\": np.zeros(lambdas.size),\n",
|
||
" \"lasso_sk\": np.zeros(lambdas.size)\n",
|
||
"}\n",
|
||
"\n",
|
||
"plot_counter = 1\n",
|
||
"\n",
|
||
"fig = plt.figure(figsize=(32, 54))\n",
|
||
"\n",
|
||
"for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n",
|
||
" for key, method in zip(\n",
|
||
" [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n",
|
||
" [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n",
|
||
" ):\n",
|
||
" method = method.fit(X_train, y_train)\n",
|
||
"\n",
|
||
" train_errors[key][i] = method.score(X_train, y_train)\n",
|
||
" test_errors[key][i] = method.score(X_test, y_test)\n",
|
||
"\n",
|
||
" omega = method.coef_.reshape(L, L)\n",
|
||
"\n",
|
||
" plt.subplot(10, 5, plot_counter)\n",
|
||
" plt.imshow(omega, **cmap_args)\n",
|
||
" plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n",
|
||
" plot_counter += 1\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We see that LASSO reaches a good solution for low\n",
|
||
"values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too\n",
|
||
"much. Ridge is more stable over a larger range of values for\n",
|
||
"$\\lambda$, but eventually also fades away.\n",
|
||
"\n",
|
||
"## Finding the optimal value of $\\lambda$\n",
|
||
"\n",
|
||
"To determine which value of $\\lambda$ is best we plot the accuracy of\n",
|
||
"the models when predicting the training and the testing set. We expect\n",
|
||
"the accuracy of the training set to be quite good, but if the accuracy\n",
|
||
"of the testing set is much lower this tells us that we might be\n",
|
||
"subject to an overfit model. The ideal scenario is an accuracy on the\n",
|
||
"testing set that is close to the accuracy of the training set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"\n",
|
||
"colors = {\n",
|
||
" \"ols_sk\": \"r\",\n",
|
||
" \"ridge_sk\": \"y\",\n",
|
||
" \"lasso_sk\": \"c\"\n",
|
||
"}\n",
|
||
"\n",
|
||
"for key in train_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" train_errors[key],\n",
|
||
" colors[key],\n",
|
||
" label=\"Train {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"\n",
|
||
"for key in test_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" test_errors[key],\n",
|
||
" colors[key] + \"--\",\n",
|
||
" label=\"Test {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"plt.legend(loc=\"best\", fontsize=18)\n",
|
||
"plt.xlabel(r\"$\\lambda$\", fontsize=18)\n",
|
||
"plt.ylabel(r\"$R^2$\", fontsize=18)\n",
|
||
"plt.tick_params(labelsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n",
|
||
"achieves a very good accuracy on the test set. This by far surpasses the\n",
|
||
"other models for all values of $\\lambda$.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## Logistic Regression\n",
|
||
"\n",
|
||
"In linear regression our main interest was centered on learning the\n",
|
||
"coefficients of a functional fit (say a polynomial) in order to be\n",
|
||
"able to predict the response of a continuous variable on some unseen\n",
|
||
"data. The fit to the continuous variable $y_i$ is based on some\n",
|
||
"independent variables $\\boldsymbol{x}_i$. Linear regression resulted in\n",
|
||
"analytical expressions for standard ordinary Least Squares or Ridge\n",
|
||
"regression (in terms of matrices to invert) for several quantities,\n",
|
||
"ranging from the variance and thereby the confidence intervals of the\n",
|
||
"parameters $\\boldsymbol{\\beta}$ to the mean squared error. If we can invert\n",
|
||
"the product of the design matrices, linear regression gives then a\n",
|
||
"simple recipe for fitting our data.\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## Classification problems\n",
|
||
"\n",
|
||
"\n",
|
||
"Classification problems, however, are concerned with outcomes taking\n",
|
||
"the form of discrete variables (i.e. categories). We may for example,\n",
|
||
"on the basis of DNA sequencing for a number of patients, like to find\n",
|
||
"out which mutations are important for a certain disease; or based on\n",
|
||
"scans of various patients' brains, figure out if there is a tumor or\n",
|
||
"not; or given a specific physical system, we'd like to identify its\n",
|
||
"state, say whether it is an ordered or disordered system (typical\n",
|
||
"situation in solid state physics); or classify the status of a\n",
|
||
"patient, whether she/he has a stroke or not and many other similar\n",
|
||
"situations.\n",
|
||
"\n",
|
||
"The most common situation we encounter when we apply logistic\n",
|
||
"regression is that of two possible outcomes, normally denoted as a\n",
|
||
"binary outcome, true or false, positive or negative, success or\n",
|
||
"failure etc.\n",
|
||
"\n",
|
||
"## Optimization and Deep learning\n",
|
||
"\n",
|
||
"Logistic regression will also serve as our stepping stone towards\n",
|
||
"neural network algorithms and supervised deep learning. For logistic\n",
|
||
"learning, the minimization of the cost function leads to a non-linear\n",
|
||
"equation in the parameters $\\boldsymbol{\\beta}$. The optimization of the\n",
|
||
"problem calls therefore for minimization algorithms. This forms the\n",
|
||
"bottle neck of all machine learning algorithms, namely how to find\n",
|
||
"reliable minima of a multi-variable function. This leads us to the\n",
|
||
"family of gradient descent methods. The latter are the working horses\n",
|
||
"of basically all modern machine learning algorithms.\n",
|
||
"\n",
|
||
"We note also that many of the topics discussed here on logistic \n",
|
||
"regression are also commonly used in modern supervised Deep Learning\n",
|
||
"models, as we will see later.\n",
|
||
"\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## Basics\n",
|
||
"\n",
|
||
"We consider the case where the dependent variables, also called the\n",
|
||
"responses or the outcomes, $y_i$ are discrete and only take values\n",
|
||
"from $k=0,\\dots,K-1$ (i.e. $K$ classes).\n",
|
||
"\n",
|
||
"The goal is to predict the\n",
|
||
"output classes from the design matrix $\\boldsymbol{X}\\in\\mathbb{R}^{n\\times p}$\n",
|
||
"made of $n$ samples, each of which carries $p$ features or predictors. The\n",
|
||
"primary goal is to identify the classes to which new unseen samples\n",
|
||
"belong.\n",
|
||
"\n",
|
||
"Let us specialize to the case of two classes only, with outputs\n",
|
||
"$y_i=0$ and $y_i=1$. Our outcomes could represent the status of a\n",
|
||
"credit card user that could default or not on her/his credit card\n",
|
||
"debt. That is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i = \\begin{bmatrix} 0 & \\mathrm{no}\\\\ 1 & \\mathrm{yes} \\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Linear classifier\n",
|
||
"\n",
|
||
"Before moving to the logistic model, let us try to use our linear\n",
|
||
"regression model to classify these two outcomes. We could for example\n",
|
||
"fit a linear model to the default case if $y_i > 0.5$ and the no\n",
|
||
"default case $y_i \\leq 0.5$.\n",
|
||
"\n",
|
||
"We would then have our \n",
|
||
"weighted linear combination, namely"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto13\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\\boldsymbol{y} = \\boldsymbol{X}^T\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
|
||
"\\label{_auto13} \\tag{13}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\boldsymbol{y}$ is a vector representing the possible outcomes, $\\boldsymbol{X}$ is our\n",
|
||
"$n\\times p$ design matrix and $\\boldsymbol{\\beta}$ represents our estimators/predictors.\n",
|
||
"\n",
|
||
"## Some selected properties\n",
|
||
"\n",
|
||
"The main problem with our function is that it takes values on the\n",
|
||
"entire real axis. In the case of logistic regression, however, the\n",
|
||
"labels $y_i$ are discrete variables. A typical example is the credit\n",
|
||
"card data discussed below here, where we can set the state of\n",
|
||
"defaulting the debt to $y_i=1$ and not to $y_i=0$ for one the persons\n",
|
||
"in the data set (see the full example below).\n",
|
||
"\n",
|
||
"One simple way to get a discrete output is to have sign\n",
|
||
"functions that map the output of a linear regressor to values $\\{0,1\\}$,\n",
|
||
"$f(s_i)=sign(s_i)=1$ if $s_i\\ge 0$ and 0 if otherwise. \n",
|
||
"We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron\" model in the machine learning\n",
|
||
"literature. This model is extremely simple. However, in many cases it is more\n",
|
||
"favorable to use a ``soft\" classifier that outputs\n",
|
||
"the probability of a given category. This leads us to the logistic function.\n",
|
||
"\n",
|
||
"## Simple example\n",
|
||
"\n",
|
||
"The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>ID</th>\n",
|
||
" <th>Age</th>\n",
|
||
" <th>Agegroup</th>\n",
|
||
" <th>CHD</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>21</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>2</td>\n",
|
||
" <td>23</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>25</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>4</td>\n",
|
||
" <td>29</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>5</td>\n",
|
||
" <td>21</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>...</th>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>95</th>\n",
|
||
" <td>96</td>\n",
|
||
" <td>61</td>\n",
|
||
" <td>8</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>96</th>\n",
|
||
" <td>97</td>\n",
|
||
" <td>69</td>\n",
|
||
" <td>8</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>97</th>\n",
|
||
" <td>98</td>\n",
|
||
" <td>65</td>\n",
|
||
" <td>8</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>98</th>\n",
|
||
" <td>99</td>\n",
|
||
" <td>64</td>\n",
|
||
" <td>8</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>99</th>\n",
|
||
" <td>100</td>\n",
|
||
" <td>63</td>\n",
|
||
" <td>8</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"<p>100 rows × 4 columns</p>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" ID Age Agegroup CHD\n",
|
||
"0 1 21 1 0\n",
|
||
"1 2 23 1 0\n",
|
||
"2 3 25 1 1\n",
|
||
"3 4 29 1 0\n",
|
||
"4 5 21 1 0\n",
|
||
".. ... ... ... ...\n",
|
||
"95 96 61 8 1\n",
|
||
"96 97 69 8 1\n",
|
||
"97 98 65 8 1\n",
|
||
"98 99 64 8 1\n",
|
||
"99 100 63 8 0\n",
|
||
"\n",
|
||
"[100 rows x 4 columns]"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import os\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.utils import resample\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"from IPython.display import display\n",
|
||
"from pylab import plt, mpl\n",
|
||
"plt.style.use('seaborn')\n",
|
||
"mpl.rcParams['font.family'] = 'serif'\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"chddata.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the chd data as csv file and organize the data into arrays with age group, age, and chd\n",
|
||
"chd = pd.read_csv(infile, names=('ID', 'Age', 'Agegroup', 'CHD'))\n",
|
||
"chd.columns = ['ID', 'Age', 'Agegroup', 'CHD']\n",
|
||
"output = chd['CHD']\n",
|
||
"age = chd['Age']\n",
|
||
"agegroup = chd['Agegroup']\n",
|
||
"numberID = chd['ID'] \n",
|
||
"display(chd)\n",
|
||
"\n",
|
||
"plt.scatter(age, output, marker='o')\n",
|
||
"plt.axis([18,70.0,-0.1, 1.2])\n",
|
||
"plt.xlabel(r'Age')\n",
|
||
"plt.ylabel(r'CHD')\n",
|
||
"plt.title(r'Age distribution and Coronary heart disease')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Plotting the mean value for each group\n",
|
||
"\n",
|
||
"What we could attempt however is to plot the mean value for each group."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
|
||
"group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
|
||
"plt.plot(group, agegroupmean, \"r-\")\n",
|
||
"plt.axis([0,9,0, 1.0])\n",
|
||
"plt.xlabel(r'Age group')\n",
|
||
"plt.ylabel(r'CHD mean values')\n",
|
||
"plt.title(r'Mean values for each age group')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We are now trying to find a function $f(y\\vert x)$, that is a function which gives us an expected value for the output $y$ with a given input $x$.\n",
|
||
"In standard linear regression with a linear dependence on $x$, we would write this in terms of our model"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f(y_i\\vert x_i)=\\beta_0+\\beta_1 x_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"This expression implies however that $f(y_i\\vert x_i)$ could take any\n",
|
||
"value from minus infinity to plus infinity. If we however let\n",
|
||
"$f(y\\vert y)$ be represented by the mean value, the above example\n",
|
||
"shows us that we can constrain the function to take values between\n",
|
||
"zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking\n",
|
||
"at our last curve we see also that it has an S-shaped form. This leads\n",
|
||
"us to a very popular model for the function $f$, namely the so-called\n",
|
||
"Sigmoid function or logistic model. We will consider this function as\n",
|
||
"representing the probability for finding a value of $y_i$ with a given\n",
|
||
"$x_i$.\n",
|
||
"\n",
|
||
"## The logistic function\n",
|
||
"\n",
|
||
"Another widely studied model, is the so-called \n",
|
||
"perceptron model, which is an example of a \"hard classification\" model. We\n",
|
||
"will encounter this model when we discuss neural networks as\n",
|
||
"well. Each datapoint is deterministically assigned to a category (i.e\n",
|
||
"$y_i=0$ or $y_i=1$). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a \"soft\"\n",
|
||
"classifier that outputs the probability of a given category rather\n",
|
||
"than a single value. For example, given $x_i$, the classifier\n",
|
||
"outputs the probability of being in a category $k$. Logistic regression\n",
|
||
"is the most common example of a so-called soft classifier. In logistic\n",
|
||
"regression, the probability that a data point $x_i$\n",
|
||
"belongs to a category $y_i=\\{0,1\\}$ is given by the so-called logit function (or Sigmoid) which is meant to represent the likelihood for a given event,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p(t) = \\frac{1}{1+\\mathrm \\exp{-t}}=\\frac{\\exp{t}}{1+\\mathrm \\exp{t}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Note that $1-p(t)= p(-t)$.\n",
|
||
"\n",
|
||
"## Examples of likelihood functions used in logistic regression and nueral networks\n",
|
||
"\n",
|
||
"\n",
|
||
"The following code plots the logistic function, the step function and other functions we will encounter from here and on."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"The sigmoid function (or the logistic curve) is a\n",
|
||
"function that takes any real number, z, and outputs a number (0,1).\n",
|
||
"It is useful in neural networks for assigning weights on a relative scale.\n",
|
||
"The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n",
|
||
"\n",
|
||
"import numpy\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import math as mt\n",
|
||
"\n",
|
||
"z = numpy.arange(-5, 5, .1)\n",
|
||
"sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n",
|
||
"sigma = sigma_fn(z)\n",
|
||
"\n",
|
||
"fig = plt.figure()\n",
|
||
"ax = fig.add_subplot(111)\n",
|
||
"ax.plot(z, sigma)\n",
|
||
"ax.set_ylim([-0.1, 1.1])\n",
|
||
"ax.set_xlim([-5,5])\n",
|
||
"ax.grid(True)\n",
|
||
"ax.set_xlabel('z')\n",
|
||
"ax.set_title('sigmoid function')\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\"\"\"Step Function\"\"\"\n",
|
||
"z = numpy.arange(-5, 5, .02)\n",
|
||
"step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n",
|
||
"step = step_fn(z)\n",
|
||
"\n",
|
||
"fig = plt.figure()\n",
|
||
"ax = fig.add_subplot(111)\n",
|
||
"ax.plot(z, step)\n",
|
||
"ax.set_ylim([-0.5, 1.5])\n",
|
||
"ax.set_xlim([-5,5])\n",
|
||
"ax.grid(True)\n",
|
||
"ax.set_xlabel('z')\n",
|
||
"ax.set_title('step function')\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\"\"\"tanh Function\"\"\"\n",
|
||
"z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n",
|
||
"t = numpy.tanh(z)\n",
|
||
"\n",
|
||
"fig = plt.figure()\n",
|
||
"ax = fig.add_subplot(111)\n",
|
||
"ax.plot(z, t)\n",
|
||
"ax.set_ylim([-1.0, 1.0])\n",
|
||
"ax.set_xlim([-2*mt.pi,2*mt.pi])\n",
|
||
"ax.grid(True)\n",
|
||
"ax.set_xlabel('z')\n",
|
||
"ax.set_title('tanh function')\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Two parameters\n",
|
||
"\n",
|
||
"We assume now that we have two classes with $y_i$ either $0$ or $1$. Furthermore we assume also that we have only two parameters $\\beta$ in our fitting of the Sigmoid function, that is we define probabilities"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
|
||
"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
|
||
"\n",
|
||
"Note that we used"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p(y_i=0\\vert x_i, \\boldsymbol{\\beta}) = 1-p(y_i=1\\vert x_i, \\boldsymbol{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- !split -->\n",
|
||
"## Maximum likelihood\n",
|
||
"\n",
|
||
"In order to define the total likelihood for all possible outcomes from a \n",
|
||
"dataset $\\mathcal{D}=\\{(y_i,x_i)\\}$, with the binary labels\n",
|
||
"$y_i\\in\\{0,1\\}$ and where the data points are drawn independently, we use the so-called [Maximum Likelihood Estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) (MLE) principle. \n",
|
||
"We aim thus at maximizing \n",
|
||
"the probability of seeing the observed data. We can then approximate the \n",
|
||
"likelihood in terms of the product of the individual probabilities of a specific outcome $y_i$, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"P(\\mathcal{D}|\\boldsymbol{\\beta})& = \\prod_{i=1}^n \\left[p(y_i=1|x_i,\\boldsymbol{\\beta})\\right]^{y_i}\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]^{1-y_i}\\nonumber \\\\\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"from which we obtain the log-likelihood and our **cost/loss** function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left( y_i\\log{p(y_i=1|x_i,\\boldsymbol{\\beta})} + (1-y_i)\\log\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## The cost function rewritten\n",
|
||
"\n",
|
||
"Reordering the logarithms, we can rewrite the **cost/loss** function as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The maximum likelihood estimator is defined as the set of parameters that maximize the log-likelihood where we maximize with respect to $\\beta$.\n",
|
||
"Since the cost (error) function is just the negative log-likelihood, for logistic regression we have that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathcal{C}(\\boldsymbol{\\beta})=-\\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"This equation is known in statistics as the **cross entropy**. Finally, we note that just as in linear regression, \n",
|
||
"in practice we often supplement the cross-entropy with additional regularization terms, usually $L_1$ and $L_2$ regularization as we did for Ridge and Lasso regression.\n",
|
||
"\n",
|
||
"## Minimizing the cross entropy\n",
|
||
"\n",
|
||
"The cross entropy is a convex function of the weights $\\boldsymbol{\\beta}$ and,\n",
|
||
"therefore, any local minimizer is a global minimizer. \n",
|
||
"\n",
|
||
"\n",
|
||
"Minimizing this\n",
|
||
"cost function with respect to the two parameters $\\beta_0$ and $\\beta_1$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_0} = -\\sum_{i=1}^n \\left(y_i -\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_1} = -\\sum_{i=1}^n \\left(y_ix_i -x_i\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## A more compact expression\n",
|
||
"\n",
|
||
"Let us now define a vector $\\boldsymbol{y}$ with $n$ elements $y_i$, an\n",
|
||
"$n\\times p$ matrix $\\boldsymbol{X}$ which contains the $x_i$ values and a\n",
|
||
"vector $\\boldsymbol{p}$ of fitted probabilities $p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We can rewrite in a more compact form the first\n",
|
||
"derivative of cost function as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
|
||
"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Extending to more predictors\n",
|
||
"\n",
|
||
"Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with $p$ predictors"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\log{ \\frac{p(\\boldsymbol{\\beta}\\boldsymbol{x})}{1-p(\\boldsymbol{\\beta}\\boldsymbol{x})}} = \\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here we defined $\\boldsymbol{x}=[1,x_1,x_2,\\dots,x_p]$ and $\\boldsymbol{\\beta}=[\\beta_0, \\beta_1, \\dots, \\beta_p]$ leading to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p(\\boldsymbol{\\beta}\\boldsymbol{x})=\\frac{ \\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}{1+\\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Including more classes\n",
|
||
"\n",
|
||
"Till now we have mainly focused on two classes, the so-called binary\n",
|
||
"system. Suppose we wish to extend to $K$ classes. Let us for the sake\n",
|
||
"of simplicity assume we have only two predictors. We have then following model"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\log{\\frac{p(C=2\\vert x)}{p(K\\vert x)}} = \\beta_{20}+\\beta_{21}x_1,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and so on till the class $C=K-1$ class"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\log{\\frac{p(C=K-1\\vert x)}{p(K\\vert x)}} = \\beta_{(K-1)0}+\\beta_{(K-1)1}x_1,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and the model is specified in term of $K-1$ so-called log-odds or\n",
|
||
"**logit** transformations.\n",
|
||
"\n",
|
||
"\n",
|
||
"## More classes\n",
|
||
"\n",
|
||
"In our discussion of neural networks we will encounter the above again\n",
|
||
"in terms of a slightly modified function, the so-called **Softmax** function.\n",
|
||
"\n",
|
||
"The softmax function is used in various multiclass classification\n",
|
||
"methods, such as multinomial logistic regression (also known as\n",
|
||
"softmax regression), multiclass linear discriminant analysis, naive\n",
|
||
"Bayes classifiers, and artificial neural networks. Specifically, in\n",
|
||
"multinomial logistic regression and linear discriminant analysis, the\n",
|
||
"input to the function is the result of $K$ distinct linear functions,\n",
|
||
"and the predicted probability for the $k$-th class given a sample\n",
|
||
"vector $\\boldsymbol{x}$ and a weighting vector $\\boldsymbol{\\beta}$ is (with two\n",
|
||
"predictors):"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p(C=k\\vert \\mathbf {x} )=\\frac{\\exp{(\\beta_{k0}+\\beta_{k1}x_1)}}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It is easy to extend to more predictors. The final class is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p(C=K\\vert \\mathbf {x} )=\\frac{1}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and they sum to one. Our earlier discussions were all specialized to\n",
|
||
"the case with two classes only. It is easy to see from the above that\n",
|
||
"what we derived earlier is compatible with these equations.\n",
|
||
"\n",
|
||
"To find the optimal parameters we would typically use a gradient\n",
|
||
"descent method. Newton's method and gradient descent methods are\n",
|
||
"discussed in the material on [optimization\n",
|
||
"methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n",
|
||
"\n",
|
||
"\n",
|
||
"## Friday September 24\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Wisconsin Cancer Data\n",
|
||
"\n",
|
||
"We show here how we can use a simple regression case on the breast\n",
|
||
"cancer data using Logistic regression as our algorithm for\n",
|
||
"classification."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n",
|
||
"Test set accuracy with Logistic Regression: 0.96\n",
|
||
"Test set accuracy Logistic Regression with scaled data: 0.96\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/opt/homebrew/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Using the correlation matrix\n",
|
||
"\n",
|
||
"In addition to the above scores, we could also study the covariance (and the correlation matrix).\n",
|
||
"We use **Pandas** to compute the correlation matrix."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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2g4mJSZFR4zt3biMg4Af88stBAMD582dfu65GjRojNvY+XFya49Gjh6+8Xtzc5GXLFuG77/6NWrVqISMj/bXLA5Du3HP37h00a+b82riIdEHZXWh4Nxki5VQqjv/++2+cOHECq1atgpmZGXx9fbFq1SoWx0QViLYPljdv3kBY2BUYGeVhwgRPeHt/BgBITk7G8ePHkJj4FFFR99CoUSOsX78GDRo0QkLCExw9eggdO3bBvXt3cPz4MdSpUxfnz5/F8+fPERUVienTZ2PLlg24d+8uatasKRW3f/0VjPj4OBw9egiDBr2LsLAriIy8i65de2D48H9h82YfuLq2RXj4VcTERKNLl244fvwY7t27g5s3byAy8h7S0tJw+vQp9OnTH9269cD27VsBgMVxGXGKl3IvFrVWVuZIT88GwKKWSBtUKo4dHR1hbFz0rm8vPyYiKo3mzVvC1/crODraICHhufS8nZ0dlixZIT1+661B0v/Hjv3/Hx769tsA6f+ff/6F9P/Y2Bh4e38OGxsbxMXF4c8//wsA6NixC3755ZC0nK/vV9L/p03zkv4/fvxE6f8vxtG8eUu8884Q6fGcOQtUbywRERkMlYrjpKQkHD58GM+fP8fVq1dx/vx5pKSkaDi0ioNz04i0Jy7uMb777hs0adIUDx7EYtasT3QdEukIcy8RlYVKxfH8+fPx+eef48KFC7hw4QJ69eqFZcuWaTo2IqJS69ixMzp27KzrMEgDNF3sspgmIkDF4rhatWrYsGFDkedycnI0EhARERERka6oVBw/evTolee2bduGdevWqT0gIiKiykL5aHVTrcZBRP9PpeJ4yJAhsLW1hRACubm5SExMRM2aNTUdG+k5ZUl9ouO/tBwJERERkXqoVBwvWLAAo0ePlh4/efIEBw8e1FhQ+qQyFYC8rVLlpu75ltxviLRH2f2MS7s8bxVHpGJx/GJhDAA1atRAdHS0JuIhokrixo1w7NzpCyMjATe3DkhKSsSzZ8/g7f0ZTE1NS7Wu9PQ0LFo0F9u3+2soWiLtupf3l/R/00wTyPNyAQBB53QVEVHloVJxvGTJEun/QggkJCTwPsdEVC4tW7ZGu3ZvwMgoD5MnTwUAzJo1FSEhF9CjR+9SrcvKyhrbtvlpIkzSgYp414ibMckaXf+LxfSLmsg6lmo9HFEmUrE4jouLw9ChQwEU/JRq9erV0bkzb5VUWVTEAxXpn/z8fKSmPoOtrR3Cwq7g6NFDaNSoMWJi7mPatFl4/jwVa9eugoODA+ztHXD79i1MmDAZ3br1wG+/HcGXX27E77+fBgD88MN3iI6+hwYNGuHatTCYmpri44/nY8OGtRAiHw0bNsbdu7fx1luDMHToCN02nIiI9IpKxfGMGTPQsWPx3z7j4uJQq1YttQZlyFhIKscRCSrO1atX8cMP3+HOnVto2rQZnJ2bY+TIYfj6671wdKyBY8cO4/vvd2P27HkYMmQ4QkIuYu7cRYiIuI49e75Bt249MGjQu9i9u2DkODLyLo4fP4p9+34BAKxevRwdOnRCrVq1MX78B/Dz24E5c+YjOTkZH388jcUxEREVoVJx/P3338PIyAhCiFde27NnD3bu3Kn2wPTdz+FHkKH4rXsiVfELwqtcXV3h4TERAPDDD3uwbdsWpKam4vffjwEAnj9/BmNjmbR8gwYNAQC2tnbIyEh/ZX1RUVGoW7ee9LhOnbpFXq9fvwGAgp+pzsjIUGtbiDRN2fSJ0i5f2ukWRJWJSsVxbGwspk6dimbNmgEA7ty5g2bNmsHU1BT379/XaIBkeH48fhPp/OJAZeDgUB23bt2Era0thg1zR9WqVfHsWQrCw6+pvI5GjRrjwYNY6fGjRw+LFMhGRkZqjZmoMivNXTKsrMzxZvu6r1+QSMdUKo7d3Nywd+9eVKtWDQCQmpqK7du3Y+nSpfjPf/6j0QCp4lPXaGpx61G2jtJus7S3STLEkWBt33rt5s0bCAu7AiAfe/fuRl5eHiIj72LKlGlIS3uOXbu2oU6duoiPj8N7741CUlIizp8/i+fPn+PBg1gcP34M8fFx+PvvS0hKSkRaWhqCgn7F8OHv4a23BsHbeymaNnVGTk4OjIyMkJOTg+PHj+HevTu4efMGIiPvIS0tDadPn0KfPv212nYyHMoupGvewK5Uy+sbQxhR5pk20hWViuOsrCypMAaAqlWrIjExEcCrt3kzVJwrrFxpDw5EqmjevCV8fb+Co6MNEhKev/J6mzZtX3nu88+/kP4/ZcpUTJkyVXr81luDpP936tQFH3wwBQCwdu0q1KlTD2ZmZliyZEWR7b/zzhC1tIWIiCoOlYrjhIQEfPfdd9JFeZcuXUJKSoom4yIDoKxodq2q5UDUqLQjxJreLkdIyuaXX/6DBg0aIj8/H46ONdC2rZuuQ6IKxlBGiNVFXbmRuY4MgUrF8dq1a/H5559j165dAIAuXbpg7dq1Gg1MUzhCzJFgqvhWrFij6xDoBcy7FVdpp2cov6CQxTHpD5WK45o1a8LX11fTsZCOGcpISGlGMPRpJNjKylwHkRARVW7KvpzxJ+5JGZV+5i4xMRGLFi3CnDlzkJmZiRUrVuDZs2eajo2IiIiISKtUGjnesGEDOnTogEuXLsHS0hKjR4/GF198gc8++0zT8ZUZT+MZzkiwMroa9TUEnLdH9HqGngOJSDdUnlbx/vvvIzw8HADQsmVL2NjYaDQwMlwRmcGQ5+W+8rw+3SLIUOjTtBCAxXdlU9pBBp6mpkLFzS02zVSp5HitTad/KtXypb2ehtMwSKU9tfDOFIU3z8/IyEBsbGwJ71C/yrSzcrSDiAyRps/Y8WJizTOE+x+XlrL9ZrCS7/qlXZ4qHpWK4y5duuDdd99FTk4OPD09ER4ejmXLlmk6NpUYwvQJJvQCpf3ZU2UMOUkTERGRfjMSQghVFoyMjMTFixcBAF27doWTk/KvUMXd0F9VhlDsAkAVK3NkqPgTyZVtJNjU1ARy+avTKjStuKJZn0ZBrKzM9e5ntdX1i4Dl2Wbhj4Bo+lcI1dWm8kwtcXTU3HQ0deXdF3Obun4dTl0DAaVZfxUrc1yOiFPLdnVNVzlV3UpqR2lysroGWkqrcD97+fivbL9U1iZ1/XKrsukl8/qMKvb5lyn7ASZdKsuUvte1oyx5V6XiuEuXLpg9ezbGjh1b6g0QERERERkKlW7l5uzs/EphnJSUpJGAiIiIiIh0RaXi+J133sGZM2cgl8ul53bu3KmxoIiIiIiIdEGlaRXNmzf//zcYGUEIASMjI0RERGg0OCIiIiIibSrxbhWPHj2CiYkJ+vfvjx07dhR57csvv9RoYERERERE2lbiyPG//vUvvPfee+jduzcAwMLCAvb29loLjoiIiIhIm0qcc9y6dWuMGTMGBw4cwNSpU3Hu3DltxUVEREREpHUlFseFv4jn5eWFZs2aYdiwYdJrOTk5mo2MiIiIiEjLVP6h88JCudCGDRv05lfyNC0hIQFbt27FzZs3sX//fgBAdnY2fHx8ULNmTURHR8PT0xONGzfWcaTaV1zfHDhwAP/5z39gbm4OoGB6zvDhw3UYpXbFxMRg69ataNmyJeLi4mBrawsvLy+kpKRg06ZNqF+/PqKjozF37lxUr15d1+FqjbJ+2bZtGy5duiQtN23aNHTv3l2HkVYeFSW3VZQ8VFFyR0X5W8/Pz8e0adPg6uoKuVyO2NhYrF27FllZWQb1eShrx9dff21Qn0ehrKwsvP/+++jRowcWLVqkkZxVYnF88uRJ3Lx5EwAQHR2N0aNHS689ePCg0hTH//zzD/r371/k7hx79+5F7dq18dFHH+HWrVv49NNP8eOPP+owSt0orm8AYPPmzahXr56OotKtlJQUvPPOOxgwYACAglsh9unTBz///DO6du2Kd955B//973/h4+ODL774QsfRao+yfgGAH374QYeRVV4VJbdVlDxUUXJHRfpbd3Nzw4wZMwAA06dPx4kTJ/D3338b1OcBFN8OwPA+DwDSF69CmshZJRbHTZo0wYgRI4p97dChQ+XasCEZOHAgQkJCijx3+vRpzJ07FwDg4uKCmzdvIi0tDdbW1roIUWeK6xsACAgIQPXq1ZGZmYnx48fD1tZW+8HpiKura5HH+fn5sLS0xJkzZzB9+nQAQPv27bF48WJdhKczyvoFAHbt2gUzMzPk5eXBw8NDep40q6LktoqShypK7qgof+vGxsZSQZmbm4v4+Hg0btwYmzZtMqjPQ1k77t+/b1CfBwAEBQWhffv2uHXrFjIyMgBoJmeVWBzPmTMH7du3L/Y1fT/NpmmJiYmwsrKSHltbWyMxMVGvDyDa0rFjR/Tp0wf29vY4c+YMPv74Y+zdu1fXYenEyZMn0aNHDzRp0qTIPmNtbY1nz54hNzcXJiYqz26qMF7sl4EDB6Ju3bqoUqUKAgICsGbNGqxdu1bXIVZaFSW3GXoeqii5oyL8rZ87dw7fffcd+vTpgzZt2hjs5/FyOywsLAzq87h79y4iIyMxd+5c3Lp1S3peEzmrxAvylBXGQMEQfWXm4OCA9PR06XFaWhocHBx0GJH+qF+/vnTLvy5duuCvv/5CXl6ejqPSvuDgYISEhGDp0qUAiu4zaWlpqFatmt4nU014uV+aNWuGKlWqACjYX4KDg3UZXqVXUXKbIeehipI7Ksrfes+ePbF79248ePAAAQEBBvt5vNwOQ/s8Tp48CTMzM/j7++Off/7B1atX8d1332kkZ6n089H0qj59+uDKlSsAgFu3bqF58+YGN7KiKZs2bUJubi6AgrnqdevWhUwm03FU2nX69Gn873//w6effoqEhARcuXIFvXv3lvaZy5cvS/cPr0yK6xcfHx/p9fv376NBgwY6jJAqSm4z1DxUUXJHRfhbv3v3Lk6fPi09rlevHh48eGBwn4eydhja5zF9+nR4eXnB09MTb7zxBlxdXTFx4kSN5CyVfj66srt06RKCgoJw7tw5jBkzBpMnTwYA+Pj4wNHRETExMZg6dWqlnGpSXN/89NNPuHPnDurVq4fbt29jwoQJlepMQ3h4ODw8PNC6dWsAQEZGBsaNG4d+/fph48aNqFOnDmJjYzFv3jy9vsJZ3ZT1S1RUFDIzM+Hg4IDbt29j9uzZlfJvSRcqSm6rKHmoouSOivK3HhMTgw0bNqBly5bIzc3FvXv3sGzZMpiamhrU56GsHd9//71BfR6Fjh8/joCAAMjlcowbNw4DBgxQe85icUxEREREpMBpFURERERECiyOiYiIiIgUWBwTERERESmwOCYiIiIiUmBxTERERESkwOKYJP/88w88PDzQrVs3rFixQvrn7u6OBw8elGmdHh4exf6sa0XzySef4OzZswCAkJAQeHh4lHodcXFxmDZtWpneS0REROqh/z/pQlrzxhtvYMSIEfjPf/6D1atXS88HBATA1NRUh5Hpv8WLF8POzq5c66hVqxYmTZqE7du3qykqIiIiKi0Wx1Sibdu2YcSIEahZsyaOHTuGCxcuwNbWFvHx8Vi4cCEcHR1x9OhR/PHHH6hbty4ePXqEGTNmoGnTpjh48CCio6Px/fff4/jx4xg2bBi2bNmCWrVqYf369fj3v/+NL774AocOHYK9vT2mTJmC+Ph4uLu749y5c8jOzkZQUBC+//57REdHw9zcHM+fP8eSJUuK/I46APj6+uKHH37AhAkTcOPGDURHR2PlypX47bffcPXqVbi4uGDdunUAoDReAPj999+xd+9euLi4wNTUFPv374enpyecnJzg4+ODzp07IzMzExEREfjggw8wZswYhISE4IsvvkDv3r3h4eEhxbt69Wq0a9cOiYmJ8PX1xaFDh2BsbIylS5dKfQAAP/zwA06cOIHGjRu/0i5lfU5EREQaIohesH//ftGpUycxZ84cMWfOHDF48GARGxsr7t69K9555x2Rl5cnhBDi559/FgsWLBBCCHH69Gnx/PlzIYQQYWFhYsqUKdL6xo8fL4KDg4usf9GiRdLjvn37itjYWCGEELGxsaJFixbixo0bQggh9u3bJy5cuCA++OADafnNmzeLrVu3Fhv7+PHjxZdffinF1717d5GSkiLy8vJE7969RVRUVInxPn36VHTo0EHEx8dL6+jbt6+0fl9fXzF+/HiRn58vIiMjRffu3Yu85uvrK4QQIjg4WIwfP75IbC+288U+iIiIEN26dROZmZlS+wrfW1KfExERkWZw5Jhe0bBhQ2zZsgUAEBQUBAsLC5w+fRrZ2dlYuXIlACA9PR1yuRxAwe+0r1u3DpaWlkhPT0d0dHSZt21vb48WLVoAAMaNGwcfHx8kJydjxYoVAICUlJQSR07btWsHAKhfvz7q1q2LatWqSTEmJCSgUaNGSuMNDQ1FzZo1UaNGDQAF00xe5ubmBiMjIzRo0ABPnz4tczsLXbp0Ca1bt4aFhQUAoEOHDrh8+TIA4OLFi0r7nIiIiDSDxTGVaPjw4dL/GzVqVGQucnp6OgBgxowZmDt3Lt5++208ePAAEyZMULo+IyMj5OfnS49fLvbMzMxeeY+bmxtWrVoFABBCIDMzU+n6C99vZGRUZF0vbrc08Spbv0wmgyjlL68XLp+bm6vye5T1OREREWkG71ZBKunatSvCw8ORlpYGALhx44Y0hzclJQW2trYAgMePHxd5n5mZGfLz8xEeHo5bt26hevXqSEhIAAA8efIEiYmJJW63Z8+eCAkJkQrKP/74A3v37i1XW5TF6+bmhri4ODx58gRAwd07ysLc3Bx5eXkAgP379wMAHB0dpfVGRERIy3bq1Anh4eHIysp6ZZsl9TkRERFpBkeOSXLlyhUcOnQIDx8+xOrVq7Fw4ULpdH+TJk2wfPlyLFy4EA0aNEBqaioWLFgAAFi6dCl8fHzQoUMHZGdnIyUlBXv37sUHH3yAgQMH4ptvvoGpqSlWrVqFxo0b47vvvsOSJUvQuHFj1KxZE9u2bYO3tze2bduGlJQUrF69GkuXLoWJiQm6deuG0aNHY968eahduzays7OxePHiV2IPCgqSLv6rWbOmdFHcwYMHAUB6rVmzZiXG+9lnn+Hjjz9G48aNUatWLekuHVeuXMGZM2cAAP369cO5c+cAFFwI2LlzZ+m1Tp06wdXVFUIILFmyBPXq1QMAfPTRR9i4cSPatWuH/Px8hIWF4fjx43j77bcxbdo0fPjhh3B2dkZ2djaio6Px73//G2PGjFHa50RERKQZRqK054aJKrALFy6gW7duAIDTp08jMDAQX375pY6jIiIiIm3hyDHRC06cOIHjx4/DwsICT548waJFi3QdEhEREWkRR46JiIiIiBR4QR4RERERkQKLYyIiIiIiBRbHREREREQKLI6JiIiIiBRYHBMRERERKbA4JiIiIiJSYHFMRERERKTA4piIiIiISIHFMRERERGRAotjIoUhQ4bg/v37ug6DiIiIdIg/H02kkJqaiqpVq6p9vYsXL0bdunUxa9Ysta+biIiI1Isjx0QKmiiMiYiIyLCY6DoA0m8//fQT/Pz80LZtW9jY2ODy5cto3rw5vLy8sHnzZkRERGDixIkYN24cAEAul2Pz5s24cuUKjIyM0L17d8ycORNGRka4c+cOvvjiC8jlcmRkZMDd3R2jRo0CAHh5eeHMmTOYNWsWQkNDcefOnSLrfdGpU6fwxRdfwM7ODs2aNcPt27eRk5ODNWvWoFWrVgCAmJgYrFy5Ejk5OcjPz8f8+fPRvn176b3Vq1dHmzZt8M8//+Dp06d466238Ouvv2Lp0qVwd3cvEs+VK1dw+/ZtzJ8/H9nZ2Thw4ACSk5Oxbds2NGrUqMTt7d27F+fOnYO5uTkuXbqEoUOH4v3330d4eDjWrVsHIyMjyGQyrFixAk2aNCnS31ZWVrh27RqqVq2KH374QTsfOBEZPH3M2wBw8uRJ7Nu3D0ZGRpDL5Zg7dy7eeOMNPHr0CHPmzEFYWBjWrVuHI0eO4NKlS/j9999haWkJb29vJCcnIy8vDx9++CEGDBhQ4vqIyk0QvYavr6/o1auXSE1NFdnZ2aJr165i2bJlIj8/X4SHhws3Nzchl8uFEELs3LlTeHh4iNzcXJGTkyNGjRolgoKChBBChIaGitDQUCGEEDk5OWLgwIEiKipK2k7fvn2Ft7e3EEKIsLCwIut92f79+0WLFi3EzZs3hRBCHDp0SPTt21fk5OQIuVwuBg4cKH755RchhBARERGiU6dO4vnz59J7XV1dxd27d4UQQqxfv14IIcT48ePF/v37i8SzZs0aIYQQJ0+eFF26dBEnTpwQQgixZs0asXz5ciGEeO32Fi1aJHx9faX1pqamis6dO4sLFy4IIYT4888/xVtvvSXy8vKk/u7WrZtITEwUeXl5YsOGDap+VEREQgj9zNtBQUEiOTlZCCFEbGys6N27t/RabGyscHZ2FoGBgUIIIb799lsRHx8vJk6cKLZu3SqEECI+Pl506tRJxMbGvnZ9ROXBaRWkEldXV9jY2MDMzAwNGzaEs7MzjIyM4OLigoyMDCQmJgIAAgMDMWLECMhkMpiammLgwIE4dOgQAKBhw4b49ddfMXr0aEyePBkJCQm4ceNGke307NkTAF5Zb3GaNm0KFxcXAMA777yDJ0+eIDQ0FGFhYYiNjcWwYcMAAM2bN0fNmjVx+vRp6b2NGzdGkyZNAACLFi1Suo1u3boBAJo1a4akpCR07dpViu/BgwcAoNL2XvTnn3+iSpUq0rr69OmDp0+fIiwsTFrGzc0N9vb2MDY2xoIFC5TGR0SkjL7l7ebNm2PJkiUYM2YMlixZgsePH7+ybP/+/QEAkyZNghACFy5cwHvvvQcAqFGjBtq3b4+jR4+qvD6isuC0ClKJlZWV9H8TExPpsYlJwS4kl8sBAHFxcdizZw8OHDgAAEhPT5fm8q5fvx6pqakICAiATCaDh4cHsrKyimzH2toaAGBubl5kvcWpVq2a9H+ZTAYbGxskJCRIz02ePFn6f05ODp4/fy49trGxKVW7ZTJZkfhkMpkUW3x8/Gu396K4uDg8e/YMHh4e0nP29vZISUkpdXxERMroW96ePn06xo0bhylTpgAoKKYzMzOLLPNi7ouLiwNQMIBhZGQEAEhOToazs7PK6yMqCxbHpFa1a9fG9OnTMWjQIABAfn4+UlNTAQBXr17F2LFjpUKzpMJXFS8Wk7m5uXj+/DkcHR2l0Y8X5+lmZGTA2FgzJ0pq1apVqu3Vrl0btWrVKrJ8WloazMzMNBIfEVFJtJG3ExMT8fDhQ2mUWZX11KpVCwDg6+sLe3t7AEB2djZyc3PLtD4iVXFaBanViBEjcOTIEeTl5QEoOF331VdfAQAaNGggTR148uQJbt26Va5tRUdHS+s4evQoatSoATc3N7Rt2xa1a9fGiRMnABQUzjNnzkR0dHS5tqfM67ZnZWWFzMxMZGRkYN68eejbty+Sk5Nx9epVAAWF9IQJE5CWlqaR+IiISqKNvG1ra4uqVatK6zp37txr31OzZk10794dBw8elJ7z9vZGSEhImdZHpCre55hKdPjwYWzZsgXZ2dmYOXMmkpKS8N1336F69epYt24ddu/ejZMnT6Jt27bw9/eHlZUVvvzyS1y6dAnm5uaoVasWVq9eDUtLS9y7dw8LFiyAqakpnJycEB4eDrlcDm9vbwQGBuK3336Dk5MTtm/fDh8fnyLrtbW1LRLXgQMHcODAAbRo0QLh4eHIzs7G6tWr0bp1awAFd49YtWoVsrOzkZ+fD3d3d7z33nu4ePEiVq1ahadPn8LV1RXffvstgIJTh7/++iuqV6+OxYsX49ixY1I8W7ZsweLFixEWFoZ+/fph+vTpWLhwIZ4+fYqRI0di4cKFSrcHAFeuXMGSJUtgbW2NDz74AEOGDEF4eDh8fHwghIAQAh9++CH69u1bpL+7d++ODRs2aPXzJiLDp695+48//sC6devQqFEjtG7dGl999ZW0rKenJ8LCwtCpUyd4e3ujadOmAApGnAtzNgD06tUL06ZNe+36Xt42UWmwOCaDdODAAQQGBvIWZ0RERKRWnFZBRERERKTA4pgMzqlTp+Dv74+IiAisWbNG1+EQERFRBcJpFUREREREChw5JiIiIiJSYHFMRERERKSgkR8BSUgo/pfBAMDOrgqSkzM0sVm1YYzqwRjVgzGqhz7E6OiouV8+LCnvVkT68HnqCtvOtlc25Wl7WfKu1n8hz8REpu1Nlpq2YjwaeaLY5wc7vfXa97If1YMxqgdjpLKo6DlQU9j2yolt1x5OqyAiIiIiUtD6yDEREVFJyjOiTERUXiyO9VBpDww8kBARERGpB6dVEBEREREpcOSYiIgMwotnyarEmyMjPRsAz5IRkXpx5JiIiIiISIHFMRERERGRAqdVVEK8gI+IiIioeCyODYiy+XZEREREpB6cVkFEREREpMDimIiIiIhIgdMqtEDZHF8iIiIi0i8cOSYiIiIiUmBxTERERESkwGkVFRincxARERGVDotjIiIyaLx3OxGpE6dVEBEREREpcOSYiIjUQt+mcnFEmYjKgiPHREREREQKLI6JiIiIiBQ4raKMeLqOiIiIqOJhcazwYrFbJd4cGenZAFjsEhEREVUmLI7ptdQ1Sh50LrLY54f3dCp1TERERESawOL4NfTt6msiIiIi0hwWx2pWmYppzrvmaDhVToae55i7iKgkLI6JiIhQfNHMgpmo8mFxTHqrIo7KVsQ2ERERVSQsjum1bsYkF/t88wZ2Wo6kZMUVniw6iag8+IWWqPJhcUxlpqxoHmzAxwweCIkqDkP5Yk9E+oXFMUk2nf5J1yGonbJit5CVlTnSFfe01uZ2iciwqeuLNL+QE+mfClsc82pk5ZSNpqhLYbJXtfAsbSGpi8KTxS5RxVdcbmwiK906DKVo1nROY3FPhqzCFsdERFQ+hn7LNmU0PUCgC/wCT6Q+LI4rsIp4AKioeGqV6PVezGmmpiaQy3N1GI1uBJ2L1Nh0MCIqwOK4AmARXHGV9kCob6duiYiIDI3BFMfqmkNcUU8TGoJ7eX+Vavkmso4aioSIXsS8qHmVbdpDadtb3Bfy4tZhZWWON9vXLXNcr1u/sliocjGY4rgiKs+Ib2U9pUglM4RkbwgxAoYTZ0WkT2fD+KWeqPLRu+K4tCMYhjDioU+JXhsKDyammSaQ55W9gFd2UFJ28ClueR6oyqY0oz6aLhbVMQIFAD8ev1ns9BQWu5pXmXKguorp0uY/Q1eav3NdfXEt7XbVfeeSl6fYabK9+tbHH7m31eh2X2YkhBBa3SIRERERkZ4y1nUARERERET6gsUxEREREZECi2MiIiIiIgUWx0RERERECiyOiYiIiIgUWBwTERERESmwOCYiIiIiUtD4j4BkZWXh/fffR48ePbBo0SJkZ2fDx8cHNWvWRHR0NDw9PdG4cWNNh1GiyMhIHD16FObm5vjrr78wa9Ys2NvbY+fOnWjYsCEePnyIRYsWwcrKSmcxfvPNN3j48CHs7Oxw//59fP7558jKysKmTZtQv359REdHY+7cuahevbrWYkpISMDWrVtx8+ZN7N+/HwBK/HwPHjyIiIgIGBsbo0GDBhg9erROYvT398fTp0/h6OiI8PBwzJ49G02aNNGrGAsdOnQICxYswOXLl6X978KFCzhx4gQcHBxgZGQELy8vncQohMAPP/wAAHj48CFSU1Oxbt06AAX7a1paGlJTU9G9e3f0799fJzHGxsZiw4YNaNOmDSIiIvDuu+9KsejisybVjRw5Eubm5gAAY2Nj7N27FykpKUpzni72OXVSVz598OCBXh27VFFc2w8cOID//Oc/0j7wr3/9C8OHDwdQcdoeExODrVu3omXLloiLi4OtrS28vLzKtJ9HREQgICAA9erVQ2JiIhYtWgQTE737nTeJsrZv27YNly5dkpabNm0aunfvDkDLbRcatm7dOrFw4UKxfv16IYQQfn5+wt/fXwghxM2bN8WYMWM0HUKJcnNzxUcffSTy8vKEEELEx8eLxMREMXnyZBEWFiaEEOL7778XW7Zs0VmMT548ER07dpRinDZtmjh48KBYvny5OHr0qBBCiFOnTon58+drNa7ffvtNnDp1SowYMUJ6Ttnn+/jxYzF06FCRn58vhBDC3d1dREVF6STGLVu2SHEcPXpUTJ06Ve9iFEKIu3fvis2bNwtnZ2eRlpYmhBAiIyNDDBgwQGRnZwshhPDy8hIXLlzQSYyBgYEiMDBQehwRESGEECI0NFR8+OGHQggh5HK5ePPNN0VqaqpOYlyxYoXYs2ePEEKI69evizfffFMIobvPmlTn6+v7ynPKcp6u9jl1Ulc+1adjl6qKa/v+/ftFbGzsK8tWpLaHhYWJkydPSo8HDRokrl27Vur9PD8/XwwePFg8efJECFFQd/38889abk3pKGt7cX/3Qmi/7RqdVhEUFIT27dujXr160nOnT59Gu3btAAAuLi64efMm0tLSNBlGia5duyaNgPn5+eHPP/+EjY0NQkJC0KZNGwBA+/btcebMGZ3FaGlpCVNTU6mfMjIy0KxZM5w5c0bqS13EOHDgwFe+lSv7fM+dO4dWrVrByMgIANCuXTucPXtWJzHOmTNHiiM/Px9VqlQBAL2KMTMzE9988w1mzpxZ5PnQ0FDUqVMHZmZmAAo+99OnT+skxsOHDyMlJQXff/89Nm/eLL3+559/ws3NDQBgYmICJyenIiMB2oyxevXqSEpKAgAkJSWhVatWAHT3WZPqbt++DX9/f2zbtk3ax5XlPF3tc+qkjnwql8v16tilquLaDgABAQHYvXs3tm/fjpSUFADK/3YNse2urq4YMGCA9Dg/Px+Wlpal3s9jY2ORlZUFR0fHV96jr5S1HQB27dqF3bt3w9/fH5mZmQC033aNjbnfvXsXkZGRmDt3Lm7duiU9n5iYWOSPwNraGomJibC2ttZUKCV69OgRQkNDsXnzZtjY2GD+/PlISUmBhYWF9MdXGKOuWFtbY8GCBfjkk0/g6OiIWrVqoUGDBkX60traGs+ePUNubq5OT6Uo+3yTkpKKPG9lZaXTPgWAnJwcBAYGwtvbGwD0KsYtW7ZgxowZUhFcSFn/6sKjR4+QlpYGLy8vREVF4cMPP8SxY8eQlJQEJyenIjEWFqjaNmnSJMycORPr1q3D1atXMWPGDAD69VlT8T766CO4uroiLy8P48aNkz6j4nKePu1z6lTafJqcnKxXx67y6NixI/r06QN7e3ucOXMGH3/8Mfbu3Vth237y5En06NEDTZo0KfV+rk/HhbJ4se0DBw5E3bp1UaVKFQQEBGDNmjVYu3at1tuusSrq5MmTMDMzg7+/P/755x/I5XJ89913cHBwQHp6urRcWloaHBwcNBXGa1lZWcHJyQk2NjYAgDfeeAN///03srKyIISAkZGRzmOMiIjA7t27ERgYCBMTE6xfvx47duyQ+rJq1apIS0tDtWrVdD7HSNnna29vj/v370vPp6eno0GDBroIEUBBYbxy5Up88sknUhz6EuPjx4+RmpqK3377TXpuz5496N27t179/VhbW6Nt27YAgMaNGyMtLQ2PHz+Gvb39KzHa29vrJMbFixfj/fffx7vvvoukpCS89dZb+OOPP/TmsyblXF1dAQAymQwdOnRASEiI0pynT/ucOpU2n9rZ2enVsas86tevL/2/S5cumD59OvLy8ipk24ODgxESEoKlS5cCQKn3c306LpTWy21v1qyZ9FqXLl2we/duANB62zU2rWL69Onw8vKCp6cn3njjDbi6umLixIno06cPrly5AgC4desWmjdvrrNRYwBo27YtUlJSkJeXB6BgNKxZs2bo3Lkzrl27BgC4fPkyevfurbMY4+PjYWtrKxW+jo6OyMnJQe/evaW+1HWMhZR9vj179sT169chhAAAXLlyBb169dJJjJmZmfD29sakSZPQunVrHD9+HAD0JsbatWtj/fr18PT0hKenJ4CCEdA2bdrAzc0Njx49Qk5ODoCCz71Pnz5ajxEAunbtitjYWAAFCSkvLw+Ojo7o06cPQkNDAQByuRyRkZHo2LGjTmJ8/PixdLqtatWqMDY2Rn5+vt581lS8e/fu4ZdffpEe379/H/Xr11ea8/Rpn1On0uZTU1NTvTp2lcemTZuQm5sLAIiOjkbdunUhk8kqXNtPnz6N//3vf/j000+RkJCAK1eulHo/r1+/PiwsLJCQkPDKe/RZcW338fGRXr9//740aKHtthuJwj1MQ44fP46AgADI5XKMGzcOAwYMgI+PDxwdHRETE4OpU6fq/G4VJ0+eRHBwMOzs7PD48WMsX74cT58+xY4dO1C/fn08fvwYixcv1tlVr3l5efjss89gbm4OGxsb3LlzB0uXLoWZmRk2btyIOnXqIDY2FvPmzdPq3SouXbqEoKAgnDt3DmPGjMHkyZMBQOnne/DgQYSHh0Mmk6FRo0ZauTtAcTHOnz8fd+7cQY0aNQAUzOEuvEJaX2K0sLBAUlIS/vOf/+DLL7/EjBkzMHr0aNSsWRPnz5/H8ePHYWdnB1NTU63craK4GOVyOb744gvUqVMHMTExePvtt6Wk9M033yA1NRXPnj1Dr169tHLngOJiDA8Px/fff4+WLVviwYMHaNWqFcaMGQNAN581qSY+Ph5r1qxBixYtkJaWhtzcXCxZsgSpqalKc54u9jl1Ulc+ffDggd4cu1RVXNt/+ukn3LlzB/Xq1cPt27cxYcIEac5pRWl7eHg4PDw80Lp1awAFx6Jx48ahX79+pd7PIyIi8MMPP6BOnTp49uyZ3t+tQlnbo6KikJmZCQcHB9y+fRuzZ8+W9nlttl3jxTERERERkaHgj4AQERERESmwOCYiIiIiUmBxTERERESkwOKYiIiIiEiBxTERERERkQKLYyIiIiIiBRbHREREREQKLI6JiIiIiBRYHBMRERERKbA4JiIiIiJSYHFMRERERKTA4piIiIiISIHFMRERERGRAotjIiIiIiIFFsdERERERAosjomIiIiIFFgcExEREREpsDgmIiIiIlJgcUxEREREpMDimIiIiIhIgcUxEREREZECi2MiIiIiIgUWx0RERERECiyOiYiIiIgUWBwTERERESmwOCYiIiIiUmBxTFQKP/30E/r164fFixfrOhQiIiLSABbHRCXYtm1bkUJ41KhRGDFihA4jIiKiF72cp4nKi8UxEREREZGCkRBC6DoI0r2ffvoJfn5+aNu2LWxsbHD58mU0b94cXl5e2Lx5MyIiIjBx4kSMGzcOACCXy7F582ZcuXIFRkZG6N69O2bOnAkjIyPcuXMHX3zxBeRyOTIyMuDu7o5Ro0YBALy8vHDmzBnMmjULoaGhuHPnTpH1FhfX/v37YWlpCQsLCyxcuBCWlpaYM2cOwsLCsG7dOgQFBSExMRFbt27FwYMHceHCBTg4OGD79u0wNzcHAJw9exY7d+6ETCaDhYUFli9fjkaNGgEAoqOjsWbNGmRlZSEvLw/Tp09H7969cezYMWzcuBHZ2dlwcnJCt27dMH36dGzbtg2RkZGwsbHBtWvXUL16dWlbK1euxJEjRzB+/HhERkbi1q1bePvttzF37lypTd988w1OnDgBExMTtGjRAosWLYKZmRnu3buHVatWAQByc3Px3nvvwd3dHU+fPsXixYuRnZ2N3Nxc9O3bF56enpraFYhIg/Q116anp2PdunW4d+8eAKBx48aYP38+7O3tlebIq1evYvny5Xj+/DnGjh2LP/74A7m5udi6dSv8/f1x5coVtGzZEj4+PsjJycGUKVNw6dIlzJ07FyEhIYiPj8ewYcOkfPb3339j165dyMvLQ1ZWFj788EMMGDBAivHbb7/F77//DnNzc1hYWGDOnDm4f//+K3na3t6+SB+/nKcB4Ny5c9i+fTtMTU1hbW2NVatWoWbNmsjMzMTixYuRmJiIvLw8tGnTBkuXLkV+fj5WrVqF27dvw9jYGI0aNcKnn36KKlWqaGxfIR0SRAq+vr6iV69eIjU1VWRnZ4uuXbuKZcuWifz8fBEeHi7c3NyEXC4XQgixc+dO4eHhIXJzc0VOTo4YNWqUCAoKEkIIERoaKkJDQ4UQQuTk5IiBAweKqKgoaTt9+/YV3t7eQgghwsLCiqz3RWlpaaJTp04iOztbCCHEd999J/bv3y+EECI2NlY4OzuL48ePCyGE+Oyzz0T//v3Fw4cPRX5+vhg6dKg4cuSIEEKImJgY4ebmJiIjI4UQQgQFBYm3335byOVyIZfLxdtvvy2tNzo6WrRr107cv39f6pNFixa90k89evQQKSkpIi8vT7z77rvi8OHD0uvjx48XH330kcjPzxfx8fGiZcuWIi4uTgghxMGDB8XAgQNFRkaGyM/PF7NnzxY7duwQQggxe/ZscfToUSGEEE+ePBFTpkwRQgjh4+Mj/Pz8hBBCpKeni9GjR6v6kRKRHtK3XCuEEMuWLROLFy8WQgiRl5cnpk6dKoKDg1+bI4ODg0WrVq3ElStXhBBCTJ8+XYwYMUJqW5cuXaTXhBDC2dlZbNiwQQghRHJysujevbs4d+6cEEKI06dPi+joaCGEEM+fPxc9evQQqampQgghDh06JAYPHiwyMjKEEEJ88803wtfXV+rP1+XpwYMHS3m68Jhw7949IYQQ+/btEx988IH0/xUrVgghhMjNzRXu7u5SbIU5WQghZsyYIWJjY4vtSzJ8nFZBRbi6usLGxgZmZmZo2LAhnJ2dYWRkBBcXF2RkZCAxMREAEBgYiBEjRkAmk8HU1BQDBw7EoUOHAAANGzbEr7/+itGjR2Py5MlISEjAjRs3imynZ8+eAPDKel8kk8kAAEFBQcjMzMS4cePw7rvvFlmmW7duAABnZ2dUrVoVderUgZGREZo1a4bY2FgAwJEjR9CmTRs0btwYAPDuu+/i0aNHuHLlCsLCwvDgwQMMHTpUir1t27ZSW5Rp27YtqlWrBmNjYzRr1gwPHjwo8nqPHj1gZGSEGjVqwNbWFg8fPpT6bfDgwbC0tISRkRHeffddHDx4EABQrVo1/P7773jw4AEcHR2xbds2AICtrS3OnTuHO3fuoEqVKvj2229LjI2I9J8+5dr8/HwEBQXB3d0dAGBsbIzFixejadOmKuVIKysruLm5AQCaNWuGunXrSm1r1KiRlIsLDR48GEBBbuvVqxeOHj0qvffLL7/E6NGjMX36dKSkpCAqKgoAcODAAQwcOBCWlpYAgJEjR+Ltt98usY+V5ekjR46gdevWcHJyAlBwTLh48SKePHkCW1tb/PPPPwgLC4NMJsO+ffsAAFWrVsXt27dx/vx55OfnY/PmzahTp06J2yfDZaLrAEi/WFlZSf83MTGRHpuYFOwqcrkcABAXF4c9e/bgwIEDAApOyVWtWhUAsH79eqSmpiIgIAAymQweHh7Iysoqsh1ra2sAkE5xFa73RRYWFti3bx/8/PywdetW9OnTRzrN9/J6ZDLZK7G/GOuL75HJZKhatSri4uKk/xe2DwDs7e0RHx9fYj8VbhcAzMzMXon/xdfNzc2LxHL48GGEhIQAALKzs2FsXPAddenSpfj222/xwQcfoEaNGpg9eza6du2KKVOmwNLSEp988glkMhmmTZuGQYMGlRgfEek3fcq1SUlJyMnJKZInC6edhYSEvDZHKmtL4eOXt1kYP1BQIN++fRsAsGjRIjg7O2Pz5s0AgH79+iEzM1Pqhxfjs7GxgY2NzSttKa7the1/sU/v3bsHDw8P6fW6desiMTERgwcPRm5uLj7//HOkpKRg4sSJGDt2LNq1a4c1a9bg66+/xtKlSzFq1ChMnTq1xO2T4WJxTGVSu3ZtTJ8+XSrS8vPzkZqaCgC4evUqxo4dK438FpeMVSGXy+Hg4ICNGzfi+fPnWLx4MXx8fODj41PqWAtHHwAgLy8PqampqFWrFmQyGVJTU5Gbmysl/6SkJGmUWd1q166Nbt264cMPP5SeS0pKAgCkpqZixowZmD59Og4ePIjp06fjwoULSEtLg4eHBzw8PHDhwgVMnToVrVq1QoMGDTQSIxHpD23kWnt7e5iZmSEpKQlNmjQBAMTHx8PY2Bi1atVSe4589uwZ6tWrBwBITk6Go6Oj1J7JkydLy73Yntq1a0u5EgAyMjIQFxcnjf6WRu3atdG6dWv4+/sXicna2hpJSUl45513MGzYMNy4cQOTJk2Ck5MTWrVqhU6dOqF3796IiYnBhx9+iJo1a+Jf//pXqbdP+o/TKqhMRowYgSNHjiAvLw9Awam/r776CgDQoEEDhIWFAQCePHmCW7dulWkb8fHxWL58OYCCUYIWLVpI2yuNwYMHIzw8HPfv3wcAHDt2DHXq1EG7du3Qtm1bNGjQAEeOHAEAxMbGIiwsTDqFaGVlhczMTAghMHPmzDK140UjRozA77//juzsbABAcHAwvL29AQBLlizB06dPYWRkhI4dOyI3NxdGRkbSRTpAwalYU1NTCF5HS1QpaCPXGhsbY/jw4dLodH5+Pj799FM8ffr0tTmyLI4fPw6goDA+e/asNM3ixfbcvHkTCQkJ0nsKc2fhSPLevXtx7tw5AKXP04MHD0ZYWJg03S0xMREeHh7Iz89HQEAAzpw5A6Bgul61atWQn5+PkydP4qeffpLirFmzJvLz88vcB6TfeLcKAgAcPnwYW7ZsQXZ2NmbOnImkpCR89913qF69OtatW4fdu3fj5MmTaNu2Lfz9/WFlZYUvv/wSly5dgrm5OWrVqoXVq1fD0tIS9+7dw4IFC2BqagonJyeEh4dDLpfD29sbgYGB+O233+Dk5ITt27fDx8enyHptbW2lmDIyMvDZZ58hKioKxsbGMDc3x2effYYqVarA09MTYWFh6NevH6ZPn46FCxfi6dOnmDBhAmrWrAlfX1+Ym5vjk08+wZAhQ/C///0P27dvL/ZuFTExMVi9ejUyMzOLXIkNAPfv38eMGTNgbW2NN998EzVr1izSTzKZrMi2IiIi8PPPP0v9dvDgQezfvx9OTk7YtGkTmjZtim+//Ra//fYbLC0tYW1tjTVr1sDBwQGBgYH46aefYGZmhrS0NHz44Yd45513cPr0aXz99deQyWRIS0vD8OHDMWHCBB3sJURUXvqYa4GC6Rpr165FZGQkhBAYMmSIdGcLZTny7t27mDdvHiIjIzFixAj07t0bn3/+ebFt8/b2RteuXeHi4oKlS5fi7NmzePz4MYYNGyZNT/jnn3+wbNkyVK9eHS4uLvj999/h4OBQJHf+/vvv0lzmlStXwsTEpNR5+sVjgqmpKYyMjDB37ly4ubkhNDQUW7ZsgRACaWlp6N69u9TG9evXIysrCxkZGXBxcYG3tzfMzMy0vQuRFrA4JiIiIq1wcXHBqVOnpGkVRPqI0yqIiIiIiBRYHBMREZFG5eTkSHeHmDt37mvvCESkS5xWQURERESkwJFjIiIiIiIFjdznOCHhuSZWWyZ2dlWQnJyh6zDUqiK2CWC7DElFbBOg+XY5Opb8owXloU9593UMdf8xxLgNMWbAMOM2xJgBw4y7NDGXJe9W+JFjExOZrkNQu4rYJoDtMiQVsU1AxW2XvjHUfjbEuA0xZsAw4zbEmAHDjFvTMfMX8iqho5Enin1+sNNbWo6EiKj8mNOISJ1YHBuQwgNAlXhzZKRnS8/zAEBERESkHiyOiYhIJzjiS0T6qMLPOSYiIiIiUhWLYyIiIiIiBU6rqMCUnbIkIiIiouKxOCYiIr3CuchEpEucVkFEREREpMDimIiIiIhIgdMqSOd4/2Yi0gROzyCisuDIMRERERGRAkeOiYjIIPAOPESkDRw5JiIiIiJS4MgxvVZp5+0pW/5mTHKxzzdvYFe2wIiIiIjUjMUxSUp7ypKnOImIiKii4bQKIiIiIiIFjhwTEZFGvXyW6eXbNmqbJm/xxtvHERk+FscVgK6mN+jbHOLi+oEHJCJSFXMIEQEsjomIqJR4vQERVWQsjsngbDr9U7HP864XREREVF4sjum1lE2fUPf6TU1NIJfnSs8Pdirbel5U2nUQEemDoHORxT4/vCeTGpGmsTgmvaVshJiIiIhIU1gcExER6YiyEWIi0h0Wx1rAW/voDk9NEpE2KZuGxileRIaDxbEe4pXg6nMv7y8lr5TuSMUim6hyejEfv3h/Zg5uEFVcLI6pUlJXscuimYiIqGJhcaxD+jZCrOm7UhARGZoX8+KLd9S5GVO6C4Y1PbdY2fo/cm+rlvXwCz9VJiyOiYiI9Iy6poT9ePwm0ov5qW4Wu0TKsTguI15kVzHxynEiIqLKjcVxBaZsmgR/SU455aM1xWsi66ihSIhIU3SRG5XlFuYQIv3D4rgC0Le5wvoWDxGRvirtF3J10dUcaE7nIEPA4rgSYvGqfzhNh+j1eDZMd1jsUmXC4phIi5QdYEzrajkQIj2mri/wHAjQPHWNQL+8Hisrc7zZvvjEyEKdNI3FMRERFUvfbjdJpS9GIzKDIc/LfeV5Xc115kXPZAhYHBMREcGwR5qVzV02NS7dYV6fLhzU1Kh0IWUjzfo2Ml3afuAIevmxOFZQ15xPjrRULsoOJEHn/v//Vlbm0n1GlV58E1P80/KH/CU/0jxN562Xi84Xf0xDE+unyklZnlMlT5dn/cyjFY/eFceavjCptAcBdRw01J241X1gqYw0fYX4i+s3zTQp9rRmeWw6Xfyvc6lrdEfZfi9/2BRA0YK/tAzlQMKLJEkfqSt36Wo9ynLUy+sxzTRBA7TTaCyaZsgjvrr6IqAvX0CMhBBCq1skIiIiItJTxroOgIiIiIhIX7A4JiIiIiJSYHFMRERERKTA4piIiIiISIHFMRERERGRAotjIiIiIiIFFsdERERERAp69yMgqrpw4QJOnDgBBwcHGBkZwcvLq8jr2dnZ8PHxQc2aNREdHQ1PT080btwYABAaGorz58/D2NgYISEhWLduHWrXrq2LZryiPO1at24dZDIZhBDIysrC8uXLYWys++8/r2sTABw7dgybN2/Gp59+ir59+5bqvbpS1nbFxMRg69ataNmyJeLi4mBra1sh2lUoKysL77//Pnr06IFFixZpK+wSladNkZGROHr0KMzNzfHXX39h1qxZcHV11Wb4BqU8Oaxfv36oW7cuAKBGjRrYtGmTXsQM6GeOKk/cI0eOhLm5OQDA2NgYe/fu1YuY/f398fTpUzg6OiI8PByzZ89GkyZNAAAHDx5EREQEjI2N0aBBA4wePVorMZc3bn3dr48dO4ZTp06hefPmuHbtGoYPH45+/foB0O++LilutfW1MEAZGRliwIABIjs7WwghhJeXl7hw4UKRZfz8/IS/v78QQoibN2+KMWPGCCGEeP78ufDy8pKWi4mJEenp6VqKvGTlaVdoaKgYMmSItNyQIUPE33//raXIlVOlTTExMeLixYti/Pjx4r///W+p3qsr5WlXWFiYOHnypPR40KBB4tq1a9oJ/DXK065C69atEwsXLhTr16/XSsyvU5425ebmio8++kjk5eUJIYSIj48XiYmJ2gvewJQnhwkhhK+vr/aCVTDUHFXev1V97estW7aI/Px8IYQQR48eFVOnThVCCPH48WMxdOhQ6TV3d3cRFRWl93ELob99vX//fvHw4UMhhBDXr18Xb775phBC//taWdxCqK+vdT+sWAahoaGoU6cOzMzMAADt27fH6dOniyxz+vRptGtX8NOTLi4uuHnzJtLS0nDmzBlUqVIFe/bswfbt23H9+nVUqVJF200oVnnaZWtri4yMDOTm5iI3NxdGRkaoV6+etpvwClXaVL9+fXTp0qVM79WV8rTL1dUVAwYMkB7n5+fD0tJSo/GqqjztAoCgoCC0b99eL/a9QuVp07Vr1yCEwA8//AA/Pz/8+eefsLOz00bYBqk8OQwA/v77b3z99dfYunUrLl++rDcx62OOKu/f6u3bt+Hv749t27bpVcxz5syBkZERgILcWHh8PnfuHFq1aiW91q5dO5w9e1bv4wb0d792d3dHnTp1AAD379+XRrr1va+VxQ2or68NclpFYmIirKyspMfW1tZITExUaZmHDx8iLCwMn332GWQyGSZMmAA7Ozt07txZa/ErU552NWzYECNHjsTHH38MY2NjdOvWDfb29lqLXRlV2qSJ92qaumI7efIkevToUeSPW5fK0667d+8iMjISc+fOxa1btzQVYqmVp02PHj1CaGgoNm/eDBsbG8yfPx+mpqZwd3fXVLgGrTw5zNraGvPmzYOrqysyMzMxYsQI+Pn5oWHDhjqPWRPvLa/ybvujjz6Cq6sr8vLyMG7cOFhZWaFjx46aCFVSmphzcnIQGBgIb29vAEBSUlKR91pZWellX78cNwC93q+zsrKwbds2XLp0CRs3bgRgGH1dXNyA+vraIEeOHRwckJ6eLj1OS0uDg4ODSstYW1ujZcuWMDU1hbGxMdzc3HDp0iWtxV6S8rTr1KlTCAkJwY4dO7Bt2zY8ePAAP//8s9ZiV0aVNmnivZqmjtiCg4MREhKCpUuXqju8MitPu06ePAkzMzP4+/vjn3/+wdWrV/Hdd99pKFLVladNVlZWcHJygo2NDQDgjTfe0Jt8oY/Kk8MASHO5LS0t0aJFC62Mshlqjirvtgv7WiaToUOHDggJCVF7jC9TNeacnBysXLkSn3zyCRo0aAAAsLe3L/Le9PR0vevr4uIG9Hu/trCwwIIFC7Bx40ZMmDABcrncIPq6uLgB9fW1QRbHbm5uePToEXJycgAAly9fRp8+fZCSkiKdnuvTpw+uXLkCALh16xaaN28Oa2trdO7cGQ8fPpTW9ejRIzRq1EjrbShOedoVFxcHR0dHaV2Ojo7SenRJlTaV9r36oDztAgpOLf/vf//Dp59+ioSEBOkz1bXytGv69Onw8vKCp6cn3njjDbi6umLixIlaiLpk5WlT27ZtkZKSgry8PAD6lS/0UXly2MWLF4ucur1//z7q16+vFzGX9r3aUJ647927h19++UV6rE99nZmZCW9vb0yaNAmtW7fG8ePHAQA9e/bE9evXIYQAAFy5cgW9evXSeMzljVuf9+vdu3dL/VmrVi0kJycjOztb7/taWdzq7GsjUbgFA3P+/HkcP34cdnZ2MDU1hZeXFzZs2ABbW1t4enoiKysLPj4+cHR0RExMDKZOnSpdER0QEICHDx/C1NQUWVlZWLx4sTS3RtfK2q6MjAysWLECdevWhbGxMR48eIBVq1bpxXzq17VJCIFdu3bh119/xRtvvIGhQ4eiZ8+eSt+rL8rarvDwcHh4eKB169YAgIyMDIwbN05vTtWX5/MCgOPHjyMgIAByuRzjxo3Du+++q8PWFChPm06ePIng4GDY2dnh8ePHWL58OSwsLHTcIv1V1hx269YtbN++Ha1atcKTJ09Qo0YNTJs2TS9i1tccVda44+PjsWbNGrRo0QJpaWnIzc3FkiVLtHJ3o9fF7OXlhTt37qBGjRoACvLj/v37ARTcQSE8PBwymQyNGjXS6h0Uyhq3Pu/Xu3btQnx8POrUqYN79+6hffv2GDVqFAD97mtlcauzrw22OCYiIiIiUjeDnFZBRERERKQJLI6JiIiIiBRYHBMRERERKbA4JiIiIiJSYHFMRERERKTA4piIiIiISIHFMRERERGRAotjIiIiIiIFFsdERERERAosjomIiIiIFFgcExEREREpsDgmIiIiIlJgcUxEREREpMDimIiIiIhIgcUxEREREZECi2MiIiIiIgUWx0RERERECiyOiYiIiIgUWBwTERERESmwOCYiIiIiUmBxTERERESkwOKYiIiIiEiBxTERERERkQKLYyIiIiIiBRbHREREREQKLI6JiIiIiBRYHBNp2IMHD/DOO+/oOgwiInoJ8zMVx0gIIXQdBFFFl5qaiqpVqwIADhw4gMDAQPzwww86joqIiF7Mz6+zePFi1K1bF7NmzdJwVKRLHDkm0gJVEy8REWkX8zO9jCPH9Fo//fQT/Pz80LZtW9jY2ODy5cto3rw5vLy8sHnzZkRERGDixIkYN24cAEAul2Pz5s24cuUKjIyM0L17d8ycORNGRka4c+cOvvjiC8jlcmRkZMDd3R2jRo0CAHh5eeHMmTOYNWsWQkNDcefOnSLrfVl6ejrWrVuHe/fuAQAaN26M+fPnw97eHtHR0VizZg2ysrKQl5eH6dOno3fv3rh69SqWL1+O58+fY+zYsTh9+jSePXsGX19fNG7cGAAQExOD1atXIysrC3K5HN27d8fs2bORnp6OlStX4unTp8jOzkazZs2wfPlyPHnyBJMmTUJSUhJGjx6NefPmYcOGDdi/fz+mTJmC8+fPIzg4GKdOncKjR4+wYsUKPH36FC1atICzszPu3buHixcvok+fPvDz80NQUBA2btyI9u3bw9fXVwufMBGpG/Nm+fKmp6cngoKC8OOPP8LMzAw1a9bEqlWrYG1tXaQ9OTk5mDJlCi5duoS5c+ciJCQE8fHxGDZsGDw9PV/pWwBo164d5s6dC1NTU3zwwQdSfjY2NsacOXMQFhaG9evX4+DBg3j8+DHWrVuH9u3bY+/evfD394e5uTnq1q2LoUOH4t1338XixYuRmJiIvLw8tGnTBkuXLlX/DkXaJYhU4OvrK3r16iVSU1NFdna26Nq1q1i2bJnIz88X4eHhws3NTcjlciGEEDt37hQeHh4iNzdX5OTkiFGjRomgoCAhhBChoaEiNDRUCCFETk6OGDhwoIiKipK207dvX+Ht7S2EECIsLKzIel+2bNkysXjxYiGEEHl5eWLq1KkiODhYyOVy8fbbb4v9+/cLIYSIjo4W7dq1E/fv3xdCCBEcHCxatWol/vrrLyGEEN7e3mL58uVCCCFyc3PFoEGDxIEDB4QQQqSmpoqePXsKIYRITk6W2iGEEIsWLRI///yzEEKIiIgI0b59e5GZmSmEECIxMVGKTQghnJ2dRWxsrBBCiP3794vx48dLr+Xk5IhOnTqJf/75R3pu6tSpIj8//3UfCxHpMebNsufNv//+W3Tq1EkkJiYKIYRYv369WLp0qdK+dnZ2Fhs2bJC22b17d3Hu3DkhhBDbt28XH3zwgcjNzRW5ubli8uTJYvv27UXeW5ifY2NjhbOzszh69KgQQgh/f38xefLkIvH7+vpKj/ft2ydWrFgh9YO7u7vSGMlwcFoFqczV1RU2NjYwMzNDw4YN4ezsDCMjI7i4uCAjIwOJiYkAgMDAQIwYMQIymQympqYYOHAgDh06BABo2LAhfv31V4wePRqTJ09GQkICbty4UWQ7PXv2BIBX1vui/Px8BAUFwd3dHQBgbGyMxYsXo2nTpggLC8ODBw8wdOhQaZtt27aVYgCAKlWqoEOHDtJ2Hjx4AAAIDQ1FTEwMhgwZAgCwsbHBli1bAADVqlXDo0ePMGbMGHh4eODSpUu4fv06AKB58+aoV68e/vjjDwDAsWPHVL7Iw9TUFIMHD0ZQUBAA4MaNG3BxcYGRkZFK7yci/cW8Wba8GRgYiH79+sHe3h4AMGTIEBw+fBiihJPdgwcPBgDY2tqiV69eOHr0KADg4MGDGD58OGQyGWQyGYYNG4YDBw6U+Ln16tXrlXYWx9bWFv/88w/CwsIgk8mwb9++EtdLhsFE1wGQ4bCyspL+b2JiIj02MSnYjeRyOQAgLi4Oe/bskZJPenq6NKdr/fr1SE1NRUBAAGQyGTw8PJCVlVVkO4WnzczNzYus90VJSUnIycmREicANGrUCAAQEhKCqlWrSnEBgL29PeLj41/ZRuF2CrcRHx//ynvfeOMNAAXJ+qeffkJQUBBsbW2xbds2PHz4UFpu+PDhCAoKwrvvvosLFy5gzJgxyrryFcOHD8eHH36IZcuW4eDBgxg5cqTK7yUi/cW8Wba8GRcXh3v37sHDwwMAkJubi+rVqyM5OblI/C96ce6wra0tbt++La3Lzs5OabuK82J/FteXhQYPHozc3Fx8/vnnSElJwcSJEzF27NgS1036j8UxqV3t2rUxffp0DBo0CEDBaEVqaioA4OrVqxg7dixkMhmA4hO4Kuzt7WFmZoakpCQ0adIEQEGCNjY2Rq1atZCamorc3FwpWSclJUlz40pS3Hvv3buHunXr4urVq3B1dYWtrS2AgmT9oiFDhmDz5s0IDg5Go0aNpDaqwtXVFQ4ODjh58iSio6OlNhFR5cC8WTRv1q5dG/Xr14e3t7e0bFJSktLCGACePXuGevXqAQCSk5Ph6OgorSs5ObnIemrWrPnadqkiKSkJ77zzDoYNG4YbN25g0qRJcHJyQpcuXdSyftINTqsgtRsxYgSOHDmCvLw8AAUjB1999RUAoEGDBggLCwMAPHnyBLdu3SrTNoyNjTF8+HBplCU/Px+ffvopnj59irZt26JBgwY4cuQIACA2NhZhYWHS6cKSvPzelJQUzJkzBzKZDA0bNsTNmzeRk5OD3NxcXLx4sch7q1evji5dumDBggUYNmyY0m1YWVkhMzMTADBr1izpYDFs2DCsW7cO3bt3L32HEJFBY94smjdHjBiBM2fO4NmzZwCAyMhITJ8+vcQ4jh8/DqCgMD579qw0zWLEiBE4dOgQ8vLykJ+fj0OHDklTS0qrMH9nZGRg3rx5CAgIwJkzZwAAzs7OqFatGvLz88u0btIfvFsFvdbhw4exZcsWZGdnY+bMmUhKSsJ3332H6tWrY926ddi9ezdOnjyJtm3bwt/fH1ZWVvjyyy9x6dIlmJubo1atWli9ejUsLS1x7949LFiwAKampnByckJ4eDjkcjm8vb0RGBiI3377DU5OTti+fTt8fHyKrLdw5KFQeno61q5di8jISAghMGTIEOkK7cIrpzMzM4tcdX337l3MmzcPkZGRGDFiBN577z0sXLgQT58+xciRI7Fw4cIiV13n5+djzpw56NSpEzIyMrBgwQJERkaiWbNmyMvLQ2hoKD788ENMmjQJQMGcOX9/f2n+MADpaui2bdti27ZtsLCwwMSJE2Fubo7WrVtj2bJlAIBHjx7hrbfewpkzZ+Dg4KCVz5aININ5s3x5EyiYKxwQEAALCwuYmppi2bJlSkeyXVxcsHTpUpw9exaPHz/GsGHDMHXqVAAFI+1bt27FP//8A6D4u1UU5udZs2YhLCwM/fr1w/LlyzF9+nRERkZi0KBB2LBhA65cuYIlS5bA2toaH3zwAerXr48tW7ZACIG0tDR0794d8+bNU+OeRLrA4phIT6SmpmLp0qXYvn27rkMhIjIoLi4uOHXqlDStgqg8OK2CSMfOnDmDpKQkHDlyhD9jSkREpGMsjol0LCYmBmPHjsXZs2fx1ltv6TocIiKDkZOTI93RYu7cua+9CwWRKjitgoiIiIhIgSPHREREREQKGrnPcULC8zK/186uCpKTM9QYTcXAfnkV+6R47JdX6UufODraaGzdFS3vMibVMCbVMKbX07d4APXEVJa8q3cjxyYmqv9wQmXCfnkV+6R47JdXsU9Kpo/9w5hUw5hUw5heT9/iAXQXk8H/Qt7RyBOlWn6wEy94IiLSB8ryN/M0EemS3o0cExERERHpisGPHJcWRyqIiIiISBmOHBMRERERKbA4JiIiIiJSqHTTKoiISLtKe+E0EZEu6V1x/HP4EWSkZ7/yPOcEExEREZGmcVoFEREREZGC3o0cExFR5XY08gSqxJsXexaxODyzSETqxJFjIiIiIiIFFsdERERERAosjomIiIiIFAxmzjFvBUREREREmmYwxbGm8WeliYiIiIjFMRERqQXP8BFRRcA5x0RERERECiyOiYiIiIgUOK3iNTgXmYiIiKjy4MgxEREREZECR46JiKhUeOEdEVVkHDkmIiIiIlLgyHEZcS4yEVUUP4cfQUZ69ivPM59VXEHnIot9fnhPJy1HQqR/WBwTEVGxDGX6BAcriEidWByT2nFEgoiIiAwV5xwTERERESlw5LgC0PRILUeCicgQcboFEZUFi2MtYIImIiIiMgwsjomIiEpJXWfU9O3MnL7FQ6QLLI7VzFCu7iYiqqx4No+ISsLiWIeUJeibMcmvPGdqaoIG+e1KtX6OABARqa64nFzagllXeVeftmtlZY4329fV6HaJNInFMVUYxSVpfhEgIk24l/dXsc83kXXUciTaoaz4JqqIWBzrUHEjxNrAJEdEZJhezt9WVuZIL+bXDZUtT0Svx+KYykxdSbe06+FoMBEREWkKi+PXUDa627yBXamWVwdlp/GUqein9143YvLisqpSVnhz/jZR5fTiPOQq8ebIeE3OUaayjeCWNmdqclpc0LnIYo8XzN+kTIUtjktb1JLmVcSDg6EXzYYeP1UupR18UEe+f3GbpqYmkMtzS1y+tHORlS0fdE7FAA2MJo8D+naMeV08LxfszLv6o8IWx6RcZbuQpDT0LbkSkfbo05k/5mn9y8ccTKg8Kl1xrKuL4AyBukY8KlPyVhdDSbqlOfVpKG1SxtDjNwQl5WNVRmk1sV1DxXxceobyN65PcepTLJpkJIQQug6CiIiIiEgfGOs6ACIiIiIifcHimIiIiIhIgcUxEREREZECi2MiIiIiIgUWx0RERERECiyOiYiIiIgUWBwTERERESno7EdALly4gBMnTsDBwQFGRkbw8vIq8np2djZ8fHxQs2ZNREdHw9PTE40bN9ZRtNrxuj4BgGPHjmHz5s349NNP0bdvXx1EqX2v6xd/f388ffoUjo6OCA8Px+zZs9GkSRMdRasdr+uTY8eO4dSpU2jevDmuXbuG4cOHo1+/fjqKVntU+RsCgEOHDmHBggW4fPkyrKystByl5pUnvx48eBAREREwNjZGgwYNMHr0aADAgwcPsHPnTjRs2BAPHz7EokWLVO67ssZz9epV7N27Fy1btkRUVBRcXV0xcuRIAMCKFSsQFRUlrWPZsmVwcXHRSh/169cPdevWBQDUqFEDmzZtKncflSemkJAQrF69Gvb29gCAxMREDBo0CLNmzdJ4PwHKj0vK3puSkoJNmzahfv36iI6Oxty5c1G9enWNxxQTE4OtW7eiZcuWiIuLg62trfTebdu24dKlS9L7p02bhu7du2s8JgAYOXIkzM3NAQDGxsbYu3cvAN3104MHDzBx4kTUrl0bAJCWlgYXFxesX79e4/1U0vFcE7lJKaEDGRkZYsCAASI7O1sIIYSXl5e4cOFCkWX8/PyEv7+/EEKImzdvijFjxmg9Tm1SpU9iYmLExYsXxfjx48V///tfXYSpdar0y5YtW0R+fr4QQoijR4+KqVOnaj1ObVKlT/bv3y8ePnwohBDi+vXr4s0339R6nNqmSr8IIcTdu3fF5s2bhbOzs0hLS9N2mBpXnvz6+PFjMXToUOnvyd3dXURFRQkhhJg8ebIICwsTQgjx/fffiy1btmg8nj/++EPaZk5OjujQoYNITEwUQgjh6+urWoeoOaaStl3WPipvTJGRkeL69evSckuXLhUPHjwoMVZ1xaTsuFTSe5cvXy6OHj0qhBDi1KlTYv78+VqJKSwsTJw8eVJ6PGjQIHHt2jUhhO76qaRt66qfkpKSxPnz54vE99dff5UYq7piUnY810RuKolOplWEhoaiTp06MDMzAwC0b98ep0+fLrLM6dOn0a5dOwCAi4sLbt68ibS0NG2HqjWq9En9+vXRpUsXHUSnO6r0y5w5c2BkZAQAyM/PR5UqVbQdplap0ifu7u6oU6cOAOD+/fsVfiQdUK1fMjMz8c0332DmzJk6iFA7ypNfz507h1atWkl/T+3atcPZs2chl8sREhKCNm3aSOs8c+aMxuPp378/XF1dpeVkMhlMTU0BAOnp6di1axf8/f2xb98+5Oaq/lPT5T0G/f333/j666+xdetWXL58GQDK1Ufljalx48Zo2bIlAODp06fIzs6WRrY13U/KjkslvffMmTNSOzTRT8picnV1xYABA6TH+fn5sLS0lB7v2rULu3fvhr+/PzIzM7USEwDcvn0b/v7+2LZtW5H36aqf7Ozs0K1bNwBATk4OwsPD0aFDB+l1TfaTsuO5JnJTSXQyrSIxMbHIkLe1tTUSExNVWsba2lprcWqTKn1SGZWmX3JychAYGAhvb29thacTqvZJVlaWdAps48aN2gxRJ1Tply1btmDGjBlScq6IypNfk5KSijxvZWWFxMREJCcnw8LCQjowlSY/qSvfBwQEYNq0abCxsQEADBkyBC4uLjAxMcGGDRvg5+en8pee8sY0b948uLq6IjMzEyNGjICfnx8sLS3L3EfqiKnQv//9b+l0M6D5firLe198zdraGs+ePUNubi5MTF5fkqjrWHny5En06NFDGjgYOHAg6tatiypVqiAgIABr1qzB2rVrVVpXeWP66KOP4Orqiry8PIwbNw5WVlbo2LGjXvTTkSNH8M4770iPtdVPLx/PNZGbSqKTkWMHBwekp6dLj9PS0uDg4FDqZSqSytZeVanaLzk5OVi5ciU++eQTNGjQQJshap2qfWJhYYEFCxZg48aNmDBhAuRyuTbD1LrX9cvjx4+RmpqK3377Df7+/gCAPXv24Nq1a1qPVZPKk1/t7e2LPJ+eng4HBwfY2dkhKysLQgil69REPIUOHz6MjIwMTJw4UXquVatWUpHQpUsXBAcHqxSPOmIqHM22tLREixYtcPny5XL1kTpiAoof5dN0P5XlvS++lpaWhmrVqqlU8JU3pkLBwcEICQnB0qVLpeeaNWsmjVJqs5+A/9+fZDIZOnTogJCQkFfWq4t+AoDff/+9SHGsjX4q7niuidxUEp0Ux25ubnj06BFycnIAAJcvX0afPn2QkpIinbbq06cPrly5AgC4desWmjdvXmFHjQHV+qQyUqVfMjMz4e3tjUmTJqF169Y4fvy4LkPWOFX6ZPfu3VKyqFWrFpKTk5Gdna2zmLXhdf1Su3ZtrF+/Hp6envD09AQATJo0STodV1GUJ7/27NkT169fl/adK1euoFevXjA1NUXnzp2lLxKXL19G7969NR4PAPzyyy9ITEzEjBkzcOvWLeniMh8fH2kb9+/fL9WX4vLEdPHiRZw9e7bItuvXr1+uPlJHPwGvjvIBmu+n0r4XAHr37i21QxP9VJLTp0/jf//7Hz799FMkJCRIceiqn+7du4dffvmlyLbr168PQLf9BAAhISFwc3OTpjIBmu8nZcdzTeSmkhiJwi1p2fnz53H8+HHY2dnB1NQUXl5e2LBhA2xtbeHp6YmsrCz4+PjA0dERMTExmDp1aoW/W8Xr+kQIgV27duHXX3/FG2+8gaFDh6Jnz566DlvjXtcvXl5euHPnDmrUqAEAyMjIwP79+3UctWa9rk927dqF+Ph41KlTB/fu3UP79u0xatQoXYetca/rF6Dg9Nx//vMffPnll5gxYwZGjx6NmjVr6jhy9SpPfj148CDCw8Mhk8nQqFGjIleE79ixA/Xr18fjx4+xePFila8IL2s8f/zxBxYtWiTNp01JScGyZcvQuXNnLFmyBA4ODrCwsEBUVBSWLFlSqiv5yxrTrVu3sH37drRq1QpPnjxBjRo1MG3atHL3UXk/NwDw9PTEjh07ihQzmu6nko5Lxb0XKPgcN27ciDp16iA2Nhbz5s3TSkzh4eHw8PBA69atARQcK8aNGwd3d3ds2rQJmZmZcHBwwO3btzF79uxS1RxljSk+Ph5r1qxBixYtkJaWhtzcXCxZsgTGxsY666dCc+fOxbJly6S7oADQeD+VdDzXRG5SRmfFMRERERGRvuGPgBARERERKbA4JiIiIiJSYHFMRERERKTA4piIiIiISIHFMRERERGRAotjIiIiIiIFFsdERERERAosjomIiIiIFFgcExEREREpsDgmIiIiIlJgcUxEREREpMDimIiIiIhIgcUxEREREZECi2MiIiIiIgUWx0RERERECiyOiYiIiIgUWBwTERERESmwOCYiIiIiUmBxTERERESkwOKYiIiIiEiBxTERERERkQKLYyIiIiIiBRbHREREREQKLI6JiIiIiBRYHBMRERERKbA4JiIiIiJSYHFMRERUgWzcuBHu7u4YMmQITp06pbM4Tp06hYEDB8LDw0Ol5desWYMOHTrgwIEDAIDs7Gz07t0bmZmZmgyzVIYMGYL79+/rOgzSMBbHRBrm4eEhJXsiIk2KiYlBQEAA/vOf/2Dbtm2wtLRU6/oPHDigcrHbv39/eHp6qrzu5cuXo0WLFtJjc3NzHD58WO1tKI+AgAA0bNhQ12GQhpnoOgAiIiJSj7i4ONjZ2cHMzAyNGjVCo0aNdB1SuVStWlXXIRShb/GQZrA4phL99NNP8PPzQ9u2bWFjY4PLly+jefPm8PLywubNmxEREYGJEydi3LhxAAC5XI7NmzfjypUrMDIyQvfu3TFz5kwYGRnhzp07+OKLLyCXy5GRkQF3d3eMGjUKAODl5YUzZ85g1qxZCA0NxZ07d4qst7i49u/fD0tLS1hYWGDhwoU4evQo/Pz80KxZM3z55ZfIysrCJ598AiEEPD094efnh+rVq8PV1RXBwcGws7PDmjVrsGXLFly7dg1vv/02PvnkE+Tk5GDKlCm4dOkSVqxYgf/+97+IjY3F559/jmvXruHEiRMQQmDXrl2wt7cHAISHh2PdunUwMjKCTCbDihUr0KRJE2zatAkRERFISEhAYGAgpkyZgtOnT+PIkSMYP3487t69i/DwcOTk5CAzMxO1atXCmjVr4OTkhClTpuDZs2fYtWsXXFxctPOBE5FK9DE3Xr16FZ9//jkSEhLg4eGBAQMGICoq6pV8869//QsDBw5Uuk0AOHToEPbt2wcLCwsAwPTp0yGTyeDv74+nT5/Cw8MDzs7OWL58OX766SccPXoURkZGAApGgJs2bapSP167dg3e3t4wNzdHmzZtIISQXps3bx5OnDiBb775Bu3atVNbXn75s7t27RqqV6+O7du3w9zcHE+fPsXixYuRnZ2N3Nxc9O3bF56enli/fj1+/fVXLF26FO7u7gCAoKAg/PjjjzA1NYWdnR1Wrlwprevf//433n77bTx//hwRERFo1aoVfHx8SrurkS4Iotfw9fUVvXr1EqmpqSI7O1t07dpVLFu2TOTn54vw8HDh5uYm5HK5EEKInTt3Cg8PD5GbmytycnLEqFGjRFBQkBBCiNDQUBEaGiqEECInJ0cMHDhQREVFSdvp27ev8Pb2FkIIERYWVmS9L0pLSxOdOnUS2dnZQgghvvvuO7F//34hhBBTp04Vu3btkpZds2aNiImJEUIIsX//fuHm5iYePnwo8vPzxbBhw8RHH30ksrOzxdOnT0WrVq1EfHy89F5nZ2fx7bffCiGE2LNnj+jVq5e4cuWKtB0/Pz8hhBCpqamic+fO4sKFC0IIIf7880/x1ltviby8PCGEEOPHj5fiKzR+/HgxadIkkZubK+7duyd+/vlnsWbNGrFs2TJpmd27d4uLFy+q9BkRkfbpW24UQojg4GDRt2/fIs8Vl29K2uY///wjunXrJhITE4UQQvz2229i0aJFQoiCPDp+/Pgi6//3v/8t5ePg4GAxZswY6bXili+UnZ0tevXqJQ4fPiyEEOLGjRuidevWRfJl3759RXBwsPRYXXnZ19dX9OjRQ6SkpIi8vDwxePBgKQ4fHx9pPenp6WL06NFF+rIwvr/++kt06dJF6qcdO3aICRMmSMsuWrRIDBs2TGRnZ4usrCzRqVMncfny5WL7gvQL5xyTSlxdXWFjYwMzMzM0bNgQzs7OMDIygouLCzIyMpCYmAgACAwMxIgRIyCTyWBqaoqBAwfi0KFDAICGDRvi119/xejRozF58mQkJCTgxo0bRbbTs2dPAHhlvS+SyWQACr6xZ2ZmYty4cXj33XcBAMOHD8fBgwcBFIzUPHr0CPXr15fe27hxY9SpUwdGRkZo2rQpnJycYGZmBgcHB9jb2+PBgwdFttWtWzcAgLOzM7KysuDm5ibFFxsbCwD4888/UaVKFXTt2hUA0KdPHzx9+hRhYWEl9mnv3r0hk8ng5OSE999/H8OGDcPvv/+O7OxsAEBISAg6d+5c4jqISLf0KTeW5OV8U9I2Dxw4gF69ekkjsAMGDMCYMWOUrrtp06aYNm0axo4di02bNuH69esqxRQaGorExEQMGjQIANCiRQuVpoGoKy+3bdsW1apVg7GxMZo1ayblf1tbW5w7dw537txBlSpV8O233xYbR1BQEPr06SP107/+9S8EBwfj0aNH0jKdO3eGmZkZzM3N0bBhw1eOMaSfOK2CVGJlZSX938TERHpsYlKwC8nlcgAF89327NkjXYCWnp4uzdFav349UlNTERAQAJlMBg8PD2RlZRXZjrW1NYCCCzFeXO+LLCwssG/fPvj5+WHr1q3o06cP5s+fD3t7e/Tr1w8rVqzA1atX8eTJE+mA8rp2FD5+eXuFr8tkMqXLxsXF4dmzZ0UuUrG3t0dKSkoxPfn/bGxsijxu06YNatSogVOnTsHJyQnNmjWTTlMSkX7Sp9xYkpfzTUnbjIuLKzKVy8TEBG3bti12vc+fP8fUqVPx+eefY+DAgXjw4AH69++vUkwJCQmoWrWqNOABFBSmr6OuvFzYp0BBvxa+d8qUKbC0tMQnn3wCmUyGadOmSQX8i17uJzs7O+n5OnXqlLgN0m8sjkmtateujenTp0uJJD8/H6mpqQAK5sONHTtWSoRlTRJyuRwODg7YuHEjnj9/jsWLF8PHxwc+Pj4wMzPDwIEDERQUhGfPnmH58uXqaVgJateujVq1auGHH36QnktLS4OZmVmp1zVs2DAcPHgQTk5O0pw2IjJ82siNpVHSNmvXro2kpCTpcW5uLu7evYvmzZu/sp6oqCikpaVJAxG5ubkqx+Do6IjU1FTk5uZKXyZeN6igqvLk5cTERHh4eMDDwwMXLlzA1KlT0apVKzRo0OCVbbzYT8nJyQCAWrVqqaUNpDucVkFqNWLECBw5cgR5eXkACk4lfvXVVwCABg0aSKe0njx5glu3bpVpG/Hx8VLRa2NjgxYtWkjbAwqmVhw9ehRCCJVGIcqrb9++SE5OxtWrVwEAGRkZmDBhAtLS0gAUjHJkZmYiOjr6tRdjDB06FOfPn8ft27fRrFkzjcdORNqhjdxYGiVtc8SIETh79qxU+B07dkwa8S7MZwAwa9Ys1KlTByYmJlL+O3funMoxuLm5wcHBAceOHQMARERE4N69e+VvHF6fl0tSeEElUDBtxtTUtMiFgoVe7qfAwEB06dJFGjUmw8WRYyrR4cOHERgYiOzsbPz4449ISkqS7r7QuHFj7N69GwAwd+5c+Pv7Y8qUKfjyyy8xZswYmJubo1atWli9ejUAYMGCBViwYAFGjRoFJycn1KtXD/7+/qhduzYCAwORkJCAtWvXYvv27VIRWbjeF4tce3t7VKtWDWPGjIGxsTHMzc3x2WefSa+3b98e1apVK3Ia7OLFi9JV1r6+vqhZsybOnTsHc3NzNG/eHOfPn5e2v2nTJqxdu1ba/vr167F27VokJCRgxYoV6N27t9Qne/bswaRJk+Dv7w8fHx8IISCEwKxZs4rMQ9u4cSMCAwMxf/58bNiwQerDZ8+eYdKkSVKctWrVQocOHV6ZDkJE+kUfc+PVq1elXOXh4YFly5bh4MGDxeabkrbZtWtXLFy4ENOnT4eZmRns7OyknNilSxd89dVXGD16NFq3bo3q1atj2bJl+PTTT9GsWTPpHsCTJ0/GuHHjpLy7Zs2aV87kmZmZYdu2bVi5ciV+/PFHNGvWDG3btoW/vz+qVauGY8eOSW3//PPPsXnzZqnt5cnLL392MplMOh40atQIAwcOxGeffQaZTIa0tDTMmTMHDRs2xPr166W+tLe3R58+fbBw4UJMmzZNulvFpk2bAAB79uwpcoy5deuW9N7CPib9ZSSK+zpEZOA+/PBD7Ny5s0xTG3Rt3rx5WLx4MRwdHXUdChERUaXDkWOqMKKjo5GcnAwbGxvUr1/foArjlJQUhIaGom3btpDL5SyMiYiIdITFMVUYz58/x7x58+Do6Cid2jIUOTk5WLlyJRwcHODt7a3rcIiIiCotTqsgIiIiIlLg3SqIiIiIiBQ0Mq0iIeF5sc/b2VVBcnKGJjZZLvoYF2NSnT7GpY8xAfoZlz7GBGgmLkdHm9cvVEbK8q6q9PVz0LTK2m6g8ra9srYbqJxtL0ve1erIsYmJ7PUL6YA+xsWYVKePceljTIB+xqWPMQH6G5emVLb2Fqqs7QYqb9sra7uByt320uAFeRXY0cgTxT4/2OktLUdCRKR9zIFEVBacc0xEREREpMDimIiIiIhIgdMqSMJTkERERFTZceSYiIiIiEiBI8dEREQo/uwZz5wRVT4cOSYiIiIiUmBxTERERESkwOKYiIiIiEiBc44rIWV3pSAi0me8ow4RaQOL4wpAV8UuD1RERERU0bA4Jq1hMU1ERET6jnOOiYiIiIgUOHJMasc5zURERGSoWByT3uI0DCIyNMxbRIaPxbEeOhp5AlXizZGRnl3k+YqaXIPORRb7vGldLQdCRJXCiwVscblW2bJEVDmwODYg+pakb8YkF/t88wZ2pVrPvby/il8PSrceIiIiovJicUxERKRhnG5BZDhYHBMRkV7Rt7NkRFS5sDjWIUM5ABTG+bq5eYZE2Tzn4T2dtBwJEemL4qaKlXaaWGlxRJlI/7A4Jr2lbE7zYNavREREpCEsjkmirgvsiIiIiAwVi2MiIjJohjJFjYgMA4tjIiLSK/p0FktZLMrwTBuR4WNxTK9VeHAwNTWBXJ6r8vKa8vIoUUkXCvKiFiL9ten0T7oOQW/xQj0i3WFxXEalOY3HZGY4eBcLIiKiyo3FsRaoaz5caU816tOpSXV6uV2FI9qG3i4iKhlzoHIcaSZSHxbHRESkUcrOyJDmsWgmKj0WxxWApuf4EhFVJC/mTFWvpSCiyoPFMVVoyi74aSLrWKr1cC4yEWlC6Qc3eNs6Ik1jcUyV0r28v4p9vrRFs6axKCeiF1WmedREusLimCoMfZpe8uPxm0gv5vZyLGqpIuPcYsMpXoPORcLKyvyVPKUsR5V27jK/2JMhY3FMRFTJqatQApoW+6yyMzWViaa/vJe2KL+X9xdMM00gzys63/po5N1SbVddU9dKgxcZkqaxOK6E9GmElYgqDhbB+of5nqj0WBzroZsxybyC2kAoG8EwQ6tiny/tqUblxYZ6Tk1yBIZKomx/Na2r5UBegwWg5mm6j4vb1zgFg3SlwhbH6jroq+MHPJi4DUdpR76aQz3zCNX1QzHKFB54Xj51rqzIKU0Rz7mFRERUkehdcVzaora0RUVxy1eJN0dGMRdPAYZzcQXphrL9w7WqetajjPIRPWXzBYufC6p8u5obsX75b7Dw709do9XqKtZ5UaVy/MJfcanrs1U20BB0TvV1KJvPrMzgUv5p8swZKaN3xTEREekHziEmbVHHvqbsi/HL637dtEX5Q9XWU2hen1HFPq/pM9ilHTRUR9Gv6QFM+cPiB3K0PShhJIQQWt0iEREREZGeMtZ1AERERERE+oLFMRERERGRAotjIiIiIiIFFsdERERERAosjomIiIiIFFgcExEREREplPk+xxcuXMCJEyfg4OAAIyMjeHl5vbLMsWPHsHnzZnz66afo27fva9+bkpKCTZs2oX79+oiOjsbcuXNRvXp1rcQVExODrVu3omXLloiLi4Otra303m3btuHSpUvS+6dNm4bu3btrPCYAGDlyJMzNzQEAxsbG2Lt3LwDd9tWDBw8wceJE1K5dGwCQlpYGFxcXrF+/XuN95e/vj6dPn8LR0RHh4eGYPXs2mjRpAgA4ePAgIiIiYGxsjAYNGmD06NFSvDt37kTDhg3x8OFDLFq0CFZWVmrtK2VxXb16FXv37kXLli0RFRUFV1dXjBw5EgCwYsUKREVFSetYtmwZXFxctNJX/fr1Q926BT+PV6NGDWzatEnnfRUSEoLVq1fD3t4eAJCYmIhBgwZh1qxZGu+rY8eO4dSpU2jevDmuXbuG4cOHo1+/fgA0u19pw+vanp2dDR8fH9SsWRPR0dHw9PRE48aNASjfTwxFedoeGhqK8+fPw9jYGCEhIVi3bp2U8/RdWdtd0t+goSjPZ75u3TrIZDIIIZCVlYXly5fD2NgwxhDL0+6NGzfC1NQU2dnZcHR0xKRJk3TRBP0iyiAjI0MMGDBAZGdnCyGE8PLyEhcuXCiyTExMjLh48aIYP368+O9//6vSe5cvXy6OHj0qhBDi1KlTYv78+VqLKywsTJw8eVJ6PGjQIHHt2jUhhBC+vr6likNdMZW0bV32VVJSkjh//nyRGP/6668S41VXTFu2bBH5+flCCCGOHj0qpk6dKoQQ4vHjx2Lo0KHSa+7u7iIqKkoIIcTkyZNFWFiYEEKI77//XmzZskVrcf3xxx/StnNyckSHDh1EYmKiEEJ3fVXStnXZV5GRkeL69evSckuXLhUPHjwoMV51xbR//37x8OFDIYQQ169fF2+++aYQQrP7lTao0nY/Pz/h7+8vhBDi5s2bYsyYMdJr5el3XStP258/fy68vLyk5WJiYkR6erqWIi+f8rS7pL9BQ1CetoeGhoohQ4ZIyw0ZMkT8/fffWoq8fMrT7pMnT4pp06ZJy40YMUKEh4drKXL9VaavRKGhoahTpw7MzMwAAO3bt8fp06eLLFO/fn106dKlVO89c+YM2rVrJz1/5swZrcXl6uqKAQMGSI/z8/NhaWkpPd61axd2794Nf39/ZGZmaiUmALh9+zb8/f2xbdu2Iu/TZV/Z2dmhW7duAICcnByEh4ejQ4cO0uua7Ks5c+bAyMgIQMFnVKVKFQDAuXPn0KpVK+m1du3a4ezZs5DL5QgJCUGbNm2kdWqir5TF1b9/f7i6ukrLyWQymJqaAgDS09Oxa9cu+Pv7Y9++fcjNVf6LTeqMCQD+/vtvfP3119i6dSsuX74MADrvq8aNG6Nly5YAgKdPnyI7O1satdR0X7m7u6NOnToAgPv370sj7Jrcr7RBlbafPn1ayiUuLi64efMm0tLSABS/nxiK8rT9zJkzqFKlCvbs2YPt27fj+vXrRf5+9Fl52l3S36AhKE/bbW1tkZGRgdzcXOTm5sLIyAj16tXTdhPKpDztjo6OlnIfANSrVw/BwcFai11flWlaRWJiYpHTh9bW1khMTCz3e198zdraGs+ePUNubi5MTFQLszxxvejkyZPo0aOHdIAcOHAg6tatiypVqiAgIABr1qzB2rVrtRLTRx99BFdXV+Tl5WHcuHGwsrJCx44d9aavjhw5gnfeeUd6rK2+ysnJQWBgILy9vQEASUlJRd5rZWWFxMREJCcnw8LCQipuytLO8sT1ooCAAEybNg02NjYAgCFDhsDFxQUmJibYsGED/Pz8MHPmTK3ENG/ePLi6uiIzMxMjRoyAn58fLC0t9aav/v3vf0vTFwDt9FVWVpY0LWjjxo0ANLtfaYMqbVe2jLW1dbH7ScOGDbUWf3mUp+0PHz5EWFgYPvvsM8hkMkyYMAF2dnbo3Lmz1uIvq/J+5oVe/hs0BOVpe8OGDTFy5Eh8/PHHMDY2Rrdu3aTpJfquPO1u37491q9fj/z8fOTl5eHmzZtS7VOZlWnk2MHBAenp6dLjtLQ0ODg4lPu9L76WlpaGatWqqVzslTeuQsHBwQgJCcHSpUul55o1ayaNGnTp0qVU36rKG1PhqKNMJkOHDh0QEhLyynp11VcA8PvvvxcpjrXRVzk5OVi5ciU++eQTNGjQAABgb29f5L3p6elwcHCAnZ0dsrKyIBS/kl6WdpYnrkKHDx9GRkYGJk6cKD3XqlUr6TPTZl8B/79fWVpaokWLFrh8+bLe9FVxZyO00VcWFhZYsGABNm7ciAkTJkAul2t0v9IGVdpe0jLF7SeGojxtt7a2RsuWLWFqagpjY2O4ubkVuZZCn5X3MweK/xs0BOVp+6lTpxASEoIdO3Zg27ZtePDgAX7++WetxV4e5Wl3+/btMWnSJOzYsQMBAQFo06ZNkZHkyqpMxbGbmxsePXqEnJwcAMDly5fRp08fpKSkSKfjSvteAOjduzeuXLkiPd+7d2+txQUUnHb43//+h08//RQJCQlSLD4+PtIy9+/ff+VgrqmY7t27h19++aXItuvXrw9A930FACEhIXBzc5OmCQCa76vMzEx4e3tj0qRJaN26NY4fPw4A6NmzJ65fvy4VK1euXEGvXr1gamqKzp0749q1a9I6NdFXyuICgF9++QWJiYmYMWMGbt26JV1Ypqu+unjxIs6ePVtk2/Xr19eLvgJePRsBaL6vdu/eLe07tWrVQnJyMrKzszW6X2mDKm3v06ePlEtu3bqF5s2bw9raWul+YijK0/bOnTvj4cOH0roePXqERo0aab0NZVGedhcq7m/QEJSn7XFxcXB0dJTW5ejoKK1H35Wn3dnZ2XB2dsasWbMwceJEpKSkFJliWlkZicKsX0rnz5/H8ePHYWdnB1NTU3h5eWHDhg2wtbWFp6cnhBDYtWsXfv31V7zxxhsYOnQoevbsqfS9QMEdGDZu3Ig6deogNjYW8+bNK/UdGMoaV3h4ODw8PNC6dWsAQEZGBsaNGwd3d3ds2rQJmZmZcHBwwO3btzF79mzpKk9NxhQfH481a9agRYsWSEtLQ25uLpYsWQJjY2Od9lWhuXPnYtmyZUVOPWm6r7y8vHDnzh3UqFEDQMHntH//fgAFdxUIDw+HTCZDo0aNitxVYMeOHahfvz4eP36MxYsXl/quAmWN648//sCiRYukeXwpKSlYtmwZOnfujCVLlsDBwQEWFhaIiorCkiVLSvUZljWmW7duYfv27WjVqhWePHmCGjVqYNq0aTrvq0Kenp7YsWNHkS9dmu6rXbt2IT4+HnXq1MG9e/fQvn17jBo1CoBm9ytteF3bs7Ky4OPjA0dHR8TExGDq1Klo3LhxifuJoShr24GCaVAPHz6EqakpsrKysHjxYmkajb4rT7uB4v8GDUVZ256RkYEVK1agbt26MP4/9u48Lqqy/R/4B4YBFdxYxD2X3BVRSzMzcXnKfW0zQXPDJbRSE3Env6mY2yOYiZlZWWopkFi5Q6QiriA9LgkoqIEygAgIDHD//nA4P9EZZGCGWfi8X69eOWfOct1nuebinvucsbTE7du34evrazJjzcvb7rS0NMyePRs9evRAQUEBXn31VZMYPqRv5S6OiYiIiIjMjWk8wI+IiIiIqBKwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTEZn9uzZ6NSpE86cOQMAuH37NgYPHmzgqIiIiKgqYHFMRmfTpk1wcnKSXjdu3Bi7d+82YERERMbHw8MD+/fvr/B6bt++jTZt2uggIiLzwOKYTEKtWrUMHQIRERFVAVaGDoDMy549e7B161Z07twZtra2uHz5MmrVqoWvvvoKy5cvR2pqKvLy8tCqVSssWbIEVlaPT8Hw8HCsXbsWderUQa9evUqsc8KECYiMjMSxY8eQlJQEX19fODk54fvvv8eRI0ewatUqdO/eHatXrwYABAQEICIiAtbW1nBwcMDChQtRr169Z2JVKBRYtmwZ0tPTUVhYiClTpmDAgAGIiYnBkiVL8PDhQ7z//vsIDw/H2bNn4evrq7Zt33//Pf788098+eWXkMlkqFatGpYsWYJmzZpp3B/ff/+9/g8GEZmtdevW4cqVK7h//z6CgoIwefJkuLm5ISIiAgEBAZDL5bCzs4Ovry+cnZ0xduxYXLhwAUOHDsXcuXMxceJEyOVyrF27FkuXLgXwuCcaAGbOnFlqnj127Bi++OILODo6olOnTjh//jxSU1Nx/PhxxMbGYtWqVbCwsIBMJsPSpUvRsmVLtW3QNK+mvNmyZUuEhobC3d0dN27cQGxsLMaMGQMvLy9s374dhw8fhkwmQ7NmzbBo0SLY2dlh+fLlapeZNWtWpR0rMkGCSMc2bdokXn31VaFQKERhYaFYs2aNSE9PF8HBwdI83t7eYu/evUIIIRQKhXB1dRUXLlwQQghx9OhR0b59exEZGSnN37p1a5GUlCSEEGLfvn3C3d29xPa8vb2FEEL8888/YtCgQaKoqEgIIcTnn39eYj1P+uCDD8TGjRuFEEKkpKSI7t27S9uIjIwUHTp0ECdPnhRCCLF69WqNbUtMTBSurq4iPj5eCCFEcHCwePPNN4VSqdS4DBFRRbm7u4t9+/ZJr4tzUVxcnBBCiB9++EFMmDBBen/KlCni888/F0qlUsyaNUtkZ2cLIYRISkoSrVu3LrHu0vJs8fsuLi7ixo0bQojHOTIzM1P06NFDnDp1SgghxIkTJ8Qbb7whCgsLn4n9efNqypvu7u5i4sSJoqCgQMTFxYm9e/eKoKAgMXjwYJGTkyOEEGLhwoXCx8enxH56ehmi0nBYBemFq6sr7O3tYWlpiU8//RS1a9fG3bt3MXbsWHh4eCAqKgp///03gMe9xg4ODujSpQsAoH///rCxsSnXdm1tbZGamorDhw9DqVRi3rx56Nat2zPzpaSk4NSpU3jrrbcAAPXq1UPXrl1x8OBBaZ7q1avj1VdfBQB4e3trbFtoaCg6deqE5s2bAwCGDh2Ku3fv4uLFixqXISLStdDQUHTs2BEtWrQA8DgXnT59Gvfu3QMAfPbZZ9i/fz/mzZuHsWPHokaNGhXaXvPmzaVeYW9vb5w4cQI1atRAz549AQBubm5ITU1FdHT0M8uWZV5NebNPnz6QyWRo0aIF3n77bYSEhGDQoEGoXr06AGD06NH49ddfUVhYqHEZotJwWAXpRc2aNUu8DgoKwp49exAcHIw6derA398fd+7cAQDcv38fdevWLTF/nTp1yrXdBg0aYOvWrdi2bRs+++wzDBs2DB999JE0fKNYcnIygMcJ3cLCAgCQnp6O1q1ba2yDpunJycmwt7eXXstkMtSqVUvaRmnrIiLSleTkZMTFxUnDIwCgUaNGUCgUqFevHho0aICJEydi9+7dWLNmTYW3py4XPnjwoMT27e3tkZGRoTbW581b3hxsb28PpVKJ1NRUODs7l7ouInVYHFOliImJgYuLi1T0FhQUSO85OTkhLS2txPzqkmkxuVyO/Px86XVmZqb070ePHuHFF1/El19+ifv372PWrFnYtm0bZs+eXWId9evXB/D4yRjFSTUvL69EXGXVoEEDJCQkSK8LCwuRmZkpbYOIqDI0aNAAHTt2RGBgoDTtwYMHsLOzA/A4x129ehUtW7aEv78/5s6dq3FdpeXZ0rZfv379EvdUZGVlwdraukLzlmW7T36GpKWlQS6Xw9HRUet1EQF8WgVVkhdeeAFXr15Ffn4+CgoKcPr0aem9Pn36IC0tDefPnwcAHD16FDk5ORrX1bhxY9y8eRP5+fnIy8uTnocMPC7CN23aBOBx0d28efMSX60Vc3Z2Rq9evRASEiJNW7ZsWYl1ldWQIUMQGxuLW7duAQB+++03NGzYUBomQkSkD7a2tnj06BFu3rwJPz8/DBkyBNHR0dK3cgqFAh4eHigqKgIAbN68GVOnTsWKFSvw008/4fLly9J6gMedC4GBgbh06VKpeVaTvn37Ij09HTExMQCAnJwcjB8/HllZWRWa93lGjRqFP/74A7m5uQCA4OBgDB8+HDKZTOt1EQGAhRBCGDoIMh8HDhzAhg0bkJeXh169eklf3eXk5ODTTz9FfHw8WrVqhcLCQly6dAlTpkzBxIkTpadV1KpVC926dUNoaChq1qyJFStWYN26dYiMjETnzp3h7+8PZ2dnfPrpp/jf//6Hdu3aoXbt2vjjjz/g7u6Ot956C//3f/8HhUKBgoICODo6YuXKlWofBadQKODr64vU1FQAwOuvv47p06fjxo0bmDt3LuLj4+Hq6gp/f3/UqVNHY9sA4K+//kJAQMAzT6sobRkiooo4cuQI1q5di5o1a2LevHl45ZVXpFwkl8thYWGBOXPmwNXVFXPnzkVERAQWLFgAR0dHzJ8/H1ZWVpgzZw5Gjx6NuXPnIiEhAbVr18aWLVtQrVo1jXnW1dVVyp0uLi745ptvpJhiY2Ph5+cHIQSEEJgyZQr69u2rNn5N82rKm2vWrMHevXvh6OiId999FxMnTpTWVfy0CktLyxJPqyhtGSJNWBwTEREREalwWAURERERkQqLYyIiIiIiFRbHREREREQqLI6JiIiIiFT08pzj+/cfSv+uW7cG0tM1P5bLVLFdpsMc2wSwXaambt0asLLS36Olnsy75spczw1tcT9wHxTjfnistP3g5KT9D8DovedYnx8GhsR2mQ5zbBPAdpkac21XZeI+fIz7gfugGPfDY7reDyb/C3kH4w+rnT6kxRuVHAkREenT3thQ5GTnPTOd+Z6IdIljjomIiIiIVEy+55iIiKqGyzdSoVQWPDN9SAsDBENEZstkimNNwyeIiIiIiHSFwyqIiIiIiFRMpueYiIhMk7Y3TvObQiIyJPYcExERERGpsDgmIiIiIlLhsAoiItIJDocgInPAnmMiIiIiIhX2HBMRkUHou6eZv6BKROXBnmMiIiIiIhX2HBMRUZXCHmUiKg17jomIiIiIVMy255g9A0RExu1qYrpW88vl6j+y9Dl2mZ8lRFWP2RbHRERE2uCj6IgIqILFMXsBiIiqBk09022b1q3kSIjIlFS54piIiMqGnQlEVBXxhjwiIiIiIhX2HBMRUZXC4RZEVBoWx0REpBXeuKZ/HNJCZDgcVkFEREREpMKeYyIi0ittn2dsTDTFPqRFJQdCRJXG6Ipjfl1HRGSaTLkIBnQTP4dDEJk+DqsgIiIiIlIxup5jIiIic8MeZSLTweJYJTgiXu30kb05sIyIiEriEEAi88XiWCWu8KyGd1gcE5F5Y6GnPT4rmch8sTgmIiKtGNuNd8YWDxGZNhbHREREBqJpSJ+8USUHQkQSsy2ODfWVl7pEx3HLRERERKbBbItjXdH0V/3U0Z0rORIiIqrqDsYfRo0UG+Rk55WYzqdeEOmOyRfHhhprtiT4WyiVBc9Mbyl7+ZlpfBIGEREZEz5ajkgzky+OtWUKN26wmCYiMk3GNKQP4OcGUXmYTHFsCkWttjQlM12tR1NSZBIlIqpcmj7DWsq0m1/bIttQj+ljzzSZMpMpjg1F0/OP5ZaVv+t0VUzrG4tvIvNgjp0SxkbzM/Z1Q1dF9rqwPTpZjzZYYJOhsDg2Y9oW08ER8bC1tUH2Uzd6aMJil4iIiMwNi2Md03cvgDbU3RyoS/oeFqKJNkW5poKfhb3pMNQ3EVXpGxD2EJs+bT97NB9z/Q7D0NQbrM05OETDJWhsuULe6Iba6dr2fFelHnRjaauFEEJU6haJiIiIiIyUpaEDICIiIiIyFiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkYrOfgTk1KlTOHz4MBwcHGBhYQEvL68S7+fl5cHPzw/Ozs64efMmPD090bx5c11tXi+e16b9+/dj9+7dsLGxAQCMGTMGI0eONECk2rl//z42btyIq1evYt++fc+8X1RUhPXr18PW1hZ37tzBW2+9BVdX18oPVEvPa9eZM2ewcuVK1KpVCwDQp08fTJkypbLD1EpiYiI2btyI9u3bIzk5GXXq1DGLa6ss7TK166uoqAjTp0+Hi4sLlEolkpKSsHLlSlSrVk2axxSPlTF43rVdFZTlmqkKynKdVRW5ubl4++238dprr8Hb29vQ4RjEO++8I31GWFpaYufOnbpZsdCBnJwcMWDAAJGXlyeEEMLLy0ucOnWqxDxbt24VgYGBQgghrl69KsaOHauLTetNWdq0b98+kZSUZIjwKuT3338Xx44dE6NGjVL7fmhoqFi2bJkQQoj09HTxxhtviIKCgkqMsHye167IyEgRGRlZyVFVTHR0tDhy5Ij0etCgQeLy5csl5jG1a0uIsrXL1K6vwsJCsXnzZun19OnTRUhISIl5TPFYGYPnXdtVQVmumaqgLNdZVbFq1Soxf/58sXr1akOHYjCbNm3Sy3p1Mqzi0qVLaNiwIaytrQEAXbt2RVhYWIl5wsLC0KVLFwBAmzZtcPXqVWRlZeli83pRljYBwK5du7B9+3YEBAQgIyOjcoMsp4EDB8LW1lbj+2FhYVJPcZ06dWBtbY1//vmnkqIrv+e1CwBCQkKwfft2/Pe//8W///5bSZGVn4uLCwYMGCC9LioqQvXq1UvMY2rXFlC2dgGmdX1ZWlpi5syZAICCggKkpKQ80ytsisfKGJTl2jZ3Zb1mzF1ZrrOqIDg4GF27dkXjxo0NHYpBXb9+HYGBgfD391dbo5WXToZVKBSKEonLzs4OCoWiTPPY2dnpIgSdK0ubXn75Zbi5ucHe3h7h4eH46KOPdNelb0BpaWkljoudnR3S0tIMGJFuvPjii5g5cyYaN26Mf/75BxMnTsRvv/0GS0vTGHp/5MgRvPbaa2jZsmWJ6aZ2bT1NU7tM9fqKiIjAt99+Czc3N3Tq1KnEe6Z+rMg4aLpmqpLSrjNzd+PGDcTHx2POnDm4du2aocMxqKlTp8LFxQWFhYUYN24cbG1t8fLLL1d4vTqpChwcHJCdnS29zsrKgoODg9bzGJOyxNukSRPY29sDAF555RWcPXsWhYWFlRqnPtjb25fozcrKypLaacocHBykv7JbtWqFhw8fmkTvMQBERkbizJkzWLhw4TPvmdq19aTS2mWq11fv3r2xfft23L59G7t27SrxnikfKzIOpV0zVUlp15m5O3LkCKytrREYGIjz588jJiYG3377raHDMggXFxcAgEwmw0svvYQzZ87oZL06KY5dXV1x9+5d5OfnAwAuXLgANzc3ZGRkSEWWm5sbLl68CAC4du0a2rZta9S9JWVp07p161BQUAAAuHnzJho1agSZTGawmCsiJydH6h12c3PDpUuXAAAZGRnIz89Hq1atDBhd+T3ZrsDAQOmr+YyMDCiVSjg6OhowurIJCwvDX3/9hUWLFuH+/fu4ePGiSV9bxZ7XLlO7vm7cuFHia73GjRvj9u3bZnGsyDiou2aqGk3XWVUyY8YMeHl5wdPTE926dYOLiws++OADQ4dV6eLi4vDzzz9Lr2/duoUmTZroZN0WQgihixWdPHkShw4dQt26dSGXy+Hl5YU1a9agTp068PT0RG5uLvz8/ODk5ITExERMmzbN6McJPa9NO3fuxD///IPGjRvj+vXrGD9+vEk81SEqKgrBwcGIiIjA2LFjMWnSJOzbtw/Xrl3DZ599hqKiIqxbtw7Vq1fH3bt38c4775hFu3777TecOHECL774Im7cuIHBgwejb9++hg67VLGxsfDw8EDHjh0BPC72x40bhxs3bpj0tVWWdpna9ZWYmIg1a9agffv2KCgoQFxcHBYvXowdO3aY9LEyBuqu7ar2dAJN18zo0aMNHFnl0nSdOTk5GTq0Snfo0CHs2rULSqUS48aNw9ChQw0dUqVKSUnBihUr0K5dO2RlZaGgoAA+Pj46GSqps+KYiIiIiMjUmcadSERERERElYDFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMVW627dvY/DgwYYOg4iIiOgZLI6p0jVu3Bi7d+/Wy7r79euHM2fO6GXdREREZP5YHJNB1KpVy9AhEBERET3DQgghDB0EGa+AgAD89NNPcHNzQ3p6OlJSUuDg4IDVq1fD3t4eABAREYGAgADI5XLY2dnB19cXzs7O0rIDBw5ERkYGYmNj0aVLF/z777+IjIzEsWPHYGlpiY8//hjR0dFYtWoVgoODoVAosHHjRoSEhODUqVNwcHBAQEAAbGxsSt2ej48PQkND0aJFC9SqVQve3t7o2LEjgoOD8eOPP8La2hrOzs7w9fWFnZ0dli9fjtDQULi7u+PGjRuIjY3FmDFjMGvWrBL7QKlUYv369bh48SIsLCzQq1cvfPjhh1AqlZg8eTKioqKwdOlShIeH4+zZs5g5cyZCQ0Px8OFDvP/++9L0q1ev4ubNm1ixYgVyc3NRWFiIGTNmoE+fPoiJicGSJUvULkNEVB4BAQGIiooCAFSvXh2fffYZnJ2dcezYMXzxxRdwdHREp06dcP78eaSmpuL48eOIjY3FqlWrYGFhAZlMhqVLl6Jly5alrk+dxMRELF++HPn5+SgqKsK8efPQtWtXjdsePXq02s+L1atXSzlcLpejbt26WL58ORwdHTV+xqxevbpydjCZL0H0HN7e3mLAgAHi4cOHQgghFi9eLObMmSOEECIxMVG4urqKuLg4IYQQP/zwg5gwYUKJZYcOHSpycnJEZmam2Lx5sxBCiNatW4ukpCQhhBBJSUmidevW4tChQ0IIIf7v//5P9O/fX9y5c0cUFRWJ4cOHi9DQ0DJtr2/fviIyMlJ6fe7cOdG9e3ehUCiEEEKsXr1aLFy4UHrf3d1dTJw4URQUFIi4uDixd+/eZ9r/5ZdfCg8PD1FQUCDy8/PFu+++K4KDg6X3W7duLfz9/YUQQhw4cEDExsaKyMhI0aFDB3Hy5Elpu0qlUrz55pti3759Qgghbt68Kbp06SJu3bolhBBqlyEiKq/vvvtOFBUVCSGE2Ldvn5g3b5703r59+4SLi4u4ceOGEOJxvsnMzBQ9evQQp06dEkIIceLECfHGG2+IwsLC567vSUqlUgwcOFD8/PPPQgghrly5Irp37y59hqjbthDqPy/Onj0rXnnlFSmHb968WYwfP17alqbPGKKK4LAKKpM+ffrAzs4OADBixAgcOnQIhYWFCA0NRceOHdGiRQsAwNChQ3H69Gncu3dPWrZnz56oXr06atasiZkzZ2rcxquvvgoAaN26NWrVqoWGDRvCwsICrVq1QlJSEgCUaXtPCgoKQr9+/aRe7mHDhuHAgQMQT3xh0qdPH8hkMrRo0QJvv/222nWMGjUKMpkMcrkcAwcOxK+//lpingEDBkjxdOjQAcDjnpXiNnl7eyM6Ohq3b9/G8OHDAQAvvPACOnfuXGJdTy9DRFReDRo0wPjx4zFu3Djs3LkTf//9d4n3mzdvLvUKe3t748SJE6hRowZ69uwJAHBzc0Nqaiqio6PLtL5i0dHRSEpKwogRIwAAbdu2hbOzM8LCwjRuu9jTnxfBwcFwc3OTcviYMWMQGRmJu3fvalyGqKKsDB0AmYbatWtL/65Tpw6USiXS09ORnJyMuLg4eHh4SO83atQICoUC9erVAwDUrFmzTNsoLr5lMhlsbW2l6VZWVlAqlQBQpu096en5CwoK4OjoiPT0dCnZPi++5ORk7NixA/v37wcAZGdnPzNmujj2Jz293pSUFNSqVQtWVv//srO3t0dKSorGZYiIyuPmzZv4+OOP8eOPP8LFxQVnzpyBj49PiXmezjfJycl48OBBifxqb2+PjIyMMq2vWHFOmzRpkjQtPz8fDx8+1Ljt0mJq06aN9Lpu3brS9IYNG5a6LqLyYnFMZfLgwQPp3+np6dLYrwYNGqBjx44IDAwsMa+6YlEXtN1egwYN0KRJEyxbtkyalpaWJhXGZd3mjBkzMGjQIABAUVERMjMztY69fv36yMzMREFBgVQgp6WloXnz5lqvi4ioNP/73/9ga2sLFxcXAI87Bp6nQYMGqF+/Pr7//ntpWlZWFqytrXH06NEyr69+/fqQy+Ul1pOTkwNLS+2/rG7QoAHS0tKk1+np6dI2iPSFwyqoTP766y9kZWUBAIKDg/Hmm29CJpNhyJAhiI6Oxp07dwAACoUCHh4eKCoq0kscz9uera0tcnNzERkZiZ07d2LUqFEIDw+Xivv4+HjMmDFDq22OGjUKoaGhKCwsBPB4mMVXX32ldeydO3dG06ZNERoaCgBISkpCdHS0NMyCiEhXXnjhBWRmZiIhIQHA4xuZn6dv375IT09HTEwMgMcF7fjx45GVlaXV+jp37owGDRrg8OHDAB4X0h9++CFu3rypdTtGjRqFP//8UyqQg4KC8Morr0i9xkT6wKdV0HMtWLAA1atXh0KhwJ07d2Bvbw8/Pz+p9/Wvv/6Snh5hYWGBOXPmwNXVFTt27MDXX38NGxsbDBw4EPPnzwcATJgwAZGRkejcuTP8/f0xa9YsREdHo1+/fpgxYwbmz5+P1NRUjB8/Hs7Ozti0aRNsbGzwySefYNiwYRq3BwA//PADfvzxR9jZ2eHzzz9Hq1atEBISgl27dqFatWqQy+VYvHgxmjdvjjVr1mDv3r1wdHTEu+++i4kTJ6ptv1KpxH//+19ERUXBxsYG9evXx2effYbq1atj0qRJOHnyJDp37oxPPvkEPXv2xI0bNzB37lzEx8fD1dUV/v7+qFOnDoDHd3B/9tlnePToUYmnVZS2DBFReWzcuBG//vor2rRpAycnJwQFBWHQoEEYNWoUfH19kZqaChcXF3zzzTfSMrGxsfDz84MQAkIITJkyBX379i11fWvWrHlm24mJifD19UVeXh6KioowevRovPXWWzh9+rTabWv6vAAg5fCnn1ZR2jJEFcHimJ5rwYIFaNSo0TOPOCMiIiIyNxxWQURERESkwhvyqFQBAQGIiIiQhhOoe9QZERERkbngsAoiIiIiIhUOqyAiIiIiUmFxTERERESkopcxx/fvPyzxum7dGkhPz9HHpkwa94t63C/qcb+oZ0r7xclJf7/k9XTeLY0p7bPyMOf2mXPbAPNunzm3DTDe9pUn71ZKz7GVlawyNmNyuF/U435Rj/tFPe4X7Zn7PjPn9plz2wDzbp85tw0wr/aZzNMqDsYfVjt9SIs3KjkSIqKqgXmXiKoijjkmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUTOY5x0REpB+anmdMRFQVmXxxzIfUExEREZGucFgFEREREZEKi2MiIiIiIhWTH1ahCYdbEBEREZG22HNMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpmO1zjjXh84+JiIiISBP2HBMRERERqRhdz7Gmnl0iIiIiIn1jzzERERERkQqLYyIiIiIiFRbHREREREQqRjfm2FCCI+LVTh/Zu0UlR0JEREREhsLimIiItMJHYhKROTPb4vhqYrra6W2b1q3kSIiIiIjIVJhtcayJpqK5paySAyEiIiIio1PlimNN4grPqp0eHKHdejhGmYiqKt67QUTmgMUxERGppembNk34DRwRmQOTL461Td76pqnnRJ2pozvrMRIiIuOgTV4E2NNMRIZl8sWxOeJXk0REZfd0zrS1tUF2dh5zJhGVi8kUx4bqIdY0FlmTlrKXyzzvj4euIjs7T9uQKozFNxHpg6Z8qU1eBJijiMiwTKY4Jv3jBxIRGTNth2dwOAcRlQeLYx3TpqdZ/sgKysKCZ6Zr6mXRNtHrm77i4VeiRJVL39/M6apHWd/0mWOZz4hMh4UQQhg6CCIiIiIiY2Bp6ACIiIiIiIwFi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkovcfATl16hQOHz4MBwcHWFhYwMvLS9+bNAnvvPMObGxsAACWlpbYuXOngSMyjPv372Pjxo24evUq9u3bBwDIy8uDn58fnJ2dcfPmTXh6eqJ58+YGjrRyqdsv+/fvx+7du6XzZsyYMRg5cqQBo6xciYmJ2LhxI9q3b4/k5GTUqVMHXl5eyMjIwLp169CkSRPcvHkTc+bMgaOjo6HDNVrmkJO1zRshISG4cuUKLC0t0bRpU7z33nuGDF+j8pzjX3/9NbKyspCZmYlevXqhf//+Bm6FZkVFRZg+fTpcXFygVCqRlJSElStXIjc31yzaBwC5ubl4++238dprr8Hb29sszsti6uoWczk3nyH0KCcnRwwYMEDk5eUJIYTw8vISp06d0ucmTcamTZsMHYJR+P3338WxY8fEqFGjpGlbt24VgYGBQgghrl69KsaOHWuo8AxG3X7Zt2+fSEpKMmBUhhUdHS2OHDkivR40aJC4fPmyWLJkiTh48KAQQohjx46JefPmGSpEo2cuOVmbvPHvv/+K4cOHi6KiIiGEEKNHjxYJCQmVHnNZaHuOX7p0SUyZMkUIIYRSqRT/+c9/RGZmZuUHXkaFhYVi8+bN0uvp06eLkJAQs2mfEEKsWrVKzJ8/X6xevVoIYR7nZTF1dYs5Hbsn6XVYxaVLl9CwYUNYW1sDALp27YqwsDB9btJkXL9+HYGBgfD396/S+2TgwIGwtbUtMS0sLAxdunQBALRp0wZXr15FVlaWIcIzGHX7BQB27dqF7du3IyAgABkZGZUfmAG5uLhgwIAB0uuioiJUr14d4eHh0vnStWtXhIeHGypEo2cuOVmbvBEREYEOHTrAwsICANClSxf8+eeflR5zWWh7jp84cQKurq4AACsrK7Ro0QJRUVGVHndZWVpaYubMmQCAgoICpKSkoHnz5mbTvuDgYHTt2hWNGzeWppnDeVlMXd1iLsfuaXodVqFQKEokMDs7OygUCn1u0mRMnToVLi4uKCwsxLhx42Bra4uXX37Z0GEZBU3njZ2dnQGjMryXX34Zbm5usLe3R3h4OD766KMqOxznyJEjeO2119CyZcsS54udnR0ePHiAgoICWFnpfdSYyTHnnKypbWlpaSWm29ramkSby3KOp6WloUWLFtIydnZ2SEtLM1TIZRYREYFvv/0Wbm5u6NSpk1m078aNG4iPj8ecOXNw7do1abo5nZfq6hZzOHbq6LXn2MHBAdnZ2dLrrKwsODg46HOTJsPFxQUAIJPJ8NJLL+HMmTMGjsh48LxRr0mTJrC3twcAvPLKKzh79iwKCwsNHFXli4yMxJkzZ7Bw4UIAJc+XrKws1K5dm4WxBuZ8bWlqm729fYnp2dnZRt/msp7jT7ctKytLyhHGrHfv3ti+fTtu376NXbt2mUX7jhw5AmtrawQGBuL8+fOIiYnBt99+a1bnpbq6xRyOnTp6LY5dXV1x9+5d5OfnAwAuXLgANzc3fW7SJMTFxeHnn3+WXt+6dQtNmjQxYETGxc3NDRcvXgQAXLt2DW3btq3yvcYAsG7dOhQUFAAAbt68iUaNGkEmkxk4qsoVFhaGv/76C4sWLcL9+/dx8eJF9OnTRzpfLly4gD59+hg4SuNlzjlZU97o3bs3/v77bwghAAAXL17E66+/bshQS6XNOe7m5oZLly4BAJRKJeLj4436G8gbN26UGMbTuHFj3L592yzaN2PGDHh5ecHT0xPdunWDi4sLPvjgA7M5LzXVLeZw7NSxEMVHRk9OnjyJQ4cOoW7dupDL5SZ5Z7SupaSkYMWKFWjXrh2ysrJQUFAAHx8fWFpWvSfrRUVFITg4GBERERg7diwmTZoEAPDz84OTkxMSExMxbdq0Kve0CnX7Zc+ePfjnn3/QuHFjXL9+HePHj5fGdFUFsbGx8PDwQMeOHQEAOTk5GDduHPr164e1a9eiYcOGSEpKwty5c/m0ilKYQ07WNm+EhIQgNjYWMpkMzZo1M9qnApTnHP/666+RmZmJBw8e4PXXXzfqJwIkJiZizZo1aN++PQoKChAXF4fFixdDLpebRfsA4NChQ9i1axeUSiXGjRuHAQMGmPx5CWiuWzIzM83m2D1J78UxEREREZGpqHpdlUREREREGrA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRm358uV46aWXsH//fkOHQkRERFUAi2MyKh4eHiUK4eXLl6Ndu3YGjIiIiIo9naOJzBGLYyIiIiIiFStDB0DGo6ioCL6+vrh+/TosLS3RrFkzLFq0CKdPn8YXX3wBR0dHuLi4IDIyEnXr1sWKFSuwYcMGXL58GW+++SY++eQTAIAQAtu3b8fhw4chk8mk9djZ2QEA/vzzT3z55ZeQyWSoVq0alixZgmbNmmHdunW4cuUK7t+/j6CgIEyePBlubm4AgMTERMyePRvXrl3Dm2++iTlz5iA/Px+TJ09GVFQUli5dirCwMCQkJMDb2xv/+c9/AADZ2dn4v//7P9y8eRNCCIwYMQJjx44FABw9ehTbtm1DtWrVYGlpidmzZ6NLly64cOECvvjiC8jlcgghMGnSJPTt21ftPvv6669x+PBhWFlZoV27dvD29oa1tTW8vLwQHh6Ojz76COfOncOlS5fg7u6OP//8E9HR0Vi1ahVCQ0MRFRWFP/74A9WqVYOvry/S0tKgVCoxduxYjBo1Cnfv3sXHH3+sdpnGjRvr+YwgIn1ITEzEZ599htzcXCiVSvTq1QuzZ88GoDk/7tmzB1u3bkXnzp1Rs2ZNXLhwAW3btoWXlxfWr1+PK1eu4IMPPsC4ceMQExODJUuW4OHDhxg2bBjOnz+PBw8eYP78+ejduzcAYM+ePTh48CAsLCwAAEuWLMGLL74I4HHeXLVqFeLi4gAAzZs3x7x587Bjx45ncnRYWBhCQ0Ph7u6O+Pj4Ejm6mKY8GRcXB19fXwBAQUEB3nrrLYwePRqpqalYsGAB8vLyUFBQgL59+8LT01PtvoyIiEBAQADkcjns7Ozg6+sLZ2dnBAQE4KeffsLAgQORkZGB2NhYdOnSBVlZWc/k5vnz52PYsGFYv349Ll68CADo0qUL5syZA7lcrjafz58/H6NHj9bD2UFGQRCphIWFicmTJ0uvZ86cKZKSkoQQQuzbt0+4urqKO3fuiKKiIjFixAgxdepUkZeXJ1JTU0WHDh1ESkqKEEKIoKAgMXjwYJGTkyOEEGLhwoXCx8dHCCFEYmKicHV1FfHx8UIIIYKDg8Wbb74plEqlEEIId3d3sW/fvhJxubu7C09PT1FUVCRSUlJE+/btRXJysvR+69atRWBgoBBCiIMHD4o33nhDem/RokVi/vz5QgghHj58KPr16yfOnj0rhBDilVdeEffv3xdCCHHkyBGxadMmIYQQY8aMEZcuXRJCCHHlyhXh7e2tdn+FhISIgQMHipycHFFUVCRmz54tNm/eLL3ft29fsWDBAiGEEJGRkeLEiRMiKSlJtG7dWgQFBQkhhPjmm29ESkqKmDBhgrR9hUIhevXqJcWpaRkiMj0FBQVi0KBBYv/+/UIIITIzM0Xv3r2FEM/Pj5s2bRKvv/66yMzMFHl5eaJnz55i8eLFoqioSMTGxgpXV1dp3sjISNGmTRtx4sQJIYQQ58+fF66uriItLU0IIcRPP/0k8vLypHnHjh0rxbh48WIpdxUWFopp06aJyMhIIYTmHD116lS1Obq0PDl79mxx8OBBIYQQ9+7dkz5//Pz8xNatW4UQQmRnZ4v33ntP7b4s3l9xcXFCCCF++OEHMWHCBOl9b29vMXToUJGTkyMyMzOl7arLzQEBAWLChAmioKBAFBQUiEmTJomAgABpXeqWIfPFYRUkqVWrFq5fv46TJ0+iqKgI69evR8OGDaX3mzdvjoYNG8LCwgIvvvgiWrRoAWtrazg4OMDe3h63b98GAISEhGDQoEGoXr06AGD06NH49ddfUVhYiNDQUHTq1AnNmzcHAAwdOhR3796V/lrXpFevXrCwsEC9evVQt25d3Llzp8T7xb0hbdq0kd4rKipCSEgIxowZAwCws7ND37598euvvwIAateujb179yIzMxP9+vWTeiZq166NkJAQpKamom3btli2bJnamIKCgjBkyBBUr14dFhYWGDp0KEJCQkrM079/fwBAjx49pF7wJ6dPnDgRQgicPn1aitPe3h5ubm7Yt2+f2nVNnDgR9erVK3V/EZFxunTpEhITEzFs2DAAQM2aNbFhwwYAKFN+dHFxQc2aNWFtbY0XXngBrVu3hoWFBdq0aYOcnBwoFAppXltbWynvdO3aFQ4ODggPDwcAvPjii5g+fTref/99rFu3Dn///TeAx3kzODhY6hW1tLTEggULpF5lTV577TUpR9epU0fKw6Xlydq1a+OPP/7A7du34eTkBH9/fwBAnTp1EBERgX/++Qc1atTAN998o3aboaGh6NixI1q0aCHtr9OnT+PevXvSPD179kT16tVRs2ZNzJw5U5r+dG4OCQnByJEjIZPJIJPJMGLEiGfGVmvK52R+OKyCJF26dMGKFSuwbds2LFy4EO+++y6mTZsmvW9rayv928rK6pnXSqUSAJCcnAx7e3vpPXt7eyiVSqSmpj7znkwmQ61atZCcnFxqbMVDMgDA2tpa2tbT79vY2EjvpaWlIT8/H1988QWqVasGAMjMzJRu8NuxYwe++uorDBo0CN26dcOnn36KJk2aYN26dQgMDMSoUaPQunVrzJs3T+1NgcnJyThw4ADOnDkDAMjLy4OlZcm/N2vWrKm2PU9OL2770/ssNja2TOsiItORkpKCWrVqwcrq/3/8duvWDcCzuVNdftSUh4vX92RurF27dolt16lTB/fu3cPDhw8xbdo0fP755xg4cCBu374tFX7FefPJOJo1a/bcdj2Zo5/Mw6XlyYULF+Kbb77BhAkTUK9ePcyePRs9e/bE5MmTUb16dXzyySeQyWSYPn06Bg0a9Mw2k5OTERcXBw8PD2lao0aNoFAopA6EsuTg4nXVrVtXem1vb4+UlJRSlyHzxeKYJA8fPkT37t3Rp08fJCYmYsqUKXB2dpZ6NMuqQYMGSEtLk16npaVBLpfD0dERDRo0QEJCgvReYWEhMjMzUb9+fZ21o5i9vT2sra2xZMkSuLi4AHj8wZGbmwvg8QePr68vfHx84OfnBx8fH/zwww/Iz8/H/PnzMWfOHHz99deYOXMmTpw4obadr776KqZMmVKirdoqbntaWprUU5+WlgZnZ2et10VExq1+/frIzMxEQUGBVNDGxcWhUaNGOs+PDx48KPE6PT0d9erVQ0JCArKysqRv3AoKCqR5ivNmWloaWrZsCeBxQW9paQknJyetYygtT2ZmZmLmzJmYMWMGQkJCMGPGDJw6dQpZWVnw8PCAh4cHTp06hWnTpqFDhw5o2rTpM+vu2LEjAgMDS7T5yUJdmzjT09NLxMgcXHVxWAVJjhw5gj179gAAmjZtCmdnZxQVFWm9nlGjRuGPP/6QitDg4GAMHz4cMpkMQ4YMQWxsLG7dugUA+O2339CwYUN06dIFwONekUePHuHmzZvw8/OrUHssLS0xcuRIaRgFAGzZsgXBwcEAgOnTp6OwsBDVqlWDi4sLCgsLAQCzZ8/Go0ePYGVlha5du0rTNbUzLy8PABAZGalxCEZpnJ2d0atXL+krvPT0dISFhWn9RwkRGb/OnTujadOmCA0NBQBkZGTg448/LlN+1FZubi7CwsIAAOfOnUNaWhr69OmDhg0bwsrKCjExMQAe39RWrDhvFuejoqIiLFq0CKmpqQC0z9Gl5UkfHx+kpqbCwsICL7/8MgoKCmBhYSHdYAg8HkZSfHP004YMGYLo6GhpCIdCoYCHh0e5P7eKh/8VFRXh119/5Q13VZiFUHfGUZUUHx+P1atXIzc3Fzk5OWjTpg2WLVuG8+fPw9fXF6mpqRg/fjycnZ2xadMm2NjYwMfHBydPnsS+ffvQokULrFu3Di+++KL0tIonn3pR/Nf8X3/9hYCAgGfuxgYeF+hr165FzZo1MW/ePPz555/Yu3cvHB0dsWrVKoSEhJTY1sqVK3Hy5El07twZ27dvx+TJkxEdHY1evXrhm2++QXZ2NlauXIm4uDjpTukFCxZAJpNh1apViI6OhlwuR2FhIZYuXYq2bdti27ZtOHbsGORyOXJzczFnzhz07NlT7T775ptv8Pvvv6N69eqws7PDihUr4ODggPnz5+P3339HixYtMGXKFAwbNgwZGRnw9PREdHQ0unfvjmXLlknj+BQKBXx9faFQKEo8raK0ZYjIND35tIqioiJ8/PHH6N69OwDN+fHAgQPYsGED8vLy8OGHHyItLQ3ffvutlBu3b9+OI0eOoHPnzggMDMS1a9fg4+ODt99+G6dOnUJGRgY+/fRTvP766wCAn376Cdu2bUOrVq3wwgsvYOfOnc/kzfj4eAghMGzYMIwbNw6A9jn6xRdf1Jgng4KCsGfPHlhbWyMrKwtTpkzB4MGDERYWhm3btkEmkyErKwsjR47E+PHj1e7L4v0ll8thYWGBOXPmwNXVFTt27MDXX38NGxsbDBw4EPPnzwcAtbkZePyt4saNG3H+/HkAJZ9WoWkZMl8sjomIiMzMmTNn4OPjg+PHjxs6FCKTw2EVREREREQqLI6JiIjMSExMDFauXIn79+9LPy5CRGXHYRVERERERCrsOSYiIiIiUtHLc47v33+oj9VWmrp1ayA9PcfQYeiEubTFXNoBmE9b2A7tOTnp70cEypp3TfG4mVrMphYvwJgrg6nFC5hezOriLU/eZc+xGlZWMkOHoDPm0hZzaQdgPm1hO0yTKbbX1GI2tXgBxlwZTC1ewPRi1lW8/IW85zgYf1jt9CEt3qjkSIiIjBvzJRGZA/YcExERERGpsDgmIiIiIlJhcUxEREREpMIxx+XEsXVERGXDfElEpoQ9x0REREREKuw5rgTsNSEiIiIyDew5JiIiIiJSqXI9x/ruxdW0fiIic6GrPMdv1YjIGFW54lhbVxPT1U5v27RuJUdCRERERPrGYRVERERERCosjomIiIiIVDisQuXJsW81UmyQk51nwGiIiIiIyBDYc0xEREREpMKe43LijXpERERE5oc9x0REREREKuw5VnmyJ1gut4JSWVDh9RRjbzIRERGRaWDPMRERERGRCotjIiIiIiIVFsdERERERCocc0xERCbhyefRP2lIizcqORIiMmfsOSYiIiIiUjHbnmNNPQyank9sCMER8WqnyxvdUDudvSNEVBU8nb/5q6VEVJnMtjg2BXGFZ9VObws++o2IiIjIEFgcExGRWpq+gSMiMmcsjs0Ab1IhInPy9PC34h9m0vSDSpqGqGlrZO8WOlkPEZk2FseVQFfjnLXtxTkYf1jtWD0WzURERETqsTgmIiKToKmjoaVMN+tX1wOtqTdZU281e5+JTB+LYyIi0gltvyXTNEzCUNTfJM1il6iqMfniuCrdMKLpg8fYPmCIiMrCUI/W1PSkICIiwAyKY02M6XnGRESkPyx2iUiXzLY4NmXaFvbsUSaiiqhK38ARET0Pi2MqNz5CjojMnaYb7zT1VgdHALa2Nsh+6ilBmm7U05RHlXdeVDudN/wR6R+LYzN2NTFdej5oyel71M6vqaeZxS4RVVUcskFU9Zh8ccyxxfpXnucrq6OrIps91kSGxbyrWVzhWcgfWUFZWLJTYl2YdkW2to+n0/bRck/PX9zbzZ5pIhMqjnX1C0hkfFjsEhGVVNqwDWOiq/ytbj38DCBDMbriWNOFFlfIngp903dvkLbDOZ48F9T90l9p8xfTlFy1TejG1huu7fz8wQLtcZ+RMdJUNLeUvax2elnHTBf3dmsqvuWNbpQ9yFK2a4jrx5hiIdNgIYQQhg6CiIiIiMgYWBo6ACIiIiIiY8HimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREakY3Y+A6MOpU6dw+PBhODg4wMLCAl5eXiXez8vLg5+fH5ydnXHz5k14enqiefPmAICQkBBcuXIFlpaWaNq0Kd577z0AwNKlS5GQkCCtY/HixWjTpo3RtuPWrVvw8/ODlZUVNm3aJC2TkZGBdevWoUmTJrh58ybmzJkDR0dHk2uHv78/oqKipNfTp09Hr1699NqOirQlJiYGO3fuRPv27ZGQkAAXFxe88847AIDbt2/jyy+/xAsvvIA7d+7A29sbtra2JtcOQ1wjFWmLQqGAj48PunXrBoVCAaVSiSVLlsDS0tIgx6Q89JHrjDHe0s47Y425mEKhwMiRIzFt2jS4u7sbfcyXLl3CyZMnYWlpiTNnzmDVqlVo0KCB0ca7atUqyGQyCCGQm5srXcP69ryYAeC3337D+vXrsWjRIvTt21erZY0l3sTERGzcuBHt27dHcnIy6tSpUynxViTmYrm5uXj77bfx2muvwdvbu/SNCTOXk5MjBgwYIPLy8oQQQnh5eYlTp06VmGfr1q0iMDBQCCHE1atXxdixY4UQQvz7779i+PDhoqioSAghxOjRo0VCQoIQQohNmzZVUgseq0g7hBAiJCRE7N69W8yaNavEMkuWLBEHDx4UQghx7NgxMW/ePH02Q2/tqOzjIUTF2nL06FERHR0thBAiPz9fvPTSS0KhUAghhJg0aZL03nfffSc2bNhgku0wtWOSnJws9uzZI803bNgwce7cOSFE5R+T8tBXrjPGeEs774w1ZiGEKCwsFIsXLxbTp08X33//vd7jrWjMDx8+FF5eXtJ8iYmJIjs722jjvXTpkhg2bJg035PXsKFjTkxMFKdPnxbu7u7i+PHjWi1rTPFGR0eLI0eOSK8HDRokLl++rNd4KxpzsVWrVon58+eL1atXP3d7Zj+s4tKlS2jYsCGsra0BAF27dkVYWFiJecLCwtClSxcAQJs2bXD16lVkZWUhIiICHTp0gIWFBQCgS5cu+PPPPwEA2dnZ2LJlCwIDA/HDDz+goKDAaNsBAMOHD4dcLn9mveHh4dIyXbt2RXh4uB5bob92AMCWLVuwfft2BAYG4tGjR/prhEpF2tK/f3+4uLhI88lkMsjlciiVSpw5cwadOnWS1mnMx0RTO4DKv0Yq2hZnZ2ep9zErKws5OTlo1KiRQY5Jeegr1xljvKWdd8YaMwBs27YNb731FmrXrq33WHURc3h4OGrUqIEdO3YgICAAf//9N2rUqGG08dapUwc5OTkoKChAQUEBLCws0LhxY73GW9aYmzRpgldeeaVcyxpTvC4uLhgwYID0uqioCNWrV9drvEDFYgaA4OBgdO3atczng9kXxwqFosTXn3Z2dlAoFGWaJy0trcR0W1tbadlhw4Zh6tSp8PT0xN27d7F161ajbUdZ12tnZ4cHDx7otYjRVzsGDhyICRMmYPLkybC1tcWKFSt0G7gaumrLrl27MH36dNSsWRPp6emoVq2aVKSUpe0VpY92AJV/jZQ1zufNc/DgQUyfPh1TpkxB/fr1DXJMykNfuc4Y433S0+edPlUk5tOnT6NatWro3Lmz3uMsSzxlmefOnTuIjo6Gu7s7Zs6ciR9++AFnzpwx2nhfeOEFvPPOO/joo4/wySef4NVXX4W9vb1e4y1rzPpYtrx0tc0jR47gtddeQ8uWLXUZnloVifnGjRuIj4/HG2+8UebtmX1x7ODggOzsbOl1VlYWHBwcyjSPvb19ienZ2dnSsh06dICV1eMh26+88goiIyP12YwKtaOs683KykLt2rWldumDvtrRqlUrqUejMo4HoJu2HDhwADk5Ofjggw8AAHXr1kVubi6EEBrXqWv6aAdQ+ddIWeIsyzxDhgzBd999h4MHDyI8PNwgx6Q89JXrjDHeYurOO32qSMzHjx9HXl4eAgMDcf36dZw8eRL79u0z6pjt7OzQvn17yOVyWFpawtXVtcS9HcYW77Fjx3DmzBls3rwZ/v7+uH37Nvbu3avXeMsasz6WLS9dbDMyMhJnzpzBwoULdR2eWhWJ+ciRI7C2tkZgYCDOnz+PmJgYfPvtt6UuY/bFsaurK+7evYv8/HwAwIULF+Dm5oaMjAzpqy43NzdcvHgRAHDt2jW0bdsWdnZ26N27N/7++2/pQ/HixYt4/fXXAQB+fn7SNm7duoWmTZsabTtK06dPH2mZCxcuoE+fPnpshf7aUdnHA6h4W37++WcoFArMnDkT165dQ0JCAuRyOXr06IHLly9L6zT2Y6KuHYDpHZOoqCjExMQAACwtLdGwYUMkJSUZ5JiUh75ynTHGC2g+74w15kWLFsHT0xOenp5o3bo1evXqhTFjxhh1zD169MCdO3ekdd29exfNmjUz2niTk5Ph5OQkrcvJyUlaj6Fj1nZZY40XeDys5a+//sKiRYtw//596VjoU0VinjFjBry8vODp6Ylu3brBxcXluX9QW4jibGjGTp48iUOHDqFu3bqQy+Xw8vLCmjVrUKdOHXh6eiI3Nxd+fn5wcnJCYmIipk2bVuIO7tjYWMhkMjRr1ky6g9vHxwcODg6oVq0aEhIS4OPjo/enPFSkHUePHkVISAgSEhIwYsQITJ06FcDjp1WsXbtWKgTmzp1rku1Yt24dHj16BAcHB1y/fh2zZ88ucYe4sbXl6NGj8Pb2Rvv27QE8Pg6LFy9Gjx49cPv2bWzevBlNmjTBv//+iwULFuj9yQj6aIchrpGKtCU6Ohrbt29H+/btkZ2djZSUFCxfvhw1atQwyDEpD33kOmOMt7TzzlhjLvbLL79g165dcHZ2xtixYyvlD62KxLxr1y7cuXMHcrkcubm5WLBggTTEyNjizcnJwdKlS9GoUSPpKTO+vr56HyddlpiFENiyZQt++eUXdOvWDcOHD0fv3r01Lmus8cbGxsLDwwMdO3YEAOTk5GDcuHEYPXq00cZc7NChQ9i1axeUSiXGjRuHoUOHatxWlSiOiYiIiIjKwuyHVRARERERlRWLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHZHYOHDiARYsWGToMIiJ6CvMzmQILIYQwdBBEulRYWIjc3FzY2toCABYsWIBGjRph1qxZBo6MiKhqezo/P0+/fv2watUq9OjRQ8+REf1/7DkmsyOTycqceImIqPIwP5MpYM8xlVliYiI+++wz5ObmQqlUolevXpg9ezYA4M8//8SXX34JmUyGatWqYcmSJWjWrBn27NmDrVu3onPnzqhZsyYuX74MR0dHBAQEwMbGBgBw8uRJ+Pv7Qy6Xo6ioCO7u7hg0aBD++ecffPHFF1AqlcjJycHo0aPx7rvv4tixY1i8eDGqV6+OefPmYfDgwfDw8EB8fDymT5+OX375BQ8fPsTx48exc+dOBAYGwsbGBo0aNcLw4cOxbds2pKen4/3338cnn3yC1atXIygoCFOnTsWUKVOeaffXX3+Nw4cPw8rKCu3atYO3tzesra3h5eWF8PBwfPTRRzh37hwuXboEd3d3/Pnnn4iOjsaqVasQGhqKqKgo/PHHH6hWrRp8fX2RlpYGpVKJsWPHYtSoUbh79y4+/vhjtcs0bty4Uo8xEemWKeTNVatWoWfPnli/fj0uXrwICwsL9OrVCx9++CEsLCxKtCcmJgZLlizBw4cPMWzYMJw/fx4PHjzA/Pnz0bt3bwBAamqq2lx37do1zJ8/X8rPx44dwxdffAFHR0d07twZZ8+ehaWlJTZv3gwHBwf4+PggNDQULVq0QK1ateDt7Y3q1avD19cXAFBQUIC33noLo0ePVrvvg4OD8eOPP8La2hrOzs7w9fWFnZ0dli9fjtDQULi7u+PGjRuIjY3F8OHDcfHiRURFRWHp0qUIDw/H2bNn8dVXX6FDhw5YuXIlEhISUFRUhP79+2Pq1KlQKpWYPHmy2mXY023iBFEZFBQUiEGDBon9+/cLIYTIzMwUvXv3FkIIkZiYKFxdXUV8fLwQQojg4GDx5ptvCqVSKYQQYtOmTeK1114TGRkZorCwUAwZMkQcOHBAWrZLly4iISFBCCFEdHS0cHd3F0IIcenSJXHp0iUhhBD5+fli4MCB0nw7d+4UEydOlOI7cuSI2LNnjxBCiMjISNG3b1/pPW9vb7Fp0ybpdWxsrOjWrZvIzc0VQghx//594ePjo7bdISEhYuDAgSInJ0cUFRWJ2bNni82bN0vv9+3bVyxYsEDa7okTJ0RSUpJo3bq1CAoKEkII8c0334iUlBQxYcIEKQ6FQiF69eolzp49K4QQGpchItNlSnnzyy+/FB4eHqKgoEDk5+eLd999VwQHB6ttV2RkpGjTpo04ceKEEEKI8+fPC1dXV5GWliaEEKXmuqfz8759+0Tnzp1FYmKiEEKIKVOmiK+++kp6v2/fviIyMlJ6PXv2bHHw4EEhhBD37t0TkydPVhvjuXPnRPfu3YVCoRBCCLF69WqxcOFC6X13d3cxceJEUVBQIOLi4sTevXuFEEK0bt1a+Pv7CyGEOHDggIiNjRU+Pj7C29tbCCHEo0ePxNChQ6VcrWkZMm0cVkFlcunSJSQmJmLYsGEAgJo1a2LDhg0AgNDQUHTq1AnNmzcHAAwdOhR3797FxYsXpeU7d+6M2rVrw9LSEq1atcLt27elZTt27IhmzZoBAFxcXPDxxx8DAF544QX88ssveO+99zBp0iTcv38f//vf/6RtnD17FikpKQCAP/74A4MGDSpTWzp06ID69evj6NGjUgxDhgxRO29QUBCGDBmC6tWrw8LCAkOHDkVISEiJefr37w8A6NGjB9zc3J6ZPnHiRAghcPr0aYwZMwYAYG9vDzc3N+zbt0/tuiZOnIh69eqVqT1EZJxMKW8GBQVh1KhRkMlkkMvlGDhwIH799VeNbbO1tZXyXdeuXeHg4IDw8HCkpKSUKdc9qXnz5mjSpAkAoE2bNlI71alduzb++OMP3L59G05OTvD391c7X1BQEPr16wd7e3sAwLBhw3DgwAGIJ74s79OnD2QyGVq0aIG3335bmj5gwABpf7Vr1w4HDhyQ2lOtWjUMHjwY+/fvL7G9J5fp0KGDxvjJNFgZOgAyDSkpKahVqxasrP7/KdOtWzcAQHJyspSAgMdjymrVqoXk5GRpmp2dnfRvGxsbKJVKtcs+ud7Vq1cjMzMTu3btgkwmg4eHB3JzcwE8Tri9evVCSEgI3n33XchkMtSsWbPM7RkxYgSCg4MxZMgQnD59GuPHj1c7X3JyMg4cOIAzZ84AAPLy8mBpWfJvSk3bfXJ68b54sq329vaIjY0t07qIyPSYUt5MTk7Gjh07pKIvOzsbtWrV0ti22rVrl3hdp04d3Lt3r8y57kma2qnOwoUL8c0332DChAmoV68eZs+ejZ49ez4zX3JyMuLi4uDh4QHg8RAMR0dHpKenS7FpyrdPxpOWlob8/Pxn2lP8B4a6Zcj0sTimMqlfvz4yMzNRUFAgJfq4uDg0atQIDRo0QEJCgjRvYWEhMjMzUb9+/eeu9+llASA2NhYdO3ZETEwM3n//fchkMgB4JmGOHDkS/v7+qFmzZpl7jYsNHz4c//3vf3Hq1Cm0aNHimYL3yfheffXVEmOR09LStNoWAGlfpKWloWHDhtK/nZ2dtV4XEZkGU8qbDRo0wIwZM6RpRUVFyMzM1BjDgwcPSrxOT09HvXr19J7rMjMzMXPmTMyYMQMhISGYMWMGTp06hRo1apSYr0GDBmjSpAmWLVsmTUtLS3vmj4rnsbe3h7W1NdLS0tCyZUtpPczd5o3DKqhMOnfujKZNmyI0NBQAkJGRgY8//hgymQxDhgxBbGwsbt26BQD47bff0LBhQ3Tp0uW563162fPnz2PLli0AgKZNmyI6OhoAcO/ePVy7dq3Esv369cP9+/exd+9evPbaaxq3YWtri0ePHiEnJwdz584FADg7O6N79+6YP38+RowYoXHZUaNG4Y8//kBeXh4AIDIyskSyLStnZ2f06tVL6pVJT09HWFiY9FUdEZkfU8qbo0aNQmhoKAoLCwE8Hpbw1VdfaYwhNzcXYWFhAIBz584hLS0Nffr00Xmus7W1RW5uLiIjI7Fz5074+PggNTUVFhYWePnll1FQUPDMTYPF7QkPD5eK+Pj4eMyYMUPr7VtaWmLkyJEICgqS2v37779rvAmQzAOfVkFl9uRd10VFRfj444/RvXt3AMBff/2FgICAZ+66PnDgADZs2IC8vDx8+OGHkMlk2LRpE2xsbPDJJ59g2LBh0rJyuRzVqlXDihUrUL9+fcTFxeHTTz+FXC5HixYtEBsbC6VSiWXLlklfoy1btgw2NjZYuHAhAEh3Q8fHx6Nv377YtGkTLl68CB8fH9jZ2WHChAnS+L+QkBBs37691HF1APDNN9/g999/R/Xq1WFnZ4cVK1bAwcEB8+fPx++//44WLVpgypQpGDZsGDIyMuDp6Yno6Gh0794dy5Ytw4svvggAUCgU8PX1hUKhKHEHd2nLEJFpM4W8CTzuYf7vf/+LqKgo2NjYoH79+vjss89QvXr1Z9p05swZ+Pj44O2338apU6eQkZGBTz/9FK+//joAzbnu6fw8duxY+Pr6IjU1FePHj0eHDh3w+eefIy8vD1OmTMHEiRPxww8/4Mcff4SdnR0+//xzxMbGYs+ePbC2tkZWVhamTJmCwYMHq933ISEh2LVrF6pVqwa5XI7FixejefPmWLNmDfbu3QtHR0e8++67mDhxIgBg0qRJOHnyJDp37oxPPvlE2l/Z2dlYuXIl4uPjUVhYiAEDBmDq1KmwsLDQuAyZNhbHVGWFh4fjn3/+Ufv4NiIiUq+4OD5+/LihQyHSCw6roConODgYAPDrr79KvchEREREAItjqoJOnDiBkSNHomnTprypgohICzExMVi5ciXu378v/ZgJkbnhsAoiIiIiIhX2HBMRERERqejlOcf37z8s97J169ZAenqODqPRDWOMizGVnTHGZYwxAcYZlzHGBGgfl5OT/n7kxRzzrq6Ye/sA828j22faDNm+8uRdo+s5trKSGToEtYwxLsZUdsYYlzHGBBhnXMYYE2C8cWnLXNqhibm3DzD/NrJ9ps3U2mfyv5B3MP6w2ulDWrxRyZEQEZEh8HOAiHTJZIpjTcmPiIiIiEhXTKY4JiKiqoE9wURkSEY35piIiIiIyFDYc0xERCaBw+uIqDKw55iIiIiISIU9x0REZBDsCSYiY8SeYyIiIiIiFfYcExGRWSruma6RYoOc7DxpOp96QUSlYc8xEREREZEKe46JiKhK4XOUiag07DkmIiIiIlIxup7jvbGhJcaGERERERFVFqMrjomIiIxFcES82ukje7eo5EiIqLJwWAURERERkQqLYyIiIiIiFQ6rICIi0iCu8KyGdzisgshcseeYiIiIiEiFxTERERERkYrZDqvgHcZERKQv/IwhMl9mWxxznBgREWlD0y/nEVHVYrbFsSb8a5+IiIiINKlyxTEREZE6VxPTDR0CERkBFsdERKQTxjYsobjYlcutoFQWVMo2NX07qYmmby35LSeR4bA4VmEiIiIiIiKTL475NRgRUcXsjQ1FTnbeM9OHtHjDANFoz5g+BzTdDN5S9nIlR0JE5cXnHBMRERERqbA4JiIiIiJSMflhFURERKZK2xv4iEj/qlxxrPnHQdQLjnj8f1tbG2Q/MSaPN+oREVFFcYwykfGpcsUxERFRRWnb0UJEpoPFcTnx0W9ERERE5ofF8XMU9w7IH1lBWfj/HyLPr7yIiKisdNXTrKljZurozjpZPxGxOCYiIi3p+5fwND23uG3Tunrdrin78dDVEvfFPI+uvuXkt6hkjkymODamh7wTEVHl4+eA7qwL26N2+ly3dys5EiLjYzLFsbHR9BVZ8dMtyoJ/WRMRkTraDsNwwWt6iuQxXT1yjj3NZApYHOuYNgltXZj6eTV9dai882KJ18WPl2NSISJTxJ5g06HvR86pG6pjKj9fTuaHxbER0vyBUTI5Fd8kqKm3WlMyK2vxXUxT8a3uazm53AotG9RUOz8TnenQNKa0Kh1D7gPdjS1mEax/Vx5FlrhpvLx01UOs6dyJK9QwnhzPfi49GcuTvzWgbYeQplg0febJG91QO11X1766ffz0byk8qSp1gBlL3rUQQohK3SIRERERkZGyNHQARERERETGgsUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREalU6nOOT506hcOHD8PBwQEWFhbw8vIq8X5eXh78/Pzg7OyMmzdvwtPTE82bNwcAhISE4MqVK7C0tETTpk3x3nvvGTymfv36oVGjRgCAevXqYd26dZUSEwD89ttvWL9+PRYtWoS+fftqtawh4nrnnXdgY2MDALC0tMTOnTsrJabAwECkpqbCyckJsbGxmD17Nlq2bAlAf+dUReMy1Hn122+/4dixY2jbti0uX76MkSNHol+/fgAMu69Ki8uQ1yAA/Prrr/j0009x4cIF2NraarVsZTHGvKtLFWnfrVu34OfnBysrK2zatMkQ4T9XedsXExODnTt3on379khISICLiwveeecdA7VCs/K2T6FQwMfHB926dYNCoYBSqcSSJUtgaWl8fX4VOUcBQKFQYOTIkZg2bRrc3d0rO/znMsY6qsJEJcnJyREDBgwQeXl5QgghvLy8xKlTp0rMs3XrVhEYGCiEEOLq1ati7NixQggh/v33XzF8+HBRVFQkhBBi9OjRIiEhwaAxCSHEpk2bKhxDeWJKTEwUp0+fFu7u7uL48eNaLWuIuIQw3L7asGGDdN4cPHhQTJs2TQihv3OqonEJYbh9tW/fPnHnzh0hhBB///23+M9//iOEMPy+0hSXEIbbV0IIcePGDbF+/XrRunVrkZWVpdWylcUY864uVTSHh4SEiN27d4tZs2ZVXtBaqEj7jh49KqKjo4UQQuTn54uXXnpJKBSKSoz++SrSvuTkZLFnzx5pvmHDholz585VUuRlV9FztLCwUCxevFhMnz5dfP/995UXeBkZYx2lC5X2J9alS5fQsGFDWFtbAwC6du2KsLCwEvOEhYWhS5cuAIA2bdrg6tWryMrKQkREBDp06AALCwsAQJcuXfDnn38aNCYAOHfuHLZt24aNGzfiwoULFY6nrDE1adIEr7zySrmWNURcAHD9+nUEBgbC39+/UmP6+OOPpfOmqKgINWrUAAC9nVMVjQsw3Hk1evRoNGzYEMDjHrXinmxD7ytNcQGG21ePHj3C119/jQ8//FDrZSuTMeZdXapoDh8+fDjkcnmlxqyNirSvf//+cHFxkeaTyWRG19aKtM/Z2VnqCc/KykJOTo7UA2lMKnqObtu2DW+99RZq165dqXGXlTHWUbpQacMqFAqF9LUjANjZ2UGhUJRpnrS0tBLTbW1tn1m2smOys7PD3Llz4eLigkePHmHUqFHYunUrXnjhBb3HpI9l9b3uqVOnwsXFBYWFhRg3bhxsbW3x8ssvV1pM+fn5CAoKwrJlywBAb+dUReMCYNDzKjc3F/7+/oiKisLatWsBGMe+UhcXYLh9tWHDBsycOVP6QNC2PZXFGPOuLlU0hxs7XbVv165dmD59OmrWrKn/oLWgi/YdPHgQP/30E6ZMmYL69etXTuBaqEgbL1++jGrVqqFz58746aefKi1mbRhjHaULldZz7ODggOzsbOl1VlYWHBwcyjSPvb19ienZ2dnPLFvZMQGQ/iqvXr062rVrp5O/esoSkz6W1fe6i/eVTCbDSy+9hDNnzlRaTPn5+Vi+fDk++eQTNG3aFAD0dk5VNC7AsOdVtWrV8Omnn2Lt2rUYP348lEqlUewrdXEBhtlX//77LzIzM/H7778jMDAQALBjxw5cvnxZr9dgeRhj3tWliuZwY6eL9h04cAA5OTn44IMP9B6vtnTRviFDhuC7777DwYMHER4erv+gtVSRNh4/fhx5eXkIDAzE9evXcfLkSezbt6/SYi8LY6yjdKHSimNXV1fcvXsX+fn5AIALFy7Azc0NGRkZUve6m5sbLl68CAC4du0a2rZtCzs7O/Tu3Rt///03hBAAgIsXL+L11183aEynT58u8RXjrVu30KRJk0qJSdtldaEiccXFxeHnn3+WXlfmvnr06BGWLVuGiRMnomPHjjh06BAA6O2cqmhchjyvtm/fLu2P+vXrIz09HXl5eQbfV5riMtS+atCgAVavXg1PT094enoCACZOnIhOnTrp9RosD2PMu7pUkfaZgoq27+eff4ZCocDMmTNx7do1JCQkGKYhGlSkfVFRUYiJiQHw+Cbvhg0bIikpyTANKUVF2rho0SIpz7Ru3Rq9evXCmDFjDNYWdYyxjtIFC1Gc+SrByZMncejQIdStWxdyuRxeXl5Ys2YN6tSpA09PT+Tm5sLPzw9OTk5ITEzEtGnTStw1HRsbC5lMhmbNmunsrunyxnTt2jUEBASgQ4cOuHfvHurVq4fp06dXSkxCCGzZsgW//PILunXrhuHDh6N3794al9WV8saVkpKCFStWoF27dsjKykJBQQF8fHx0clfx82Ly8vLCP//8g3r16gEAcnJypL+89XVOVSQuQ55XW7ZsQUpKCho2bIi4uDh07doV7777LgDD7itNcRlyXwGPh5vs3r0b//3vfzFz5ky89957cHZ21us1qI+2GCLv6lJF2nf06FGEhIQgISEBI0aMwNSpUw3cmmeVt31Hjx6Ft7c32rdvDwDIyMjA4sWL0aNHDwO3qKTyti86Ohrbt29H+/btkZ2djZSUFCxfvrzE/RvGoiLnKAD88ssv2LVrF5ydnTF27Fj06dPHgK15ljHWURVVqcUxEREREZExM74HAhIRERERGQiLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHRERE5ZSTkwNPT0+89957GDFiBO7cuWOwWAICAtCrVy/4+/s/d97CwkJ4eHigTZs2uH37NgDg3LlzmDRpkr7DLLPbt29j8ODBhg6DqiAWx2R2nkz2RET6dPDgQRQUFGD37t34+OOPYWmp24/VBQsWlKnYBQAvLy/07t27TPPKZDJ8//33JaZ169YN//3vf7WOUV8aN26M3bt3GzoMqoKsDB0AERGRqUpJSUG9evUAAH379jVwNBVjYWGBmjVrGjqMEmrVqmXoEKgKYnFMz1VUVARfX19cv34dlpaWaNasGRYtWoSZM2fi9OnTcHNzw9atWxEcHIy1a9eia9euaN26NX766Se8+eabyMzMxOXLlzFgwAC8+eab+Oqrr3Dt2jX4+PhgwIABiImJwZIlS/Dw4UO8//77OHr0KAoKCrBx40YEBgbi4sWLaN++Pfz8/KSYgoOD8eOPP8La2hrOzs7w9fWFnZ0dpkyZAgCYM2cObGxssHr1aixYsABRUVFYunQpwsPDcfbsWTg6OiIxMRGurq745ptvcOnSJSxduhS1a9fG/v37n9kHsbGxWLVqFSwsLCCTybB06VK0bNkSe/bswdatW9G5c2fY2tri8uXLqFWrFlq2bInQ0FC4u7vjxo0biI2NxZgxY+Dl5YXt27fj8OHDkMlk0r60s7PD8uXL1S4za9asSjvWRFR2e/bswf79+5GXlwcPDw/MmjUL/v7+z+Sbr776CpmZmfjhhx9gYWEBpVKJOXPmoFu3bgAg5btz585BJpPB0dER8+bNw/HjxxEREQEbGxtERUVh+PDhePvtt7F8+XIkJCSgqKgITk5O+Oyzz2BnZ1emmPft24cdO3bA0dERQ4YMkaanpaVh+vTpiI6OxrVr13Sal5/MbfHx8bh27RrefPNNzJkzBwBw4cIFfPHFF5DL5RBCYNKkSejbty8mTJiAyMhIHDt2DI0bN4ZSqcT69etx8eJFAECXLl0wZ84cyOVyeHl5ITw8HLNmzcKlS5fwzz//4IMPPsC4cePU7ofs7Gz83//9H27evAkhBEaMGIGxY8fi7t27+PjjjxEdHY1Vq1YhNDQUUVFRmD9/Pn788Uc4OjqiU6dOOH/+PFJTU3H8+HHExMRgzZo1EELAwsIC8+fPh4uLC44dO4YvvvhC7TJk5ATRc4SFhYnJkydLr2fOnCmSkpJEfn6+6N69uzh//rz03rRp00RRUZEQQghvb28xatQokZeXJxQKhejQoYPYvHmzEEKIQ4cOiTfffFNaLjIyUnTo0EFcvHhRCCHEjBkzxKhRo0RmZqbIy8sTr7zyivTeuXPnRPfu3YVCoRBCCLF69WqxcOFCaV2tW7cWSUlJJdrQunVr4e/vL4QQ4sCBAyI2NlYMHTpU/Prrr9I8H3/8scjKynqm/ZmZmaJHjx7i1KlTQgghTpw4Id544w1RWFgohBBi06ZN4tVXXxUKhUIUFhaKNWvWCCGEcHd3FxMnThQFBQUiLi5O7N27VwQFBYnBgweLnJwcIYQQCxcuFD4+PtK21C1DRMZr06ZNwtvbu8Q0dfkmODhYpKenCyGESEpKEn369JHm37Jli/jggw9EQUGBEEIIX19fsW/fPiHE4zy6adOmEuvfuXNnie1v2LBBeq1u/mLXr18XLi4uIjExUQghxK5du0rky6SkJNG6dWtpfl3mZXd3dzF16lRRVFQkUlJSRPv27UVycrIQQogxY8aIS5cuCSGEuHLlSon9+WR8AQEBYsKECaKgoEAUFBSISZMmiYCAAGnevn37imXLlgkhhIiOjhaurq5CqVSq3ReLFi0S8+fPF0II8fDhQ9GvXz9x9uzZEvshKChICCHEN998I1JSUsS+ffuEi4uLuHHjhtTGzMxM0b17dxEZGSmEEOLs2bOie/fu4sGDB0IIoXYZMn4cc0zPVatWLVy/fh0nT55EUVER1q9fj4YNG0Iul2PIkCEIDg4GAPzvf/9DmzZtYGFhIS3bvXt3WFtbw97eHvb29mjbti0A9eOCbW1t4erqCgBo1aoVGjVqhJo1a8La2hrNmjVDUlISACAoKAj9+vWDvb09AGDYsGE4cOAAhBCltmPAgAEAgKFDh6JDhw4YOXKkFHtaWhpsbGxga2v7zHInTpxAjRo10LNnTwCAm5sbUlNTER0dLc3j6uoKe3t7WFpa4tNPP5Wm9+nTBzKZDC1atMDbb7+NkJAQDBo0CNWrVwcAjB49Gr/++isKCws1LkNEpufpfNO2bVv4+Phg7Nix8PHxwb///guFQgEA2L9/P0aMGAGZTAYAmDZtGl5++WWN67axscH7778Pd3d3HDx4EH///XeZYjp06BBcXV3RpEkTACjTzW66zMuvvfYaLCwsUK9ePdSpU0e6ebF27doICQlBamoq2rZti2XLlqmNJSQkBCNHjoRMJoNMJsOIESOe+aaveMx1mzZtkJOTI+3jJxUVFSEkJARjxowBANjZ2aFv37749ddfS8zXv39/AMDEiROloTPNmzdHy5YtAQDe3t44ceIE7Ozs0KNHDwDASy+9hNq1a5foHX56GTJ+HFZBz9WlSxesWLEC27Ztw8KFC/Huu+9i2rRpAICRI0diypQpWLx4MUJCQvDOO++UWPbJYtPKykp6LZPJoFQqyzRv8evi+ZOTkxEXFwcPDw8Aj7+SdHR0RHp6upSY1Xn6a8dhw4Zhw4YNuHfvHn7//XeNHxTJycl48OCBtD0AsLe3R0ZGhvRa0zi9p6cnJyeXiNHe3h5KpRKpqalwdnYudV1EZDqezjczZszAuHHjMHnyZACPi7dHjx4BeJwX6tatK81bnAvUOXPmDFavXo0DBw6gcePG2L9/P4KCgsoU071790psp06dOs9dRpd5+cl9YmNjIy27bt06BAYGYtSoUWjdujXmzZuHdu3aPRPL0/vJ3t4eKSkpJeYp3oaNjQ0APPM5AzzuDMnPz8cXX3yBatWqAQAyMzOf2aa6XPy8nF4cV3JycqnrIePG4pie6+HDh+jevTv69OmDxMRETJkyBc7OzhgzZgxcXFzg4OCAI0eO4ObNm9Jfx/rUoEEDNGnSpETvQlpaWqmFsTr16tVDjx49cODAAURFRcHd3V3j9urXr1/izu6srCxYW1uXK/a0tLQSccvlcjg6Omq9LiIyDQqFAnfu3JF6NZ8u2Bo0aID09HTpdXp6OrKzs9G4ceNn1hUTE4PmzZtL7xUUFJQ5jnr16uHmzZsltqMrFcnL+fn5mD9/PubMmYOvv/4aM2fOxIkTJ9Ru48mY09LSSv1DQhN7e3tYW1tjyZIlcHFxAfD4mOTm5mq9rqdzenFc9evX13pdZDw4rIKe68iRI9izZw8AoGnTpnB2dkZRUZH0/ogRI7Bq1Sr06tWrUuIZNWoUwsPD8eDBAwBAfHw8ZsyYIb1fo0YN5ObmIiQkBH/88Uep6xo5ciR27NiBZs2aSV9pPq1v375IT09HTEwMgMfPNR0/fjyysrLKFfsff/whJeHg4GAMHz5c47aJyPTVqVMHtWrVkoZiRURElHh/1KhRCAkJkYZXrVu3DlevXgXwuOf20aNHyMnJwdy5c/HCCy8gMTFRKhL/+uuvMsfx5ptv4tKlS9JQiNDQ0Aq37ck2lJaXSzN79mw8evQIVlZW6Nq1a4lhZk9vo3gYWlFREX799VeMHj1a61gtLS0xcuTIEsMotmzZIg2z00bfvn2RnZ2Ns2fPAgDOnz+PBw8eoF+/flqvi4wHe47puVxdXbF69WocP34cOTk5aNOmDUaMGCG9P3z4cAQEBJS483nHjh3SXdZt27bFyZMncf/+faxcuRIbNmzAggULAACTJk3CwoULsXLlSty/fx9Lly5Fnz59EBQUhLy8PPz4449IS0vDlStXcP/+fTRo0AA9e/bERx99hKlTp6JatWqQy+VYvXq1tO1x48bhk08+gZ2dHTZt2iQ91H7OnDn45JNPpLHDAPCf//wHy5YtK9Gep9nZ2SEwMBB+fn4QQkAIgVmzZsHe3h4HDhyQYp0/fz7WrFkDAFizZo0U84MHDzBx4kQAj4dy3Lt3DxMmTCjx5I/SliEi47Rnzx7p+p8wYQJ27typNt/IZDKsWrUKq1atwh9//IGOHTtK8wQGBmLy5MnIysrC+++/D0tLS3Tv3r3EmGUfHx9ERUVhwoQJGDBgAMLDw/HOO++gTZs2qFGjBq5cuYI1a9agRo0aUt6tX7/+M/cstGrVCsuWLcP06dPh4OAgFXBz5szBhg0bpKdHeHh4YOnSpTrLy0/mtubNmyMkJET6PFi3bh369++PiRMnQi6XIzc3V3oCxoQJE6T4/P39MXnyZDx8+FB6AkWXLl3g6ekJAJg/f760zoCAAGkdxfv46SEkCxYswMqVK/Hee+/BysoK7dq1w4cffoiMjIwS+2HZsmV48cUXcfr0aQQGBiI1NRWTJk3CN998A+Dx58PXX38NPz8/FBUVwcLCAtu2bUOtWrU0LkPGz0I87y4moufIzMzEwoULERAQYOhQtFZUVITJkydjx44dhg6FiIiIjAB7jqncwsPD0alTJ/zxxx8m9xOf0dHRqFWrFhITE/Hqq68aOhwiIiIyEiyOqdwSExOxatUqNGvWzOR6je/fv4958+ahfv36+PLLLw0dDhERERkJDqsgIiIiIlLh0yqIiIiIiFT0Mqzi/v2H+litpG7dGkhPz9HrNnTBFOI0hRgBxqlrphCnKcQIaBenk5P+fgxAU941lf1YFubUFsC82sO2GCdzagtQvvaUJ++aZM+xlZVpPBPWFOI0hRgBxqlrphCnKcQIGH+cxh6fNsypLYB5tYdtMU7m1Bag8trDG/LK6WD8YbXTh7R4o5IjISKqXMx/RGTOTLLnmIiIiIhIH1gcExERERGpsDgmIiIiIlLhmGMVjqEjIipJU14kIjJn7DkmIiIiIlJhcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhU+rULHnry7u0aKDXKy8/jECyIiIiITUeWK4+CIeLXT5Y0qORAiIiIiMjocVkFEREREpFLleo6JiEg/+GNKRGQOzLY41pSk4wrT1U5vi7r6DIeIiIiITIDZFse6wp9PJSKqGPYoE5EpYXGscjVRQ49y04r3KPODgYiIiMg08IY8IiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGp8Ia859DnjXq6whv+iMiYacqjQ1pUciBERGXA4ricNCX7J8nlVlAqCzQW0ixqiYiIiIwLi2MiItKJsnQaEBEZOxbHJoQ/SEJE5iQ4Il7tdHmjG2qnf+A0Rp/hEBEBMOPimD0YRETGLa7wrNrpbWE893QQUdVjtsWxMTGFm/qIqOrS9K0UOxmIqCoy+eLYHIcamGObiIjKSmNR3qNy4yCiqonPOSYiIiIiUjH5nmN+7UdEREREumLyxTEZDp/TTESV6cdDV5GdnffM9JG9+WsiRKQ7LI4NSNteb0038PHXp4ioKlsXtkft9Llu71ZyJERkDlgcm7Gy3NhXI8UGOWp6Yp7EnmAiIiKqKkymOH6yZ6D4Z5lJt9gDTUTmRNOPjHAYBhGVxmSKYzIcY3u0HMc6E1VNVx5FQllY8Y4R5hAiKg2LYzNWljHN+uiF1/TBo7zzotrphujFYY8SET1NXe5iwUxU9bA4NiGm/tg6TT8VezD+htrppvyhxOKbTImp5xZNNOUcJGqzFu16mdkrTWT6jK441lRUUNWjaZy5pqd26LPXp6znpa2tjdpHTT1vPZqKZm2vh7KupzhOeSPz+8NEV/gHDgGa/3C4mqj+CRma1/Ps/KV9c9dS9rLa6ZoKfm2fZmTKT/IwlT9AtB2SaGzxG4KxHFsLIYSo1C0SERERERkp/nw0EREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkYlQ/AnLq1CkcPnwYDg4OsLCwgJeXV4n38/Ly4OfnB2dnZ9y8eROenp5o3rw5AODWrVvw8/ODlZUVNm3aZJRxxsTEYOfOnWjfvj0SEhLg4uKCd955x+jiVCgU8PHxQbdu3aBQKKBUKrFkyRJYWurnb6mKHHcAUCgUGDlyJKZNmwZ3d3eji7Ffv35o1KgRAKBevXpYt26dXmKsaJyXLl3CyZMnYWlpiTNnzmDVqlVo0KCBUcV55swZfPbZZ7C3twfw+NgPGjQIs2bNMqo4AWDVqlWQyWQQQiA3N1cn11BF4gkJCcGVK1dgaWmJpk2b4r333gMA3L59G19++SVeeOEF3LlzB97e3rC1ta1QnIZsz9KlS5GQkCCtY/HixWjTpo1Rt0XT51dGRgbWrVuHJk2a4ObNm5gzZw4cHR1Nsi3+/v6IioqSXk+fPh29evUy2raU9nltitdMae0xtWumtBpFZ8dGGImcnBwxYMAAkZeXJ4QQwsvLS5w6darEPFu3bhWBgYFCCCGuXr0qxo4dK70XEhIidu/eLWbNmmW0cR49elRER0cLIYTIz88XL730klAoFEYXZ3JystizZ48037Bhw8S5c+eMLk4hhCgsLBSLFy8W06dPF99//71Rxrhp0ya9xKXLOB8+fCi8vLyk+RITE0V2drbRxRkfHy/+/vtvab6FCxeK27dvG12cly5dEsOGDZPm08U1VJF4/v33XzF8+HBRVFQkhBBi9OjRIiEhQQghxKRJk6S89N1334kNGzZUKM6y0ld7Kut6e5K+Pr+WLFkiDh48KIQQ4tixY2LevHn6bIYQQn9tMbXjUtrntSleM6W1x9SOTWk1iq6OjdEMq7h06RIaNmwIa2trAEDXrl0RFhZWYp6wsDB06dIFANCmTRtcvXoVWVlZAIDhw4dDLpcbdZz9+/eHi4uLNJ9MJtNbzBWJ09nZWfqLMisrCzk5OVLPpzHFCQDbtm3DW2+9hdq1a+slPl3EeO7cOWzbtg0bN27EhQsXjDLO8PBw1KhRAzt27EBAQAD+/vtv1KhRw+jibN68Odq3bw8ASE1NRV5enlGem3Xq1EFOTg4KCgpQUFAACwsLNG7c2GDxREREoEOHDrCwsAAAdOnSBX/++SeUSiXOnDmDTp06SesMDw+vUJyGbA8AZGdnY8uWLQgMDMQPP/yAggL1P89sLG0BNH9+hYeHS8tU1rHR52fxli1bsH37dgQGBuLRo0f6a4SKPj6vTfWaKa3+MLVrRlONostjYzTFsUKhKNH1bWdnB4VCofU8+qarOHft2oXp06ejZs2aRhvnwYMHMX36dEyZMgX169c3ujhPnz6NatWqoXPnznqJTRcxAsDcuXMxdepUTJs2DQsXLsStW7eMLs47d+4gOjoa7u7umDlzJn744QecOXPG6OJ80k8//SR9lW5scb7wwgt455138NFHH+GTTz7Bq6++Kg0FMUQ8aWlpJabb2tpCoVAgPT0d1apVk4rMysyp+mgPAAwbNgxTp06Fp6cn7t69i61bt+q5Jfr7/HpyGTs7Ozx48EDvhYu+2jJw4EBMmDABkydPhq2tLVasWKHbwNXQx+e1qV4zT3q6/jDVa+bpGkWXx8ZoimMHBwdkZ2dLr7OysuDg4KD1PPqmizgPHDiAnJwcfPDBB0Yd55AhQ/Ddd9/h4MGDevvLuCJxHj9+HHl5eQgMDMT169dx8uRJ7Nu3z6hiBCD9tV69enW0a9dOb73HFYnTzs4O7du3h1wuh6WlJVxdXUuMDzSWOIvl5+cjNjYWL730kl5irGicx44dw5kzZ7B582b4+/vj9u3b2Lt3r8Hisbe3LzE9OzsbDg4OqFu3LnJzcyGE0LhOfdFHewCgQ4cOsLJ6fDvNK6+8gsjISH02o9Q4tZ2ntPVmZWWhdu3aUtv0RV9tadWqlfRtlCkdl6c/r031mimmrv4w1Wvm6RpFl8fGaIpjV1dX3L17F/n5+QCACxcuwM3NDRkZGdLXNW5ubrh48SIA4Nq1a2jbti3s7OxMKs6ff/4ZCoUCM2fOxLVr10oMgjeWOKOiohATEwMAsLS0RMOGDZGUlGR0cS5atAienp7w9PRE69at0atXL4wZM8aoYjx9+rT0dS/w+GaVJk2a6DzGisbZo0cP3LlzR1rX3bt30axZM6OLs1hoaCgGDx6sl/h0EWdycjKcnJykdTk5OUnrMUQ8vXv3xt9//y19aFy8eBGvv/465HI5evTogcuXL0vr7NOnT4XiNGR7AMDPz0/axq1bt9C0aVOjbktp+vTpIy1TWcdGX20xxeOi7vPaVK8ZTe0BTO/YaKpRdHlsLERxdjECJ0+exKFDh1C3bl3I5XJ4eXlhzZo1qFOnDjw9PZGbmws/Pz84OTkhMTER06ZNk+6QPXr0KEJCQpCQkIARI0Zg6tSpRhfn0aNH4e3tLY2ZzMjIwOLFi9GjRw+jijM6Ohrbt29H+/btkZ2djZSUFCxfvlxvY1ArctwB4JdffsGuXbvg7OyMsWPH6iVRlTfGa9euISAgAB06dMC9e/dQr149TJ8+XefxVTRO4PFXbXfu3IFcLkdubi4WLFggfT1lTHECgKenJzZv3qz3+wzKG2dOTg6WLl2KRo0aSXdQ+/r6Vvgaqsh+CwkJQWxsLGQyGZo1a1biaRWbN29GkyZN8O+//2LBggWVdue9Ptrj4+MDBwcHVKtWDQkJCfDx8amUJzzo4/MrIyMDa9eulT78586da7JtWbduHR49egQHBwdcv34ds2fPLnFNG1tbSvu8NsVrprT2mNo1U1qNoqtjY1TFMRERERGRIRnNsAoiIiIiIkNjcUxEREREpMLimIiIiIhIhcUxEREREZEKi2MiIiIiIhUWx0REREREKiyOiYiIiIhUWBwTEREREamwOCYiIiIiUmFxTERERESkwuKYiIiIiEiFxTERERERkQqLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKTC4piIiIiISIXFMRERERGRCotjIiIiIiIVFsdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUz0HLNnz0anTp1w5swZAMDt27cxePBgA0dFRERE+sDimEza/v374eHhoddtbNq0CU5OTtLrxo0bY/fu3XrdJhGRsSlLvvXw8MD+/fsrvK3bt2+jTZs2FV4PUXmwOCYqh1q1ahk6BCIiItIDK0MHQOZhwYIFCAoKwksvvYTvvvsOSUlJcHd3R0REBO7du4epU6ciPz8fP/74I6ytrbFy5UokJCSgqKgI/fv3x9SpU6FUKjF58mRERUVh6dKlCA8Px9mzZ/HVV1/h5s2b2LdvH6pXr45q1aph/vz5UCgUCAwMRGpqKjw8PNC6dWssWbKkRFx79uzB1q1b0blzZ9ja2uLy5cuoVasWvvrqKyxfvhypqanIy8tDq1atsGTJElhZPb4kwsPDsXbtWtSpUwe9evUqsc4JEyYgMjISx44dQ1JSEnx9feHk5ITvv/8eR44cwapVq9C9e3esXr0aABAQEICIiAhYW1vDwcEBCxcuRL169SrnwBCR2THWfLtu3TpcuXIF9+/fR1BQECZPngw3NzdEREQgICAAcrkcdnZ28PX1hbOzM8aOHYsLFy5g6NChmDt3LiZOnAi5XI61a9di6dKlACD1VM+cObPUXHvs2DF88cUXcHR0RKdOnXD+/Hmkpqbi+PHjiI2NxapVq2BhYQGZTIalS5eiZcuWlX7cyIQIIh15/fXXxYULF4QQQuzYsUO0a9dOXL58WQghRGBgoPRvHx8f4e3tLYQQ4tGjR2Lo0KEiKChIWk/r1q2Fv7+/EEKIAwcOiKioKNG9e3eRl5cnhBDi22+/Ffv27RNCCLFv3z7h7u5ealybNm0Sr776qlAoFKKwsFCsWbNGpKeni+DgYGkeb29vsXfvXiGEEAqFQri6ukptOXr0qGjfvr2IjIwsEWNSUpLaGDZt2iS1759//hGDBg0SRUVFQgghPv/88xLrISIqD2PNt+7u7tL8QgiRmJgoXF1dRVxcnBBCiB9++EFMmDBBen/KlCni888/F0qlUsyaNUtkZ2cLIYRISkoSrVu3LrHu0nJt8fsuLi7ixo0bQgghVq9eLTIzM0WPHj3EqVOnhBBCnDhxQrzxxhuisLCw1HZQ1cZhFaQzffr0QVhYGADg8uXL+M9//oPw8HAAwP/+9z906NABRUVFOHDgAMaMGQMAqFatGgYPHvzMGLUBAwYAAIYOHYpOnToBAIKDg/Ho0SOMGzcOQ4cO1So2V1dX2Nvbw9LSEp9++ilq166Nu3fvYuzYsfDw8EBUVBT+/vtvAI97jR0cHNClSxcAQP/+/WFjY1OufWJra4vU1FQcPnwYSqUS8+bNQ7du3cq1LiKiYsacb58UGhqKjh07okWLFtI2Tp8+jXv37gEAPvvsM+zfvx/z5s3D2LFjUaNGjXJvCwCaN28u9Qp7e3vjxIkTqFGjBnr27AkAcHNzQ2pqKqKjoyu0HTJvLI5JZ9zc3HDixAnk5OSgevXq6NevH8LDw/HgwQPUrFkTFhYWSEtLQ35+Puzt7aXl7O3tkZKSUmJddnZ20r+rVauGH374AVFRUejfvz+WLl2KrKwsrWKrWbNmiddBQUHYs2cPtmzZgu+//x6jRo1Cbm4uAOD+/fuoW7duifnr1Kmj1faKNWjQAFu3bkVISAjc3Nywfv16KJXKcq2LiKiYMefbJyUnJyMuLg4eHh7w8PCAl5cXGjVqBIVCAeBxjpw4cSLOnz+vk46Dp3N9cnIyHjx4IG3fw8MD9vb2yMjIqPC2yHyxOCad6dmzJ27duoX9+/fj1Vdfxeuvv47//e9/CAkJweuvvw7gcWK2trZGWlqatFxaWhqcnZ01rlepVMLBwQFr167FoUOH8ODBA/j5+VUo1piYGLi4uEhFb0FBgfSek5NTifgAlJpI5XI58vPzpdeZmZnSvx89eoQXX3wRX375JYKDg3Hp0iVs27atQrETEZlKvm3QoAE6duyI77//XvovKCgIrVu3BgDk5eXh6tWraNmyJfz9/UtdV2m5trTtCUrDAwAAcWhJREFU169f/5ntP30vCdGTWByTzlSvXh3du3fHl19+id69e6Nu3bro2LEjAgMDpa+0LC0tMXLkSAQFBQEAcnNz8fvvv2P06NEa15uSkiLd+FGzZk20a9cOhYWFAB4PW3j06BEAYNasWSWK3NK88MILuHr1KvLz81FQUIDTp09L7/Xp0wdpaWk4f/48AODo0aPIycnRuK7GjRvj5s2byM/PR15envQ8ZOBxEb5p0yYAj4vu5s2bS7ETEZWXsebb4nlu3rwJPz8/DBkyBNHR0bhz5w4AQKFQwMPDA0VFRQCAzZs3Y+rUqVixYgV++uknXL58WVoP8LiDITAwEJcuXSo112rSt29fpKenIyYmBgCQk5OD8ePHV6g3nMwfi2PSKTc3N7z44ovSV1tubm5o06aNlOiAx3daW1hYYOzYsRg/fjyGDh2KESNGAAAmTZoEAJgzZ45UsNrb26N27doYO3Ysxo0bhwsXLmDOnDkAgFdeeQWFhYV477334OzsLD1totiBAwcQFBSEiIgIzJ8/X5r+7rvvolWrVhgxYgTmzJkDJycnREREYMeOHbC3t8fGjRuxfPlyjBs3DjExMWjYsCFWrlyJmJgYTJgwQYoxJSUFXbp0weuvv45Ro0Zh0aJFePnllxEREYEtW7agRYsWuHfvHtzd3fHee+/h4cOHmDx5sp72PhFVJcaWbwFgzJgx+O677zBv3jz06dMHTZo0wbp16zB37lx4eHjgk08+wWeffQa5XI65c+di9+7duHHjBhISEmBlZYUZM2Zg//79qFu3LoYOHYpx48bh9OnTaNu2bam59vTp0wgMDMSVK1ekdgGPh4wEBgbiiy++gLu7O6ZOnYpZs2aVGGpC9DQLIYQwdBBERERERMaAPcdERERERCosjomIiIiIVFgcExERERGpsDgmIiIiIlJhcUxEREREpPLsc1h04P79h/pYbYXUrVsD6eman1VrisytTebWHoBtMhWV1SYnp5rPn6mcjDHvFjPmc8aYYwOMOz5jjg1gfBVhzLEB2sVXnryrl+LYGFlZyQy27YPxh9VOH9LijQqt15Bt0gdzaw/ANpkKc2yTMTHm/avr2HSd76vSvtM1xld+xhwboP/4OKyCiIiIiEiFxTERERERkQqLYyIiIiIiFRbHREREREQqVeaGPCIiIqDkTXM1UmyQk51nwGiIyNiw55iIiIiISIU9x0REREamuHf76Z7tij4ClIiejz3HREREREQq7Dk2IH39OAgRERERlQ+LYyIiMkuaOiCIiErD4piIiMhE8BtHIv3jmGMiIiIiIhX2HJcT/3onIqpc5ph3DTX0IzgiXu30kb1bVHIkRMaHxbERMscPACIiMj8ssskcsTg2IU8XzcXPv2TRTERERKQbLI51jHdHExFRRV1NTAcAyOVWUCoLpOltm9ZVO7+23zjGFZ7VsGX2+BLxhjwiIiIiIhX2HKtwnC8RUeXiN226U9zT/LQhWnYE6/uzkGOUyRSwOCYiIpNmCkW2rmLUVAQbG01FMIdzkCngsAoiIiIiIhX2HJsBDgkhIiJ1NPXgEpFmLI6JiEiv9saGIic7z9BhkInRtrDnuGXSFQ6rICIiIiJSYc8xERGRmdJ8A5x21PXi2tra6GTdRMaGPcdERERERCrsOTZjvFGPiIiISDssjp/DFJ6faeqKv66ztbVB9hM37fDmCiIyd6by3GJ941M1yJiwOK6C2KNMREREpF6VK47ZE6w9/twn9wERVYyp9BBrirOlrJIDITKgKlcck2bG9rUWC1IiMlamUuzqm6anYbSUvVzJkWjGzxLSltkWx0/3ENdIsTHbh9DrKklr2zOgbcLRVfGtzXaNreAnIiIi42byxTGHSVAxUyiE2YNBRFWBrp6vrI2n8+vTN3mXdz3FmKerDpMvjokMiUmUyHhp+latbdO6FV4H6Z+uhmxoWk9whHbzA9rldX4+mC4Wxybk6SQtl1tBqSzQ2fp1lYhMoQdX3zQ9nu558z+NSZSIiKhysTgmMiMssqk8tH28o74fB6ltb602PcFUPuo6T+SPdFdCaDMMo6zzyh9ZQVmouw4k7YdxvqjX7fLxq/pjMsWxKY8t1sVXe4ak7dgxY7pL2dTpqtjV5XrK2huuq4KcBb/haJt3Nc1fw9ZGF+FopG0x/eT8uv4GjkyHtp9t2p5n2t7kvi5sj1bzD9GQAnVxs7ymPK/tDfeG+qyqKKMrjk25CAa0u3g4lu2x4gT19F/5LLI1M8STP/S9bmMbjmMsSZqIiCqXhRBCGDoIIiIiIiJjYGnoAIiIiIiIjAWLYyIiIiIiFRbHREREREQqLI6JiIiIiFRYHBMRERERqbA4JiIiIiJSYXFMRERERKRidD8Cogv379/Hxo0bcfXqVezbtw8AkJeXBz8/Pzg7O+PmzZvw9PRE8+bNDRxp2alr0/79+7F7927Y2Dz+9akxY8Zg5MiRBoyy7BITE7Fx40a0b98eycnJqFOnDry8vJCRkYF169ahSZMmuHnzJubMmQNHR0dDh1smmtrk7++PqKgoab7p06ejV69eBoy0bIqKijB9+nS4uLhAqVQiKSkJK1euRG5urskeI01t2rZtm0keI2NkzLnKmPOOsecPY84HpnBd5+bm4u2338Zrr70Gb29vo6tJno7PWK5ZAHjnnXekOCwtLbFz5069X7NmWRyfP38e/fv3x5UrV6RpO3fuRIMGDTB16lRcu3YNixYtwo8//mjAKLWjrk0AsH79ejRu3NhAUZVfRkYGBg8ejAEDBgAABg8eDDc3N+zduxc9e/bE4MGDcfz4cfj5+eGLL74wcLRlo6lNAPD9998bMLLyc3V1xcyZMwEAM2bMwOHDh3Hu3DmTPUaA+jYBpnuMjI0x5ypjzjumkD+MOR8Y+3Vd/IdPMWOrSZ6ODzCOaxYAevfujVmzZpWYtn79er2ed2Y5rGLgwIGwtbUtMS0sLAxdunQBALRp0wZXr15FVlaWIcIrF3VtAoBdu3Zh+/btCAgIQEZGRuUHVk4uLi7ShwDw+C//6tWrIzw8XDpOXbt2RXh4uKFC1JqmNgHAli1bsH37dgQGBuLRo0eGClErlpaW0odNQUEBUlJS0Lx5c5M+RpraBJjmMTJGxpyrjDnvGHv+MOZ8YOzXdXBwMLp27Vqi0DSmmkRdfIBxXLMAcP36dQQGBsLf3x9hYWEAoPfzziyLY3UUCkWJhG1nZweFQmHAiCru5ZdfxtSpUzF58mR06tQJH330kaFDKpcjR47gtddeQ8uWLUscJzs7Ozx48AAFBQUGjlB7T7Zp4MCBmDBhAiZPngxbW1usWLHC0OFpJSIiAtOmTYObmxs6depkFsfo6TaZ+jEydsaYq4w57xhz/jDmfGCM1/WNGzcQHx+PN954o8R0Y6lJNMVnTNfs1KlT4enpiZkzZ+Krr77C2bNn9X7eVZni2MHBAdnZ2dLrrKwsODg4GDCiimvSpAns7e0BAK+88grOnj2LwsJCA0elncjISJw5cwYLFy4EUPI4ZWVloXbt2rCyMq3RP0+3qVWrVqhRowaAx8cpMjLSkOFprXfv3ti+fTtu376NXbt2mcUxerpNpn6MjJ2x5SpjzjvGnj+MOR8Y43V95MgRWFtbIzAwEOfPn0dMTAy+/fZbo6lJNMVnTNesi4sLAEAmk+Gll17CmTNn9H7eVZni2M3NDRcvXgQAXLt2DW3btoWdnZ2Bo6qYdevWSX8p3bx5E40aNYJMJjNwVGUXFhaGv/76C4sWLcL9+/dx8eJF9OnTRzpOFy5cQJ8+fQwcpXbUtcnPz096/9atW2jatKkBIyy7GzduSF9hAUDjxo1x+/Ztkz5GmtpkqsfIVBhTrjLmvGPM+cOY84ExX9czZsyAl5cXPD090a1bN7i4uOCDDz4wmppEU3zGcs3GxcXh559/ll7funULTZo00ft5ZyGEEDpdoxGIiopCcHAwIiIiMHbsWEyaNAkA4OfnBycnJyQmJmLatGkm9bQKdW3as2cP/vnnHzRu3BjXr1/H+PHj4erqauhQyyQ2NhYeHh7o2LEjACAnJwfjxo1Dv379sHbtWjRs2BBJSUmYO3euyTwJQVObEhIS8OjRIzg4OOD69euYPXv2/2vvzgOiqvr/gb/ZQUBZRNxTe1xRxDXJDbesxP2p5BEyNXEJTa0ENDWtR9w1l1LKx9Ss7CsCohWZCpGKaIqC4b6AqMgqIjtzfn8w3p8oIzMwK75ffzkzd+68zx3uuR/PPfeOQfztJScnY+XKlejQoQNKS0tx7do1fPrppzAzMzPY70hRm3bu3GmQ35E+0ue+Sp/7HX3vP/S5PzCE/ToyMhK7d+9GSUkJxo8fj8GDB+tVTfJ0vszMTL3YZ9PS0vD555+jffv2yMvLQ2lpKQIDA5Gbm6vRv7taWRwTEREREVXHCzOtgoiIiIioKiyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQkx+KYiIiIiEiOxTERERERkRyLYyIiIiIiORbHRERERERyLI6JiIiIiORYHBMRERERybE4JiIiIiKSY3FMRERERCTH4piIiIiISI7FMRERERGRHItjIiIiIiI5FsdERERERHIsjomIiIiI5FgcExERERHJsTgmIiIiIpJjcUxEREREJMfimIiIiIhIjsUxEREREZEci2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTAbh9+zbefPNNXccgIiIiHWNxTHpn37598PHx0epnNm3aFD/99JNG1j1w4ECcPHlSI+smItIXuui7iTSBxTGRXN26dXUdgYiIiHTMSAghdB2C9FNAQABCQ0PRvXt37Ny5EykpKfD29kZMTAzu37+PKVOmoLi4GD/88APMzc2xbNky3LhxAzKZDIMGDcKUKVNQUlKCyZMnIy4uDosWLUJ0dDROnTqFLVu24ObNmwgJCYGVlRUsLS0xb948ZGZmYtGiRcjIyED79u3Rpk0bLFy4sEKuTZs24ccff4SHhweys7ORlpYGR0dHLF++HA4ODgCAmJgYbNq0CWZmZrCxscGSJUvg7Owsvff1119HTk4OEhMT0aVLF9y9exexsbE4fPgwjI2NMXv2bJw7dw5BQUEICwtDZmYm1q9fj/DwcBw/fhyOjo7YtGkTLCwsnvt5gYGBOHDgAFq1aoW6devC398fHTt2RFhYmLTdnJ2dsWTJEtjY2OCzzz7DgQMH4O3tjatXryIxMRFjx47FzJkztf79E5Fh0te+Gyjvv+Pi4gAAVlZWWLp0KZydnXH48GGsWrUK9evXR6dOnfD3338jIyMDR44cQWJiIoKCgmBkZAQTExMsWrQIL7/88nPXR1Qjgug5+vXrJ86cOSOEEGL79u2iffv2IiEhQQghRHBwsPTvwMBA4e/vL4QQoqCgQHh6eorQ0FBpPW3atBEbN24UQggREREh4uLiRM+ePUVRUZEQQojvvvtOhISECCGECAkJEd7e3s/N5e/vLwYPHiwePnwohBDi008/FXPnzhVCCJGcnCzc3NzEtWvXhBBCfP/992LChAkV3uvp6Sny8/NFbm6u2Lx5s5QxJSVFCCFESkqKaNOmjYiMjBRCCPHFF1+IQYMGidTUVCGTycSIESPEgQMHlPq8AQMGiNjYWOnx6dOnRc+ePUVmZqYQQojly5eL+fPnS697e3uLiRMnitLSUnHt2jXx888/P3dbEBE9TV/77p07dwqZTCYt//HHH0uvhYSECFdXV3H16lUhRHnfmJubK1555RVx/PhxIYQQR48eFa+99pooKyurcn1E1cVpFfRc/fv3R1RUFAAgISEBQ4YMQXR0NADgn3/+gYuLC2QyGSIiIjB27FgAgKWlJd58803s27evwroGDx4MAPD09ESnTp0AAGFhYSgoKMD48ePh6empcjYbGxsAwMiRIxEZGYmysjIcOHAAHTt2RKtWraTPO3HiBO7fvy+9193dHVZWVrC1tcWMGTMUfsarr74KAGjTpg3q1q2Lxo0bw8jICK1bt0ZKSgoAKPV5TwoNDcXAgQOlUe7hw4cjIiIC4omTOP3794eJiQlatWqFt956S6XtQkSkr313o0aN8O6772L8+PHYsWMHLly4UOH1li1bSqPC/v7+OHr0KOrUqQN3d3cAgIeHBzIyMnDu3Dml1kdUHaa6DkD6zcPDA+vXr8fUqVNhZWWFHj16YPfu3fD29oatrS2MjIyQmZmJ4uJiqdgDAAcHB6SlpVVY1+NCFijvhL///nts3boV69evh4eHBz7++OMK66hKvXr1pH/b2dmhpKQE2dnZuHfvHq5du1bhwpAmTZogMzMTDRo0AADY2toq9RmPM5uYmMDa2lp63tTUFCUlJQCg1Oc96enlS0tLUb9+fWRnZ0vtVzYfEVFl9LHvvnnzJmbPno0ffvgBrq6uOHnyJAIDAyss83Tfd+/ePTx48KBC/+rg4ICcnByl1kdUHSyO6bnc3d0xZ84c7Nu3D6+++irc3d2xYMEChIeHo1+/fgDKOypzc3NkZWVJ/+PPysp67ryvkpISODo6YvXq1Xj48CECAgKwYsUKrFixQulsDx48kP6dnZ0NMzMz2Nvbo1GjRujYsSOCg4MrLPtkB69Oqn5eo0aN0KxZMyxevFh6LisrS6X/GBARPY8+9t3//PMPrK2t4erqCqB8YKAqjRo1QsOGDbFr1y7puby8PJibm+OPP/5QeX1EyuC0CnouKysr9OzZE1999RX69u0Le3t7qRB8fJrL2NgYo0aNQmhoKACgsLAQv/76K8aMGaNwvWlpadLFGra2tmjfvj3KysoAANbW1igoKAAAzJw5U2GH99dffyEvLw9A+Sm+oUOHwsTEBMOGDcO5c+eQmpoKAMjMzISPjw9kMpkatsizqvo8a2trFBYWIjY2Fjt27MDo0aMRHR0tFffXr1/H9OnTNZKNiF5M+th3v/TSS8jNzcWNGzcAlF/IXJUBAwYgOzsb58+fBwDk5+fj3XffRV5eXrXWR6QMjhxTlTw8PFBUVCSd7vLw8MCpU6cqTDMICAjAsmXL4OXlhbKyMnh6emLkyJEAgEmTJgEA5s6dizlz5sDd3R0ODg6oV68evLy8YGxsDAsLC3zxxRcAgF69emHLli0YN24cOnbsCFPTyv9M3d3dMX/+fKSmpsLBwUEauWjWrBnWrFmDjz76CGZmZjAyMsLSpUthZmaG7du3IyYmBhYWFigoKMC8efMAABMmTJAybty4EXPnzgUATJ8+HdOnT0dwcDAyMjKwYcMGODs7S+to0aIFhg8frvDzAOCdd97BihUrYGNjg//+979o3bo1PvzwQ0yZMgWWlpYwMzPD8uXLAQArV65EUlIS0tPT8eDBA0ycOFF9XyQRvVD0re92cXHB1KlTMXnyZLRt2xZOTk5IT0/HvHnzMHr0aKmfnTRpEv73v/8BKJ/SERwcjBUrVkAIASEEZs6cCQcHBzg4OChc38qVKzW+fan24q3cyCAFBASgSZMmvMUZERERqRWnVRARERERyXFaBRmcTZs2SdMaGjZsyFudERERkdpwWgURERERkRynVRARERERyWlkWkV6+sNqvc/evg6ys/PVnKZmmEk5zKQcZlJObc3k5KS5H3d53O/q27bTtzyA/mXStzyA/mXStzyA/mXStzyAfmSqTr+rVyPHpqYmuo7wDGZSDjMph5mUw0zVp2859S0PoH+Z9C0PoH+Z9C0PoH+Z9C0PoJ+ZlMEL8tTs4PXfn3luWKvXdJCEiEg/VNYvAuwbiUg/sTjWAh4YiIiIiAyDXk2rICIiIiLSJRbHRERERERyLI6JiIiIiORYHBMRERERybE4JiIiIiKSY3FMRERERCTH4piIiIiISI73OSYiIrWo7J7uddIsdJCEiKj6OHJMRERERCTHkWMd4i/nEREREekXFsd6iEUzERERkW6wOK4mRQUsEREphwMBRKSPOOeYiIiIiEiOxTERERERkRynVcgpOr33ntNYLSdR7HHGOmkWyH9UJD3PU5BERERE6sHimIiIVKLpay44F5mIdInTKoiIiIiI5FgcExERERHJcVpFFX5OPFBhfi8RERER1V4cOSYiIiIiknvhRo754x1EREREpMgLVxyT5oXFXK/0+VF9W2k5CREREZFqOK2CiIiIiEiOI8dERFQpfZuGxvsfE5E2sDiuBXjAICIiIlIPFsdUbU/OLba2tsAjPbzlHec/ExERkSpYHNditXVEWZMFL4tpIiKiF1utLY71ba6cJl1MzlZx+T2VPv+ySY9Kn9dVYaioUCWiF5Oivm6YDroo/keaqPaqtcUxqQ+LVCIyRIr6riljOms5CREZEhbHpHO6KL5Z8BPVHprcn3XVV3Bkmkh3WByT1mj6IPP0+q2tLTS27sd4oCIiZairD2FfRKR5BlMcv0hziKn2+iHyYqV39eCBjej/U/U6imtlpyp9XtF1FIr2QyIiwICKY/r/BwwzM1OUlJTqOA0Bmh/F4SgRaQMHH9RH1TNkYTHX1XIrTHWfmXs6E/scepGwONYhRaMj7ZrbazlJOVVHX0gxRQcqRVM99G0OtCpFOQt4qoqu+jpFfZor+mj0c4nIsOldcWzoIxiqng7U1DrUSdWimUW25qlakD6v+Nb2D7ioK7umi+/K5rA/elTEor8WSCqIRUnZs2ff2Ecppq7/wFenjwKU66cM5YwdBxT0n5EQQug6BBERERGRPjDWdQAiIiIiIn3B4piIiIiISI7FMRERERGRHItjIiIiIiI5FsdERERERHIsjomIiIiI5FgcExERERHJ6fRHQN5++21YWJT/YpixsTF27NiBnJwcrFmzBs2aNcPNmzcxd+5c1K9fXyt5bt++jffeew+NGjUCAOTl5aFt27Zo0qQJ4uLipOWmTZuG3r17ayxHeno61q9fj4sXLyIkJAQAUFRUhBUrVsDZ2Rk3b96Er68vWrZsCQAIDw9HUlISjI2N0bx5c4wbN04rmYKDg5GRkQEnJyckJiZi1qxZePnllwEAAwcORJMmTQAADRo0wJo1a7SSad++ffjpp5+kv6uxY8di1KhRAHS3nebPn4+UlBRpmcuXLyMkJARNmzbV+HZKTk7G+vXr0aFDB9y7dw92dnbw8/N77n727bffIi8vD7m5uejduzcGDRqklUzLli2DlZUV6tSpg4sXL2L+/PlwcnLC7du38f7778PJyQkA4OLigoCAAK1k2rhxo8J9X9PbSVXHjx/H77//DkdHRxgZGcHPz08rn6tqP66J7aauPvP27dv46quv8NJLLyE1NRX+/v6wtrZWW6bq9E/qyqTOviApKQm7d+9G06ZNkZmZCX9/f5iaqlZOqHOfU0ceAJDJZJg2bRpcXV1RUlKClJQULFu2DIWFhTrZRoryfPPNNzrbRgBQWFiIt956C3369IG/v7/O9zWNEDq0YcOGZ55buHChOHjwoBBCiMOHD4uPP/5Ya3mysrLEsWPHKuQ7depUpTk16ddffxWHDx8Wo0ePlp7bunWrCA4OFkIIcfHiReHl5SWEEOLu3btixIgRQiaTCSGEGDNmjLhx44ZWMq1bt0763IMHD4qpU6dKr2ljm1WWKSQkRKSkpDyzrC630+O/ZyGEePjwofjggw+kx5reTufOnROHDh2SHr/xxhsiISFB4X4WHx8v3n//fSGEECUlJWLIkCEiNzdXK5nWrl0rPbd161axdOlSIYQQKSkpIiQkRK0ZlM2k6PvRxnZSRX5+vhg8eLAoKioSQgjh5+cnjh8/rpXPVqUf19R2U1efOWnSJHHu3DkhhBA7d+4U69atU2um6vRP6sqkrr5AJpOJYcOGifv37wshhAgKChI///yz2vKous+pK48QQpSVlYnNmzdLj6dNmybCw8N1to0U5dHlNnr8/nnz5only5cLIXS/r2mCTqdVXL58GcHBwdi4cSOioqIAANHR0ejSpQsAoGvXroiOjtZaHnt7e7z66qsAgOLiYiQmJqJ79+4AgK+//hrbtm1DcHAwCgoKNJrj9ddff+Z/UFFRUdJ2adu2LS5evIi8vDzExMTAxcUFRkZGAIAuXbrgzz//1Eqm2bNnS58rk8lQp04d6bXTp0/jm2++wfr163HmzBm151GUCQB2796Nbdu2YdOmTcjJyQEAnW6nN998U/r33r17MXbsWOmxpreTq6srBg8eLD2WyWSwsrJSuJ8dPXoUbm5uAABTU1O0atWqwgiFJjPNmTNHek4IUeHv6ejRo/j222+xbt06XL16Va15npcJqHzf18Z2UkV8fDwaN24Mc3NzAOXf6eM+VdNU6cc1td3U0WeWlJTg5MmT6NSp0zO51ZUJUK1/UmcmdfUFKSkpKCwslM7kVDeTuvY5deUBys98zJgxAwBQWlqKtLQ0tGzZUmfbSFEeQHfbKCwsDF27dkXTpk2l53S9r2mCTqdVTJkyBa6urigrK8P48eNhbW2NzMxMqUOxsbHBgwcPUFpaWu3h/+o6cOCAVNS8/vrraNKkCerUqYPdu3fj888/x7Jly7Sa58ntApRvm8zMTGRlZVV4/vE21Kbi4mKEhoZi8eLF0nMfffQRXF1dUVBQgNGjR2Pr1q146aWXNJ6lR48e8PDwgIODA6Kjo/Hhhx9ix44derGdZDIZ/vrrL0yYMEF6Tpvb6dChQ+jTpw9efvllhftZVlYWWrVqJb3HxsYGWVlZGsnzdKbHcnNz8ddff2Hjxo0AAAcHB8yaNQutW7dGRkYG3n77bYSFhaFu3boaz6Ro39f2dqqKov5BG1Tpx7W53VTtM7Ozs2FpaSkdyDWxDVXtnzSVqSZ9gSb+1mqyz2kiT0xMDL777jt4eHigU6dOOt9GT+extLTUyTa6evUqrl+/jrlz5+LSpUvS8/q4r9WUTkeOXV1dAQAmJibo3r07Tp48CUdHRzx69AhA+ZzfevXqab0wBoDffvtNKo5bt24tjWL16tULsbGxWs/z5HYByreNo6MjHBwcKjz/6NEjODo6ai1XcXExPvvsM8yZMwfNmzeXnn/83VpZWaF9+/YaGz1+WrNmzeDg4ACg/Ls6deoUysrKdL6dAODIkSPw8PCQOgRAe9spNjYWJ0+exPz58wFA4X729HbKy8uTtqemMwHAw4cPsWTJEixbtgx2dnYAgDp16qB169YAgPr166N+/fq4ePGiVjIp2ve1uZ2Uoah/0AZV+nFtbjdV+0x7e3sUFhZCCFFheXVStX/SRKaa9gXq/lur6T6nib/9vn37Ytu2bbh9+zZ2796t8230dB5dbaNDhw7B3NwcwcHB+Pvvv3H+/Hl89913ermv1ZTOiuNr167h//7v/6THt27dQrNmzdC/f3+cPXsWAHDmzBn0799f69lOnjwJNzc3mJmZAQBWrFhRIeeTRaC2eHh4SNvl0qVLaNeuHWxsbNC3b19cuHBB+iM7e/Ys+vXrp5VMBQUFWLx4MSZOnIiOHTsiMjISAHDixIkKUxYef7fasGbNGpSWlgIAbt68iSZNmsDExESn2+mx0NBQjB49Wnqsre0UFRWFv/76CwsWLEB6ejrOnj2rcD/z8PBAfHw8AKCkpATXr19Hjx49tJIpKysLS5Yswbx589CsWTPp7yksLEwapSgpKcG9e/ekixg1nUnRvq+t7aQsNzc33LlzB8XFxQDKv1MPDw+Nf66q/bg2t5uqfaaZmRleeeUVJCQkPJNbXVTtn9SdSR19QbNmzWBpaYn09PQaZ1LHPqfOPFevXq0wHalp06a4ffu2zraRojy62kbTp0+Hn58ffH190a1bN7i6uuK9997Ty32tpozE49RalpaWhs8//xzt27dHXl4eSktLERgYiNzcXKxevRqNGzdGSkoKPvroI63dreKxuXPn4tNPP5X+h79mzRoUFBTA0dERly9fxqxZs6R5P5oQFxeHsLAwxMTEwMvLC5MmTQJQXqQ7OTkhOTkZU6dOrXA1aGJiIkxMTNCiRQuN3IWhskwff/wxrly5ggYNGgAA8vPzERISgkuXLmHTpk1wcXHB/fv30aBBA0ybNk0rmfbs2YMrV66gadOmuHz5Mt59911pDpautpOlpSWSkpKwf/9++Pv7S8tqYzslJibCx8cHHTt2BFD+HY0fPx4DBw5UuJ99++23yM3NxYMHD9CvXz+134VBUaZdu3ahtLRUGjG2trbGli1bcOLECezZswft27fHrVu30K1btwrztjWZ6caNGwr3fU1vJ1UdO3YMkZGRsLe3h5mZmVbuVlGdflwT201dfebt27exefNmNGvWDHfv3kVAQEC1r6BXV/+krkzq7AuSkpKwa9cuNG7cGA8ePKjWnQ/Uuc+pIw9QfgeNlStXokOHDigtLcW1a9fw6aefwszMTCfbSFGenTt36mwbAUBkZCR2796NkpISjB8/HoMHD9bpvqYJOiuOiYiIiIj0DX8EhIiIiIhIjsUxEREREZEci2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQkx+KYiIiIiEiOxTERERERkRyLYyIiIiIiORbHRERERERyLI6JiIiIiORYHBMRERERybE4JiIiIiKSY3FMRERERCTH4piIiIiISI7FMRERERGRHItjIiIiIiI5FsdERERERHIsjomIiIiI5FgcExERERHJsTgmIiIiIpJjcUxEREREJMfimIiIiIhIjsUxEREREZEci2MiFX322Wfo3r079u3bp+soREREpGYsjkmn9u3bBx8fH13HeC4fH58KhfBnn32G9u3b6zAREZHyDKGfrYmn+2iimmJxTEREREQkZySEELoOQboXEBCA0NBQdO/eHTt37kRKSgq8vb0RExOD+/fvY8qUKSguLsYPP/wAc3NzLFu2DDdu3IBMJsOgQYMwZcoUlJSUYPLkyYiLi8OiRYsQHR2NU6dOYcuWLbh58yZCQkJgZWUFS0tLzJs3D5mZmVi0aBEyMjLQvn17tGnTBgsXLqyQSyaTYcmSJbh8+TKMjY3RokULLFiwACdOnMCqVatQv359uLq6IjY2Fvb29vj888+xbt06JCQkYOjQoZgzZw4AQAiBbdu24ffff4eJiYm0HhsbGwDAn3/+ia+++gomJiawtLTEwoUL0aJFC6xZswY//vgj6tevDycnJ0yePBkeHh7w8fFBt27dcP36dVy6dAlDhw7F3LlzUVxcXGEbREVF4caNG/D398eQIUMAAI8ePcIXX3yBmzdvQgiBkSNHwsvLCwDwxx9/4JtvvoGlpSWMjY0xa9YsdOnSBWfOnMGqVatgZmYGIQQmTZqEAQMGaPEvhIhqSl/7WQBITk7G0qVLUVhYiJKSEvTu3RuzZs0CoLh/3LNnD7Zu3YrOnTvD1tYWZ86cQbt27eDn54e1a9ciKSkJ7733HsaPH4/z589j4cKFePjwIYYPH46///4bDx48wLx589C3b18AwJ49e3Dw4EEYGRkBABYuXIh//etfAMr7zaCgIFy7dg0A0LJlS3z88cfYvn37M310VFQUDhw4AG9v72f66Me+/fZb/P777zA1NUX79u3h7+8Pc3NzXLt2DUuWLAEAlJaW4t///jfGjBmDjIwMBAQEoKioCKWlpRgwYAB8fX0198dCuiWI5Pr16yfOnDkjhBBi+/bton379iIhIUEIIURwcLD078DAQOHv7y+EEKKgoEB4enqK0NBQaT1t2rQRGzduFEIIERERIeLi4kTPnj1FUVGREEKI7777ToSEhAghhAgJCRHe3t4KM0VFRYnJkydLj2fMmCFSUlKk97q5uYnU1FQhk8nEyJEjxZQpU0RRUZHIyMgQLi4uIi0tTQghRGhoqHjzzTdFfn6+EEKI+fPni8DAQCGEEMnJycLNzU1cv35dCCFEWFiYGDp0qCgpKRFCCOHt7S3lfczb21v4+voKmUwm0tLSRIcOHcS9e/cqbIPg4GAhhBAHDx4Ur732mvTaggULxLx584QQQjx8+FAMHDhQnDp1SgghRK9evUR6eroQQohDhw6JDRs2CCGEGDt2rIiPjxdCCJGUlCRtfyIyLPrYz5aWloo33nhD7Nu3TwghRG5urujbt68Qour+ccOGDaJfv34iNzdXFBUVCXd3d/Hpp58KmUwmEhMThZubm7RsbGysaNu2rTh69KgQQoi///5buLm5iaysLCGEED/++KOUPzY2Vnh5eUkZP/30UxEQECCEEKKsrExMnTpVxMbGCiEU99FTpkyptI8ODw8Xr7/+usjPzxcymUzMmjVLbN68WQghxKxZs8TBgweFEELcv39fOv6sWLFCbN26VQghxKNHj8S4ceMUbk8yfJxWQZL+/fsjKioKAJCQkIAhQ4YgOjoaAPDPP//AxcUFMpkMERERGDt2LADA0tISb7755jPzvQYPHgwA8PT0RKdOnQAAYWFhKCgowPjx4+Hp6alUprp16+Ly5cs4duwYZDIZ1q5di8aNG0uvt2zZEo0bN4aRkRH+9a9/oVWrVjA3N4ejoyMcHBxw+/ZtAEB4eDjeeOMNWFlZAQDGjBmD/fv3o6ysDAcOHECnTp3QsmVLKfOdO3dw9uzZ52br3bs3jIyM0KBBA9jb2yM1NbXC649HQ9q2bSu9JpPJEB4eLm0/GxsbDBgwAPv37wcA1KtXDz///DNyc3MxcOBAaWSiXr16CA8PR0ZGBtq1a4fFixcrtf2ISL/oYz8bHx+P5ORkDB8+HABga2uLdevWAYBS/aOrqytsbW1hbm6Ol156CW3atIGRkRHatm2L/Px8ZGZmSstaW1vDw8MDANC1a1c4OjpK7f/Xv/6FadOm4T//+Q/WrFmDCxcuACjvN8PCwjBmzBgAgLGxMQICAqRRZUX69Okj9dF2dnZSPxwaGophw4bBysoKRkZG8PT0RHh4OIDyvva3337D7du34eTkhI0bNwIA7OzsEBMTgytXrqBOnTr43//+p9S2JcPE4pgkHh4eOHr0KPLz82FlZYWBAwciOjoaDx48gK2tLYyMjJCVlYXi4mI4ODhI73NwcEBaWlqFdT2ergCUd+zff/894uLiMGjQICxatAh5eXlKZerSpQs+//xzfPPNNxgwYAC2bdsG8cRMIGtra+nfpqamzzwuKSkBANy7d++ZzCUlJcjIyHjmNRMTE9StWxf37t17brYn22hubi591tOvW1hYSK893n6rVq2Cj48PfHx8cOrUKRQXFwMAtm/fjrS0NLzxxhuYPXs27t+/DwBYs2YNLC0tMXr0aEyePBk3b96seuMRkd7Rx342LS0NdevWhampqfRct27dADzbd1bWPyrqhx+v78m+sV69ehU+287ODvfv38fDhw8xdepUvP322/jhhx+wdu1aFBYWAkCl26NFixZwdHR8brue3D5P9sP37t1DRESE1Ad/8803MDYuL4fmz5+Pdu3aYcKECfDy8kJ8fDwAYPLkyXjttdcwZ84cjBw5UvoPDtVOLI5J4u7ujlu3bmHfvn149dVX0a9fP/zzzz8IDw9Hv379AJR30Obm5sjKypLel5WVBWdnZ4XrLSkpgaOjI1avXo3IyEg8ePAAK1asUCrTw4cP0bNnT3z33XfYtWsXwsLCEBYWpnLbGjVq9ExmMzMz1K9f/5nXysrKkJubi4YNG6r8OVV5vP0WLlyIXbt2YdeuXdi7dy8WLFgAoPzAs2TJEhw+fBiOjo4IDAwEABQXF2PevHk4evQoevTogRkzZqg9GxFpnj72sw0bNkRubi5KS0ul565du4bCwkK1948PHjyo8Dg7OxsNGjTAjRs3kJeXJ51xezJLZdsjLS0N6enp1crQqFEjvPXWW1If/PPPP2P37t0AgNzcXMyYMQN//PEH3nnnHUyfPl0a/fbx8cGBAwfg7++PefPmITk5uVqfT/qPxTFJrKys0LNnT3z11Vfo27cv7O3t0bFjRwQHB8Pd3R1A+emsUaNGITQ0FABQWFiIX3/9VTrdVZm0tDTpAhBbW1u0b98eZWVlAMpHHAoKCgAAM2fOrNAhAsChQ4ewZ88eAEDz5s3h7OwMmUymcttGjx6N3377TRqJCAsLw4gRI2BiYoJhw4YhMTERt27dAgD88ssvaNy4Mbp06VIh482bN5U+2CjyePs9nkYBAF9//bVU8E+bNg1lZWWwtLSEq6urtJ1mzZqFgoICmJqaomvXrtLzRGRY9LGf7dy5M5o3b44DBw4AAHJycjB79myl+kdVFRYWSqOup0+fRlZWFvr374/GjRvD1NQU58+fBwDExMRI73m8PR5PK5HJZFiwYAEyMjIqtE/ZPvrx8aCoqAgAEBsbK01VCwwMREZGBoyMjNCjRw+UlpbCyMhIusAQKJ9G8vjiaKqdTKtehF4kHh4eKCoqgq2trfT41KlTFU6bBQQEYNmyZfDy8kJZWRk8PT0xcuRIAMCkSZMAAHPnzsWcOXPg7u4OBwcH1KtXD15eXjA2NoaFhQW++OILAECvXr2wZcsWjBs3Dh07dqxwWg8A3NzcsHz5chw5cgT5+flo27YtRo4ciRMnTiA4OBgZGRnYsGEDnJ2dERMTAwsLC7Rr1w7Hjh1Deno6li1bhjVr1mD48OG4f/8+JkyYUOGuFwDQrFkzbNiwAf7+/tLV2Fu2bJGyjB07FqtXr0ZoaCg+/vhjrFy5EklJSUhPT0fLli0RHh5e4bOWLVsmbYNt27ZJV0hPmjQJ//vf/6TtN27cOOlK6Q8++AAA0KNHD4wfPx5mZmYoKyuTOuxBgwZh4sSJMDMzQ2FhYY2LdCLSHX3rZ01MTLBlyxYsXboUe/fuhUwmw8KFC2FmZvbc/jEiIgKhoaEoKirCDz/8gKysrAp947Zt26ScwcHBAABnZ2ckJSVh27ZtyMnJwZdffgl7e3sAwKeffooFCxagdevWeOmll6S2Ptlvenl5QQiB4cOHS/ebV7WPHj58ONLT0+Ht7Q0rKyvY2Njg888/B1A+p9rPzw/m5ubIy8vDypUrYWVlhddffx1ffPEFTExMkJeXh9mzZ0sZqfbhrdyIiIhI406ePInAwEAcOXJE11GInovTKoiIiIiI5FgcExERkUadP38ey5YtQ3p6uvTjIkT6itMqiIiIiIjkOHJMRERERCSnkbtVpKc/1MRqlWZvXwfZ2fk6zfA8+pyP2aqH2apPn/OpO5uTk63a1vW05/W7+ryN1YntrD1ehDYCL0Y7dd3G6vS7tXLk2NTURNcRnkuf8zFb9TBb9elzPn3Opora0o6qsJ21x4vQRuDFaKchtpH3OSa1O3j990qfH9bqNS0nIaLahH0LEWkDi2MiItIriopgIiJtYHFMkoPXf0edNAvkPyqq8DxHZYiIiOhFUSvnHBMRERERVQdHjomISC04J5iIagMWx0REpBOcW0xE+ojTKoiIiIiI5FgcExERERHJsTgmIiIiIpJjcUxEREREJMcL8oiISKN44R0RGRIWx0REpBJ9K3Yf53n6R4x4Czkiqg5OqyAiIiIikmNxTEREREQkx2kVBkTffn1K1VOr6sq/JmpPpc9/5PGOSushotpN3/pMIjIMLI5J53gAIyIiIn3B4rgWU1fRqW8X3xARERFpCotj0ltPT58wMzNFSUmpjtIQUW3Bs1VE9Dy8II+IiIiISI4jx7WAui6Me5GExVyv9PlRfVtpOQkRERHpExbH1aSO03I8tUdE+oz/kSaiFxGLYy14+gDz9K84VbU8aQ9HlIkMz8XkbADPXpfQrrm9riIRkQFjcUxVenzgeZohHHgUFbtERERElWFxTEREZCDCYq7D2toCj546+8izW0Tqw+KYao3Kp6P8S+s5iMgwVdaH8BoQohcPi2PSOUXTNtSxnpdNVFvHtbJTCl7hqAwRVZ+q1zNwShiR7rA4pmoz5LnImsYL+4hqB03vyyyCifQPi2NSOxbNRKTP1NFHPf0Lno995PFOtTLVFP9DTqQ+LI6JiIgUUDzViohqKxbHL6AXaWT3RTuwVTZ6ZG1tgSFdm+ggDZFuqXo9gzquf+A0CSLDx+JYzfgDHvQ8qh44eUqUXkTqukhXnyj6j/rLJj20nKQcp2EQKcbimCQXk7Of+YUpda/fUFVV1FZ231EievGoerZK00UzR7KJVMfiuAqGMBJsyEVnbaVvo0SKcPSIAMPo54iItIXFMRERkYHTtxHomt6/+Xln41RdN/+zT6p64YpjQx4h4QgxaQsPMkQvJnVNw+B0DjJkL1xxrE9Y7BqOquYRmhWYoqSs+nO1Fa1/TVTlz+vqXqpE1cG+TnXP63Nq2t9Q9ejboIG+5alN9K44VjSyq+rv26s6Qqzq7c1UWf7pZTV50RvpN3XdWk7RDxBUxqzAFI9iuqiUR9Gp2Mo+V9VC/el9s06aBfIfFam8j6vrwPC8Ea7KTu2+SAceFrWGT119jrqmZyibx6zAFM1Reb+lLvowSv5kH6NvRXZlNJ1RXwp+IyGE0OonEhERERHpKWNdByAiIiIi0hcsjomIiIiI5FgcExERERHJsTgmIiIiIpJjcUxEREREJMfimIiIiIhIjsUxEREREZGc3v0ISFWOHz+O33//HY6OjjAyMoKfn1+F14uKirBixQo4Ozvj5s2b8PX1RcuWLQEAQUFBMDExgRAChYWFWLhwIYyN1ff/g6qyAcAvv/yCtWvXYsGCBRgwYIBK79VFtuTkZKxfvx4dOnTAvXv3YGdnpzfZHissLMRbb72FPn36wN/fX63Zaprv+vXrOHjwICwsLHDq1CnMnDkTrq6uepHt22+/RWpqKuzt7XHr1i3897//haWlpdayBQcHIyMjA05OTkhMTMSsWbPw8ssvAwDCw8ORlJQEY2NjNG/eHOPGjVNbrppkO3/+PHbs2IEOHTrgxo0bcHV1xdtvv63WbDVRk/7RkNTkb8tQKHtM2L9/Pz755BOcOXMG1tbWWk5Zc1W1UwiBXbt2AQBSU1ORm5uLoKAgXUSttqramJKSgpUrV6JTp05ISkqCp6cnBg0apKO01Zeeno7169fj4sWLCAkJeeZ1mUyGtWvXwtraGqmpqfj3v/8NNzc37QdVhjAg+fn5YvDgwaKoqEgIIYSfn584fvx4hWW2bt0qgoODhRBCXLx4UXh5eQkhhIiPjxfDhw+Xlhs+fLg4ffq0VrMlJyeLEydOCG9vb3HkyBGV3qurbOfOnROHDh2SHr/xxhsiISFBL7I9FhQUJObNmyeWL1+utlzqyFdaWiqmTJkiysrKhBBCpKWliczMTL3Idv/+fdGjRw8p27Rp00R4eLhWs61bt07IZDIhhBAHDx4UU6dOFUIIcffuXTFixAjptTFjxogbN27oRbY//vhDnDt3TgghRHFxsejevbtav9OaqEn/aEhq8v0ZCmWPCVevXhVr164Vbdq0EXl5edqOWWPKtDM0NFSEhoZKj5OSkrQZscaUaeOiRYvE9u3bhRBCXLhwQQwZMkTbMdXi119/FYcPHxajR4+u9PUDBw6IxYsXCyGEyM7OFq+99pooLS3VYkLlGdS0ivj4eDRu3Bjm5uYAgK5duyIqKqrCMlFRUejSpfwnJ9u2bYuLFy8iLy8PdnZ2yM/PR2lpKUpLS2FkZISmTZtqNVuzZs3Qq1evar1XV9lcXV0xePBg6bFMJoOVlZVeZAOAsLAwdO3aVa3fpbryJSQkSKMeW7duxdGjR2FvX/nPkWs7m5WVFczMzJCXlwcAyM/PR+vWrbWabfbs2TAyMgJQ/ndVp04dAEBMTAxcXFyk17p06YI///xTL7INGjSowsi/iYkJzMzM1JatJmrSPxqSmnx/hkKZNhYUFODbb7/FBx98oIOE6qFMOyMiIpCTk4OdO3dKo46GRJk21q9fH1lZWQCArKwsuLi4aDumWrz++uvP/X6ioqKkkWI7OzuYm5vjypUrWkqnGoMqjjMzMytseBsbG2RmZiq1zEsvvYS3334bH374IebMmYNXX30VDg4OWs2mifdqc/2HDh1Cnz591Hp6sibZrl69iuvXr+O1115TW56n1STfnTt3EB8fjzFjxmDq1Kk4deoUQkND9SKbjY0NPvnkE8yZMwcBAQFo2LAhmjdvrpNsxcXFCA0NxezZswGUHxyefK+1tbXO9oensz1p9+7dmDZtGmxtbdWWrSZq0j8aEnV9f/pMmTauW7cOM2bMkIouQ6RMO+/cuYO8vDy8++67GD16NN5//32UlZVpO2q1KdPGiRMn4ty5cwgKCsLmzZsxZswYbcfUiqysLNjY2EiPbWxspP8U6BuDKo4dHR3x6NEj6XFeXh4cHR2VWubw4cM4efIkNm/ejI0bN+L27dv4+eeftZpNE+/V1vpjY2Nx8uRJzJ8/X225aprt0KFDMDc3R3BwMP7++2+cP38e3333nd7ks7a2RqtWraTiqVu3boiLi9OLbElJSdi2bRu2bt2K5cuXw97eHps3b9Z6tuLiYnz22WeYM2eOVJw7ODhUeO+jR490sj9Ulu2xiIgI5Ofn47333lNbrpqqSf9oSNTx/em7qtp49+5d5Obm4tdff0VwcDAAYPv27UhISNB61ppQ5ru0sbFB586dAQAtW7ZEXl4e7t69q9WcNaFMGwMCAvDWW28hMDAQmzdvxpw5c5CTk6PlpJrn4OBQ4UxVXl6eWgcp1cmgimM3NzfcuXMHxcXFAIAzZ87Aw8MDOTk50gb38PDA2bNnAQCXLl1Cu3btYGNjg3v37sHJyUlal5OTk7QebWVT9b36kA0oPxXy119/YcGCBUhPT5e2r66zTZ8+HX5+fvD19UW3bt3g6uqq9mKlJvk6d+6MnJwcaZTjzp07aNGihV5kS0tLg52dHUxNy6/J1cX+UFBQgMWLF2PixIno2LEjIiMjAQB9+/bFhQsXIIQAAJw9exb9+vXTi2wA8H//93/IzMzEjBkzcOnSJdy4cUNt2WqiJv2jIanp92cIqmpjo0aNsHz5cvj6+sLX1xdA+ehjp06ddBlbZcp8l+7u7khJSQFQXkyVlZVVOJbrO2XaePfuXalNdevWhbGxMWQymc4yq1N+fr40Ouzh4YH4+HgAQE5ODoqLi9U6nU+djMTjI5CBOHbsGCIjI2Fvbw8zMzP4+flh5cqVsLOzg6+vLwoLC7FixQo4OTkhOTkZU6dORcuWLZGfn49FixahSZMmMDY2xu3bt7FkyRK1zkWrKpsQAl9//TX27t2Lbt26YcSIEejbt6/C96pTdbMlJibCx8cHHTt2BFD+hz5+/Hi1nvapyXYDgMjISOzevRslJSUYP348PD091ZatpvkOHTqE2NhY2Nvb4+7du1i4cKFa7whR3WxlZWX44osvYGFhAVtbW1y5cgXz589HgwYNtJbNz88PV65ckT4zPz9fusI5PDwciYmJMDExQYsWLdR+t4rqZvvjjz/g7++PDh06ACjv4D/99FO88soras1XXdXtHw1NTf62DEVVbQTKT1P/9NNP+PLLLzFjxgyMGzcOzs7OOk6umqra+fDhQ6xatQqNGzdGcnIyhg4div79++s6tkqqauPp06exc+dOdOjQAbdv34aLiwu8vLx0HVtlcXFxCAsLQ0xMDLy8vDBp0iSEhITg0qVLWLp0KWQyGdasWQMrKyvcuXMHb7/9tt7ercLgimMiIiIiIk0xqGkVRERERESaxOKYiIiIiEiOxTERERERkRyLYyIiIiIiORbHRERERERyLI6JiIiIiORYHBMRERERybE4JiIiIiKSY3FMRERERCTH4piIiIiISI7FMRERERGRHItjIiIiIiI5FsdERERERHIsjomIiIiI5FgcExERERHJsTgmIiIiIpJjcUxEREREJMfimIiIiIhIjsUxEREREZEci2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQkx+KYiIiIiEiOxTGRFkRERGDBggW6jkFERE9g30yVMRJCCF2HIKrMvn37EBoail27duk6So2VlZWhsLAQ1tbWAICAgAA0adIEM2fO1HEyIqotalOfqS1P981VGThwIIKCgvDKK69oOBnpEkeOibTAxMRE6c6XiIi0g30zVYYjx1SlgIAAhIaGonv37ti5cydSUlLg7e2NmJgY3L9/H1OmTEFxcTF++OEHmJubY9myZbhx4wZkMhkGDRqEKVOmoKSkBJMnT0ZcXBwWLVqE6OhonDp1Clu2bMHNmzcREhICKysrWFpaYt68ecjMzMSiRYuQkZGB9u3bo02bNli4cOEz2ZKTk7F06VIUFhaipKQEvXv3xqxZswAAf/75J7766iuYmJjA0tISCxcuRIsWLbBnzx5s3boVnTt3hq2tLRISElC/fn1s2rQJFhYWAIBjx45h48aNMDMzg0wmg7e3N9544w1cuXIFq1atQklJCfLz8zFmzBi88847OHz4MD799FNYWVnh448/xptvvgkfHx9cv34d06ZNw969e/Hw4UMcOXIEO3bsQHBwMCwsLNCkSROMGDEC33zzDbKzs/Gf//wHc+bMwfLlyxEaGoopU6bg/fff1+r3TUQ1wz6zZn1mUFAQ3N3dsXbtWpw9exZGRkbo3bs3PvjgAxgZGVVoz/nz57Fw4UI8fPgQw4cPx99//40HDx5g3rx56Nu3LwAgIyMDS5YsQVZWFkpKSuDl5YXRo0fj0qVLmDdvntQ3Hz58GKtWrUL9+vXRuXNnnDp1CsbGxti8eTMcHR0RGBiIAwcOoFWrVqhbty78/f1hZWWFJUuWAABKS0vx73//G2PGjNHknxdpgyBSQr9+/cSZM2eEEEJs375dtG/fXiQkJAghhAgODpb+HRgYKPz9/YUQQhQUFAhPT08RGhoqradNmzZi48aNQgghIiIiRFxcnOjZs6coKioSQgjx3XffiZCQECGEECEhIcLb21thptLSUvHGG2+Iffv2CSGEyM3NFX379hVCCJGcnCzc3NzE9evXhRBChIWFiaFDh4qSkhIhhBAbNmwQffr0ETk5OaKsrEwMGzZMRERESO/t0qWLuHHjhhBCiHPnzkk54uPjRXx8vBBCiOLiYvH6669Ly+3YsUNMnDhRynfo0CGxZ88eIYQQsbGxYsCAAdJr/v7+YsOGDdLjxMRE0a1bN1FYWCiEECI9PV0EBgYqbDsR6Tf2mTXrM7/66ivh4+MjSktLRXFxsXjnnXdEWFhYpe2KjY0Vbdu2FUePHhVCCPH3338LNzc3kZWVJYQQYsKECVJ/m5mZKXr37i1OnTolvffJvjkkJER07txZJCcnCyGEeP/998WWLVuk1wcMGCBiY2Olx7NmzRIHDx4UQghx//59MXnyZIXbnwwHp1WQUvr374+oqCgAQEJCAoYMGYLo6GgAwD///AMXFxfIZDJERERg7NixAABLS0u8+eab2LdvX4V1DR48GADg6emJTp06AQDCwsJQUFCA8ePHw9PTU6lM8fHxSE5OxvDhwwEAtra2WLduHQDgwIED6NSpE1q2bCl91p07d3D27Fnp/Z07d0a9evVgbGyM1q1b4/bt29J7O3bsiBYtWgAAXF1dMXv2bADASy+9hL1792LcuHGYNGkS0tPT8c8//0ifcerUKaSlpQEAfvvtN7zxxhtKtcXFxQUNGzbEH3/8IWUYNmyYUu8lIv3DPnM2gOr3maGhoRg9ejRMTExgZmaG119/Hfv371fYNmtra3h4eAAAunbtCkdHR0RHRyMtLQ0nTpyQtrGDgwM8PDwQEhKicF0tW7ZEs2bNAABt27aV2lmZevXq4bfffsPt27fh5OSEjRs3KlyWDAeLY1KKh4cHjh49ivz8fFhZWWHgwIGIjo7GgwcPYGtrCyMjI2RlZaG4uBgODg7S+xwcHKSO7zEbGxvp35aWlvj+++8RFxeHQYMGYdGiRcjLy1MqU1paGurWrQtTU1PpuW7dugEA7t27VyGHiYkJ6tati3v37lWaw8LCAiUlJZW+98n1Ll++HJmZmdi9ezd27dqF9u3bo7CwUGpr7969ER4ejgcPHsDExAS2trZKtQUARo4cibCwMADAiRMn4O7urvR7iUi/sM+sWZ957949bN++HT4+PvDx8cH+/ftRVlamsG316tWr8NjOzg7379+X8le1jZ+kqJ2VmT9/Ptq1a4cJEybAy8sL8fHxCpclw8HimJTi7u6OW7duYd++fXj11VfRr18//PPPPwgPD0e/fv0AlHc45ubmyMrKkt6XlZUFZ2dnhestKSmBo6MjVq9ejcjISDx48AArVqxQKlPDhg2Rm5uL0tJS6blr166hsLAQjRo1qpCjrKwMubm5aNiwYZXrffq9AJCYmAigfH7bq6++ChMTEyn/k0aNGoXw8HD88ssvSo8aPzZixAicOHECx48fR6tWrWBszN2TyFCxz6xZn9moUSNMnz4du3btwq5du7B3716sX79eYYYHDx5UeJydnY0GDRpI+VXZxqrIzc3FjBkz8Mcff+Cdd97B9OnTkZ+fr5Z1k+7w6EtKsbKyQs+ePfHVV1+hb9++sLe3R8eOHREcHCyNcBobG2PUqFEIDQ0FABQWFuLXX3997sUJaWlp0kUjtra2aN++vTQ6YG1tjYKCAgDAzJkzK3ToQPkpvubNm+PAgQMAgJycHMyePRsmJiYYNmwYEhMTcevWLQDAL7/8gsaNG6NLly5VtvXp9/7999/4+uuvAQDNmzfHuXPnAAD379/HpUuXKrx34MCBSE9Px88//4w+ffoo/IzHbcvPz8dHH30EAHB2dkbPnj0xb948jBw5ssqcRKS/2GfWrM8cPXo0Dhw4ILUtNDQUW7ZsUZihsLBQmsZy+vRpZGVloX///nB2dkbv3r2lqSrZ2dmIioqSplmoytraGoWFhYiNjcWOHTsQGBiIjIwMGBkZoUePHigtLX3mokEyPKZVL0JUzsPDA0VFRdJpLw8PD5w6darCbXACAgKwbNkyeHl5oaysDJ6enlKhN2nSJADA3LlzMWfOHLi7u8PBwQH16tWDl5cXjI2NYWFhgS+++AIA0KtXL2zZsgXjxo1Dx44dK5wKBMpP+23ZsgVLly7F3r17IZPJsHDhQpiZmaFZs2bYsGED/P39pSuvt2zZAlNTU0RERCA0NBRFRUX44YcfYGJigpiYGFhYWKBFixYYPny49F4zMzNYWlri888/BwB88skn+OSTT/DOO++gVatWaNq0KYKDg9GoUSO4u7vD3Nwcb7zxBiwsLKS8ly5dwrJly5Ceno5Zs2Zhw4YN8PT0RGBgIOLi4jBhwgSpTSNHjsS2bdvQrl07DX2LRKQt7DOr12cCwOTJk/Hll1/Cy8sLFhYWaNiwIZYuXapwWzs7OyMpKQnbtm1DTk4OvvzyS9jb2wMAVq1ahSVLlmD8+PEoKSnBRx99hO7duz/TN3t5eSE4OBgZGRnYsGEDXFxcpHZv374dEydOxDvvvIMVK1bAxsYG//3vf1G3bl34+fnB3NwceXl5WLlyJaysrGr6p0M6xlu5EemR6OhoXLlyhbdvIyJS0smTJxEYGIgjR47oOgrVEpxWQaQHHl+It3//fulKciIiItI+FsdEeuDo0aMYNWoUmjdvrrYLRYiIarvz589XmBpBpA6cVkFEREREJMeRYyIiIiIiOY3crSI9/WG132tvXwfZ2YZ5j0BDzg4Ydn5Dzg4Ydn5Dzg5oN7+Tk/I/CqOqF7XffRrbop/YFv30IrSlOv2u3o0cm5qa6DpCtRlydsCw8xtydsCw8xtydsDw86tDbdoGbIt+Ylv0E9uiYF1qW9ML5uD13595rk6aBQY499dBGiIi0geVHRsAYFir17SchIiqS+9GjomIiIiIdIXFMRERERGRHItjIiIiIiI5vZtz/HPiAeQ/KnrmeU3P1+I8MSIiIiLSu+JYXVjsEhEREZGqOK2CiIiIiEiOxTERERERkVytnVahiKLpFkREREREHDkmIiIiIpJjcUxEREREJPfCTatQFadhEBEREb04WBwTEdELRZVBD97+k+jFYzDFMe9bTERERESaZjDFsSKc9kBERERE6mLwxTGpLizmeqXPTxnTWctJiIg0R5ODJxyYIaq9eLcKIiIiIiI5FsdERERERHKcVkFERGQgeHE6keaxOCYiIoP2ZMFYJ80C+Y+KNLJuInoxsDgmIiLSMFWLbI4EE+kOi2MiIiLSCkV3SxrVt1Wt+kwybCyOtYBzxIjoRcY+kIgMCYtjIiIiPXPw+u9qnz9NRMphcWxAOPpCRJrwc+KBSoswXfUt7OtIHz2enmFtbYFHT+wvnJ5R+7A4VjNVLrrQ9AFA0TwrRX6IvFhhh3+MOz4RERG9KFgcG5CLydmVPl+SqloRTERkiHhbtdqrssEcRQMzvMCONI3FsQ4pKnaHcf8mIiID9nQB+/RUBG18prbWo+ryLOL1H4tjPaSuHZyIiEiTFI/m/0urOWoDjojrDxbHWqBohFiRa2Wn1LL8yyY9VFqPIur6X7Eh7PiGkJGotuA0CfXhj4wQqQ+LY9I5VQvSypa3trbAkK5N1JqLiOhFo093CuFZVNIVFsekdrqa96XKOjgSTKR+HAmuvfjd1l6qXAz5omBxXItperoFEdVu+jSKSM+naPpeu+b2Gl2/Ii+bqOVjNaq2jkxzUKjmWByrmaodCBkGdjZEZIhUvSsSj2Gap6uiXNGURE2tGzDcYySLY6o1ausoAJG+4Sl2w7cmao9G1//0mUuzAlOUlJUqXJ5nNFWni2Oepj9TX4psFscvIEXTLVzRR6PrZ+enOn3pKIiIiF4ULI6pSrWx2NX0RYP6VrwaSk4iQ6fqtARFc4IvJmfDzMwUJSWKR1uJNOVFPxOrd8VxwtWMSjuD53UglVF1eXUwM9O7zamSpILY5572epqq92NWdT2qFt+VrUfROlTNrup61kSp1qZ6bVKQX+mvR2n2RvqG8MtO6rjV3/OWV4QXo6mPpi8WUxdVjg+6utCtttJF/20oDLlQNdSBGSMhhNB1CCIiIiIifWCs6wBERERERPqCxTERERERkRyLYyIiIiIiORbHRERERERyLI6JiIiIiORYHBMRERERyensxrzHjx/H77//DkdHRxgZGcHPz6/C60VFRVixYgWcnZ1x8+ZN+Pr6omXLljpKW1FV2YODg5GRkQEnJyckJiZi1qxZePnll3WUtqKqsj+2f/9+fPLJJzhz5gysra21nFKxqvILIbBr1y4AQGpqKnJzcxEUFKSLqM+oKntKSgpWrlyJTp06ISkpCZ6enhg0aJCO0laUnp6O9evX4+LFiwgJCXnmdZlMhrVr18La2hqpqan497//DTc3N+0HVaCq/Pv27UN8fDyaN2+Of/75B97e3ujatasOkqpfTfra8PBwJCUlwdjYGM2bN8e4ceN00QRJTdoycOBANGnSBADQoEEDrFmzRuv5n6RMX/zLL79g7dq1WLBgAQYMGKDSe7WpJm15++23YWFhAQAwNjbGjh07tJa7MjU5vhva/vK8thja/vLLL7/g8OHDaNeuHRISEjBq1CgMHDgQQDW/F6ED+fn5YvDgwaKoqEgIIYSfn584fvx4hWW2bt0qgoODhRBCXLx4UXh5eWk9Z2WUyb5u3Tohk8mEEEIcPHhQTJ06Ves5K6NMdiGEuHr1qli7dq1o06aNyMvL03ZMhZTJHxoaKkJDQ6XHSUlJ2oyokDLZFy1aJLZv3y6EEOLChQtiyJAh2o6p0K+//ioOHz4sRo8eXenrBw4cEIsXLxZCCJGdnS1ee+01UVpaqsWEz1dV/q+++koUFhYKIYSIj48Xnp6e2oynMTXpa+/evStGjBgh9WVjxowRN27c0F74p9T0uLFhwwbtha2CMm1JTk4WJ06cEN7e3uLIkSMqvVebatIWIQzve1F0fDfE/eV5tYqhfS8hISEiNTVVCFHx+Fnd70Un0yri4+PRuHFjmJubAwC6du2KqKioCstERUWhS5cuAIC2bdvi4sWLyMvL03bUZyiTffbs2TAyMgJQPqJWp04dbceslDLZCwoK8O233+KDDz7QQcLnUyZ/REQEcnJysHPnTmkkUx8ok71+/frIysoCAGRlZcHFxUXbMRV6/fXXn7sto6KipJFiOzs7mJub48qVK1pKV7Wq8k+fPl0avdKnfbamatLXxsTEwMXFRerLunTpgj///FOr+Z9U0+PG6dOn8c0332D9+vU4c+aMVrM/TZm2NGvWDL169arWe7WpJm0BgMuXLyM4OBgbN27UaTuAmh3fDXF/eV6tYmj7y5gxY9C4cWMAwK1bt6QR8Op+LzqZVpGZmVnhQGVjY4PMzEyllrGxsdFazsook/2x4uJihIaGYvHixdqK91zKZF+3bh1mzJgh/RHqE2Xy37lzB3l5efDz88ONGzfw/vvv45dffoGJiYm241agTPaJEyfigw8+QFBQEM6fP48ZM2ZoO2a1ZWVlVdg3bWxspELfkAghsHPnTgQEBOg6ilrUpK/Nysqq8Ly1tbXCvk4banrc+Oijj+Dq6oqCggKMHj0aW7duxUsvvaS1/Mrk1PR7NaGmeaZMmQJXV1eUlZVh/PjxsLa2Ro8euvm555oc3w1xf3msslrFEPeXwsJCbNy4EXFxcVi9ejWA6n8vOhk5dnR0xKNHj6THeXl5cHR0VHkZXVA2V3FxMT777DPMmTMHzZs312ZEharKfvfuXeTm5uLXX39FcHAwAGD79u1ISEjQetbKKLPtbWxs0LlzZwBAy5YtkZeXh7t372o1Z2WUyR4QEIC33noLgYGB2Lx5M+bMmYOcnBwtJ60eBweHCmd28vLy4ODgoMNEqhNCYOXKlRg9erQ0+mjoatLXOjg4VHj+0aNHOu2Da3rccHV1BQBYWVmhffv2Oh0Nq8nxTd+OjTXN8/h7MTExQffu3XHy5Em1Z1RWTY7vhri/AIprFUPcXywtLfHJJ59g9erVePfdd1FSUlLt70UnxbGbmxvu3LmD4uJiAMCZM2fg4eGBnJwc6QDr4eGBs2fPAgAuXbqEdu3a6XzUGFAue0FBARYvXoyJEyeiY8eOiIyM1GVkSVXZGzVqhOXLl8PX1xe+vr4AykczO3XqpMvYEmW2vbu7O1JSUgCU70BlZWVwcnLSWebHlMl+9+5dKWvdunVhbGwMmUyms8xVyc/Pl0aHPTw8EB8fDwDIyclBcXExWrdurcN0VXsyf1lZGf773/9iwIAB6Nevn97sszVVk762b9++uHDhAoQQAICzZ8+iX79+umkIataWEydOVDiVeuvWLTRr1kz7jZBTpi2qvldXatKWa9eu4f/+7/+kx4bwvSg6vhvi/qKoLYa4v2zbtk3a9g0bNkR2djaKioqq/b0Yicfv0LJjx44hMjIS9vb2MDMzg5+fH1auXAk7Ozv4+vqisLAQK1asgJOTE5KTkzF16lS9uVtFVdn9/Pxw5coVNGjQAED5QbiyK+R1oarsQPlpiJ9++glffvklZsyYgXHjxsHZ2VnHyctVlf/hw4dYtWoVGjdujOTkZAwdOhT9+/fXdWwAVWc/ffo0du7ciQ4dOuD27dtwcXGBl5eXrmMDAOLi4hAWFoaYmBh4eXlh0qRJCAkJwaVLl7B06VLIZDKsWbMGVlZWuHPnDt5++229ultFVfmDgoIQGRkpHQCSk5MRHR2t49TqUZO+Njw8HImJiTAxMUGLFi10fvV9ddty6dIlbNq0CS4uLrh//z4aNGiAadOm6XVbhBD4+uuvsXfvXnTr1g0jRoxA3759Fb7XENuSlpaGzz//HO3bt0deXh5KS0sRGBgIY2Pd3WW2Jsd3Q9tfFLXFEPeXr7/+GmlpaWjcuDGuXbuGrl274p133gFQve9FZ8UxEREREZG+4Y+AEBERERHJsTgmIiIiIpJjcUxEREREJMfimIiIiIhIjsUxEREREZEci2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQkx+KYiIiIiEiOxTERERERkRyLYyIiIiIiORbHRERERERyLI6JiIiIiORYHBMRERERybE4JiIiIiKSY3FMRERERCTH4piIiIiISI7FMRERERGRHItjIiIiIiI5FsdERERERHIsjomIiIiI5FgcExERERHJsTgmIiIiIpJjcUxERFRL5Ofnw9fXF+PGjcPIkSORmpqqsyybNm1C7969sXHjxiqXLSsrg4+PD9q2bYvbt28DAE6fPo1JkyZpOqbSbt++jTfffFPXMUgLWByT3tm3bx98fHx0HUNtnuzsiYiqS5m+8eDBgygtLcVPP/2E2bNnw9hYvYf5gIAApYpdAPDz80Pfvn2VWtbExAS7du2q8Fy3bt3w5ZdfqpxRU5o2bYqffvpJ1zFIC0x1HYCIiIjUIy0tDQ0aNAAADBgwQMdpasbIyAi2tra6jlFB3bp1dR2BtIDFMSkUEBCA0NBQdO/eHTt37kRKSgq8vb0RExOD+/fvY8qUKSguLsYPP/wAc3NzLFu2DDdu3IBMJsOgQYMwZcoUlJSUYPLkyYiLi8OiRYsQHR2NU6dOYcuWLbh58yZCQkJgZWUFS0tLzJs3D5mZmQgODkZGRgZ8fHzQpk0bLFy4sEIumUyGJUuW4PLlyzA2NkaLFi2wYMECzJgxAydOnICHhwe2bt2KsLAwrF69Gl27dkWbNm3w448/YujQocjNzUVCQgIGDx6MoUOHYsuWLbh06RICAwMxePBgnD9/HgsXLsTDhw/xn//8B3/88QdKS0uxfv16BAcH4+zZs+jQoQNWrFghZQoLC5O2g7OzM5YsWQIbGxu8//77AIC5c+fCwsICy5cvR0BAwDPbo379+khOToabmxv+97//IT4+HosWLUK9evWwb98+rX7vRPR8+to37tmzB/v27UNRURF8fHwwc+ZMbNy4sdLPyM3Nxffffw8jIyOUlJRg7ty56NatGwBI/d3p06dhYmKC+vXr4+OPP8aRI0cQExMDCwsLxMXFYcSIEXjrrbfw2WefSe1zcnLC0qVLYWNjo9S2DAkJwfbt21G/fn0MGzZMej4rKwvTpk3DuXPncOnSJbX2y5999hkOHDgAb29vXL9+HZcuXcLQoUMxd+5cAMCZM2ewatUqmJmZQQiBSZMmYcCAAZgwYQJiY2Nx+PBhNG3aFCUlJVi7di3Onj0LAOjSpQvmzp0LMzMz+Pn5ITo6GjNnzkR8fDyuXLmC9957D+PHj6/R3x5piSB6jn79+okzZ84IIYTYvn27aN++vUhISBBCCBEcHCz9OzAwUPj7+wshhCgoKBCenp4iNDRUWk+bNm3Exo0bhRBCREREiLi4ONGzZ09RVFQkhBDiu+++EyEhIUIIIUJCQoS3t7fCTFFRUWLy5MnS4xkzZoiUlBRRXFwsevbsKf7++2/ptalTpwqZTCaEEMLf31+MHj1aFBUViczMTOHi4iI2b94shBAiMjJSDB06VHpfbGyscHFxEWfPnhVCCDF9+nQxevRokZubK4qKikSvXr2k106fPi169uwpMjMzhRBCLF++XMyfP79C21NSUiq04entkZiYKDw9PcX+/fulZWbPni3y8vIUbgci0h197BuFEGLDhg3S5yn6jMTERBEWFiays7OFEEKkpKSI/v37S8t//fXX4r333hOlpaVCCCGWLFkiZfD39xcbNmyosP4dO3ZU+Px169ZJjytb/rHLly8LV1dXkZycLIQQYvfu3RX6y5SUFNGmTRtpeXX2y97e3mLKlClCJpOJtLQ00aFDB3Hv3j0hhBBjx44V8fHxQgghkpKSKmzPJ/Nt2rRJTJgwQZSWlorS0lIxadIksWnTJmnZAQMGiMWLFwshhDh37pxwc3MTJSUllW4L0i+cc0zP1b9/f0RFRQEAEhISMGTIEERHRwMA/vnnH7i4uEAmkyEiIgJjx44FAFhaWuLNN998ZsRz8ODBAABPT0906tQJQPn/7AsKCjB+/Hh4enoqlalu3bq4fPkyjh07BplMhrVr16Jx48YwMzPDsGHDEBYWJuVr27YtjIyMpPf27NkT5ubmcHBwgIODA9q1aweg8nnB1tbWcHNzAwC0bt0aTZo0ga2tLczNzdGiRQukpKQAAEJDQzFw4EA4ODgAAIYPH46IiAgIIZ7bjie3h4uLC0aNGiVlz8rKgoWFBaytrZXaJkSkXfrYNz7P0/1Nu3btEBgYCC8vLwQGBuLu3bvIzMwEUD63eeTIkTAxMQEATJ06FT169FC4bgsLC/znP/+Bt7c3Dh48iAsXLiiVKTIyEm5ubmjWrBkAKHWxmzr75T59+sDIyAgNGjSAnZ2ddPFivXr1EB4ejoyMDLRr1w6LFy+uNEt4eDhGjRoFExMTmJiYYOTIkc98t4/nXLdt2xb5+fnSNib9xuKYnsvDwwNHjx5Ffn4+rKysMHDgQERHR+PBgwewtbWFkZERsrKyUFxcLHVCAODg4IC0tLQK63ryNJulpSW+//57xMXFYdCgQVi0aBHy8vKUytSlSxd8/vnn+OabbzBgwABs27ZN6vBGjRqF3377DcXFxQgPD8eIESMqvPfJYtPU1FR6bGJigpKSEqWWffz48fL37t1DbGwsfHx84OPjg88//xz169dHdnb2c9vx9GnH4cOH4+TJk7h//z4iIiJ4VTSRHtPHvvF5nu5vpk+fju7du+PHH3+ULoQrKCgAUN6n2dvbS8s6OztLBezTTp48ieXLl2PlypX4/vvv4evri8LCQqUy3b9/v8Ln2NnZVfkedfbLT24TCwsL6b1r1qyBpaUlRo8ejcmTJ+PmzZuVZnl6Oz3vu7WwsACAZ44zpJ9YHNNzubu749atW9i3bx9effVV9OvXD//88w/Cw8PRr18/AOUdgrm5ObKysqT3ZWVlwdnZWeF6S0pK4OjoiNWrVyMyMhIPHjyoMFfseR4+fIiePXviu+++w65duxAWFiaNuLq6usLR0RGHDh3CzZs38fLLL1e/8Upq1KgRPDw8sGvXLuzatQs//vgj9u7dW+GAqIwGDRrglVdeQUREBI4fP47evXtrKDER1ZQ+9o3KyszMRGpqqjSq+XTB1qhRowpFZHZ2tsI77pw/fx4tW7ZE06ZNAZTPV1ZWgwYNKmybqgYUVFGTfrm4uBjz5s3D0aNH0aNHD8yYMUPhZzyZuarvlgwHi2N6LisrK/Ts2RNfffUV+vbtC3t7e3Ts2BHBwcFwd3cHABgbG2PUqFEIDQ0FABQWFuLXX3/FmDFjFK43LS1NupjE1tYW7du3R1lZGYDykYHHIxgzZ858prM9dOgQ9uzZAwBo3rw5nJ2dIZPJpNdHjhyJoKAgrRWXo0ePlkaMAOD69euYPn269HqdOnVQWFiI8PBw/Pbbb89d16hRo7B9+3a0aNFCOqVJRPpHH/tGZdnZ2aFu3bo4d+4cACAmJqbC66NHj0Z4eLj0uWvWrMHFixcrZMjPz8dHH32El156CcnJyVKR+NdffymdY+jQoYiPj5emQhw4cKBa7alMVf3y88yaNQsFBQUwNTVF165dpe1Q2Wfs378fZWVlkMlk2L9//3O/WzIcvFsFVcnDwwNFRUXSLXU8PDxw6tSpCqezAgICsGzZMnh5eaGsrAyenp4YOXIkAEg3cZ87dy7mzJkDd3d3ODg4oF69evDy8oKxsTEsLCzwxRdfAAB69eqFLVu2YNy4cejYsSNMTSv+mbq5uWH58uU4cuQI8vPz0bZtW+mzAGDEiBHYtGlThSuft2/fLl1l3a5dOxw7dgzp6elYtmwZ1q1bh4CAACnr/PnzsWzZMqSnp2PRokXo378/QkNDUVRUhB9++AFZWVlISkpCeno6GjVqBHd3d3z44YeYMmUKLC0tYWZmhuXLl0ufPX78eMyZMwc2NjbYsGFDpdvjsSFDhmDx4sUV2kNE+knf+sY9e/ZIfdWECROwY8eOSj/DxMQEQUFBCAoKwm+//YaOHTtKywQHB2Py5MnIy8vDf/7zHxgbG6Nnz54V5iwHBgYiLi4OEyZMwODBgxEdHY23334bbdu2RZ06dZCUlISVK1eiTp06Ur/bsGFDvPXWWxXytm7dGosXL8a0adPg6OiIgQMHSjnWrVsn3T3Cx8cHixYtUlu/vHLlSmnZli1bIjw8XDoerFmzBoMGDcLEiRNhZmaGwsJCaeR+woQJUr6NGzdi8uTJePjwoXQHii5dusDX1xcAMG/ePGmdmzZtktbxeBsrM4WEdMdIVHXVEJGByc3Nxfz587Fp0yZdR1GZTCbD5MmTsX37dl1HISIieiFx5JhqjejoaHTq1Am//fabwV3Mdu7cOdStWxfJycl49dVXdR2HiIjohcXimGqN5ORkBAUFoUWLFgY3apyeno6PP/4YDRs2xFdffaXrOERERC8sTqsgIiIiIpLj3SqIiIiIiOQ0Mq0iPf2hJlarNvb2dZCdna/rGFrBttY+L0o7gdrXVicnW42tWxv9rj5/H8xWPcxWPcymOl3lqk6/+0KOHJuavjj3j2Vba58XpZ3Ai9VWQ6DP3wezVQ+zVQ+zqU5fc1WGF+TpoYPXf6/0+WGtXtNyEiIi/cG+kYi0gcUxERFpFItaIjIkLI7VrLKDAA8ARERERIaBxbEOKRpNISJ6EXBEmYj00Qt5QR4RERERUWVYHBMRERERybE4JiIiIiKS45xjA8L5eURERESaxeJYC3jhHRGR5hy8/jvqpFkg/1FRhec5cEBE1cFpFUREREREciyOiYiIiIjkOK2imjhVgohIM9i/EpEuceSYiIiIiEiOI8e1AO9iQURERKQeLI6rwNN7RESGiQMHRFQdLI5rMUW3N1KEBwwiqgkOJhBRbcDiuBa7mJwNMzNTlJSUVni+XXN7HSUiIiIi0m+8II+IiIiISI7FMRERERGRHKdVkCQs5nqlz4/q20rLSYiIiIh0g8WxAbmYnF3p85xDTERERKQeLI6JiEivqDoQwIuPiUidWByT5FrZKQWvcFoFERERvRhYHBMR0QtFlR8H4Q+JEL14eLcKIiIiIiI5jhzrIUXz7XS1fo6cEBER0YuCxbEcf/ZU83irOKLawVD6S1Uv7NNku9j/ERkOFsdaoOlbsGl6pJmISB+wryMibWBxTERElXp6JLVOmgXyHxXpKI36qKPIHqamAV+OKBPpHxbHOsRRECIiw6SoqK2MtbWFBpMQkbqxOK4m/lqdYqocNIio9mN/SUSGhMUxVUnRga0kVb+K4B8iL+LRU6d8eWqSiIiIVFFri2PefoyISLtUnSpmyFPLFP2i6MsmPdSyPBHpTq0tjhU5eP13jV5UYsidvarU1dnzghQiw/Ii9XOqqqxfNCswnEMt+2OiWlAcG8r9Nl8kiopmRdRVTKty0QsPAERVe7oINjMzRUlJqY7S1E6K+ss1UZU//5HHO5U+r6hPM2tytdLnS1L/BaC833x6OhrRi07vimN9K1o4QkLVoa6LElmskzbwIlrDoep3pegY9rKJOtJoVmXXkQDsF0nz9K44VjzqqJ6d4WJydqWjH7xqWv/o4oCtb/85I9IGVc/20ItnTdSeSp9X9cyfor60sr6Xt8AjXdG74lgRTU+f4Aix/lHHnGZFHboiitZtKCNr6iruVWmvKge76mTRFUPPT7WTuq71eLweswJTlJRVf6qMqnkUH8v/pfRnqjqFxFAuxGefoz/bwEgIIbT6iUREREREespY1wGIiIiIiPQFi2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQkZzA/AlIdx48fx++//w5HR0cYGRnBz8+vwuvBwcHIyMiAk5MTEhMTMWvWLLz88ss6SlszVbX1l19+weHDh9GuXTskJCRg1KhRGDhwoI7SVl9V7Xxs//79+OSTT3DmzBlYW1trOaV6VNXWffv24aeffoKFRfmvSI0dOxajRo3SQdKaqaqdQgjs2rULAJCamorc3FwEBQXpImqtVdV3UFRUhBUrVsDZ2Rk3b96Er68vWrZsCQCIj4/HsWPHYGxsjJMnTyIoKAiNGjXSi2xBQUEwMTGBEAKFhYVYuHAhjI3VNyakTH/0yy+/YO3atViwYAEGDBig0nt1kS05ORnr169Hhw4dcO/ePdjZ2elNtscKCwvx1ltvoU+fPvD399ebbNevX8fBgwdhYWGBU6dOYebMmXB1ddWLbN9++y1SU1Nhb2+PW7du4b///S8sLS21lu159VZ4eDiSkpJgbGyM5s2bY9y4cWrLVW2ilsrPzxeDBw8WRUVFQggh/Pz8xPHjxysss27dOiGTyYQQQhw8eFBMnTpV6znVQZm2hoSEiNTUVCGEEBcuXBBDhgzRes6aUqadQghx9epVsXbtWtGmTRuRl5en7Zhqoex3mpKSoot4aqNMO0NDQ0VoaKj0OCkpSZsRaz1lvoOtW7eK4OBgIYQQFy9eFF5eXkIIIR4+fCj8/Pyk5ZKTk8WjR4/0Ilt8fLwYPny4tNzw4cPF6dOntZotOTlZnDhxQnh7e4sjR46o9F5dZTt37pw4dOiQ9PiNN94QCQkJepHtsaCgIDFv3jyxfPlyteWqabbS0lIxZcoUUVZWJoQQIi0tTWRmZupFtvv374sePXpI2aZNmybCw8O1mk1RvXX37l0xYsQI6bUxY8aIGzduqC1bddXaaRXx8fFo3LgxzM3NAQBdu3ZFVFRUhWVmz54NIyMjAIBMJkOdOnW0HVMtlGnrmDFj0LhxYwDArVu3DHKEXJl2FhQU4Ntvv8UHH3ygg4Tqo0xbAWD37t3Ytm0bNm3ahJycHO2GVANl2hkREYGcnBzs3LkTa9euNdgzAfpKme8gKioKXbp0AQC0bdsWFy9eRF5eHqKjo1GnTh1s374dmzZtwoULF9Taj9Ykm52dHfLz81FaWorS0lIYGRmhadOmWs3WrFkz9OrVq1rv1VU2V1dXDB48WHosk8lgZWWlF9kAICwsDF27dlXrd6mObAkJCdJZrq1bt+Lo0aOwt7fXi2xWVlYwMzNDXl4eACA/Px+tW7fWajZF9VZMTAxcXFyk17p06YI///xTbdmqq9ZOq8jMzKxwELWxsUFmZmalyxYXFyM0NBSLFy/WVjy1UrathYWF2LhxI+Li4rB69WptRlQLZdq5bt06zJgxQ9pJDZUybe3Rowc8PDzg4OCA6OhofPjhh9ixY4e2o9aIMu28c+cO8vLy4Ofnhxs3buD999/HL7/8AhMTE23HrZWU+Q4ULZOamopz587hiy++gImJCd59913Y29vjlVde0Xm2l156CW+//TY+/PBDGBsb49VXX4WDg4NacimbTRPv1eb6Dx06hD59+qh1MKUm2a5evYrr169j7ty5uHTpktoyqSPbnTt3EB8fj7Vr18LW1hYff/wxzMzMMGbMGJ1ns7GxwSeffII5c+bAyckJDRs2RPPmzdWSS9VsT9dbWVlZFd5rbW2t1n2humrtyLGjoyMePXokPc7Ly4Ojo+MzyxUXF+Ozzz7DnDlz1PrHok3KttXS0hKffPIJVq9ejXfffRclJSXajFljVbXz7t27yM3Nxa+//org4GAAwPbt25GQkKD1rDWlzHfarFkz6WDfq1cvnDp1CmVlZVrNWVPKtNPGxgadO3cGALRs2RJ5eXm4e/euVnPWZsp8B4qWsbGxQYcOHWBmZgZjY2O4ubkhLi5OL7IdPnwYJ0+exObNm7Fx40bcvn0bP//8s1azaeK92lp/bGwsTp48ifnz56stV02zHTp0CObm5ggODsbff/+N8+fP47vvvtOLbNbW1mjVqhVsbW0BAN26ddP6vqBIUlIStm3bhq1bt2L58uWwt7fH5s2btZ6tsnrLwcGhwnsfPXqk1n2humptcezm5oY7d+6guLgYAHDmzBl4eHggJydHOrVQUFCAxYsXY+LEiejYsSMiIyN1GbnalGnrtm3bIIQAADRs2BDZ2dkoKirSWebqqKqdjRo1wvLly+Hr6wtfX18AwMSJE9GpUyddxq4WZb7TNWvWoLS0FABw8+ZNNGnSxOBGU5Vpp7u7O1JSUgCUd7plZWVwcnLSWebaRpnvwMPDA2fPngUAXLp0Ce3atYONjQ1eeeUVpKamSuu6c+cOWrRooRfZ7t27V+HvxMnJSVqPtrKp+l59yAaUT1X566+/sGDBAqSnp0vbV9fZpk+fDj8/P/j6+qJbt25wdXXFe++9pxfZOnfujJycHGmAQhf7giJpaWmws7ODqWn5ZAFd7AuK6q2+ffviwoULUn1y9uxZ9OvXT23ZqstIPE5UCx07dgyRkZGwt7eHmZkZ/Pz8sHLlStjZ2cHX1xd+fn64cuUKGjRoAKB8Hk5ISIiOU1dPVW39+uuvkZaWhsaNG+PatWvo2rUr3nnnHV3HVllV7QTKT9P89NNP+PLLLzFjxgyMGzcOzs7OOk6uuqraumPHDly5cgVNmzbF5cuX8e6778LNzU3XsVVWVTsfPnyIVatWoXHjxkhOTsbQoUPRv39/XceuVar6DgoLC7FixQo4OTkhOTkZU6dOle4IsXv3bqSmpsLMzAyFhYUICAiQ5g/qMlt+fj4WLVqEJk2awNjYGLdv38aSJUvUOie6qmxCCHz99dfYu3cvunXrhhEjRqBv374K36tO1c2WmJgIHx8fdOzYEUD5cXH8+PFqmx5Qk2yPRUZGYvfu3SgpKcH48ePh6empF9kOHTqE2NhY2Nvb4+7du1i4cKFa7whR3WxlZWX44osvYGFhAVtbW1y5cgXz58+Xah9tZHtevRUeHo7ExESYmJigRYsWenG3ilpdHBMRERERqaLWTqsgIiIiIlIVi2MiIiIiIjkWx0REREREciyOiYiIiIjkWBwTEREREcmxOCYiIiIikmNxTEREREQk9/8AlbMXItfkET8AAAAASUVORK5CYII=\n",
|
||
"text/plain": [
|
||
"<Figure size 720x1440 with 30 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 1080x576 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"import pandas as pd\n",
|
||
"# Making a data frame\n",
|
||
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"\n",
|
||
"fig, axes = plt.subplots(15,2,figsize=(10,20))\n",
|
||
"malignant = cancer.data[cancer.target == 0]\n",
|
||
"benign = cancer.data[cancer.target == 1]\n",
|
||
"ax = axes.ravel()\n",
|
||
"\n",
|
||
"for i in range(30):\n",
|
||
" _, bins = np.histogram(cancer.data[:,i], bins =50)\n",
|
||
" ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)\n",
|
||
" ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)\n",
|
||
" ax[i].set_title(cancer.feature_names[i])\n",
|
||
" ax[i].set_yticks(())\n",
|
||
"ax[0].set_xlabel(\"Feature magnitude\")\n",
|
||
"ax[0].set_ylabel(\"Frequency\")\n",
|
||
"ax[0].legend([\"Malignant\", \"Benign\"], loc =\"best\")\n",
|
||
"fig.tight_layout()\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"import seaborn as sns\n",
|
||
"correlation_matrix = cancerpd.corr().round(1)\n",
|
||
"# use the heatmap function from seaborn to plot the correlation matrix\n",
|
||
"# annot = True to print the values inside the square\n",
|
||
"plt.figure(figsize=(15,8))\n",
|
||
"sns.heatmap(data=correlation_matrix, annot=True)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Discussing the correlation data\n",
|
||
"\n",
|
||
"In the above example we note two things. In the first plot we display\n",
|
||
"the overlap of benign and malignant tumors as functions of the various\n",
|
||
"features in the Wisconsing breast cancer data set. We see that for\n",
|
||
"some of the features we can distinguish clearly the benign and\n",
|
||
"malignant cases while for other features we cannot. This can point to\n",
|
||
"us which features may be of greater interest when we wish to classify\n",
|
||
"a benign or not benign tumour.\n",
|
||
"\n",
|
||
"In the second figure we have computed the so-called correlation\n",
|
||
"matrix, which in our case with thirty features becomes a $30\\times 30$\n",
|
||
"matrix.\n",
|
||
"\n",
|
||
"We constructed this matrix using **pandas** via the statements"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"correlation_matrix = cancerpd.corr().round(1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Diagonalizing this matrix we can in turn say something about which\n",
|
||
"features are of relevance and which are not. This leads us to\n",
|
||
"the classical Principal Component Analysis (PCA) theorem with\n",
|
||
"applications. This will be discussed later this semester ([week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html)).\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Other measures in classification studies: Cancer Data again"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n",
|
||
"Test set accuracy with Logistic Regression: 0.96\n",
|
||
"Test set accuracy Logistic Regression with scaled data: 0.96\n",
|
||
"[1. 1. 1. 1. 1. 1.\n",
|
||
" 1. 1. 0.92857143 0.92857143]\n",
|
||
"Test set accuracy with Logistic Regression and scaled data: 0.96\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/opt/homebrew/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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jaJj8pCBL9eC1XXh48uEXgH/i07qZKxLYAIQAYUBiGusB3P3/f+lRAs8zsJ4AaNYs9RETIYTIyooWLYaxsTE1a9bGzW0FJUtmZNQy477qHrz+BT9MnS6i6xtOXNncGMzoBSTdIBcVFcfIkcfZv/8RJXV1+NssF7Z5jAk63TWdrWo3OSPPHNLO6idtrH7Sxp8mMTGR337bzLffdiBXLnMA/PxekCdPXnR00r7n/XN78F/1VLXvkntqcubUZ82aNrTSf8bQHA+x09VB1z/1m6KEEEKIj3n06CHt2rVk7NgRzJnjpFpuZ5fvo8n9v/iqE7yubzgxjfITq1Qmm33oHYVCwZ9xGzFWJA27J+Q3SbGOEEIIkZaYmBgWLZpHkyb1uHr1MjY2tjRs2DhT9v1VJ/iLnYrSM+gtdd++Jb0rFQn5TQhzqpNJkQkhhNB2ly5dpEmTeri6LiIuLo4+fQZw/vxV2rVrnyn7/ypusnv/WnvwLnuiS1nQr98B/vrLS7XO0VxpN8WQ8B10PL42M0IVQgiRDXh4PKZ9+1YolUqKFSuOm9sK6tSpl/4Hv6CvIsF/eK1dT08nRUGUBUYffkoIIYT4PCVKlKRHj97kyZOHUaPGkyNH2nOUqMtXMUT/fnI3+ukmAMOH10i2TkB8AoRn/hcghBBC+7169ZJBg/py7doV1bIlS1YyadJ0jSR3yMYJPjIyjl9+uUl4eCwRwyoRVzZprntDd18AqlTJQ4MGBalRw46tWzvg7t4XTKI1GbIQQggtk5iYyObNG6hfvyYHD+5n+vTJqnu6FIqUU+Jmpmw3RB8cHMWvv95i/fp/CAyMIjY2gR8cq2HgnjRX+ft3wm/a9G2a07UKIYQQH+Ph8ZixY0dw6VLSDKctWrRi0SI3jSf2d7R6opuePTtz4sSHtdcbAu8/ghAKLOOa+RgsFEYMCd/BibhHqW/8xP//3yzlW9o2FernkokrMoe0s/pJG6vf19rGsbGxrFixhCVLXIiNjcXKypr5851p376TWpL7VzlVbcrkDnAVqA+8KwZgBlSkeojLZ+9HpkIVQgjxTkhICGvW/ERsbCw9e/Zh5sw5WFhkrOR5ZtLqBP/Oh73rqVP/Zt26fzA1NWDgwMp8//0QbGyM093Ou2IzX0tvXQghRMaEh4dhaJgDfX19bGxscHNbSa5cuWjQoKGmQ0tTtrrJrqdXZ2xumxGut4yFRkb46BtT9uVmzs8ejc1ts3T/E0IIIT50/PhRGjSoxapVK1XL7O2/zdLJHbJZgn9Xz90kVzQTjXKSS0cHh1P1cDiV8ckF0qrlLoQQ4uvy5s0bHBz607t3N1688OXEiWMkJn6sYmjWonVD9O/PSqe0WgEkVWB/n2v+5cBF1euE/Ca8qSjD7kIIIdKnVCrZvn0rTk5TCQkJwcjIiEmTpjF48FC1FYZRB61L8B+rAJcamUNeCCFERoWEBDNoUF/Onj0NQOPGTXFxWUrBgoU0HNmn07oEn1pyHznyGEZG+qCsD1ZhvB1elOiuJTUQnRBCCG1mZpaL2NhYLC0tmTNnId991zXLPNf+qbT2OXijlTcx/vkW8UolBkFBvH8Uvr4jMTDQ1VCE2u1rfa41s0k7q5+0sfpllzb+55/rWFpaqXrpPj7eGBkZY2lpqeHIknzuc/DaczHhA5GOlVEEDEc/cFqy5I55hCR3IYQQ6QoPD2f69Mm0bt2U8eNHqaaYLVCgYJZJ7v+F1g3Rp/TBmY2l3EwnhBDi406d+ovx40fj4+ONjo4OZcqUIz4+Hn19/fQ/rCW0KsGnfh0kmNWr2/DyZTiz7i4C84hMj0sIIYR2CAgIYPr0SezZsxOAChUq4ea2nEqVqmg4si9PqxJ8apo1q0+nTqUBmHX7mIajEUIIkVVFRkbSuHFdXr9+RY4cOZgwYSpDh/6Inp7Wp8JUad1RyTSyQgghPoeRkRG9evXh6tWrLF68lCJFimo6JLXSugSfY+fjZK/lcTghhBCpiY+PZ+3aVRQsWAh7+28BGDduMrq6ulr76Nun0LoEb+p0MdlrSfBCCCE+dOfOLUaPHs7t2zextrahceOmGBsbZ9vh+NR8PUcqhBAi24uMjMTFZQGrV68kISGB/PkL4OKyBGPj9CuKZjda+xz8Oz4+ocTExGs6DCGEEBp2+vTfNGxYm59+WoZSqWTIkGGcOXOZpk2/ziJiWteDj+pSQvVzWGwC1aqtB8DSMidYD4YV6zUVmhBCCA2Ji4tjwoTRPH/+jDJlyrFkyQqqVq2u6bA0SusSfPisuqqfnz4Jgl+uAhAYGAX6xpD975sQQghBUtW3uLg4DAwM0NfXZ/HiZdy4cY1hw0ZkqwlrPpfWJfj3vXz5QeEZS+2fE1kIIUT6fHy8mTBhNPnzF8TFZQkADRo0pEGDhhqOLOvQ6mvw0dHx2NgYo3raQRK8EEJkawkJCaxd+zMNGtTi5Mm/OHBgD0FBgZoOK0vS6h588+ZFuXt3CPHxibx5E0Hle2U1HZIQQgg1uXfvLmPHDufGjesAfPttR+bNcyZ3bu0vDKMOWp3g39HT08HOzhQC3mo6FCGEEF+YUqlkwYI5rFy5lPj4ePLmtWPRIjdatWqj6dCyNK0eohdCCJH9KRQKfHy8SUhIYODA7zl37ook9wzQuh68eeeDyV6H7G6noUiEEEKoS0hIMAEBARQvnvRo9Jw5Cxk48Htq1Kil4ci0h9YleP37QZoOQQghhJoolUr++GMfU6ZMwMrKir/+OoOBgQFWVlZYWVlpOjytIkP0QgghsoQXL3zp27c733/fH3//N5iamhEcHKzpsLSW1vXg3wlKTGRmZBTmy6+QJ48JBQuagZGmoxJCCPGpEhMT2bBhPXPnOhEREY6pqRnTp8+ib98B6OhIP/RzaV2CD95lD8Dtx4GsHHII5p4DoFQpS/hJk5EJIYT4HH36dOOvv44B0Lq1PQsXLiZvXjsNR6X9tO7UKL6cJfHlLPE10k22PE8eEw1FJIQQ4r9o06YdtrZ5+PXXrWzatE2S+xeidT34d169ikj2Om9eSfBCCKENLl26yLNnnnTv3guAnj378O23HTA1NdNwZNmL1ib46tXzMnPmN7x6Fc6rV+HUrGnHDk0HJYQQIk2hoW+ZM8eJTZt+IUeOHNSqVYciRYqiUCgkuauB1ib4cuWsKVfOOtmyMbc1FIwQQoiPOnz4IJMnj+PVq5fo6+szbNgIGYpXM61N8EIIIbK+V69eMmnSOI4cSZqkrFq1GixZspLSpctoOLLsT+sSvN695FWD4stJkQEhhMiqxowZzokTxzE2NmHatJn07z8YXV3d9D8o/jOtS/BmnQ+iq6oPC/73+2kwGiGEEB9SKpUo/v932slpHoaGOZg7dyH58uXXcGRfFy17TM6WciEh3IyP13QgQgghPhAbG4ur6yL69++FUqkEoGTJUmzYsFWSuwZoWQ++N48SEmn4NpRDZqY00NfXdEBCCCGAq1cvM3bsCB4+fADA9etXqV69poaj+rqpLcFfuHCB48ePY2lpiUKhwNHRMdn7Pj4+ODs7U6FCBR48eIC9vT1NmzZNZ6umAIQqlbQIC+Na1YLYqCl+IYQQ6QsPD2PevFn8+us6lEolRYoUxdV1uST3LEAtCT4qKoqZM2dy+PBhDAwMGD58OBcvXqROnTqqddavX0+1atXo378/9+/fZ9SoURlI8P/qM6gy1nMbqSF6IYQQGXH48GEcHIbg5/cCPT09fvxxJGPGTCBnzpyaDk2gpmvwN2/exM7ODgMDAwCqVq2Ku7t7snWsrKwICkoq/RoUFES5cuUysOWTAHTuXIY5cxqpbuIQQgiR+S5evIif3wuqVKnK8eOnmTp1piT3LEQtPfjAwECMjY1Vr01MTAgMTP5424ABA/jxxx9ZsGABt2/fZtiwYRnY8lkOHVpPixbF0NdP+zELa2vTzw1dIO2XWaSd1U/a+MtSKpU8f/6cwoULAzBt2jQKFy7MgAED5NG3LEgtCd7S0pKIiH/nig8PD8fSMvnz6pMmTaJLly7Y29sTFBREixYtOHHiBObm5h/dds2aeQkJifzoOv7+YZ8d+9fO2tpU2i8TSDurn7Txl+Xp+YSxY0fy+PEjzp+/irm5BdbWprRv342goI//TRb/zeeeqKpliL5y5cr4+fkRGxsLwI0bN2jUqBEhISGEh4cD8PLlS6ytk6aaNTMzQ0dHh8TERHWEI4QQ4jPFxcWxbJkrDRvW4fz5syQmJuDh8VjTYYkMUEsPPmfOnDg5OTF37lwsLCwoVaoUderUwdnZGXNzcxwcHJg8eTKbN2/mn3/+wdfXl9GjR5M7d251hCOEEOIz/PPPdUaPHs79+3cB6Nq1B7NmzU8xIiuyJoXy3WwEWkChUBD5w5/JloXPqqv62eZ2UjWiNxVDMzWu7ESGNTOHtLP6SRv/NytXLmPu3JkkJiZSsGBhFi9eSqNGTZKtI22cOT53iF7LJrqBnLs8kr1+P8ELIYT4MipUqIhCoeDHH0cyfvxkjIyMNB2S+ERal+CFEEJ8ef7+/pw8eZzu3XsB0LBhY65cuUWBAgU1HJn4XFo2F70QQogvSalUsmPHb9SvX50RI37g8uVLqvckuWs3revBhznVSX8lIYQQ6fLy8mT8+NGcOfM3AN980xhbW1sNRyW+FK1L8NFdS2o6BCGE0Grx8fGsXv0TLi7ziYqKwsLCgtmzF9C1aw+ZITQb0boEL4QQ4r9xcZnPkiWLAfjuu67MmbMQKysrDUclvjRJ8EII8ZUZPPgHTp06yaRJU2natIWmwxFqIjfZCSFENufufoq+fXsQFxcHgLW1NcePu0tyz+YkwQshRDYVFBSIo+MQunbtwJ9/Hmbr1k2q9+Rae/YnQ/RCCJHNKJVK9u7dxbRpEwkMDCRHjhyMGzeJ3r37aTo0kYm0LsFbl92U7LX/ffmFFUKId3x8vBk/fhSnTp0AoH79b1i8eClFixbXcGQis2ldghdCCJG2M2fcOXXqBLlymTNr1jx69Ogtw/FfKUnwQgih5d6+DSFXLnMAevbsw6tXL+ndu79MWvOVk5vshBBCS0VFRTF3rhNVq5bn2TMvIOnmubFjJ0pyF9rXg5dr7kIIAefOnWHs2BF4eXmiUChwdz9F//6DNB2WyEK0LsELIcTXLDg4iFmzprNt2xYASpcug6vrcmrUqKXhyERWo1UJ/ntDqf0uhPh6nTnjztChgwgI8MfAwIDRo8czfPhoDAwMNB2ayIK0KsELIcTXzNY2D2/fhlCrVh3c3FZQooQU3xJp07qb7IxW3tR0CEIIkSkSEhI4fPggSqUSgFKlSnPkyAkOHDgqyV2kS6sSvJNRG4x/vqXpMIQQQu0ePLiPvX0LBgzoxb59u1XLK1Wqgo6OVv3pFhqiVUP0drq5NB2CEEKoVXR0NEuXLmbFiiXExcVha5sHU1NTTYcltJBWnQaujT5PVJcSmg5DCCHU4tKlCzRpUg83N2fi4uLo128Q589fpXnzVpoOTWghrerBD9m/gyHsgNuajkQIIb6so0cP069fDwBKlCiJq+tyateWJ4fE59OqBJ8RzUylvrEQQvs0btyUMmXK0qZNO0aNGoehoaGmQxJaTusS/JuKoZoOQQgh/rNXr16yaNE8Zs6cg7m5BTly5ODEibPo6+trOjSRTWhdghdCCG2WmJjI5s0bmDNnJmFhoRgaGrJwoSuAJHfxRUmCF0KITPL48SPGjh3B5csXAWjVqg0jRozRcFQiu5IEL4QQahYbG8vy5W4sXbqY2NhYbGxsWbDABXv79lKrXaiNVj0md23yeMw7H9R0GEII8UmuX7+Ks/N8YmNj6d27H+fOXaFduw6S3IVapduDv3fvHtOmTcPS0pJ27dphbGxMs2bNMiO2FKp5FQSCNLJvIYT4FLGxsaoiMHXq1GPMmAk0aNCQevUaaDgy8bVItwf/+++/s3LlSmrWrEn79u25ceNGZsQlhBBa688/j1C7dhWuXLmsWjZp0jRJ7iJTpZvgCxUqRL58+VRDSebm5uqOSQghtNLr168ZNKgvfft2x9fXh40b12s6JPEVS3eI/vHjxxw+fBh/f3/+/vtvvL29MyOuVFWb78yJEmc0tn8hhEiNUqnkt982M2vWdN6+DcHIyJgpU6YzaNAQTYcmvmLpJvgxY8bg7OzMo0ePCAoKYuLEiZkRV6puFPUhvpylxvYvhBAf8vX1YfjwoZw/fxaAZs1asGiRGwUKFNRwZOJrl26Cj4yMxNU1aRIGLy8vHj58iLW1tdoDE0IIbWBomIP79+9iZWXF3LmL6Nixs9wdL7KEdK/BHz58WPVzvnz5cHd3V2c8QgiR5d2+fZO4uDgArK2t2bRpO+fOXaVTpy6S3EWWkWYP/sSJE5w8eZKHDx/y4sULIOk60+vXrzMtOCGEyErCw8NZuHAO69atZsqUGYwcORZAqr6JLCnNBF+mTBnMzMzYt28fHTt2BEBHR4cSJaQeuxDi63PixDEmTBiDr68Purq6REVFaTokIT4qzQSfL18+8uXLR5UqVZIVQPDx8SFXrlyZEtyHqnoWQE83UG60E0JkGn9/f6ZNm8C+fXsAqFixMkuWrKBChUoajkyIj0v3JrvY2Fh27dpFUFDSDHLXrl1j48aN6o4rVdenTAAO4X+/n0b2L4T4unh6PqF166YEBweTM2dOJk6choPDD+jpSRkPkfWl+1vq5OREuXLl8PDwoF69epiZmWVGXEIIoXGFCxelTJly6Ovr4+KylMKFi2g6JCEyLN0EX7JkSfr3709sbCxdu3YlJCQkE8ISQojMFx8fz5o1P9O2bTsKFy6Cjo4Omzdvx9TUTO6OF1on3cfkvLy8CA8PJzg4mGvXrnH58uX0PqI214t4E1c2t8b2L4TIvm7fvknLlo2ZNWsa48ePQqlUAmBmlkuSu9BK6fbgmzRpwsOHD7G3t2fatGl07tw5M+JKVfUFLrypGKqx/Qshsp+IiAicneezZs1PJCYmUqBAQX74YbgkdaH10k3w75eG3bdvH2fPnlVrQEIIkVn+/vsk48ePxtv7GTo6OgwZ8iMTJ07FxMRE06EJ8Z99dIj+1q1bPH/+XPX6/v37rFy5Uu1BCSGEur169ZI+fbrh7f2McuUqcPToSebMWSDJXWQbafbgZ8yYwa1bt4iMjGTGjBns3buXJ0+e8MMPP2RmfEII8cW8u66uUCjIkycvEyZMART88INjsvk+hMgOPjpEf+DAAeLj4+nRowe9evXCzc1NrksJIbSSt/dzxo8fRffuvejYMeleohEjxmg4KiHUJ80hehsbGwD09PT45ptv6NChAwqFgjt37mRacEII8V8lJCSwevVKvvmmFn//fRIXlwUkJiZqOiwh1C7NHvydO3f47bffAHj48KHq53PnzrFq1ap0N3zhwgWOHz+OpaUlCoUCR0fHZO8rlUq2bNkCwIsXLwgNDWXBggUf3eaatd0xsbxA+Cwp7CCESN/du3cYM8aRmzf/AaBDh07MneuMjk66TwgLofXSTPCvX7/m7t27AJiZmal+zkg1uaioKGbOnMnhw4cxMDBg+PDhXLx4kTp16qjWOXDgAGZmZnTo0AFIOolIj8OpeoCHJHghxEdFR0czefJ8XFxcSEhIwM4uH87ObrRo0VrToQmRadJM8OPHj6devXopll+8eDHdjd68eRM7OzsMDAwAqFq1Ku7u7skS/MGDB2nQoAGbN28mICCALl26fE78QgiRglKpZM+ePSQmJjJ48BCmTJmBiYmppsMSIlOlmeBTS+5AsiSdlsDAQIyNjVWvTUxMCAwMTLaOn58f4eHhODo64uXlxeDBgzly5Ai6urrpbt/aWv6hqpO0b+aQdv6ygoKC0NXV/X+1S1M2bdqEQqGgdu3amg4tW5Pf46xLLSWRLC0tiYiIUL0ODw/H0jJ5iVcTExMqVUoqt1ikSBHCw8N5+fIl+fPnT3O7DoO345p/OdH+YeoIW5D0j9Vf2lftpJ2/HKVSyYEDe5kyZQKtW9vj6roMSOqM+PuHSTurkfweZ47PPYlSy50mlStXxs/Pj9jYWABu3LhBo0aNCAkJITw8HEj6x+fj4wMknQAkJCRgbW390e2ua3aB6K4l1RGyEEIL+fr60Lt3VxwcBhAQ4M/Tpx6qvztCfO0UynczP3xEYmIiISEhWFhYZPg5+PPnz3Ps2DEsLCzQ19fH0dERZ2dnzM3NcXBwICwsDBcXF+zs7PD29qZly5Y0bNjw48GeVMhc9GomZ+SZQ9r5v0lISGDDhnXMmzebiIhwzMxyMXPmHHr16qu6Q17aWP2kjTPH5/bg003w586dY8aMGZQsWZK2bdsSERFB9+7dP2tn/5UkePWTf7CZQ9r580VFRdGpkz3Xr18FwN6+PQsWuGBrmyfZetLG6idtnDnUNkT/999/c/ToUapWrUq7du148+bNZ+1ICCG+hJw5c1K0aDHy5MnLxo3b+PXXLSmSuxAiAzfZ2draYmhoqBqaf/fomxBCZJaLF8+TI0cOqlSpBsC8eYvQ0dHBzCyXhiMTIutKtwf/7Nkz1q5dy9OnT9m6dWuGJroRQogv4e3bEMaOHUn79q0ZOXKY6gY6c3MLSe5CpCPdBD9lyhTCw8MJDg7G39+fcePGZUZcqVJ2X4F12U0a278QInMolUoOHjxA/fo12bJlA/r6+tjbt9d0WEJolXSH6A8fPsyYMVJxSQiROV6+9GPixLH8+edhAGrUqIWb2wpKlSqt4ciE0C7pJvg//viDhw8fUq9ePZo2bSrlYoUQahMfH0+7di3x9n6OiYkp06fPol+/gVIcRojPkG6CX7JkCTY2Npw7d46ZM2dSqFAhBg0alBmxCSG+Mnp6eowdO5GjRw+zcOFi7OzyaTokIbRWugne29sbHR0dbt68yYULF0hISMiMuFKl2DFcnoMXIhuJiYlh+XI3TExM+eGHpJLS3bv3onv3XjJaKMR/lG6CnzBhAvr6+nTp0oXdu3djbm6eCWEJIbK7K1cuM2aMI48fPyJnzpx06dIdKysrSexCfCHpJvgWLVowYcIEuQYmhPgiwsJCmTvXiY0bf0GpVFK0aDFcXZdjZWWl6dCEyFbSzdqTJk1Kltx///13tQYkhMi+jh49TP36NdmwYT26urqMHj0Od/eL1KvXQNOhCZHtpNmD79OnD1u2bKFGjRqYmZkBSc+mRkRE0K1bt0wLUAiRPSiVSlavXsnLl35UrVoNN7eVlC1bTtNhCZFtpZngV61aBcDUqVPp0KGDavnBgwfVHpQQIntITEwkPDwMM7NcKBQKXF2X8/ffJxg40AFdXV1NhydEtpZmgjcxMQFIdl3s4cOH+Pn5qT+qNHx/oi45Hj6WmvBCaIEnTzwYO3YEBgYG7Ny5H4VCQfHiJShevISmQxPiq5DuNfibN2+qfi5dujSRkZHqjOej1q7vganTRY3tXwiRvtjYWJYscaFx47pcvHiee/fu4Ovro+mwhPjqpNmD37RpE5s2bSI8PJx9+/YBoKOjQ7lycs1MCJG669evMmbMcB48uA8kPdPu5DSX3LktNRyZEF+fNBN8v3796NevHzt37qRr166ZGZMQQgs5OU1j1aoVKJVKChUqzOLFy2jYsLGmwxLiq5XuEP2Hyf3s2bNqCyY9a5ucJ6qLXL8TIivKmTMnOjo6ODqO4vTpS5LchdAwhVKpVKb2hrOzMxMmTKBPnz6qmaWUSiUvX77kxIkTmRrkO4qTCpmqVs2srU3x9w/TdBjZXnZo5zdv3uDl5UmtWrWBpGlnPTweU758BQ1HliQ7tHFWJ22cOaytTT/rc2kO0TdokDTxRLly5ejTpw+QlOC3b9/+WTsSQmQPSqWSHTt+Y+bMKejp6XP+/FUsLHJjaGiYZZK7EOIjCb5OnTpA0kx274SGhjJ+/Hj1RyWEyJI8PZ8yfvxozp51B6BRoyZER0drMiQhRBrSvQbv5OTEzZs3+e233+jQoQOLFi3KjLiEEFlIXFwcy5cvoVGjOpw9607u3Ln56ae1/P77PvLmtdN0eEKIVKSb4O3s7KhcuTIHDhzg8OHDqglwhBBfj6FDBzF37kyio6Pp3Lkb585do0uX7lL5TYgsLN1qchEREVy7do0CBQqQM2fOzIhJCJHFDBgwmFu3buLs7EaTJs00HY4QIgPS7cHb2toyd+5cvv/+e/7++29evXqVGXGl6trk8Zh3lrnwhVC3v/8+yeLFC1Wv69f/hosXr0tyF0KLpPmY3IeCg4OxsLBQdzwfZ70SAP/7/TQbRzYmj71kjqzazoGBgUyfPondu5PKQh89epJq1WpoOKrPk1XbODuRNs4cn/uYXLo9+Bs3btCwYUOaNm1K48aNk81NL4TIHpRKJbt27aBevWrs3v07OXLkYPr02VSsWFnToQkhPlO61+D379/P3r17sbS0xN/fn6VLl1K5cuVMCE0IkRmeP3/GhAmj+fvvkwA0aNAQF5elFC1aTMORCSH+i3QTfKFChbC0TCoUYW1tTaFChdQeVFqqzXfmRIkzGtu/ENnR0qWL+fvvk5ibmzN79gK6despd8cLkQ2km+C9vLw4fvw4BQoUwNvbm2fPnmVCWKm7UdSH+HJSlUqI/youLg59fX0Apk2bhY6ODhMnTsPGxkbDkQkhvpR0E/yIESNYtGgRjx49onTp0kyYMCEz4hJCqEFkZCSLFy/E3f0Uf/55CgMDAywtLXF1Xa7p0IQQX1iaCT4oKIhff/0VCwsLFi1ahJ5euucCQogs7MwZd8aNG8mzZ14oFArOnTsjj70JkY2leRe9k5MThoaGPH/+nHXr1mVmTEKILyg4OIiRI4fRufO3PHvmRZkyZTly5IQkdyGyuTS75YUKFWL48OEAuLi4ZFpAQogv5/Dhg4wfP4qAAH8MDQ0ZM2YCP/44EgMDA02HJoRQszR78IaGhqqf35+iduPGjWoN6GOqehZA716gxvYvhLZ5+zaEgAB/6tatj7v7BUaPHi/JXYivRJoz2TVo0ABbW1sAXr9+ja2tLUqlkoCAAE6fPp2pQarITHZqJzNTZQ51tXNCQgJ3796mUqUqQNIENn/+eYSWLVujo5PuvFbZivwuq5+0ceb43Jns0hyir1+/Ph07dkyx/MCBA5+1IyGEet2/f48xYxy5f/8e7u4XKVq0GAqFgtat22o6NCGEBqSZ4MePH0/u3LlTLC9evLhaAxJCfJro6Gjc3JxZuXIp8fHx5M1rx5s3r2UmOiG+cmmO2aWW3D+2PDNcL+JNXFnN7V+IrObChXM0alSHpUsXEx8fz4ABgzl37gq1a9fVdGhCCA3Tqofbqy9w4U3FUE2HIUSWsGbNT0yfPhmAkiVL4eq6glq1ams4KiFEVvF13XUjRDbSpElzTExMGT9+MidPnpPkLoRIJkM9+FOnThEeHk6ZMmXInz9/ssfmhBCZ4+VLP7Zv38ro0eNRKBSUKFGSf/65R65c5poOTQiRBaXbg3d2duavv/7i2rVrxMXF4erqmhlxCSH+LzExkV9/XUe9ejVYuHAuu3f/rnpPkrsQIi3pJngzMzMWLFhA/vz5KVu2rFSbEiITPXr0kHbtWjJp0ljCw8No3dqe+vW/0XRYQggtkO4QfXBwMICqPnRQUJB6IxJCEBMTw9Kli1m+3I24uDhsbGxZuNAVe/tvNR2aEEJLpJvgCxcuTJs2bdDR0eHYsWN069YtM+JK1Zq13TGxvED4LHkESGRvGzasw9V1EQB9+gxgxoxZMhwvhPgkaU5V+76nT5/i4eFByZIlKVq0aGbElTqZqlbtZOrJzJFaOyuVStVIWUxMDN9/348ffhhOnTr1NBGi1pPfZfWTNs4cnztVbYYekytWrBitWrWiaNGiHDly5LN2JIRI29Gjh2nevCHBwUmXwAwNDdm8eYckdyHEZ0t3iL5JkyaqXoVSqSQiIoI2bdqoPTAhvgavX79i8uTxHDqUVONh48ZfGD16vIajEkJkB+km+KFDh9K1a1cA/Pz8uHr1aoY2fOHCBY4fP46lpSUKhQJHR8dU1/vjjz8YP348N27cwNjY+KPbdBi8Hdf8yzO0fyGyssTERDZv3sDs2TMIDX2LsbEJU6fOYMCA7zUdmhAim0g3wb9L7gB2dnb4+fmlu9GoqChmzpzJ4cOHMTAwYPjw4Vy8eJE6deokW+/p06c8ffo0w8Gua3aBeRVLZnh9IbKip0896Nx5NGfOnAGgefOWLFrkRv78BTQcmRAiO0k3wU+ePFn1c0REBImJielu9ObNm9jZ2WFgYABA1apVcXd3T5bgo6KiWL9+PbNmzWL16tWfE7sQWsnPz48zZ85gZWXN/PnOtG/fSXUZTAghvpQMTVX7ri68sbExZcqUSXf9wMDAZMPtJiYmBAYGJltnyZIlDBs2THUSkFGfezehyDhp4y/v2bNnFC5cGIBOnezZsGED3377rUarM34N5HdZ/aSNs650E7yBgQFmZmaULl06wxu1tLQkIiJC9To8PBxLS0vV65cvXxIaGsrRo0dVyzZs2EDDhg2pUKHCR7ctj2Solzz28mWFh4cxf/5sNmxYz759h1VlXPv374+/f5i0tRrJ77L6SRtnjs89iUo3wfv6+lKqVKlP2mjlypXx8/MjNjYWAwMDbty4Qc+ePQkJCUFPT4+8efOycOFC1fqurq4MGDAg3ZvshNAmx48fZeLEsbx44Yuuri53796WOu1CiEyT7nPwVapUSdYb37hxY7obzZkzJ05OTsydO5clS5ZQqlQp6tSpw9q1a9m2bZtqvaCgIH7++WcA1q9fz+vXrz/jEITIWt68eYODQ3969+7Gixe+VK5chePHTzN48FBNhyaE+IqkO5Nd48aNCQoKUg2xR0REcPny5UwJLgWZyU7tZMjtv7lw4Rz9+yeNVhkZGTFp0jQGDx6Knl7ywTJpZ/WTNlY/aePMobYh+rZt2zJu3DjV6127dn3WjoT4GpQsWRodHR0aN26Ki8tSChYspOmQhBBfqTQT/OTJk6lZs2ay5A7QpUsXtQclhLaIi4tj27Yt9OjRGwMDA6ysrDh+/DQFChSUR9+EEBqVZoI3NzdXPR4nhEjp5s0bjB49nHv37hAUFKiaYlZ67UKIrCDNm+zS6n3s3btXbcGkR7FjuFx/FxoXERHB9OmTadWqCffu3aFgwcJUqVJN02EJIUQyafbgd+7cybFjx5Ite1dsplOnTmoPTIis6NSpvxg/fjQ+Pt7o6OgwbNgIxo+fLI94CiGynDQTfPPmzRk4cGCyZUqlkp07d6o9KCGyovPnz9K9+3cAVKhQCTe35VSqVEXDUQkhROrSTPAWFhaUKFEixfLx46WUpfg61a1bn+bNW1KnTn2GDv0xxaNvQgiRlaR5Df7WrVvs27cvxXJDQ0O1BiREVvH8+TP69u2Op2dSxUOFQsHWrTtxdBwpyV0IkeWl+Vfqt99+y8w4hMgy4uPjWbPmZ5yd5xEVFYWurh4bNmwF0r75VAghshqt6oZ8f6IuOR4+Jrqr1IQX6nHnzi1Gjx7O7ds3AejUqTNz5izSbFBCCPEZtCrBr13fA7goCV58cZGRkSxevJBVq1aQkJBA/vwFcHZ2o1mzlpoOTQghPku6xWaE+Bq8eOHL2rU/k5iYiIPDD5w5c1mSuxBCq2lVD16ILyk09C2mpmYoFApKlCjJokVulC5dhmrVamg6NCGE+M+0qge/tsl5orqkfHRPiE+hVCrZu3cXtWtXYc+ef+d16NWrryR3IUS2oVUJfojDDsJn1dV0GEKL+fh407NnZ4YOHURAQABHjx7WdEhCCKEWWpXghfhcCQkJrF37Mw0a1OLkyb/IlcscN7cVrFu3UdOhCSGEWsg1eJHt+fm9YODA3ty4cR2Ab7/tyLx5ztja2mo4MiGEUB9J8CLby53bkrdv35I3rx2LFrnRqlUbTYckhBBqJwleZEsXL56nTJmymJtbkCNHDjZt2k7evHkxNTXTdGhCCJEp5Bq8yFZCQoIZM2Y47du3Ztas6arlJUuWkuQuhPiqaFWCvzZ5POadD2o6DJEFKZVKDh7cT716Ndi6dRMGBgbkz18ApVKp6dCEEEIjtGqIvppXQSBI02GILMbP7wWTJo3lzz+PAFCrVh1cXZdTsmQpDUcmhBCao1UJXogPvX79mgYNahEWFoqpqRnTp8+ib98B6Oho1eCUEEJ8cZLghVaztbWlbdt2hIaGsmCBC3nz2mk6JCGEyBK0KsFXm+/MiRJnNB2G0KCYmBiWLl1Mo0ZNqVWrNgCLFy/DwMBAw5EJIUTWolUJ/kZRH+LLWWo6DKEhly5dZOzY4Xh4PObQoQO4u19EV1dXkrsQQqRCqxK8+DqFhr5lzhwnNm36BYDixUvg7LwEXV1dDUcmhBBZlyR4kaUdOXKISZPG8urVS/T19Rk+fDSjRo0jR44cmg5NCCGyNEnwIssKDX3LmDGOBAUFUa1aDdzcVlCmTFlNhyWEEFpBErzIUhITE0lMTERPTw8zs1wsWLCYoKBA+vcfLEPyQgjxCbTqYeGqngXQuxeo6TCEmnh4PKZDhzasXLlUtaxjx84MGjREkrsQQnwirUrw16dMwKLLIU2HIb6w2NhYXF0X0bhxXS5dusCWLRuJiYnRdFhCCKHVtCrBi+zn6tXLNGvWgEWL5hEbG0uvXn05efIshoaGmg5NCCG0mlyDFxoRExODk9NUfv11HUqlkiJFiuLqupz69b/RdGhCCJEtaFUP/noRb+LK5tZ0GOILMDAw4OHDB+jo6DBy5Fjc3S9KchdCiC9Iq3rw1Re48KZiqKbDEJ/p9evXxMfHkS9ffhQKBW5uK4iIiKB8+QqaDk0IIbIdrerBC+2kVCr57bfN1K9fgxEjhqlqtBcpUlSSuxBCqIlW9eCF9vH0fMLYsSM5f/4sAPr6ekREhGNiYqrhyIQQInuTHrxQi7i4OJYtc6VhwzqcP38WS0tLVq1az/bteyS5CyFEJpAevPjiEhISsLdvzj//3ACga9cezJo1H0tLqQQohBCZRRK8+OJ0dXVp3rwVgYFBLF68lEaNmmg6JCGE+Opo1RD9mrXdMZl5QdNhiFScOvUXf/55RPV6xIgxnD59UZK7EEJoiFYleIdT9ci5y0PTYYj3BAQEMHToILp3/47Ro38kKCipVoCBgQHGxsYajk4IIb5eWpXgRdahVCr5/fdt1K9fnb17d5EzZ04cHUdjZpZL06EJIYRArsGLz/DsmRfjx4/i9Om/Afjmm8YsXryUwoWLaDgyIYQQ72hVgncYvB3X/Ms1HcZXTalUMnBgH+7evY2FhQWzZy+ga9ceKBQKTYcmhBDiPVo1RL+u2QWiu5bUdBhfpXezzykUCubOXUinTl04d+4a3br1lOQuhBBZkFb14EXmi4yMxNl5PhEREbi4LAGgbt361K1bX8ORCSGE+Bit6sGLzHX69N80bFibn39eztatG3n2zEvTIQkh1CAhIUHTIWS6r+GY1daDv3DhAsePH8fS0hKFQoGjo2Oy99euXUtAQADW1tbcvXuXESNGUKxYMXWFIz5BUFAgM2dO5ffftwFQpkw5lixZITfRiY+6f/8uP/+8nPj4eGrUqEVYWBgBAf5Mnz4bQ0NDAP788zAeHo8xMjIiKiqKAgUK8u23HVWXeS5fvsjlyxcwNTUjPDyMN2/e0KtXX0qXLqvJQ8uw69ev8tdff2JiYkrx4iVo1aptmutGRkawbJkriYmJTJ3q9MVjOXbsCI8fP0JXVwc7u/x06PBdqusdPLgfS0urLD0qt23bZiIiIggLC6VmzdrUr98wxTpXr17m5Mnj5M9fAG/v5/9/qseM0NC3rFy5lIIFC+Hr60Pz5q2oVq0G/v5v2Lt3Jw4OP6Knlz0Hs9VyVFFRUcycOZPDhw9jYGDA8OHDuXjxInXq1FGtExkZyeTJk1EoFBw5cgQXFxdWr16tjnDEJ9i+fTsjRowgICAAQ0NDxo2bxLBhI9DX19d0aCKLK1u2PFWqVCMqKopBg4YAMGnSGM6c+ZvmzVuxf/8enj3zZNSo8arPrF69kr17d/Ldd924ceMaBw7sZd48Z1XC37t3F7dv39SaBH/ixDFVAomPj//oukZGxrRs2YajRw998TjevHnN9u1b2bDhNxQKBYMH96VatRoUKFAw2Xo3b97g3r07TJo0/YvH8KXcu3eXGzeusXhx0slj795dqFy5GiYmJqp1EhISmDVrKr/9tptcuczZvXsHv/66llGjxrFhw3qKFStOt269CA0NpV+/7uzYsY88efJSrlwFfv11LQ4OwzR4hOqjlgR/8+ZN7OzsMDAwAKBq1aq4u7snS/CjRo1S/ZyYmIiRkZE6QhGf6NixYwQEBFCvXgMWL15KsWIlNB2S+Aw9e3bmxInjX3SbzZq1YNu23Z/0mbdv32JhkRuA7du3sGDB4mTvt2/fiREjhvLdd93YseM3OnT4LtlNm99+25Ho6OgU2719+yZHjx6iQIGCPHhwnx49euPn94LFixfw55/u3L9/Fze3hQwbNorixUvi5DQVUFKwYGFu3LhK//7fM2/eTEaPnoC9fXsWLJhNdHQUs2YtYP361SQkJKCjo4ORkRG9evVLsf8DB/bi4+ONiYkJISEhDB8+mjt3bvHgwX3i4+MJDAykRYtWyT6zYcM64uLiMDAw4MmTx8yd65zs/bt377Br1zZKliyNh8djhg4dTp48eTh9+hQ3b/6DlZUVDx8+YM6chakue9+VKxcpVaq0qi3Ll6/ApUsXUiT4P/7YR6NGTVWvFy2ai5WVNVFRUVhaWtGjR2/u3r3N4sULKVWqNPr6Bri7n2T79r2cOHEMf38/DAyMiIiIYNiwESgUCiZPHkeZMmV58+YNFStWokWL1inab8OGddy5czvF8vr1v6FTpy7Jll24cJby5SsCoKenR6FChbl583qyXnxoaCgxMbHkymUOgJ1dfg4c2AuAr683lSpVBsDMzIy4uFi8vJ5SunRZateui5vbIgYPHoqOTva7Yq2WBB8YGJhsFjMTExMCAwNTXTc2NpZ9+/Yxc+bMdLer7L4C2AT+jumuKzImISGBly9fkj9/fgBcXV1p1KgR/fr1k7vj1czaWn1V9QwMvvw/bQMDvXRjNjY25M6df9i5czNnz56lZ8/utG6dlEBev35FyZKFsbD4dxtmZoV59eolFhY5efXqBcWKFUh3H0qlklmzprJ3716srKx4/PgxUVFRNGzYmXXrfsba2pSGDetw9GgZzM2NKFYsH46OP+Di4sK8ebPw9/cnMTGRq1dbkDevFdbWptjaWuHo6MiNGzfw8HjAr7/+CkCfPn1o2bIpZcqUUe3/6dOnHDiwm4MHDwIwc+ZMTp8+Rrdu3Th58igdO3akVq1ayWI+e/YsHh4PWLduHQC7du3C2toUc3MjcuTQx9raFDs7SyZPnkiBAgU4fvw4R47sZeLEiZw6dYzmzZvTsWNHbty4gbW1aarL3hcbG4mlpblquZWVBTEx4SnW8/F5RokShVTLW7VqTrNmzQBo3749Awf2oXHjety924KoqCgmTJjAw4d9iIsLY9++nRw5cgSFQsGkSZO4ffsKzZo1o3v3LjRr1oyEhATatGlDr15dU3yHEyaM+eh3/L7o6HDs7IqqYsyd25z4+Khkx2JtbUqePLaEhLyiRIkSPH/uQXR00jp16tTC0/MRXbp0wNvbm7dv36Knl/j/z5uiVCpRKGKwtrbJcEzaQi0J3tLSkoiICNXr8PDwVCuJxcbG4uTkxOjRoylYsGCK99Pi7x/2ReL82t29e4exY4cTERHByZPnMDQ0xNrakrZtvyMgIFzT4WVr1tamav093rhxh1q2m17MERExFC9emq5d+1KiRDlWrVpB/frNUCgU2Nrm4fHjZxQt+u+fnZcv/cidOzfBwVHkzm3F06c+2NoW+ug+goODCQsLR6k0xN8/DAuLvFhYJMWWkJCYLMaQkEj8/cMICYkkX76C/38vBzo6YG//HatWLadEiQrExSmJjEzkxo3bhIaG4+a2AgALC0u8vHyxssqv2ua1a7extrZV7cfSMg///HOHJk3aEB0dp9rn+27cuI2NTV7V8kaNWqniio6Ow98/jMjIBH77bQPm5ub4+fkRH5+03MFhOFu3bmTDhk3UqVOP/PmLp7rs/RNyAwMjAgNDVPsLCAgmX74CKeKKioomLCxGtdzLy4e5cxdiZGTM27dheHq+IG9eOyIiYsiTJx/+/mFYWubj1KkTJCbCunXrCA+PIT5eycuXAbx8Gczt2/e5du0mBgaGBAQEpvo788sva7h9+1aK5d9805DvvuuWbFmOHCb4+werthMUFIKeXs4U2124cAk7duzG0tIK0MfKygZ//zC+/bYrO3duY9mynzEyyknhwkXIkSOX6vM6Orr4+QWiUORMEU9W8bmdAbUk+MqVK+Pn50dsbCwGBgbcuHGDnj17EhISgp6eHiYmJkRFRTF79mwGDhxIiRIlOHbsGC1btlRHOOIDUVFRuLouUt0QZWeXj+fPn1GyZClNhyaykSpVqmFiYsqZM3/TsGETevTozR9/7Et2Df7Agb306NEHgO7de3Po0H7q1KmnSlYbN64nT568yW5WMzc3x8TEhODgICwscvPkiQdRUZFUqFAJIyMjIiLCMTY2wc/PL1k8H45IlStXnpiYaFauXEKfPgMAKF68JHfv3qFPn/5A0k1z+fIVSPa5YsWK8/Llv9v29fWmVKkyfEzx4iX555/rqteHDh2gZcs2ydb56adlfPNNI1q3tufKlUv89defAHh5eTJx4jTi4+NxdHSgQYNG+Pu/SbGsVKnSqm3VrFmH3bt3/r93quDu3TspEieAjY0toaGhAHh4POa337awa9cBAM6fP5Nm+xUrVhxDQ0McHBzw9w/j0aOH6OnpcfHiOa5evczy5Un3U+3Z83uq7fHuHo2MqFOnPhs3Jo18xMfH8/z5MypVqgokjQpZWVmjq6tLZGQEQ4cmje4eOLBX1b5BQYG0afMt5ubmhIaG4u5+ivz5k75TpVJJVFQkVlbWGY5Hm6glwefMmRMnJyfmzp2LhYUFpUqVok6dOjg7O2Nubo6DgwPjx4/Hw8MDX19fIOmmO0nw6nfu3BnGjh2Bl5cnCoWCQYMcmDp1JiYm6hsuFl+Hhw/vc+vWP8TFxXH16iVq1KjNwIEOzJs3k9jYWDp06Myffx5mxYolGBkZERMTTcGChbC37wBA7dp1AVi5cgnGxiaEhYVhYWGRIhEqFAqcnOaxevVK8ucvSGCgP99//wMAnTp1ZckSF8qVq4COjg7Hjh2hZMnSHDt2hKdPPXB3P5nsmnOnTl05efK46tp0zZq1uX//LqtXr8TIyIiwsDBV0ninUKHCfPddN5Ytc8XExAR9fX3atv2WW7du8vSpB8eOHcHY2OSDhFube/fusHr1SgwMDMiVKxdxcbGquO7cuUXLlq3Zvft3Xr70482b1zx96sHDh/e5d+8O9+7dIUeOHBQpUoyiRYvh7n4yxbL32djY0qNHb5Yvd0NHRwd7+/Yprr8DfPNNI+7du0P16jUpWLAghQsXZuHCORQsWBh//zccPvwHLVq05tatf/D0fELRosUoXboshQoVpn37TixYsABDQ2MCAvwZMsSR3Llz8/vv21iyxBlraxuio6M4dOgA9vbtP/O3Kun+gapVq7NmzU+EhYXi6DgKU9Okv1czZ07hhx9GUKlSZQ4c2Iuuri62tnlJSIinZ8++QNLU2rt3/06FChUJCwtl0qQZqm0/efKYKlWqqZ7yyG4UyndTlGkBxUkFbyqGajoMreXkNI2ff06a6rd06TK4ui6nRo3k1wrVPXQskkg7q5+0cfri4+OZN8+JQYOGqHq1n0Kb2zgmJgZn57kMHvwDefPaaTqcj/rcIfrsd9ugSFPp0mUwMDBg4sSpnDhxNkVyF0J8XfT09Jg2bRaxsbGaDiXThYa+ZeTIcVk+uf8X2fPpfgHAixe+3LhxnXbtkobHunXrSZ069ShUqLBmAxNCZBm6urophvi/BtnxrvkPSQ8+G0pISOCXX9ZQv35Nhg0bzNOnHkDStUtJ7kII8XWQHnw28+DBfcaMGc7161cBaNv2W7mBTgghvkKS4LOJ6Oholi5dzIoVS4iLi8PWNg8LF7rStm07TYcmhBBCA7RqiP77E3XJsfOxpsPIkiZOHIObmzNxcXH06zeI8+evSnIXQmTI11BZ7UNfwzFrVQ9+7foewEWiu5bUdChZzogRo7lz5zbz57tQu3ad9D8gxBcm1eSyVjU5X18ffvppKbq6uinmvX/f2bPuhIeH07q1/ReP4UvJSGW8x48fsmvXDgoXLoKXlyeDB/9Anjx5iI2NZdmyxdjY2BIYGEDFipVp1qwlUVFR/PLLGgYPHoKxsUkqe9V+WtWDF/86dOgPHB2H8G4ag2LFSnDy5FlJ7kJj3lWTK1++IoMGDWHUqHHEx8dx5szfAOzfv4eHD+8zfPhoBg0agqPjKF6+9GPv3p0Aqmpyw4ePYcCA7xk+fAxVqlTj9u2bGjyqT/Oumpyj4yiaNfv4xF3vqsmpy/37d6ldu95H1/Hx8eaPP/Zl6eT+rjKeo+Mohg0byaFDB/Dx8U6x3vz5s+nSpTu9evWjUaOmLF2adFKzf/9u9PUN6NdvECNGjGXVqhUEBARgYmJCq1ZtcXVdlNmHlGm0qgcv4NWrl0yaNI4jR5IKXdjbt6dVq6Q/ElIcRrzT06szJ8K+cDU50xZsKyLV5CDrV5MDaNGitervRFqOHj2UbD6MdetWERcXh76+PrGxsfz440h8fLyZP38WlpZWWFpacv78WRYsWIyfnx+3b1/DwsKaV69eMXz4aAwNDVOtSPeh/fv3cOaMe4rl5cqVTzGNbUYr4/n6emNrmwcAO7t8XL9+DQAfHx/s7PIBSc/9W1jk5s6dmzRu3IxSpUpz+/ZN3r4NUVWiy060KsGvbXKePpb9NR2GRiQmJrJ58wbmzJlJWFgoxsYmTJs2k+bNZXpfkbU8eHCPjRvXc+nSBb79tiPVq9cEkk5OkwqB/Ct3bktevXpJfHw8L174kDt38qJU72pXvE+pVDJz5hR++WULuXNb4un5hKioaJo1a8nq1SuBpNGEdxXgzMzM6N27H6tWLWfUqHEEBgaQmJhIw4ZNVFUvzcxyMXLkOC5fvsi9e3dYsuQnABwdHahZszYlSvxbp+HZMy/27t3Jpk1JBX0WL17AoUMHaN++EyVKlKR1a3uqVq2eLOZ32128OGkmyUOH9qdot5w5czJkiCN2dvk4ffoUe/b8zo8/juTPPw/zzTeNad3anjt3kgq0pLbsc3h5edK8+b8nIqVLl6FBg0YATJw4Gk/PpxQtWox27Tpw8eJ5Ro+eQNeuPTE1NWPcuBGcOnWKsLA4fvllDQcO7KVr1x7UrVtftY3+/XvSvn1HjIyMk+23Q4fvUh1mT01wcHCyzxsZGRMcHJRivYoVK3Pv3l3q1q3Pgwf3iI6OIj4+nooVK3H6dNIoUlhYGD4+z5MVQ7OwsMDHx1sSvKYNcdhBx4prNR1GpvPweMyYMcO5fPkiAC1btmbhQlfy5cufzifF1+pTe9pfUpky5ejffzCVKlVh1aoVtG5tj0KhIE+evAQGBiT7QxoUFEju3LnR09PD2tqGoKDUy0q/LyQkhIiICNXJQNGixTMUV6FCRQBUJxnffdeNVauWU61aTfT09DAyMuLpUw+io6PZsmUjALa2toSEBCfbjqfnU/Lkyat6nS9fAZ488fjovp8+9Ug2Fey7+fffZ2hoyJ49O5NVkwNwdBzN1q0b2b37d+rUqUf58hVTXfY5I3hxcbHo6uq+9zqen39ehqlpLvz9/ZMde+HCRf5/vPl58OAeoGDz5s2Eh8cQFhZKzpxGAAQGBrBmzU8YGRkTERHB27dvUyT4fft24+5+KkU85cqVx8FhWLJlFhYW+Pr6qF5HRkakKAAEMH36bHbt2oGvrw/GxsZYWVmjp6dHs2YtiYiIYPPmXzEyMqJMmXKqnj4knUTGxMR8QqtpD61K8F+r/fv3cPnyRaytbViwwIV27TrIcLzI8qSa3L8yu5pcRtnY2BIW9hZI6t3OnTuDY8dOo6+vr5ogKzX58hXAwMCQgQMHEhwcxYsXvgQE+Kdbke6djh0707Fj5wzF+LHKeAEBAZiammJoaEhAQIDq5ODKlUuq9g0LC6V27XrkyZOH+Ph4Tp06QZUq1VTbDw0NTZbwsxNJ8FlUaOhbzMxyATBixBgSEuIZOtQRc3MLDUcmROqkmlzWqSYHSXfHnz9/Bm/v5/z226ZU7yX45pvGnD59Cnv7DpiYmNC4cTPmzp1BqVJlefbMi2PHjlC4cBHOnz9DWFgY165doXr1mpiZmTFixGjmzZuHqWluXr9+yYAB32NiYpJqRbrBg4d+8u/TOx+rjLd8uSsNGjSkefNWnD9/hl27tlO4cFEiIsIZMGAwAP7+/qxY4UblylWJjIxk7NhJ6Oklpb7Q0LcYGhp+VqEdbSDV5LKYsLBQ5s514tChPzh79nKKa5Lqps3VobSJtLP6SRtnzOLFC2jTph1ly5b/5M9qcxsnJiayZIkLbdrYU6ZMOU2H81FSTS4b+PPPI9SvX5MNG9YTHBzEhQvnNR2SECKbGzduMgYG2bMe+sdERETQu3e/LJ/c/wsZos8CXr9+zZQp4zl4cD8AVapUxc1tJeXKffoZtRBCfKrixUtoOoRMZ2pqiqlp9q7ToVU9+GuTx2Pe+ePPdWqbgwcPUL9+DQ4e3I+RkTFz5izgyJGTktyFEEL8J1rVg6/mVRBI+fyjNsudOzdv34bQtGlznJ2XpJi8QQghhPgcWpXgs4O4uKSpO5s2bQFAvXoNOHr0JFWrVpdH34QQQnwxWjVEr+1u3LhG8+YN6dGjMxcunFMtr1athiR3IUS29zVUcEuNpo5bq3rw1eY7c6JE6hMnZGXh4eEsXDiH9evXkJiYSKFChdHRkXMr8XU6dOgA0dFRdO7cXdOhaNyBA3tZtWo5zZq1wtzcnGfPPKlZsw7fftsRSJp8ZsuWDapqfMHBwXTo8J3qprjY2Fh++20TiYmJAPj5+WJqasaPP45CX19fMweVBm/vZxw+fJAffhiu6VDS5OHxiL17d5E3rx3BwcH8+ONI1TPz74SGvmXlyqUULFgIX18fmjdvRbVqNQD4/fff8Pf3J2fOnMTGxjJ0qCMKhYKNG9fTqFFTihXL2KyLX4pWJfgbRX2IL5e5z4X/VydOHGPChDH4+vqgq6vLjz+OZPz4yRgZGWk6NJHNWZfdlOy1//2UE50A5Nj5GFOni6rXUV1KED6rrtrisrdvjxZNv6FW7dt3YsuWDXTq1JmiRYsTGhpKx46tsbdvj0KhYOLE0YwYMUZVLjcqKgpHRwcWLnTF2tqGxYsXUK/eNzRs2BhI6ikOGzaY6OjoLJXgExISmDvXiSVLVmo6lDQplUpmz57O0qU/Y2lpxYoVS/jzz0MpphXesGE9xYoVp1u3XoSGhtKvX3d27NjH8+deHD16mI0btwEwdep4zpxxp2HDxvTq1Y+RI3/gp5/WpThhUCetSvDaZtOmXxk/fhSQVAhhyZIVVKhQSbNBCaEmhw//wZo1P9G9ey+ePvUgJOQtbdq048qVi/j6+uDsvASApUuTKspNnepEZGQEK1Ysxc4uH8HBgZiZ5aJp0xapVi979eolV69extraFj+/FwwfPirFHOdnzrhz7txpChQoxIsXzxg+fBw+Pt44OU2jYsVKTJkyk6NHD3HgwF5mzpzL48ePuHz5AnZ2+VQV0Tw8HrF48UJKlSqNvr4B7u4n2b59L/Pnz6JMmbK8efOGihUr0aJFawC2bNnIs2dPKViwMHfu3EJfX5+RI8cTGRnBb79tolix4jx//oy+fQemWz/iXVUzHR0dbt26SUxMjCq5Q1JBmrp163Pw4H6++64rFy6cY8qUmar3dXV1cXFZqiqi874Pq9lNnz6HxYsXqL6LAwf2smXLBnbvPsi5c2dYscKNevUaEBkZycWL56hYsQre3s+ZPn02urq6zJvnxPDhP2JnV4TVq1dStGgxfH19ad++E6VLJ5+698aNa1haWqrqrr//PXl6PmHcuEkYG5swY8Zk/PxeULlyVe7evU2TJs2oXr1Wqu24b99uvLyeqgoWjRs3OUXyvHv3Nr/+ui5FWxgaGqaobOjn94KYmBhVrYKKFStx7NjRFAne19ebSpUqA0mFjOLiYvHyeoqfnx82Nraq9ezs8nP9+hUaNmxMjhw5sLPLx6VL56lfv2Gq3706SIJXo3bt2rN8uRuDBg3BweGHTD1zEyKztW37LUePHqJkydL07NmXyZPHEhUVweTJM1i6dDFXr16mUaOmtG5tz9GjhwDYvHkD+fPnV02jeujQAQoUKJhq9bIJE0azc+cB9PX12bp1I1u2bGTIkB+TxWBqasqIEWMxMTHh0KHd/PnnEb77riu9evXFw+MRALq6egwd6oixsQlubgvZufMAhoY5klVEa9CgITEx0QwbNpIOHb4jZ86ctGljT4MGjUhISKBXry60aNEaT88nHDt2mK1bdwEwe/Z0qlevSZ48eRgyZACOjqOoUKESN25cY+XKpSmSyjuHDiXN3f7gwT1WrFgDwOvXKavvAVhaWnLnzi18fX3JnTt3ivffTXH9vtSq2RkaGib7Lt6NJgDUr/8Np0+fIn/+gnTq1IWHD++TP39B+vfvQYECBVEqlVSqVIVmzZoxbNhw6tX7hhYtWvHypR9Tpoxjw4Ztyfbv5eWJlZVNqt/Tjh1bVd/TDz8M54cfBjF0qCOxsTEEBAQwb55Tqu1obW1D+/ad0NHRYelSF65cuUTduvWT7bd8+Yq4ua1Itc0/FBwc9ElV6xo1asqLF768ffuWiIgIypQpy5o1K4mJicHAwICHD+8nS/jW1tZ4eXlKgtdWXl6erFy5jPnznTE0NCR3bksuXryBgYGBpkMTItO866WamJhiZ5f0s6mpKZGRkSnWffrUA3v79qrX7//8YfUyMzMz1bBz/vwFOHz4j2Q9tLFjJ5IzpxEbNqz7//XsJ9jZJT122qJFKzZt+oWhQx25desG48dPUVVE27kzqezr+xXR4N/qc8WLlyA+Pp5nz7x4/PgRBgaGqiprXl5eyXrl7+qOvzu2K1cucfPmP8TGxmBklDPNNrO3b0/RosWZP38WV65comPHztjaJlXf+1BgYCDW1rZYW1sTFJSxx4YzUs0uNe++g3ejCLVr1+XkyePExsbSsmXr/2/7CRYWuXn9+hWgxMIiN4mJicnuM/qwat3739OjRw8pUqSo6r38+Qugp6eHnp4eBQsap9mOOXLk4Oefl5MrlzleXl6ULJmy2M6dO7dYv35NiuWGhoaqEaV3LCxyExn5bxnZyMgILCxSnkD16NGHnTu3sW3bFoyMclK4cBFsbfOQN68dEyZMZePG9VhYWFC0aDHViAUknVhmdtU6SfBfQHx8PKtX/4SLy3yioqIoWLAgI0eOBZDkLjQmrWvuH4ruWpLoriXVHE3qihcvyYsXvkDSNdADB/amWic8X74ChIaGEhcXh76+Pj4+PhQvXjJFD23AgJ6MHDmOypWrcurUEby8ksqMGhrmoHHjZixZ4qIaXn1XEa1Hj97o6empKqK98/6TLRcvnuPq1cssX74agD17fgeSEuD7pUz9/F6oknzx4iVp2LAJxYuXIDY2ljNn/k63PQYOHMKPPw6mdWt7KlSoqOoJvn8N/vz5M8yd64yNjS3VqtXgzBl3vvmmEQAxMdGMGzeSefNcMDMzS9bOqVWze1fSFeDVq1fpxtepU1fmz59F6dJlVN9T8eIlqF69BvXrN0SpVGJlZZ3iJmIbG1s8PZ+oXi9aNEf1PR04sDdZu38orXacNm0iGzduJ0+ePMkS8/sqVKjEsmU/p3tckHRyZmhoSGBgAJaWVty+fYu6desBSe0eHR2NhYUFQUGBtGnzLebm5oSGhuLufkp18mRmZqYaVZozZzodO3ZRbT8sLDTdqoNfmlYl+KqeBdDTDcxSN9rdvn2T0aOHc+fOLYD/Dwdm7A+rENnJ1auXeP36FUeOHKR+/YaqympWVtbcuvUPnp5PqFq1erIKan369GfFiqVs2vQL4eHh1K5dl6CgwFSrl40ZM4GlS12wtrbh1auXjBgxJkUM9vbt2bhxPVWrVufZsycEBATh6+tD/vwF6NixMw4O/Rk3bhKAqiLasmWu2NjYqiqieXs/V8VbtGgxSpcuS/nyFfn9920sWeKMtbUN0dFRHDp0AHv79rRo0ZqZM6dQvHhJYmNjVScGkyZNZ8eOreTLV4DAwAAaN26WIt5Dhw4QHh7OH3/so2/fgeTJk4fateuyYMEs+vf/HmfnpWzZsoHz588CSUli6tRZqpOIKVNmsn37FtXlh9evXzF48A/JkjukXs1OX1+fEiVKolQmqsryhoeH89dff5IvX37V92djY6tKYEWLFsPIyIgqVaqrtu3oOIr161fj5eVJaGgo5ctXSHGctWrVZevWjal+T48ePSAsLAxfXx+OHDnI69evVG37sXbs0OE73NwWUbFiJe7evY239zPq1KmPhcXnVdxUKBTMmDGHtWt/Jk+evCQmJtKqlT0AR44cxNPzCePHT+HZMy927/6dChUqEhYWyqRJM1TbWLp0MRUrVsbAwIB69RqqRkAAHj16wMCBDp8V2+fSqmpyWCfdgZnRnok6RUZG4uw8n9WrV5KYmEiBAgVxcVlCkybNNR3af6LN1aG0ibSz+mVWGz94cE9VsGT+/Fm0bdteNUqQ3X1KGx8+/AfR0VGqWu5fk0OHDhAbG0unTl3SXzkVn1tNTqt68FnJn38e5uefl6Ojo8OQIT8yceJUTExM0v+gECJb2bVrBwULFiIxMRFra5uvJrl/qrZtv+XJEw9Nh6ERpUuX1UhBH0nwn+Dd9T+Ajh07c/XqZbp27UGVKtU0HJkQQlNmzJij6RC0xtdYtQ40d9xaNZ3a9SLexJVNeVejuimVSnbv/p2aNSupbhRRKBQsWLBYkrsQQogsSasSfPUFLoTsbpep+/T2fk737p0YNux7XrzwZevWzZm6fyGEEOJzyBB9GhISEli3bhULF84lMjISc3NzZs2aT/fuvTQdmhBCCJEuSfCpePz4EY6ODty8+Q8AHTp0+v9zpzbpfFIIIURGJCQkJJv85muQ2ccsCT4VOjo6PHhwHzu7fDg7u6nmnBZCCHWIi4vj55+X88cfe+nZsy8JCQk8fvyQ/v0HU758RSCpGtvevbswNU16xj08PJx+/QZhbm4OQEBAANu3b8bU1Iy4uDi8vDypWrValqzad/asO+Hh4bRuba/pUNJ07NgRHj9+hK6uDnZ2+VOdgOnx44fs2rWDwoWL4OXlyeDBP5AnTx5iY2NZtmwxNja2BAYGULFiZZo1a0lUVBS//LKGwYOHJJvlTl0kwf/frVv/ULFiZRQKBcWLl2DTpu3UrFkLE5PPe/5QCE2zsXFL9vrNm5QTwwBs3nybceNOqF736VMBV1ftns9B2+jr69O1aw+OHz/CoEFDADh9+m9+/XUtbm4rCQgIYPr0yfz88zpVYvD0fMrkyWNYuXIdCQkJTJo0hvnzXVTznwcFBTJt2sQsl+B9fLz54499uLgs03QoaXrz5jXbt29lw4bfUCgUDB7cl2rValCgQMFk682fP5spU2ZQsmRpzp07w9Klzixc6Mb+/bvR1zegX79BxMfH061bBypXroaVlRWtWrXF1XVRpjx98dUn+ODgIJycprF9+1ZWrlxD1649AGjSJOWsU0KItGWkmpyxsUmaVcCePfNi27bNFC5chKdPPWjSpAVKpTJZVbMrVy6xd+9hNmxYR3x8PEqlEn19fQYM+D5FPEuXLuXt2wj09fWJjY3lxx9HcurUCebNm8no0ROwt2/PggWziY6OYtasBaxfv5qEhAR0dHQwMjKiV69+qmNq374Tfn6+eHs/x8lpPitXLqF8+Yp4ej6he/felChRitjYWBYunIOFhQUmJqacPPkXtWrVZvjwMZw+/XeKqnXvaryn5e3bENWsbIcO7adGjVrJen1FixZDV1eP27dv8vZtCHny5E1W3CR3bkvmzXNJsd3UKvg1btwMF5f5tGnTjubNW+HsPA9IqjK3bdtmNmxYx6BBQ7h79zYJCYkEBLzB0tKKZcuWcPHiOX75ZS0TJ04lMjKSw4f/oHDhInh7P2fo0OGqEYZ3jh49RI0atVSv161bpXoE+d335OPjnWpFQT8/v1TbcdGiuVhZWRMVFYWlpRU9evROcdz79+/hzBn3FMvLlSuvOql658qVi5QqVVo1K2H58hW4dOlCigTv6+uNrW0eIGmq2+vXrwHg4+Ojmm1QT08PC4vc3Llzk8aNm1GqVGnVd5YrV/K2+dK0KsGvWdsdE8sLX6RW9bt5r6dMmUBAgD8GBgaqAhJCiE+X0WpyaVUBW7BgNiNHjqVs2fIEBgbw6NFD6tVrkKKq2eXLF3nw4B7OzksBGDt2BFeuXKJmzdrJ4ilfvjyVKiUlkokTR+Pp+ZQmTZpx7txpVTlVM7NcjBw5TlVtbcmSnwBwdHSgZs3aqmMqW7YcgwYN4eHD++jr69O///eUKlWaR48esmnTr8ydu4iDB/djZGTE8OFjSExM5ODB/XTu3J3Q0NA0q9Z9KCYmhi1bNuLp+YTExEQmTpwGJE1BW7Bg4RTrW1pa8uKFDyEhIVhappzCO7VpW1Or4FeoUGHVI7/6+vrJqsz17NmXvXt3UatWXbp3783Dh/cJCwtj167tmJiYYGJiynffdaV48ZJ07NiGdes2YW1tw5EjB9m8+RdGjBibbP9eXp40b95K9bp06TI0aNAo2fdUtGixVCsKjhs3ItV2rFu3vmob/fv3pH37jilKCXfo8F2qw+ypCQ4O/qTKcnXr1ufBg3tER0cRHx9PxYqVOH06ac78sLAwfHyeq+b8f/e9+Ph4S4J/n8OpeoDHf07wvr4+TJw4hr/+OgZAnTr1cHVd/tVOwiDEl5ReNbm0qoC9X/HM0tIqWenP96uabdu2OVnVtvz58/PkyWP8/F5w5ow7RkY5mTvX+f/XtZdhapoLf39/1Qn8d991Y9Wq5VSrVhM9PT2MjIx4+tSD6OhotmzZCICtrW2yE/53leVKly5LUFAgJ08e49Kl80RERLxXWc5TFb+Ojg5589oB8OKFDx+rWvc+Q0ND+vTpT2xsLN9/35cXL3wpUaIktrZ5PlpZzsDAkIcPH6T/5fDxCn4f82FlueXLXfHx8eHkyb8YNmwEISEhhIaG8uefR/5/nG/R0Ul5Q9mHleXi4uJT/Z7e3+e7ioJptWNgYABr1vykKp7z9u3bFAl+377duLufShFPuXLlcXAYlmyZhYVFsiJCkZER5MtX4MOPMn36bHbt2oGvrw/GxsZYWVmjp6dHs2YtiYiIYPPmXzEyMqJMmXKqnj4k9eozo7KcViX4L+H69at07tyeiIhwzMxyMWPGbHr37pei+pEQ2i6ta+4f6tu3In37VlRzNP9KqwrYu8pyZma58Pd/w6NHD6lf/5sUn/+wMpqPjw/1639DjRq1VT20sLAwJkyYwLFjp9HX1+fp03+nSC1XrjwxMdGsXLmEPn0GqLZ59+4d+vTpDyT9nXj/D/r7leW2bt2IqakZ/foNwtv7Offv3wWgSJEieHo+BSAxMZGXL/2A9KvWpcbAwIA+fQawfv0qFi1agr19e8aOHUFERHiya/DR0dFUr16TuLg4fvttM/7+b7C2Tnrax9v7GT/9tIxFi5KXRU2rgt/7leWSSr8m934bAHTo0JmlS5dia5sPAwMD9PX1MTc3p337TpiZmfH2bQh3795JsR0bG1vCwt4CSd/T3LkzUv2ePpRWO3p4POa337awa9cBAM6fP5Pq5zt27EzHjp3T3P77atasw+7dO1EqlSgUCu7evaOaQz8gIABTU1MMDQ0JCAhQnRxcuXKJli3b/P+4Qqldux558uQhPj6eU6dOJJsULTQ0NFnCV5evLsGXL18ROzs7SpUqw4IFLpnSyEJ8DTJSTa527bppVgGbNGk627Zt5tq1q/j7v6ZPnwHcv383RVWz9yujKZVKypevQI0ayYfnTUxMaN26NXPnzqBUqbI8e+bFsWNHqFixMnp6enTq1JWTJ4+rrqnWrFmb+/fvsnr1SoyMjAgLC2PoUEfVMe3Zs5NevfphYWFBw4ZNWbNmJbGxscTHx/P69SuuXbuCvX0HFiyYzdKli7G2tiZXrlwoFIo0q9a9Lz4+nj17dhITE8O2bVvo2bMPTZo0Z+PGX1i9eiX9+g1i9uwFrF37M2ZmuYCk0rCLFy9HV1cXXV1dXF2Xs2PHbxgbGxMXF0dQUCDjxk1O8T2lVsEPoGHDxri6LiIhIZ7Q0FBVxT9/f3/Cw8PZuHE9vXv3R08vKW20bm3Phg1r2bBhG5B0AjBr1nxWrVqBnV0+Xr9+RefOKQvLfPNNY06fPoW9fQdMTExo3LhZiu+pcOEiqVYUTK0dTUxMKFy4MAsXzqFgwcL4+7/h8OE/GDx46Gf/LtvY2NKjR2+WL3dDR0cHe/v2qt+V5ctdadCgIc2bt+L8+TPs2rWdwoWLEhERzoABgwHw9/dnxQo3KleuSmRkJGPHTlK1W2joWwwNDVWjPeqkVdXkHCbXwzX/8k+qXR0dHc2qVSvo338QFhZJ09yGhARjbv55JQWzO6lyljmkndUvs9s4MjKSN29eq4aV+/Tpyq+//qaqX5EdfW4bL168gDZt2lG2bHk1RJV1JSYmsmSJC23a2KsqEGbE51aT06oErzip4E3F0Ayvf/HiecaOHcGTJx706NGbZct+VmN02YMknswh7ax+md3GwcHBLFw4m4oVKxMUFEiZMuVo1qxlpu1fE/5LGz954vHV3fcUFhZGZGTEJ48cS7nY97x9G8Ls2TPZsmUDACVKlKRHjz4ajkoIkZ1ZWFikuN4t0va1JXdIutnU1DTz5lbJdgn+0KE/mDx5HK9fv0JfX58RI8YwatS4dJ85FUIIIbKTbJXg7927y8CBSRMcVK9eEze3FZQuXUbDUQkhhBCZT+sT/LvHGCDp8ZchQ4ZRpEgx+vcfJI++CSGE+GppdQZ8/PgR7du35uLF86plc+YsZODA7yW5CyGE+KppVRZUdl+BddlNxMTE4OKygCZN6nHp0gUWLZqn6dCEEEKILEVtQ/QXLlzg+PHjWFpaolAocHR0TPZ+TEwMixYtwtbWlmfPnuHg4ECRIkXS326cJwObNeDRo4cA9O7djxkzZqvlGIQQQghtpZYEHxUVxcyZMzl8+DAGBgYMHz6cixcvUqdOHdU6mzZtIm/evHz//fc8evSIqVOnsm3bto9u1zF8Jz9Hn0P5VknRosVwc1uRbL5qIYQQQiRRyxD9zZs3sbOzw8DAAICqVavi7u6ebB13d3eqVKkCQKlSpXj48CHh4eEf3e7vMf+gi4JRo8bh7n5RkrsQQgiRBrX04AMDA1XlGCFpXujAwMAMrWNiYkJa/BNl5q/M8LmzJolPI+2sftLG6idtnHWppQdvaWmZrPZteHh4ilrFGVlHCCGEEJ9HLQm+cuXK+Pn5ERsbC8CNGzdo1KgRISEhqmH4Ro0a8c8//wDw6NEjSpcu/dHeuxBCCCEyTm3FZs6fP8+xY8ewsLBAX18fR0dHnJ2dMTc3x8HBgejoaBYtWoS1tTXe3t4MGTIkQ3fRCyGEECJ9WlVNTgghhBAZo1UT3QghhBAiYyTBCyGEENlQliw2o65Z8MS/0mvjtWvXEhAQgLW1NXfv3mXEiBEUK1ZMQ9Fqp/Ta+J0//viD8ePHc+PGjWSPjoqMSa+dlUolW7ZsAeDFixeEhoayYMECTYSqtdJrYx8fH5ydnalQoQIPHjzA3t6epk2baiha7eTv78/SpUt5+PAhe/bsSfF+YmIibm5uGBsb8+LFCzp37kzlypU/vlFlFhMZGals1qyZMiYmRqlUKpWOjo7KCxcuJFtnzZo1yrVr1yqVSqXy4cOHyh49emR6nNosI228ZMkSZWJiolKpVCoPHz6sHDJkSKbHqc0y0sZKpVL55MkTpZubm7JkyZLK8PDwzA5T62Wknfft26fct2+f6vWDBw8yM0Stl5E2njFjhnLDhg1KpVKpvHfvnrJ58+aZHabWO3r0qPLkyZPKjh07pvr+oUOHlDNnzlQqlUplcHCwskWLFsr4+PiPbjPLDdGraxY88a+MtPGoUaNUZXgTExMxMjLK7DC1WkbaOCoqivXr1/Pjjz9qIMLsISPtfPDgQUJCQti8ebOqByQyLiNtbGVlRVBQEABBQUGUK1cus8PUeq1atfro76a7u7uqx25ubo6BgQEeHh4f3WaWS/D/ZRY8kTGf0n6xsbHs27ePUaNGZVJ02UNG2njJkiUMGzZM9YdTfLqMtLOfnx/h4eH07duXjh07MnjwYBISEjI7VK2VkTYeMGAAt27dYsGCBfz000906tQps8PM9oKCgpLNFWNiYqI6qUpLlrsGL7PgqV9G2y82NhYnJydGjx5NwYIFMzNErZdeG798+ZLQ0FCOHj2qWrZhwwYaNmxIhQoVMjVWbZaR32UTExMqVaoEQJEiRQgPD+fly5fkz58/U2PVVhlp40mTJtGlSxfs7e0JCgqiRYsWnDhxAnNz80yONvvKnTt3spHq8PBwcufO/dHPZLkevMyCp34ZaeN3FQEHDBhA+fLlOXbsmCZD1jrptXHevHlZuHAhDg4OODg4AEm9IEnunyYjv8t16tTBx8cHSPqjmJCQgLW1tcZi1jYZaeOXL1+q2tTMzAwdHR0SExM1FnN2ERkZqeqlN2rUiJs3bwIQEhJCbGwsJUqU+Ojns+RENzILnvql18aOjo54eHhgY2MDJP2ipXZnp0hbem0MScNuO3bsYNmyZQwbNozu3btja2ur4ci1S3rtHBYWhouLC3Z2dnh7e9OyZUsaNmyo6bC1SnptfO3aNTZv3kzZsmXx9fWlXLly9OjRQ9Nha5UrV66wf/9+zp49S48ePRg4cCB79uzh0aNHzJ49m8TERFxdXcmZMyd+fn507do13bvos2SCF0IIIcR/k+WG6IUQQgjx30mCF0IIIbIhSfBCCCFENiQJXgghhMiGJMELIYQQ2VCWm+hGiOzo9u3buLi4EBcXR7169YCkokkxMTFMnTo1xfqPHz9m7ty5dOjQ4T/NCvb777/j4uKCvb09FhYWPH36lA4dOtCkSZNP2k6nTp3YtWsXurq6nDhxgtKlS6smipk8eTJ9+vShbNmynx1nYGAgLi4unDt3jm7duhEbG8uDBw+YNm0ahQsX/uhnN27cSP/+/T9730JkV/KYnBCZZMWKFURGRjJx4kQgKcFfuHCBxo0bp7l+vnz5/vO0n02aNGH16tWULFkSHx8funbtysWLFz9pG0qlUlWbYNKkSXTs2JFatWqleO+/uHz5MosWLWLv3r1AUuL29PRk9uzZH/1ckyZNOHXq1H/evxDZjfTghdCA+Ph4Fi9ezNSpU1m6dClxcXHo6+sTExOjOgF43/Lly9HRSbqiFhcXx+jRo/Hw8GDdunWULFkST09PfvjhBwoUKPDR/fr7+2NhYQHAypUriY+PR6lUqiYv8fT0VG3z/v37DBs2DE9PT+bNm8fmzZsJCgriwYMHANy6dYtvvvmGefPm0bFjR/LkycPYsWPp1asXjo6O/PTTT9y4cYMlS5Zw6NAhvLy8sLCwICwsjAkTJqR7UhAcHKyaijMiIoLRo0dTvXp1vLy8aNeuHXXr1uXIkSOEhoayYsUKihYtStu2bVm2bBkJCQno6OhgbGzM999//8nfjxDZgSR4ITLR5cuXmTdvXrJeb/ny5WnWrBkAQ4cOxcPDI8UUlDt37mTTpk0UK1aMGzduADBt2jQmTpxI1apVuXz5MgsXLuSnn35Kdb/btm3D3NycsLAwVq5cydmzZ7lz5w5r1qwBYPDgwZw7d44nT56gr69Pr169eP36NYaGhjRt2pSNGzcCULFiRcqUKZOsB1+zZk0A6tatS9euXcmZMycA+vr6ODk54e/vz5YtWzhy5AgKhYJJkyZx8uRJ1TG/LyAggLVr1/LPP/+QL18+JkyYAICOjg79+/enbt26hISEMGjQIOrWrUubNm1YvHgxw4cPB+Ds2bPcunWLX3/9FYA+ffpQv359ypQp8xnflhDaTRK8EJmoVq1aTJw4EaVSybNnz4CkHvm7aT/fvHmTaoUoV1dX3NzcCAwMpE+fPkBSHYbz589z7do1oqOjP1rSt2fPnpQsWVL1+tSpU8l6+4UKFeLhw4f07NmTtWvX0qtXL4oUKcKkSZM+6fh69OhBv3796NOnD69evaJAgQIcPXoUHR0d1q1bB4Cenl6a5Z2trKxwcHAgJCSEzp074+DggI2NDUqlksuXL/PPP/+gr69PcHBwqp9/9OgRUVFRrF27FoA8efKkW3FLiOxKErwQGqBQKChSpAihoaFMmDCB69evY2BgwKNHj1JdPyIigp9++onAwEDat29P27ZtKV26NM2bN6d06dLExsby119/ZXj/pUuX5sqVK6rXz549o0mTJty6dQsHBwdGjRrFokWLOHDgAAMGDEj2WR0dHZRKJd7e3imqiuXJk4dSpUoxY8YM2rdvD0DJkiUxNDRUzb9/79499PQ+/qfH3Nycrl27snbtWqZNm8auXbt48+YNCxYsIDY2lh07dqSI513hqZs3b6r2dfHiRQoVKpThdhEiO5EEL0QmuHPnDlevXiUuLo6jR4/SunVrAExNTWndujUTJ06kfPnyPHnyhAMHDmBubs7Vq1d5/Pgx9erVY9++fTx69Ijo6Gh69+4NwLx58/j1118pVKgQb968oVWrVin2u3v3bsLCwti5cyd9+vRRJbv69etz8+ZNXF1dUSqVVKlShXr16vHnn3+ycOFC8ufPT3BwMD179sTd3Z0XL16wY8cOxo0bR7169di1axcKhYLBgwcni9PW1pY+ffrg5OTEwoULAShWrBjdu3dnwYIF5M6dmzdv3jBmzJhkcQYFBXHgwAH8/f3ZtWsXXbp0oVevXrRu3RorKyuaN2/OsWPHWLRokepSw7Fjx2jZsiWNGjVi0aJFQNINgLdv38bV1RVjY2Pevn3LuHHj1Pa9CpGVyV30QgghRDYkE90IIYQQ2ZAkeCGEECIbkgQvhBBCZEOS4IUQQohsSBK8EEIIkQ1JghdCCCGyIUnwQgghRDYkCV4IIYTIhv4H/Pxb+LuHBdIAAAAASUVORK5CYII=\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 576x396 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.preprocessing import LabelEncoder\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"#Cross validation\n",
|
||
"accuracy = cross_validate(logreg,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||
"print(accuracy)\n",
|
||
"print(\"Test set accuracy with Logistic Regression and scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = logreg.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = logreg.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Friday September 25\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Optimization, the central part of any Machine Learning algortithm\n",
|
||
"\n",
|
||
"[Overview Video, why do we care about gradient methods?](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage)\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"Almost every problem in machine learning and data science starts with\n",
|
||
"a dataset $X$, a model $g(\\beta)$, which is a function of the\n",
|
||
"parameters $\\beta$ and a cost function $C(X, g(\\beta))$ that allows\n",
|
||
"us to judge how well the model $g(\\beta)$ explains the observations\n",
|
||
"$X$. The model is fit by finding the values of $\\beta$ that minimize\n",
|
||
"the cost function. Ideally we would be able to solve for $\\beta$\n",
|
||
"analytically, however this is not possible in general and we must use\n",
|
||
"some approximative/numerical method to compute the minimum.\n",
|
||
"\n",
|
||
"\n",
|
||
"## Revisiting our Logistic Regression case\n",
|
||
"\n",
|
||
"In our discussion on Logistic Regression we studied the \n",
|
||
"case of\n",
|
||
"two classes, with $y_i$ either\n",
|
||
"$0$ or $1$. Furthermore we assumed also that we have only two\n",
|
||
"parameters $\\beta$ in our fitting, that is we\n",
|
||
"defined probabilities"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
|
||
"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
|
||
"\n",
|
||
"## The equations to solve\n",
|
||
"\n",
|
||
"Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n",
|
||
"elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n",
|
||
"$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n",
|
||
"$p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We rewrote in a more compact form\n",
|
||
"the first derivative of the cost function as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
|
||
"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"This defines what is called the Hessian matrix.\n",
|
||
"\n",
|
||
"## Solving using Newton-Raphson's method\n",
|
||
"\n",
|
||
"If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. \n",
|
||
"\n",
|
||
"Our iterative scheme is then given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"or in matrix form as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The right-hand side is computed with the old values of $\\beta$. \n",
|
||
"\n",
|
||
"If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. \n",
|
||
"\n",
|
||
"\n",
|
||
"## Brief reminder on Newton-Raphson's method\n",
|
||
"\n",
|
||
"Let us quickly remind ourselves how we derive the above method.\n",
|
||
"\n",
|
||
"Perhaps the most celebrated of all one-dimensional root-finding\n",
|
||
"routines is Newton's method, also called the Newton-Raphson\n",
|
||
"method. This method requires the evaluation of both the\n",
|
||
"function $f$ and its derivative $f'$ at arbitrary points. \n",
|
||
"If you can only calculate the derivative\n",
|
||
"numerically and/or your function is not of the smooth type, we\n",
|
||
"normally discourage the use of this method.\n",
|
||
"\n",
|
||
"## The equations\n",
|
||
"\n",
|
||
"The Newton-Raphson formula consists geometrically of extending the\n",
|
||
"tangent line at a current point until it crosses zero, then setting\n",
|
||
"the next guess to the abscissa of that zero-crossing. The mathematics\n",
|
||
"behind this method is rather simple. Employing a Taylor expansion for\n",
|
||
"$x$ sufficiently close to the solution $s$, we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"eq:taylornr\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"f(s)=0=f(x)+(s-x)f'(x)+\\frac{(s-x)^2}{2}f''(x) +\\dots.\n",
|
||
" \\label{eq:taylornr} \\tag{14}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"For small enough values of the function and for well-behaved\n",
|
||
"functions, the terms beyond linear are unimportant, hence we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f(x)+(s-x)f'(x)\\approx 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"yielding"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s\\approx x-\\frac{f(x)}{f'(x)}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Having in mind an iterative procedure, it is natural to start iterating with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Simple geometric interpretation\n",
|
||
"\n",
|
||
"The above is Newton-Raphson's method. It has a simple geometric\n",
|
||
"interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
|
||
"$(x_n,f(x_n))$ crosses the $x$-axis. Close to the solution,\n",
|
||
"Newton-Raphson converges fast to the desired result. However, if we\n",
|
||
"are far from a root, where the higher-order terms in the series are\n",
|
||
"important, the Newton-Raphson formula can give grossly inaccurate\n",
|
||
"results. For instance, the initial guess for the root might be so far\n",
|
||
"from the true root as to let the search interval include a local\n",
|
||
"maximum or minimum of the function. If an iteration places a trial\n",
|
||
"guess near such a local extremum, so that the first derivative nearly\n",
|
||
"vanishes, then Newton-Raphson may fail totally\n",
|
||
"\n",
|
||
"\n",
|
||
"## Extending to more than one variable\n",
|
||
"\n",
|
||
"Newton's method can be generalized to systems of several non-linear equations\n",
|
||
"and variables. Consider the case with two equations"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
|
||
" f_2(x_1,x_2) &=0,\\end{array}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which we Taylor expand to obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
|
||
" \\partial f_1/\\partial x_1+h_2\n",
|
||
" \\partial f_1/\\partial x_2+\\dots\\\\\n",
|
||
" 0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
|
||
" \\partial f_2/\\partial x_1+h_2\n",
|
||
" \\partial f_2/\\partial x_2+\\dots\n",
|
||
" \\end{array}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
|
||
" \\partial f_1/\\partial x_1 & \\partial f_1/\\partial x_2 \\\\\n",
|
||
" \\partial f_2/\\partial x_1 &\\partial f_2/\\partial x_2\n",
|
||
" \\end{array} \\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"we can rephrase Newton's method as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
|
||
"\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
|
||
"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where we have defined"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
|
||
" -{\\bf \\boldsymbol{J}}^{-1}\n",
|
||
" \\left(\\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\\\ f_2(x_1^{n},x_2^{n}) \\end{array} \\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We need thus to compute the inverse of the Jacobian matrix and it\n",
|
||
"is to understand that difficulties may\n",
|
||
"arise in case ${\\bf \\boldsymbol{J}}$ is nearly singular.\n",
|
||
"\n",
|
||
"It is rather straightforward to extend the above scheme to systems of\n",
|
||
"more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Steepest descent\n",
|
||
"\n",
|
||
"The basic idea of gradient descent is\n",
|
||
"that a function $F(\\mathbf{x})$, \n",
|
||
"$\\mathbf{x} \\equiv (x_1,\\cdots,x_n)$, decreases fastest if one goes from $\\bf {x}$ in the\n",
|
||
"direction of the negative gradient $-\\nabla F(\\mathbf{x})$.\n",
|
||
"\n",
|
||
"It can be shown that if"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with $\\gamma_k > 0$.\n",
|
||
"\n",
|
||
"For $\\gamma_k$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq\n",
|
||
"F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n",
|
||
"we are always moving towards smaller function values, i.e a minimum.\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## More on Steepest descent\n",
|
||
"\n",
|
||
"The previous observation is the basis of the method of steepest\n",
|
||
"descent, which is also referred to as just gradient descent (GD). One\n",
|
||
"starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n",
|
||
"computes new approximations according to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The parameter $\\gamma_k$ is often referred to as the step length or\n",
|
||
"the learning rate within the context of Machine Learning.\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## The ideal\n",
|
||
"\n",
|
||
"Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n",
|
||
"minimum of the function $F$. In general we do not know if we are in a\n",
|
||
"global or local minimum. In the special case when $F$ is a convex\n",
|
||
"function, all local minima are also global minima, so in this case\n",
|
||
"gradient descent can converge to the global solution. The advantage of\n",
|
||
"this scheme is that it is conceptually simple and straightforward to\n",
|
||
"implement. However the method in this form has some severe\n",
|
||
"limitations:\n",
|
||
"\n",
|
||
"In machine learing we are often faced with non-convex high dimensional\n",
|
||
"cost functions with many local minima. Since GD is deterministic we\n",
|
||
"will get stuck in a local minimum, if the method converges, unless we\n",
|
||
"have a very good intial guess. This also implies that the scheme is\n",
|
||
"sensitive to the chosen initial condition.\n",
|
||
"\n",
|
||
"Note that the gradient is a function of $\\mathbf{x} =\n",
|
||
"(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically.\n",
|
||
"\n",
|
||
"\n",
|
||
"<!-- !split -->\n",
|
||
"## The sensitiveness of the gradient descent\n",
|
||
"\n",
|
||
"The gradient descent method \n",
|
||
"is sensitive to the choice of learning rate $\\gamma_k$. This is due\n",
|
||
"to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n",
|
||
"F(\\mathbf{x}_k)$ for sufficiently small $\\gamma_k$. The problem is to\n",
|
||
"determine an optimal learning rate. If the learning rate is chosen too\n",
|
||
"small the method will take a long time to converge and if it is too\n",
|
||
"large we can experience erratic behavior.\n",
|
||
"\n",
|
||
"Many of these shortcomings can be alleviated by introducing\n",
|
||
"randomness. One such method is that of Stochastic Gradient Descent\n",
|
||
"(SGD), see below."
|
||
]
|
||
}
|
||
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|
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