{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## MATH 382 - Scientific Computing\n",
    "## Fall 2018\n",
    "## Jorge Balbás\n",
    "<hr>\n",
    "\n",
    "## Lab 1: Introduction to Python\n",
    "## Objective\n",
    "### $\\bullet$ Basic operations in Python\n",
    "<hr>\n",
    "\n",
    "## 0. Credits/Source\n",
    "\n",
    "Notebook originally created by Xavier Bresson (CS Faculty at Singapore NTU) \n",
    "\n",
    "Original Title: Tutorial 1: Introduction to Python\n",
    "<hr>\n",
    "\n",
    "## 1. Resources\n",
    "<hr>\n",
    "\n",
    "Slides: [Python introduction by Xavier Bresson]\n",
    "[Python introduction by Xavier Bresson]: http://data-science-training-xb.s3-website.eu-west-2.amazonaws.com/All_lectures/Lecture02_python.pdf\n",
    "\n",
    "Notebook: [Python introduction tutorial by Justin Johnson]\n",
    "[Python introduction tutorial by Justin Johnson]: https://github.com/kuleshov/cs228-material/blob/master/tutorials/python/cs228-python-tutorial.ipynb\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "<br>\n",
    "## 2. Basic operations\n",
    "<hr>\n",
    "### 2.1 Elementary algebra operations\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5+6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5/8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5.0/8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2**10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2.2 Logical operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1==1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2==1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2!=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True & False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True | False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2.3 Assignment operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hello\n"
     ]
    }
   ],
   "source": [
    "x='hello'\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "x=(1==2)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=2.35789, x=2.4\n"
     ]
    }
   ],
   "source": [
    "x=2.35789202950400\n",
    "print('x={:2.5f}, x={:.1f}'.format(x,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<type 'float'>\n"
     ]
    }
   ],
   "source": [
    "x=2.35789202950400\n",
    "print(type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<type 'str'>\n"
     ]
    }
   ],
   "source": [
    "x='hello'\n",
    "print(type(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 2.4 Numpy\n",
    "\n",
    "List all libraries modules: np. + tab\n",
    "\n",
    "List properties of the module: np.abs + shift + tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<ufunc 'absolute'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.14159265359\n"
     ]
    }
   ],
   "source": [
    "x = np.pi\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 1.  1.  1.  1.]\n",
      "  [ 1.  1.  1.  1.]]\n",
      "\n",
      " [[ 1.  1.  1.  1.]\n",
      "  [ 1.  1.  1.  1.]]\n",
      "\n",
      " [[ 1.  1.  1.  1.]\n",
      "  [ 1.  1.  1.  1.]]\n",
      "\n",
      " [[ 1.  1.  1.  1.]\n",
      "  [ 1.  1.  1.  1.]]\n",
      "\n",
      " [[ 1.  1.  1.  1.]\n",
      "  [ 1.  1.  1.  1.]]]\n"
     ]
    }
   ],
   "source": [
    "print(np.ones((5,2,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "print(np.zeros(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.]\n",
      " [ 0.  0.  1.  0.  0.]\n",
      " [ 0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.eye(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(3), <type 'numpy.ndarray'>, dtype('int64'))\n"
     ]
    }
   ],
   "source": [
    "x = np.array(3.4,dtype='int64')\n",
    "print(x,type(x),x.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1,2,3],[4,5,6]])\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n",
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(X.shape[0])\n",
    "print(X.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.array([[2, 7, -2],[1, 8, 3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  7 -2]\n",
      " [ 1  8  3]]\n",
      "-2\n",
      "[ 2  7 -2]\n",
      "[2 7]\n",
      "[2 7]\n",
      "[ 7 -2]\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "print(X)\n",
    "print(X[0,2])\n",
    "print(X[0,:])\n",
    "print(X[0,0:2])\n",
    "print(X[0,:2])\n",
    "print(X[0,1:3])\n",
    "print(X[-1,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[7 8 9]\n",
      " [1 8 3]]\n"
     ]
    }
   ],
   "source": [
    "X[0,:] = [7,8,9] # assignment\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "(3, 3)\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1,2,3],[4,5,6]])\n",
    "X = np.append(X,[[7,8,9]],axis=0) # append\n",
    "print(X)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<br>\n",
    "## 3. Linear algebra operations\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[1, 2, 3],\n",
      "       [4, 5, 6]]), (2, 3))\n",
      "(array([[ 2,  7, -2],\n",
      "       [ 1,  8,  3]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1,2,3],[4,5,6]])\n",
    "print(X,X.shape)\n",
    "Y = np.array([[2,7,-2],[1,8,3]])\n",
    "print(Y,Y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 2,  1],\n",
      "       [ 7,  8],\n",
      "       [-2,  3]]), (3, 2))\n"
     ]
    }
   ],
   "source": [
    "Z = Y.T #transpose\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 2, 14, -6],\n",
      "       [ 4, 40, 18]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = X* Y # element-wise matrix multiplication\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[10, 26],\n",
      "       [31, 62]]), (2, 2))\n"
     ]
    }
   ],
   "source": [
    "Z = X.dot(Y.T) # matrix multiplication\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1,  4,  9],\n",
      "       [16, 25, 36]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = X**2\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Z = np.array(Z,'double')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.   4.   9.]\n",
      " [ 16.  25.  36.]]\n"
     ]
    }
   ],
   "source": [
    "print(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[1, 0, 0],\n",
      "       [0, 0, 0]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = 1/X\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.array(X,'double')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.        ,  0.5       ,  0.33333333],\n",
      "       [ 0.25      ,  0.2       ,  0.16666667]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = 1/X\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 0.        ,  0.69314718,  1.09861229],\n",
      "       [ 1.38629436,  1.60943791,  1.79175947]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = np.log(X)\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 2.,  3.,  4.],\n",
      "       [ 5.,  6.,  7.]]), (2, 3))\n"
     ]
    }
   ],
   "source": [
    "Z = X + 1\n",
    "print(Z,Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 2,  7, -2],\n",
      "       [ 1,  8,  3]]), (2, 3))\n",
      "8\n",
      "[2 8 3]\n",
      "[7 8]\n",
      "4\n",
      "[0 1 1]\n",
      "[1 1]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[2,7,-2],[1,8,3]])\n",
    "print(X,X.shape)\n",
    "print(np.max(X))\n",
    "print(np.max(X,axis=0))\n",
    "print(np.max(X,axis=1))\n",
    "print(np.argmax(X))\n",
    "print(np.argmax(X,axis=0))\n",
    "print(np.argmax(X,axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 2,  7, -2],\n",
      "       [ 1,  8,  3]]), (2, 3))\n",
      "19\n",
      "[ 3 15  1]\n",
      "[ 7 12]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[2,7,-2],[1,8,3]])\n",
    "print(X,X.shape)\n",
    "print(np.sum(X))\n",
    "print(np.sum(X,axis=0))\n",
    "print(np.sum(X,axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<br>\n",
    "## 4. Plotting data\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Visualization library\n",
    "%matplotlib inline\n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('png2x','pdf')\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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vbiAvbyAvcCAxMTUgL3MgL3QgMTIwIC94IC95IF0KL1R5cGUgL0VuY29kaW5n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\nMSAwIFIgL1NpemUgMzYgPj4Kc3RhcnR4cmVmCjkzMjkKJSVFT0YK\n",
      "image/png": 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CEsl5A8MjPLBtbLlWWOt8g4KjWY/s0PS6ZIfjPYM8ESgbekOGy/0mMzOuCI78\n7mg9xatFMmdPWzfbW7oAKC0q4Kq1jaG2p6SoIKG6lvqK5BsFJJLzHt91lC6/6sjiunLOXFATcouS\nApKmNk2vS1b41dYjjPgbq523ZBbza8tDbtHJfUUkGwQLP1y5poHK0vBrAKmvSD5TQCI5777ngxu8\nzc+KcoEbFtVSW+7tfN3S2c+OI10ht0gksRLdjVkwkwhw2ao5FPn1f1842Elb10DILRJJXK4VZpGU\noGBA8ps9x+gfGgmxNSKppYBEctrQSIxfbT0yej+sEqbJigoLEjbQ0rItCVtH3xCP7xrLZwp7uVZc\nTVkx5y+dPXr/sZ3qKxKul471ju4hVVJYwNXrw12uFbe4roIVDZUA9A/FeHJve8gtEkkdBSSS057Y\nfYyOPq+K1YLaMjZk0Z4fml6XbPLAtiMMjXjLtc5eWMviuoqQWzRGfUWyyS9fHJsdefnqemrKikNs\nTSL1FclXCkgkp/3yxbHlWjdkyXKtuOCJ43fN7Xm5u67kjl++kD3VtZIF+8qjTW2jeS4iYUjoK1ky\nkxingETylQISyWmbAktQrsuynWvn1pSxbl41AEMjjid2HzvNO0TSYyTmEqprXZ9lfeWM+TXUV5UC\ncLx3iBcOdoTcIomqrv4hthzw/v2ZwbXrs6uvXLpiDqVF3qXbrtZuDhxX+V/JDwpIJGe1dPSP1mIv\nLSrgvCWzQm7RybS7rmSDbYc76er3ZugaqktZ2RDexqHjKSgwrlgTLGmqviLheGrf8dEZuvXzaphd\nWRJyixKVFRdyyYo5o/d1XpF8oYBEctZv946N+J6/ZHaou+hOZOOasWRI7a4rYflNYHbk0hVzsmpp\nY9zGwD4PjzRpjwUJR3JfyUYbtc+V5CEFJJKzcuHEccHS2dpdV0L3mz1j1XguXVEXYksm9nur6onH\nSZv3n+BE72C4DZJI+m0O9JXgzPum3ccYHI6F2BqR1FBAIjkrFy6yknfXfUS760qGjcQcT+7N/uB9\ndmUJGxZ5yy5jDn4dyA8TyYTugWGePziWP3Lx8uw8r6yor2TRbG9T0+6BYZ556XjILRKZOQUkkpNa\nOvrZe7QH8PJHNizOvvyROFVFkTBtO9xJZyB/ZEV9ZcgtmtiVWooiIXqquT0hf2RWRXblj8SZmc4r\nkncUkEhOyoX8kbjgieMJ7a4rGZYL+SNxyUUglHMlmZQ4656dM4lxCt4l30Q2IDGzRWb2bTM7ZGYD\nZtZsZl9GJdx2AAAgAElEQVQ0s9mnfzeY2S1m5k7zNZL0nmWnef2d6flp808u5I/EaXddCVMuLG2M\n27BoFrXl3iZ0rV0DbG/pCrlFEiWJ55Xs7iuXraqnqMAbXNh6uJPWzv6QWyQyM0VhNyAMZrYS2AQ0\nAj8BtgMXAx8BbjCzy51zp9s0YjPw6Qme+z3gauAXEzy/Bbh3nMdfOM1nii+XLrLAG83a0+YtMXuk\nqY0rAqNbIumSK/kjcYUFxu+trudnz3k7ZT+8o43182tCbpVEQa7kj8RVlRZx4bLZo+fCR5raeNOF\ni0Nulcj0RTIgAW7HC0Y+7Jz7SvxBM/s88FHg74H3neoAzrnNeEHJSczsCf/br0/w9s3OuU9Nsc3i\nO9KZO/kjcVeuaeCOx5sB78TxyXCbIxGRS/kjcVeuaRgNSB5pauX9G1eG3CKJglzJHwm6ck2jAhLJ\nG5FbsuXPjlwPNANfTXr6b4Ae4G1mNq0zt5mdDVwKHAR+Pv2WykSC0+rnLZmV1fkjcdpdV8Lw28Dy\nwEuW12V1/khccG38U83H6R4YDrE1EhXBWfdLcmDWHWBjIOfqsZ1HRwMqkVwUuYAEuMq/vd85l1C8\n2znXBTwOVOAFFdPxJ/7tt5xzE2UvLzCz95rZx/3bc6b5WZGUS4mHcWXFhQlt3bTrdCsCRWYul3Kt\n4hpryjjDX6Y1nLTkTCRdcrGvrJtXTWN1KQAdfUO8eKgj5BaJTF8UA5K1/m3TBM/v9G/XTPXAZlYO\n/BEwAnzzFC+9Dvga3tKwrwFbzOwhM1syhc96erwvYN1U251rfpuDJw5IbOvT+1Q3XtIrFnMJBRTU\nV0TGl5w/ckmW54/EmZn6iuSNKAYktf7tREMJ8cenk5jwZv99v3TO7R/n+V7g74ALgNn+15XAQ8BG\n4IHpLhWLiiOd/ezx80dKigo4NwfyR+IuWDpWwO1pbWQlabatpZOOviEA6qtKWdmQO/+1JPQVXWRJ\nmgXzR9blSP5InPqK5IuoJrWnS3y51r+P96RzrhX466SHHzWz64FfA5cA7wa+dLoPcs5dMN7j/izJ\n+ZNtcK4JTqufnyP5I3HnLKqlqMAYjjl2tXZzoncwp058kluSK9HlQv5I3PlLxwYatuzvYHgkRlFh\nFMfPJBNyrWpjUDAgeUYBieSwKP4PH58BqZ3g+fjjJ6ZyUDM7E7gMOADcN5X3OueGGVvidcVU3hs1\nuZg/EldWXMiZC8ZKmD67f0r/xESmJBfXxMfNry1n4axyAPqGRrQfiaTVb3OoNHaydfOqKfcH5g51\n9HO4oy/kFolMTxQDkh3+7UQ5Iqv924lyTCYymWT2U4lvtZo76ypCkKv5I3HnazRLMiCX80fizlsy\nNkuipSiSLj0Dwzx3IPfyR+KKCgvYsHhsfPWZfRroktwUxYDkIf/2ejNL+PnNrBq4HC/X4zeTPaCZ\nlQFvw0tm/9Y02xWv6rVnmu/Pe7mcPxKn9b6SCbmcPxKnviKZ8NS+4zmbPxKnviL5IHIBiXNuN3A/\nsAz4YNLTn8abofiec64HwMyKzWydv3/JRN6El6D+iwmS2fGPdX5yEOQ/fg3ehowA35/szxI1uZw/\nEhc8cWzef4LhkdgpXi0yPbmcPxKniyzJhMSljbk1OxKngimSD6Ka1P4BYBPwZT8Y2IaXUH4V3lKt\nTwReu9B/fh9eEDOe+HKtiXZmj/s8sNrMNuHlmgCcA1ztf/9J59ymyf8Y0fLbHF+CAt7a+AW1ZRzq\n6Kd30Fsbf9bCidKZRKYn15c2AqyfX0NZcQH9QzEOnuijpaOfebVlYTdL8kwu51rFnbd4LCDZeqiD\n/qGRnBywk2iL3AwJjM6SXAh8By8QuQ1YiVfd6lLn3KR34jKz9cDLmVwy+/eAZ4GLgPfgBUargbuB\nK5xzn5nSDxIxwRPHJctz88QBcF4wj0SjWZJisZhLCt5zc9S3uLCADYvGlmWqr0iqBfNHAC5elpt9\nZXZlyeiyzKERN7qnikguiWRAAuCc2++ce6dzbr5zrsQ5t9Q5d6tz7njS65qdc+acWzbBcbb5zy8+\nXTK7c+5bzrlXO+eWOeeqnHOlzrklzrm3OOceS+GPl3daO/vZ0zaWPxJMeM01FyxRYrukz/aWrkD+\nSAkrG6pCbtH0qaSppFNi/kg1sytzL38kTkscJddFNiCR3PKbwIjveYtzM38kTut9JZ0SZhJXzMnJ\n/JG485eor0j65MNyrbiEvqKARHKQAhLJCfl04jhjgbc2HmB/ex+tnf0ht0jyST71lWCZ7BcOemvj\nRVIln/pK8myicy7E1ohMnQISyQm/C8yQXJKja+LjigsLOEdr4yUNnHP8rjmQP5Jjeyokq6ssYUX9\n2Nr4F7Q2XlKkf2iE5wP5I7m2/0iylQ1V1JR5dYqO9QzyUntvyC0SmRoFJJL1ugeG2dXWDUCBkZP7\njyTT9Lqkw/72Po73evkjNWVFrGrM3fyRuPO1Nl7S4MVDHQz7+SMrGipzOn8EoKDA1Fckpykgkaz3\n/IEO4rPPa+ZWU1GS+9WqlYAo6bDlwNguzRsWz8rp/JE49RVJhy37x2ZHzl2U+4NckFgwRX1Fco0C\nEsl6zwUvsvLkxHF+oErYCwc7GRjW2niZuWBfOWdRfuxvk7A2/qUTWhsvKZHvfUUBieQaBSSS9YKj\nvucszo8Tx5yqUpb7a+MHR2K8cLAz5BZJPgiO+p6TJ8H7qoYqqv218Ue7B9jf3hdyiyQfBPcfOScP\nlgGDNyta4E+K7jjSRVf/ULgNEpkCBSSS9YIXWfkyQwKJeSTaY0FmaiTmeOFQ/vWVggLjvITyv+2n\neLXI6XX0DbHnqLevVVGBccb8mpBblBqVpUWsm+f9LM4lnjtFsp0CEslqx7oHOHjCGxEtKSpg7bzq\nkFuUOucvHbtg1PS6zNSu1m56B72lf3NrSplXWxZyi1JHa+MllYLVtdbOq87pfa2SadmW5CoFJJLV\ngtPqZy6oobgwf/7JJm+QqLXxMhMJSxvzZHYkLvEi68QpXilyesnFH/KJNt6VXJU/V3eSlzbvz7+E\n9rjVjdVUl3pr49u6BjhwXGvjZfq2JPSV/Mi1ituwuHZsbXxLJ90Dw+E2SHJaYqGU/OorwYDk2X3H\nicU00CW5QQGJZLV8rIQSV1hgnLtEGyRKaiQk6eZZ8F5dVsyaud5yzZhLDL5Epiqf+8qi2eXUV5UC\n0DUwzM7W7pBbJDI5CkgkaznnEk4c+Ta1DtogUVJjYHiE7S1jldryLXgHrY2X1Gjt7OdwRz8AZcUF\nrM6DzUODzIwLlmqgS3KPAhLJWgdP9HGsZxCA6tIils+pDLlFqaeLLEmFbYe7GBrxlmYsm1PBrIrc\n3nV6POorkgpbAoNcZy2opSiP8hLj1FckF+VfT5S8ESxZePaiWgoKcn/X6WTnLplFfDPtbYc76dHa\neJmG4BKmfFuCEpe4QaLWxsv0PJfHCe1xCX1FAYnkCAUkkrWey+OqQXE1ZcWs1dp4maEteZxrFbek\nroL6Km/mp6t/mF1tWhsvU7clIX8kP/vKmQtqKfFnfvYc7aHdX2kgks0UkEjWCl5knZsnO7SP5/yk\nkV+RqQrmWp2bp6O+ZqbNRGVGvLzE/K3cGFdWXMhZC8c2e3xW5xXJAQpIJCuNxBwvHAwm6ebniQPg\n3MDPFvyZRSajq3+I3f5sQWGBceaC/A3eg0tsgrvSi0zGS+29nOgdAqC2vJilcypCblH6JPQVnVck\nByggkay0p617dK+B+qpS5ufRrtPJzgyMZOkiS6bq+YMdxPfUXN1YRXlJ/uw6neyshWPBli6yZKqS\nl2uZ5V9eYtxZgYEJnVckFyggkawUPHFsyPMTx+rG6tH1vgeO93GiV+t9ZfISSmPn8UwiwJkLxoL3\nbYc7GR6JhdgayTXP5fFGu8mCwfuLBxWQSPZTQCJZKQqVUOJKigpYO6969P6LhzTyK5MXpb4SnC0d\nGI6xu60n5BZJLnkuAgntcSsbKikt8i7xDnX0K7Fdsp4CEslKUaiEEhQc+X1R0+syBcHy2OorIuMb\nHonx/MH83mg3qKiwgHXz1VckdyggkawzOBxj26FoJLTHnam18TINR7sHOHiiD4DSpJm2fBVM2ldf\nkcna1dZN39AIAHNrSplbk795iXFnBYJ39RXJdgpIJOtsb+lk0F8bvriunLrK/Nt1OlnCiUMjWTJJ\nweVaZyyooTgPd51OlpDYrr4ik/Tc/ujkWsWpr0guyf+zl+ScxOVa0ThxrJ9fQ6G/E/3eoz3asV0m\nZUskL7LGgvethzq1Y7tMypYI5VrFBSttKbFdsp0CEsk6wUoo50bkIqusuJBVDVUAOOdVEBI5ncSE\n9vzPHwGYV1M2OmvaPTDMS+29IbdIckGUEtrj1syrosgf6Go+1ktX/1DILRKZmAISyTpRPHFAYrLu\nCxrNktPwdp2O3myimSX2FS1FkdPoHxpJGOQ5Z2E0+kppUSGr547llW1VBUfJYgpIJKv0DAyzs7UL\ngAJLXAOb7xIS23XikNM4cLyPY34pz+rSIpbPqQy5RZmjDRJlKrYd7mTYX9q3bE4FtRXFIbcocxLz\nE9VXJHspIJGs8sLBDuJLwlc1VlFZWhRugzLorIRypjpxyKkFZ0fOXlRLQUH+bh6aTKV/ZSoSNg+N\nSP5InPqK5AoFJJJVorTrdLIzAieOnUe66PdLVIqMJ0obIiZLSNY91IlzSmyXiQUT2qOytDEuccd2\nDXRJ9lJAIlkl4cQRsYus6rJils2pAGA45mg60hVyiySbJVQNilCuFcCSugqq/dnT9p5BDnf0h9wi\nyWZb9ke3r6yfX4P5k6c7W7voG9RAl2QnBSSSVaJ8kQXaIFEmJxZzPB/BhPa4ggJLmFFUEQiZSFf/\nEHuO9gBQWGAJG2tGQWVpESvqvfyymPP2+RLJRgpIJGt09A2xv93bdbq40Fg3r+Y078g/iUtRdJEl\n42s+1kOPP9JZX1XC/Nr833U62ZlJy7ZExrPtcBfxFX2rG6soLykMt0EhUF+RXKCARLLG9kBZxlWN\n1ZQURe+fZ3DTN1VEkYlsOzy2nM9bkhGdhPa4YF9R8C4TCZb7PWN+9Aa5QH1FckP0rvh8ZrbIzL5t\nZofMbMDMms3si2Y2ewrHaDYzN8FXyyned5mZ3Wdm7WbWZ2bPmdmtZha9oZuA4Ilj/fzqU7wyfwVH\nsrYd7mRoJBZiayRb6SJLpX9lchLPKxHtKwvUVyT7RaemaoCZrQQ2AY3AT4DtwMXAR4AbzOxy59yx\nSR6uA/jiOI93T/DZrwV+BPQDdwHtwGuALwCXA2+a/E+SX4KjvlG9yKqrLGFBbRmHOvoZHI6xu607\nkkvX5NR0kQUr6ispLSpgYDhGS2c/R7sHqK8qDbtZkmXUVxIrOO5o6WJoJEZxYWTHoyVLRTIgAW7H\nC0Y+7Jz7SvxBM/s88FHg74H3TfJYJ5xzn5rMC82sBvgGMAJsdM495T/+SeBB4CYzu9k5d+dkf5B8\nsq1FJw7wEtsP+VWDXjzYqYBETqKLLCgqLGD9/Bo2+xWUXjzUyZVrGkJulWSTkZhjx5Hg8sZozrzP\nqihh0exyDhzvY3Akxs4j3QlBikg2iFyI7M+OXA80A19NevpvgB7gbWaWjm2PbwIagDvjwQiAc64f\n+Cv/7vvT8LlZb3gkxo6WxHXxUZUwva71vpLkRO/gaMBaUljAiobo7NCeLCHnSpW2JMneoz30D3nL\nXhurS5kT4Rk0nVck20UuIAGu8m/vd84lLNB3znUBjwMVwKWTPF6pmf2RmX3czD5iZledIhfkav/2\nl+M89yjQC1xmZpH7X3Pv0R4Ghr0/x7yaMuoqS0JuUXgSdtbVel9JsjUwO7JmXlWkl16oKp2cSrCv\nRH1GICGxXcG7ZKEoLtla6982TfD8TrwZlDXAA5M43jzge0mP7TWzdzrnHpnsZzvnhs1sL3AmsALY\ndqoPNbOnJ3hq3embnH22KqF9VMLOuoc6iMUcBQXRq6Ik40uosBXx5XxnKllXTkFLG8ck9BVVcJQs\nFMWhtXivnGiIIP74ZHYauwO4Bi8oqQTOBv4dWAb8wsw2pPGz80pyGdMom1tTSn2VN0PUMzjCvvbe\nkFsk2UQXWWPWzKuiyA/WX2rvpaNvKOQWSTZRXxlzZmCGZNvhTkZiLsTWiJwsigFJyjjnPu2ce9A5\nd8Q51+uce8E59z7g80A58Kk0fvYF433hVQzLOTpxjDGzpJFfTa/LGPWVMaVFhayZOzajulUjvxKQ\nWB472jPvjdVlNFZ7q8F7B0fY6+9eL5ItohiQxK/uaid4Pv74iRl8xtf82ytC+OycpIusRME8EiUg\nStyQXyEnLqrlsYO06ZuMp71nkCOdAwCUFhWwbE50iz/EJS8HFskmUQxIdvi3ayZ4frV/O1GOyWS0\n+bfJ/wNO+NlmVgQsB4aBPTP47JxzrHuA1i7vxFFWXMDyep04Ek4cWhsvvj1tPQz6m2UuqC2jtqI4\n5BaFT7OJMp7gINfaedUURbj4Q1zCQJf6imSZKPbQh/zb680s4ec3s2q8zQl7gd/M4DPiFbqSA4sH\n/dsbxnnPFXjVvTY55wZm8Nk5J5g/snZuNYVK4D6pepBzWu8rmkkcT+IMiYJ38ST0lYgXf4g7M+G8\nor4i2SVyAYlzbjdwP17i+QeTnv403qzG95xzPQBmVmxm6/z9S0aZ2frx9ioxs2XAv/p3v5/09A+B\no8DNZnZh4D1lwGf8u/829Z8qt+ki62SL68qpLvOK4B3vHRrdd0KiTX3lZOvn12D+GMbutm56B4fD\nbZBkBVVuPFnyvj0a6JJsErmAxPcBoBX4spnda2b/aGYP4u3S3gR8IvDahXgleJNLAL8FaDGzn5vZ\n7Wb2WTP7of/aVcB9wOeCb3DOdQLvAQqBh83sm2b2/4DNwMvwApa7UvyzZj1dZJ3MS2zX9Lok2qq+\ncpKKkiJW+Ms8Yy5xxlWiS5UbT7ZwVjm15d4yz87+YQ4c7wu5RSJjIhmQ+LMkFwLfAS4BbgNWAl8C\nLnXOHZvEYR4Cfua/7w+BjwFXAr8G3gG82jk3OM5n3+u/7lHgjcCfAkP++292ERyy0EXW+M7S9Lok\nSbzI0qhvXDDnaquSdSNvcDjGrtaxvrJO5xXAG+hSEQjJVlHcGBEA59x+4J2TeF0zcFJSg7/pYfLG\nh5P97MeBG6fz3nwzOBxjd9tY1aB1usgapYssCWrrGuBot5deVl5cyFJVDRp11oJafrL5EKDgXbyl\ne0Mj3thecFZAvL7y+C5vzPXFQ53ccNb8kFsk4onkDIlkj12tYyeORbPLqSnTiSMuGJxtb9EylKhL\nrhqk4g9j1FckSMuAJ6a+ItlKAYmESieOia2oH9uF+sDxProHlKwbZeorE1s7b+wiq+lIFzHtQh1p\n2hBxYmvnjv3fsUMBiWQRBSQSqsQThy6ygkqKCljZUDV6XyePaEvoKwvUV4IaqkqpqywBvF2olawb\nbcFcK/WVRCsbK0dnV19q76VHA12SJRSQSKi2tWjU91SCI78KSKIt4SJLo74JzIy1c4NLUZRHElXO\nOc0mnkJpUeFoVTrwZhRFsoECEgmNd+IIXmTpxJEsGJDoIiu6BoZHEoo/rNVGbydJ7Cu6yIqqtq4B\njvV4BS4rSwpZPLsi5BZlH/UVyUYKSCQ0rV0DtPsnjqrSIhbNLg+5RdlnnU4cAuw80s2wnxexdE4F\nVaWRLZA4oXWaTRQSy8ivm19DgYo/nER9RbKRAhIJzdZAec5186p14hhH8pKtCG5TIyTt1aPZkXFp\nNlFAO7RPRnCGVX1FsoUCEgmNNkQ8vYWzyqn2R8M7+oY40jkQcoskDFoTf3prAjkkzcd66R8aCbE1\nEhbt0H56yTMkGuiSbKCAREKji6zTMzPWaOQ38rZp1Pe0KkuLWDrHyxcYiTl2tXaf5h2Sj3ReOb2F\ns8qpLCkE4HjvEG1dGuiS8CkgkdDoImtyVGkr2pKLP+gia2LBSlvqK9HTPzTCHr/4g1niTICMKShI\nHuhSX5HwKSCRUPQPjbD3aA/gnTjW6sQxISUgRtvhjn46+oYAqC5T8YdTSegrKmcaOU1Huojvibls\nTiUVJSr+MBGdVyTbKCCRUOxoGTtxLNeJ45QS91fQiSNqtiUltJup+MNEEpN11VeiRrPuk6fzimQb\nBSQSCq3znbx1gYusXW3dDI/EQmyNZJousiYvcXmj8q2iJmFpo6rRndK6wHl3xxH1FQmfAhIJhS6y\nJq+2opj5tWUADA7HaD7WE3KLJJOUPzJ5y+ZUUFLkndaOdA5woncw5BZJJqly4+QFl2ztPNLNSEyV\ntiRcCkgkFLrImhrtrBtdmk2cvKLCAlY3Vo3eV1+JDq/4Q6CvLFBfOZVZFSXMrSkFYEADXZIFFJBI\nxjnn2Naii6ypUKWtaOodHGavf6FQoOIPk6K+Ek0HT/TR1T8MQE1ZEQv8WWWZWDDnSn1FwqaARDIu\neOKoLR9bjiQTW6cZkkhqOtJNfM+y5fWVlBUXhtugHKC+Ek3bk2bdVfzh9NRXJJsoIJGMawqU41w3\nr1onjklYO1cjWVHUFPhbr9NM4qQkjvoqWTcqgmWeNes+OYn79qivSLgUkEjG7WgZ20F5zVwtQZmM\nlY2VFBZ4gdtL7b10DwyH3CLJhOBF1ppG9ZXJSN5fIaZk3UgIDnStnlt1ildKnHITJZsoIJGM2xm8\nyNKa+EkpLSpkRX3l6P0mbfoWCcG/89p5usiajMbqUmZXFAPQMzjCwRN9IbdIMqHpyNhA11oNdE3K\nqsaqhIGu3kENdEl4FJBIxiWO+uoia7KUrBs9iaO+usiaDDPTyG/EDI/E2N06FpCor0xOWXEhy+ZU\nAOBcYlAnkmkKSCSjRmKOXa1asjUdyUtRJL919A5xpHMAgJKiApbWVYTcotyxTnkkkbKvvZdBf8PY\neTVl1JYXh9yi3KG+ItlCAYlk1EvtvQwMeyeOxupSZleWhNyi3BFM1t2uE0fea2odCzpXNVRRVKj/\nridLMyTREiz+oGXAU6O+ItlCZzjJqODIvmZHpiZ5hsQ5Jevms8S+oqWNU6HljdGiZcDTp74i2UIB\niWRUQkK7ApIpWTirnMoSbx+K471DtHUNhNwiSScVf5i+4P8te472MDA8EmJrJN12BnIf1FemRkuB\nJVsoIJGMShjJ0qjvlBQUWMLJVtPr+U0lf6evqrSIxXXlgJe3tru1J+QWSToF+4oqbE3N4tkVVPgD\nXcd6BjXQJaFRQCIZpZGsmdFoVnQE+8pa9ZUpS9hM9IhyrvLVwPAIzUfHAs5VWrI1JQUFllCVTOcV\nCYsCEsmYweEYu9sCpRl14piy4OifZkjy19HuAY71DAJQUVLIwlnlIbco96zTbGIk7D3aw7C/+eXi\nunIqS4tCblHuWZdwXlHwLuFQQCIZ03xs7MSxcFY51WUqzThVwUpbGvXNX8GqQasbqyjwNy+TyVOy\nbjQE/7ZarjU96iuSDRSQSMY0KX9kxoKjvjuPdDMSU6WtfNSk4g8zpuWN0RBc2qgNEadn3fxAXzmi\nviLhUEAiGdOkkr8zNruyhLk1pQAMDMdoPqZk3Xy044g2D52pZfWVlPh7txzu6KejdyjkFkk6KKF9\n5oKbIzYd6dJAl4RCAYlkzA6N+qZEwrItjfzmpSaV/J2x4sKChARnjfzmp2BfWa2Z92mpqyyhodob\n6OofivFSe2/ILZIoUkAiGaOqQamhZN385pxLuMjSqO/0JS7bUs5VvukbHBm9eC4wWNmggGS61Fck\nbApIJCP6h0ZGlxeZThwzklBp67BOHPmmpbOfrv5hAKrLikaX6MnUBQc+til4zzu7Wrtx/uqiZfWV\nlBUXhtugHBY8r2w7rL4imaeARDJid1s38WWpS+sqKC/RiWO6ghdZTVqGkneagjOJc6sxU4Wt6Uro\nKwpI8k6TNg9NGZ1XJGyRDUjMbJGZfdvMDpnZgJk1m9kXzWz2JN8/x8zebWb3mNkuM+szsw4z+7WZ\n/bGZnfS7NbNlZuZO8XVn6n/S7JC4zlcnjplY1VhFvArsS+299A+NhNsgSamEkr/qKzMSzFXb2dqN\nc0rWzSfKtUqd5L4ikmmR3EHIzFYCm4BG4CfAduBi4CPADWZ2uXPu2GkO8ybg34DDwEPAS8Bc4A3A\nN4FXmtmb3PhnwC3AveM8/sI0fpycsKMlcdRXpq+suJAldRU0H+sl5rzZpzMX1IbdLEmRxKpBWto4\nE/Nry6gqLaJ7YJiOviHaugZorCkLu1mSIjtUSj5lggUgmo/2MDgco6QosmPWEoJIBiTA7XjByIed\nc1+JP2hmnwc+Cvw98L7THKMJ+H3g5865WOAYHweeBN6IF5z8aJz3bnbOfWomP0Cu2amRrJRa1VhN\n8zEvmXNXqwKSfKK+kjpmxqrGKjbvPwF4I78KSPLHziMa6EqVytIiFs4q5+CJPoZjjuZjPaqGKRkV\nufDXnx25HmgGvpr09N8APcDbzKzyVMdxzj3onPvvYDDiP94CfM2/uzEVbc4HGslKreDvUOt980cs\n5hJySHRBMHPqK/mpq3+Igyf6ACguNJbVn/KULZOgviJhilxAAlzl394/TjDRBTwOVACXzuAz4jtw\nDU/w/AIze6+Zfdy/PWcGn5X1egaGOXDcO3EUFRgr6hWQzNTqhBOH1vvmi4Mn+ujzc4LmVJZQX6UK\nWzO1ujGYrKu+ki+CeQ4r6qsoLozi5UxqBXPW1Fck06K4ZGutf9s0wfM78WZQ1gAPTPXgZlYEvN2/\n+8sJXnad/xV838PAO5xzL03yc56e4Kl1k3l/JgVPHMvqK7UuNQWCF1m7lICYN3a0aJO3VAv+Hne1\natQ3XwSLP2hpY2qsblRfkfBE8cowvti+Y4Ln44/Pmubx/wk4C7jPOfc/Sc/1An8HXADM9r+uxEuK\n3wg8cLqlYrkoeOLQOt/UWNVYRbwa7L5jPaq0lSd2aEPElFuTNOqrSlv5QcUfUi+5r4hkUhQDkrQx\ns3BeOYMAACAASURBVA8Dt+FV7Xpb8vPOuVbn3F87555xzp3wvx7Fm5H5LbAKePdkPss5d8F4X/5n\nZ5XEkr86caRCvNIWQMzBnraekFskqbBT5bFTLl5pC/AqbXUPhNwiSYVgQrv6SmqMV2lLJFOiGJDE\nZ0AmKksUf/zEVA5qZh8CvgRsBa5yzrVP9r3OuWG8UsEAV0zlc3OBRn3TI7hsa6em1/PCjmDVIC1D\nSYl4pa24nRr5zQs6r6RevNIWMFppSyRTohiQ7PBv10zw/Gr/dqIck5OY2a3AV/D2EbnKr7Q1VW3+\nbd4t2QpeAGitb+qoIkp+GR6Jsbst0Fe083TKBNfGq6/kvuM9g7R1eTNdpUUFLPZni2XmdF6RsEQx\nIHnIv70+eTd1M6sGLsfL9fjNZA5mZv8X+AKwGS8YaZ1mu+JVvfZM8/1ZqaN3iJbOfgBKCgtYqhNH\nygSXv2nUN/fta+8dXSIxt6aU2orikFuUP7QLdX5JXgZcWGAhtia/BJe/6bwimRS5gMQ5txu4H1gG\nfDDp6U/jzVB8zznXA2BmxWa2zt+/JIGZfRIvif1p4Brn3NFTfbaZnZ8cBPmPX4O3ISPA96f2E2W3\npsBSopWNVRSpNGPKJC7Z0okj1yVUDdISlJRalRC8a9Q31zUdUV9Jl+BsopYCSyZFsewvwAeATcCX\n/WBgG3AJ3h4lTcAnAq9d6D+/Dy+IAcDM3gH8LTACPAZ82OykUZpm59x3Avc/D6w2s03AAf+xc4Cr\n/e8/6ZzbNMOfLas0aUPEtFnZ4FXacm6s0lZZcWHYzZJp0oaI6TNepa1x/r+WHKG+kj7ai0TCEsmA\nxDm328wuxAsobgBuBA7jJaV/2jl3fBKHWe7fFgK3TvCaR4DvBO5/D3g9cBHwSqAYOALcDfyrc+6x\nqf0k2U+jvulTXuJV2tp3rHe00tYZC2rCbpZMU5OSdNNmQW0ZlSWF9AyOjFbaaqwuC7tZMk1KaE+f\n1eNU2tLeYZIJkQxIAJxz+4F3TuJ1zcBJQ2nOuU8Bn5riZ34L+NZU3pPrdOJIr9WN1ew71gt40+sK\nSHJXsK+o+ENqmRmr5lazZb9XPHHnkW4FJDnKOZc4866+klLxSlsHT/SNVtrSYKJkgsJeSaudmlpP\nKyW254eB4RGaj46V2AyOUkpqrGlUHkk+aOse4ETvEABVpUUsqFVgmWqrVWlLQqCARNLmaPcAx3oG\nASgvLmTR7PKQW5R/VKIxP+w92sNwzNtBfNHscipLIzt5nTYJF1kqApGzmlqCGyJWKRcoDdao0paE\nQAGJpE1yacYClWZMuWClrV26yMpZStJNv2Cy7i5dZOWshOVa2qsnLVap0paEQAGJpE3wAnm1Thxp\nEa+0BdDsV9qS3LMrKXiX1EuotNXahXMuxNbIdAVLnKuvpIdmSCQMCkgkbYL/kenEkR7xSlsAMect\n/ZHcs1PBe9rFK20BnOgd4mj3YMgtkunY1RoM3tVX0iE4Q7LXr7Qlkm4KSCRtglO9StJNn+DvVnkk\nuSkxIFFfSYd4pa04JbbnHq/ClvpKulX5lbaA0UpbIummgETSRku2MmO1ptdz2uBwLKHC1kpdZKWN\ngvfcdrR7kI4+r8JWZUkh81VhK21UwVEyTQGJpEV7z+Dokoiy4gIWqsJW2gQrbSkBMffsOzZWYWvh\nrHKqVGErbRL7ii6yck3w/7dVc6tVYSuNEnKuFLxLBiggkbQIzo6sbKiiUBW20iY4+6SRrNwTvDBe\npdmRtNJsYm7bpaWNGaNKW5JpCkgkLZQ/kjnJlbYGhlVpK5ckbh6qvpJOCUu2VGkr56ivZI4qbUmm\nKSCRtEissKX8kXQqLylk8eyxSlt72pSAmEsSg3f1lXRaOKtclbZymPpK5qjSlmSaAhJJC02tZ5Z2\nbM9dwb6ySqO+aWVmiUtR1Fdyyi4tb8yY5Epb+1RpS9JMAYmkxU7Vis+ohF2olaybM4ZHYgkzWrrI\nSr+EPBL1lZwRLJRSXlw4erEs6bM6YaBLfUXSSwGJpFxH3xBHOgcAKCkqYLEqbKWdypnmppfaexkc\n8ZZCzKspo6asOOQW5T/1ldyUPDtSoEIpaae+IpmkgERSLnjiWFFfSVGh/pml2xqN+uakhA0RtVwr\nI9RXcpMKpWSeZt4lk3SlKCm3S8u1Mi5YaWvfsV5V2soRWhOfeYkbvqnSVq4IFkpRrlVmaIZEMkkB\niaRcQoUtXWRlRLDS1kjMqdJWjggmVatqUGYsqC2nwq+0dVyVtnJGYqEU9ZVMCA4oqtKWpJsCEkm5\nnaqwFQrtQp17tGQr8woKLOH/JW36lhu0ZCvzVGlLMkkBiaTcLl1khWJVwo7tusjKdiMxl7hkq0F9\nJVMS+4qC92x3UqGUuoqQWxQdqxpVaUsyQwGJpFT3wDAHT/QBUFRgLJ1TGXKLoiNhhkQnjqx34Hgv\nA/4SiPqqUmZXloTcouhInE1U8J7tgnmJKxuqKFSFrYxRX5FMUUAiKbU7MOK7vL6SYlXYyphg9aAm\nnTiynnKtwpPQVxS8Zz31lfAk7NujviJppKtFSSmtiQ+PKm3lFvWV8Gi39tyivMTwqNKWZIoCEkmp\n4JTuKlVCyajykkIW+ZtQjsQczUd7Q26RnIqSdMOzcFY55cVjlbaOdQ+E3CI5FQXv4QkG783Hehga\nUaUtSQ8FJJJSuzS1HqpgOUyt981uiXuQKHjPpIICS5wlUVW6rLbriAa6wlJdVsz82jIAhkYc+45p\noEvSQwGJpFRTwqaICkgyLaGcqdb7Zq1YUoUt9ZXMW62AJCd09Q9xqKMfgOJCY+kcVdjKtGDwvksD\nXZImCkgkZXoHhzlw3KuwVWBeUrtkVsKJo00XWdnqUEcfvYNejs/simLmqMJWxgV3+96tgCRr7Q5s\n8qpCKeEIzrzvUl+RNFHPlpTZ09aDc973y+ZUUlpUGG6DIihYEWWXZkiy1s6kXafNVMY007S8MTcE\niw5oh/ZwrNamu5IBCkgkZRIT2rUEJQzB3/ueo90MKwExKwWDxVVarhUKLW/MDYm5VuorYVBfkUxQ\nQCIpk1ArXhdZoagqLUpMQGxXAmI2UoWt8C2uq6CkyDsFtnYN0NE7FHKLZDyqsBW+YCC4u62bkZgL\nsTWSrxSQSMokL0ORcKzSaFbWU18JX2GBsSKQ57arTcu2slFi8K6+EoZZFSXUV5UCMDAc48BxDXRJ\n6ikgkZTR1Hp2SExA1EVWtnHOJZbH1qhvaLQLdXYLFkopLDCW1avCVli0bEvSTQGJpET/0Aj7jnnV\nUMy8XcMlHMELXFVEyT5HOgfoGhgGoLqsiMbq0pBbFF2rG9VXslmwUMrSORUqlBKihPOKKjhKGigg\nkZTYe7SH+LLSxbMrKC/RiSMs2l8huyXnj6jCVnjUV7Kbcq2yh2ZIJN0UkEhKJK6J14kjTKuSRn2V\ngJhdEoo/aE18qDSbmN3UV7LHKi0FljSLbEBiZovM7NtmdsjMBsys2cy+aGaz030cM7vMzO4zs3Yz\n6zOz58zsVjPL2WmFXYFa8SpjGq7kBMSD/hpsyQ6qGpQ9ls6ppKjAm6E6eKKPbn8pnWQH9ZXssSpp\nNtE5DXRJakUyIDGzlcDTwDuBJ4EvAHuAjwBPmNmcdB3HzF4LPApcAdwD/CtQ4r/3zhn9YCFS1aDs\nkrgURaNZ2WSX9uvJGsWFBSwLVNrSju3ZRYVSskd9VQmzKooB6B0c4VBHf8gtknyTsoDEzOam6lgZ\ncDvQCHzYOfc659xfOOeuxgsK1gJ/n47jmFkN8A1gBNjonPtj59yfA+cCTwA3mdnNKfj5Mk5LtrKL\ndtbNTs45mhIqbCl4D5vySLKTCqVkl/+fvfuOk+Qq7/3/eSaHnZkNszubc5RWgZUMCqCAbC7IRoAR\nIGxk4GfAYMwFG4d7L2Bjm3t9r+EHxgYDJlg2wpZAgLg2kgxGCSQQKO0qbs5xdmd3cp5z/6ianqre\nCd093V3dVd/36zWv3u6erjrd22eqnjrneY6ZpeWR6EKX5Fc+R0gOmdmdZvbKPG4z7/xRjVcBB4DP\npz39Z0AvcKuZNTKNHLdzM7AQuMM59/j4g865AeCj/t33ZfF2SsLQyBgHTvem7q9TQBI5VQ8qTad7\nhujs9xbga6ypZKm/iKVER32lNAULpayc30BdddnOaI6NcB6J+orkVz4Dkl3Am4AfmtkuM/twplOf\niux6//YHzrmx4BPOuW7gEaABuKIA2xkP1u6bZHsPA33AVWZWVnVAD57pZcQ/ciybW8+c2qqIWyTB\nA4eu+paO4PS59W1NqrBVAta3KVm3FGkacOlR8F6afrr3DF//6QF+uvcMnX3DUTcnZ3kLSJxzFwEv\nB74OLAM+CRwxs2+Y2TX52k8ebPJvd03x/G7/dmMBtjPla5xzI8B+oApYO8O+MbMnJvsBNs/02nzb\nrXm+JSdUPehktxIQS8QeTW0sOZqyVZqChVKU0F4aNBW4NP3f7cf42Pee461f/hl3PXkk6ubkLK9J\n7c65R51z7wCW4iV27wHeCjxgZs+b2QezrWJVAC3+becUz48/PrcA28nXvktKuDSjDhylYEHjRAJi\n79Aox5WAWBKCfUXBe2lY09qIX2iLQx19DAyPRtsgAdIudCl/pCSsT8sh0YWu0rAnJuv1FKTKlnOu\n0zn3d4FRk38GVgGfxhs1uc3MLi/EvpPCOXfZZD/Ai8Vuy6Ur53LrFau4Yu18Ll5RVrFUbJ2XgKir\nWSUhOGVro676loS66kpWzm8AwDnYq1WoS0Lwb9ZGFX8oCYub61JTsrsGRmjvHoy4RXJ+oZTyPa4U\no+zvaeAsMAAYUAv8FvCYmd1tZvOL0Iag8VGIlimeH3/8XAG2k699l5RrNy7kL1+/lTvecyU3XbI0\n6uaIL5RHooooJWGP5sWXJCXrlpbzC6VMW2NGisTMzluPRKIVLJQyp7aKxc3lWyilIAGJmVWb2S1m\n9gDwAvAh4BTw+0Ar8MvAD4CbOL9CVaHt9G+nyhHZ4N9OlRsym+1M+RozqwLWACN4a5mIzIoSEEtL\nR+8Qp3uGAKirrmDZ3PqIWyTjQnPjT6qvRC1YKGX5vHoaalQopVSo9G9p2Z22rlU5F0rJa0BiZuvN\n7K+Bo8A3gKvxFv/7ZefcFufcZ51z55xz9zvnXgN8B3h1PtuQgQf821eZWej9m1kTXpv7gJ8VYDv3\n+7eTvedr8KpyPeqc0ziozFoosV0BSeTSF3mrqCjfA0fcKHgvLVrXqnSFjiua3hi5OBVKyefCiD/C\nGwH4Q2AI+AtgtXPuZufc/VO87AmgOV9tyIRzbi/e6Mxq4P1pT/850Ah83TnXC6nRns3+uiM5b8d3\nF94UtluCOTRmVgd8wr/7hZzfnEjAhrTSv0pAjNbuUOKhpmuVknBf0VXfqO3W4qElK9RXNJoYuV0x\nqkaXz3HQ6/FGDf4euNs5l0mpkn8DjuWxDZn6XeBR4G/N7Aa8aWUvw3sPu4CPBH53mf/8QbzgI9ft\n4JzrMrN34wUmD5rZHUAH3tS1Tf7jd+btXUqitTXXMqe2ip7BETr7h2nvGWRRU/nOLy13qrBVuoI5\nCgfO9DE0MkZNVTFSLGUy6dNQpHSs12hiSQlXOS3v4D2ff3G3OOducM59O8NgBOfcs865f8pjGzLi\nj25cDtyGF0B8GFgHfBa4wjl3plDbcc7dDVyLtxDiG4EPAMPAHwC3OF3GljxJT0Dco6tZkYrT0Hrc\nNNRUpXJ6RsccB870zvAKKST1ldK1bG49ddXeqeOZ3iHO9GiGeZTSpwKXs7yNkDjnds78W6XDOXcY\neGcGv3cArzrYrLaT9ppHgBuzeY1ILjYsmsPTh72ibbtP9XDV+taIW5RcoSlbmoZScja0zeHouX7A\nu+qoUrPRGBkdY1/7REBY7idZcVNR4V3oevZoF+CdEC+YUxtxq5LpTM8gZ3q9Qin11ZVlXyhFY9Ii\nMRZeWVdz46PS2T/MyS7vSmJNVQUr5pX3gSOOwuv2qK9E5VBHH0OjYwAsaamjqa464hZJuvT8RIlG\n3AqlKCARibENWl+hJAQ/+7WtjVRV6k9vqVFfKQ27YzQFJa6UR1Ia4laNTkdFkRjTgaM07NF0rZK3\nXmWyS4IWDy19KpNdGkIjJGVeYQsUkIjE2rK59dRXVwLeiq4d/nxTKa5wJZTyP3DEUTB439fey4g/\nbUiKa3eMypjG1XpNbywJcSslr4BEJMYqKixU0lRXs6IRt6H1OGquq6at2UvOHRod41BHX8QtSib1\nldK3cn4DNf6005Ndg3T2D0fcomSK24UuBSQiMadF36IXmoaiq74lS8m60Rodc7EqYxpXVZUVrF2o\nC11R6uwb5lR3oFDK/IaIWzR7CkhEYi40vK61SIquZ3AkVU62qsJYtaBxhldIVJRzFa0jZ/sYHPGm\nyi1sqmVuQ03ELZKphPuKLnQV2572ic983cI5VJZ5hS1QQCISe8Gh3L3tOskqtuCJ7ZrWRqpVYatk\nbVBie6TiNgUlzlSVLlpx7Cs6MorEXLCqk0ZIik9JuuVD0xujpfyR8hFe40rHlWKLY19RQCIScyvm\n1VNT5XX1E10DdA0oAbGYwnPiy78SSpyllzMdG3MRtiZ5gkHgepXHLmkbNBU4UrtjmJeogEQk5qoq\nK1jbOpG3oINHccXxSlZczWusYUGjl7cwMDzGkbP9EbcoWfaor5SNVQsaqfLzFo6e66d3cCTiFiXL\nnsDIe1wudCkgEUmA4LQtJSAWV/Cq70Zd9S154ako6ivFMpZWYUsBSWmrqapgdasqbUWhe2CYY50D\nAFRXGqsWlH+FLVBAIpIIGwMH910aISmavqGR1FX2ygpjdWs8DhxxFgwa1VeK51hnP31DowDMb6xh\nwZzaiFskM9nYFjyuKHgvlr3tval/x6lQSjzehYhMa4MOHJHY196L89MQVi1ooLaqMtoGyYzCc+PV\nV4plt9YfKTvrtW5PJEKFUmIyXQsUkIgkQnjKlg4cxRKc8qMpKOUhVJVOfaVo9sSwjGncBUdIFLwX\nT1yDdwUkIgmwan4DNf6w7vFOVdoqlnCt+PhcyYozVdqKhoL38hP8m6bpjcUT11LyCkhEEqCqsoK1\nC5WAWGxxLM0Ydwvm1KYqbfUPj3L0nCptFUO4ryh4LwdrWlVpKwrhyo3x6SsKSEQSIrxAoobXi2FP\nTIfW4045V8XlnNOUrTKkSlvFF+dCKQpIRBJigyptFdXA8CgHz3jVUMxg3UKdZJULTUUprpNdg3T7\nV9eb66pY2KQKW+UifFxR8F5oe09NVNiKW6EUBSQiCRFKQNSVrILbf7qX8fSDlfMbqKuOz4Ej7jZq\nLZKiCuWPtDVhZhG2RrKhginFFedcKwUkIgkRKtGoK1kFpxXay1d4eqNOsgptt6ZrlS2tRVJccc0f\nAQUkIomxekED1ZXelUdV2iq8PYGD8/qYHTjiTpW2iiuuZUyTQNMbiysUvMesUIoCEpGEqKqsYG1r\n+ERLCkcjJOVLlbaKa0/alC0pH2taG6lUpa2iCfaVuAXvCkhEEmSDFrIqGpX8LW/rlaxbFM650JV1\nBe/lpaaqgtULJio96UJX4QwMj3Koow+IZ6EUBSQiCbJRc+OLYmhkjAOnJ6qhxO3AkQQbtWJ7UZzu\nGaKz35s+2lhTyZKWuohbJNlSXymOfe3xLpSigEQkQUIlGnXgKJiDZ3oZ8Y8cy+bW01hbFXGLJFtK\n1i2OYNWg9aqwVZa0xlVxxLnCFiggEUkUHTiKQ9O1yl+4Kp2C90LZo1yrsqe1SIojvNBu/HKtFJCI\nJMiqtEpb3aq0VRAqY1r+giMkqrRVOOor5U9Ttooj7n1FAYlIglSnVdrSwaMwdoWG1uN3JSsJVGmr\nOIJX1DWaWJ6ClbaOnFWlrUIJHVdi2FcUkIgkTPAP2R5NRSmI3TrJioVgpS2t2J5/XoUtBe/lLr3S\n1t52HVfybWB4lINn+lL341byFxSQiCROeCErnWTl29DIGPvaJypsaV2F8hWciqJF3/LvdM8QZ/sm\nKmwtm1sfcYskV+orhbWvvZdRf9royvkNNNTEr1CKAhKRhAlVD9KUrbw7kFZha44qbJWtDaq0VVDB\nz3R9WxMVFaqwVa6COQ0qmJJ/wRHajTEddVdAIpIw4SlbOnDk284TE5/ppsUaHSlnwdFELfiWf8GA\nZFNMT7KSYoMS2wsqeFzZGNNRdwUkIgmzakFjqtLWMVXayrvgSVZcDxxJEbwSufukKm3lm/pKfISn\nbOlCV76FgveYXuhSQCKSMKq0VVjhkyxd9S1nC+bUMl+VtgommGuggKS8rW5tUKWtAtoVKvkbz76S\nyIDEzK4ys3vMrMPM+s1sh5l9yMwqs9jGBjP7EzO738wOm9mQmZ00s++Z2fVTvOYdZuam+Xlv/t6l\nyNTWq9JWwegkK142qNJWQTjn2KXpjbFRW1WpSlsF0jc0wqEOr8JWZYWxdmFjxC0qjMRlW5rZ64Bv\nAwPAnUAH8FrgM8DVwJsy3NRfAm8Bngfu8bezCbgJuMnMPuic+9spXvs94OlJHn88w32LzMrGRU18\nn+OAhtfzySvN6FXYqrB4lmZMmo1tTTy2vwPwgs1Xbm6LuEXxcLxzgG7/KnpzXRWLmmojbpHM1sa2\nJvb6FQZ3nezh4uVzI25RPATz11YvaKCuOuNr52UlUQGJmTUDXwZGgeucc4/7j38MuB+42cxucc7d\nkcHm7gP+j3PuqbR9XAv8EPikmX3LOXd8ktfe7Zy7bRZvRWRWgontmrKVP3tO9TCeZrBqQWNsDxxJ\nsiEtj0TyI31OvJkqbJW7DYvmcK//b40m5k8SEtoheVO2bgYWAneMByMAzrkB4KP+3fdlsiHn3G3p\nwYj/+EPAg0ANcNVsGyxSCOFkXR048iW8yJtGR+IgOF9bJ1n5E16hPb4nWUkSqrSl4D1vklL8IVEj\nJMAr/dv7JnnuYaAPuMrMap1zg7PYz3jZoqmyui41sw8BdcBR4AHn3JFZ7E8kK+OVtoZHXarSVlNd\nddTNKnvB/BHNiY+H9BGSsTGn9TLyINRXYnySlSRat6cwkpKXmLSAZJN/uyv9CefciJntBy4E1gIv\n5LIDM1sF3IAX3Dw8xa99MO3+qJl9BfiQP1qTyX6emOKpzRk1VBKturKCNa2NqT90e0718JKV8yJu\nVflLypWsJGn1K2119A6lKm2tmN8w8wtlWuor8bOmtZHKCmN0zHHkbD99QyOxXFG82MLTG+M78p60\nKVst/m3nFM+PP55TJpaZ1QLfAGqBjzvnzqb9yn7gA3iBUSOwFHgzcAD4HeBruexXJBcaXs8/nWTF\nkypt5dfYmAv9zVF57HhIr7SlxURnr2tgmOOd3nXqmsoKVi2IZ4UtKMOAxMwOzFA6N/3n9iK1qxL4\nOl6lrjuBT6X/jnPuIefc55xzu5xzfc654865bwHXA2eBt5rZJZnszzl32WQ/wIv5e1cSZ8GTLA2v\nz17P4AhHznrrVFRVGGta43vgSJrwVBSdZM3WkbP99A+PAtA6p4YFc1RhKy6COVfqK7MXzPFcu7CR\n6sqyO23PWDmOpe3FK9mbqWOBf4+PgLRM9ouBx89l0yA/GLkdr2TwN4G3OecyXtLXOXfYzO4BfhO4\nBtiezf5FchG8gq9KW7MXPHCsaW2kpiq+B46k2ajRxLzaGSr+oJHEONnYNof7nvP+rdHE2dt5Ihn5\nI1CGAYlz7oZZvHwncDmwEQjlYJhZFbAGLxF9X6YbNLNqvGlabwL+Bfgt59xoDm1r9291WVWKQpW2\n8is0BUUJ7bGyXlO28iq95K/Ex3oF73kVngYc76mNSbuEd79/++pJnrsGaAAezbTClpnVAN/CC0b+\nGbg1x2AE4GX+bcbBkMhsjFfaAlKVtiR3wau+qhoUL8Erk3tOeZW2JHfKtYqv0IUuBe+zlqS+krSA\n5C7gNHCLmV0+/qCZ1QGf8O9+IfgCM2sxs81mtiTt8Vrgu8DrgK8C73TOjU238+A+A49VmNl/B670\n2zZZSWKRvBuvtDVOCYizk6QrWUkzXmkLoG/Iq7QluQsv9Ka+EifjlbYADnd4lbYkd0kqJV92U7Zm\nwznXZWbvxgtMHjSzO4AO4Ca8yld34SWkB70B+Efgn4B3BB7/InAjXhBxFPjTSVaafdA592Dg/i/M\n7Fm8HJGjeDkrVwNb8coE/6Zzrmt271IkcxvamlJ/8Hae6Fbp31lI0pWsJNqwaA6P7e8AvL6i0r+5\nGRkdY197b+q+FkWMl/FKW3v9/+NdJ3u4dEVOhUsTr6N3iNM93oSduuoKVsyL99+cRAUkAM65u83s\nWuAjwBvxFifcA/wB8LdZJKOv8W9bgT+d5vceDPz7U8BL8RZonA+MAYeAzwOfds5pupYU1ea2Jr7P\ncQBePKHh9Vx19g1zsss7cNRUxbs0Y1JtXtw0EZCc7OaXL2iLuEXl6cCZPoZGvckEi5vraKnXgqxx\ns3lxcyog2XmiSwFJjnalFX+I+4KsiQtIAJxzj+CNbmTyu7cBt03y+HU57PePsn2NSCEFh4B3KiDJ\n2a7AXOn1C+ekpixIfGxa3Jz6t4L33IVGEmM+BSWpNi1u4vvP6ELXbCVt1D1pOSQiErA5cJK182Q3\nWVSrloBgMBf3eb5JFQ7eNbM2V6EKW8ofiSVd6MqPpOVaKSARSbDl8+ppqKkEvPmq7T0ZFZiTNMGy\nyRsScOBIouBJ1r72XoZGpq1hIlMITUNJwFXfJNqsgCQvklZKXgGJSIJVVFhoKFgHj9yo5G/8zamt\nYvm8egBGxhx721WVLhehqkHqK7G0Yl5D6kLXmd4h2rt1oStbzrnQcUVTtkQk9nQ1a/ZCV7IScOBI\nKvWV2RkcGWX/6YkKW8EFJyU+KiosNPqlvpK99u5BOvu9tcHm1FaxtKUu4hYVngISkYQLTkVRAmL2\nTvcMcqZ3CICGmkqWza2PuEVSKOors7OvvZdRf1HJFfPraaxNZF2dRNjcFuwryrnK1s60da0m1XI7\negAAIABJREFUWVYidhSQiCRcKLFdJ1lZ23UiWJpxTuxLMyZZuK/oJCtboapBizSSGGebl2iEZDbC\nCe3J6CsKSEQSLjgNZdfJ7tQVTMlM0kozJpmmbM2OSv4mR6jS1kn1lWwlcRqwAhKRhJvXWMOiploA\nBkfGOHimd4ZXSNDOYJKuTrJibXVrIzWV3mHzWOdAao63ZGbnCSW0J0VwNFEXurKXtIR2UEAiIqhu\n/GzsVhnTxKiurGBdIBF7l678ZmX3KZXHTor5jTUs9C90DQyPcaijL+IWlQ/nXOi4snFxMvqKAhIR\nCU1FeUEBScbSSzPqqm/8BfvKi8eVR5Kp/qHR1ElphcG6hck4yUoy9ZXcHD3XT+/QKADzGqpZOKc2\n4hYVhwISEWGTknVzcqJrgO6BEQCa6qpoa07GgSPJVGkrN3tO9eD8WTurFzRSV10ZbYOk4Da1qa/k\nIn3x0CRU2AIFJCKCknVzlb7IW1IOHEmm6Y25SeKc+KRTX8lNUhcPVUAiIqxfNIfxarUHO/roGxqJ\ntkFlIljyV1WDkmFzWvUg55SsmwlV2EqeUJls5VtlLHRcSVCulQISEaGuupLVrY0AOBcuOShTC6+r\nkJwDR5Itbq6juc5b0K97YIRjnQMRt6g87DqZzJOsJNvQNnGh68CZXvr9vAiZ3q5TyRxNVEAiIoCm\nbeVCa5Akj5lpgcQc7ErgQm9JV1ddyeoFgQtdp3RcmcnomEvkGiSggEREfJvaJk6ylIA4s5HRsdDn\ntHlJ8zS/LXGixPbsnOsbSo0k1VRWsMYfjZX4U1/Jzv7TvQyOjAHQ1lzLvMaaiFtUPApIRARIX1lX\nV31ncuBM+MAxP0EHjqRTsm52ng+UfN3QNofqSp16JIX6SnaCfWVLwi5y6a+CiACaspWt549PfEZJ\nO3AknfpKdl5QX0ks9ZXsvKCARESSbuX8Bur9tQFO9wxxumcw4haVtiQfOJIuWCVqb3sPw6NjEbam\n9KmvJFdwjStN2ZpZkvuKAhIRAaCiwkInWrqaNb0kHziSrrmummVz6wEYHnXsa++NuEWlLdxXkpOk\nK+kXugY5owtd0wr2lQsS1lcUkIhIymatrJuxJB84JDwV5UVV2prS8OhYqGrQBQreE6WywkJlnnWh\na2odvUOc7PICttqqilSFsqRQQCIiKeEERJ1kTSXpBw5Rsm6m9rX3MuRPaVvSUsfcBhV/SBpV2spM\n8CLXpsVNVCWs+EOy3q2ITEsJiJlJ+oFDFJBkSlMbZVNo3R71lamE+sri5PUVHUVFJCV4krXrZA9j\nYy7C1pSu8HSt5B04hNDiiLrqOzX1FQlNbzypvjKV5xOea6WARERSFsyppXVOLQD9w6Mc6uiLuEWl\nKcm14sWzdmEj1ZUGwNFz/XQPDEfcotKkviLBC127T3brQtcUkl4eWwGJiIRs1nzfGSX9wCFQXVnB\nuoUTybq7dOV3UuG+kryrvgKtc2ppnePlDvUNjXL4rC50pRsaGWPPqYm+sjmBxxUFJCISsknVg6Z1\n/oFDJ1lJFewrwRNv8bR3D6bWM6qvrmSVij8klvrK9Lz1jLyRo2Vz62mpr464RcWngEREQpSsO73g\ngWP5vHqa65J34BCP+sr00os/VFZYhK2RKG1qU2L7dEK5VkuTNzoCCkhEJI0qbU1PVYNknPrK9NRX\nZFyor5zUyHs69RUFJCKSZsOiJsy/kHngTC8Dw6PRNqjE6MAh4zaFKm114ZySdYO0eKiM01ok0wtO\nY0tqX1FAIiIh9TWVqYX+xhyhVZYlXDUoqQcO8SxtqaOprgqAroERTnQNRNyi0qIKWzJuY1vgQtdp\nXegKcs6pr6CAREQmsaktkICoxPYU55wqbEmKmYX6yotK1k0ZGB5lb3tv6n4SqwbJhPqaSlbNbwB0\noSvdqe5BOnqHAGisqWTFvIaIWxQNBSQicp5gUt3zxxSQjNOBQ9KF+spx9ZVxe071MOqvN7FyfgNz\naqsibpFELdxXOiNsSWkJ/t3YvKSZioQWf1BAIiLnuTBw4HjumA4c43TgkHTBvvLsUfWVcUlfdVrO\nd+HSltS/nz2q4H3cC+orQEIDEjO7yszuMbMOM+s3sx1m9iEzq8xiG6vNzE3zc8c0r327mf3czHrM\nrNPMHjSzX8vPuxOZva3LJg4czx/r0sq6vnCSrqagSPgk6zmNJqaE+0rLNL8pSaELXZPTNGBP4sZQ\nzex1wLeBAeBOoAN4LfAZ4GrgTVlucjtw9ySPPzvF/j8FfBg4AnwZqAFuAf7NzD7gnPtclvsXybtF\nTbW0zqnldM8gvUOjHDjTy9rAqtRJpQOHpNvY1kR1pTE86jjU0Udn3zAtDVqbRld9JV0weH/+eBej\nY05r06DKjeMSFZCYWTNeEDAKXOece9x//GPA/cDNZnaLc27K0Y1JPO2c+3iG+78KLxjZC/ySc+6s\n//gngSeAT5nZvzvnDmSxf5G8MzO2LmvmwZ3tADx7rEsBCTrJkvPVVFWwaXFTagrKc8c7uWpda8St\nipaKP8hkFjbV0tZcy8muQQaGx9jX3sOGtmT/HR0YHmVfu5fgbxZeryVpkjZl62ZgIXDHeDAC4Jwb\nAD7q331fAff/Xv/2f44HI/7+DwCfB2qBdxZw/yIZCw2va278eQeOTQk+cEjYhUvCUxyT7njnAJ39\nwwA01VWxfF59xC2SUrFVUxxDdp3sZnxG9OoFjTTUJGqcICRpAckr/dv7JnnuYaAPuMrMarPY5lIz\n+x0z+x/+7cU57v/etN8RiZQOHGHBA8eahB84JGzrMiW2B4VGEhc3Y6ZpOeK5cFkwsV19RaPuE5J2\nRN3k3+5Kf8I5N2Jm+4ELgbXACxlu81f8nxQzexB4u3PuUOCxRmAZ0OOcOz7Jdnb7txsz2amZPTHF\nU5szeb3ITIKJ7c8e68Q5l+gTC83zlamETrIUvOskS6a0NViVTont4amNi5N9XEnaCMn4UWOqXjD+\n+NwMttUH/CVwGTDP/7kWeAC4DviRH4QUYt8iBbd8Xj3N/irU5/qGOXquP+IWRSs8J14nWTJhy+Jm\nxnNz97b30Dc0Em2DIqb8EZlKMHh/7lgXziW7gqNWaJ9QdgGJmR2Yodxu+s/thWiHc+6Uc+5PnXNP\nOufO+T8PA68CHgPWA+8qxL79/V822Q/wYqH2KcliZqobH6ADh0ylvqaSdX7RB+fCJ+RJpNFEmcrS\nljrm+VXougdGONyR3AtdXvGHQF9Zmuy+UnYBCV6Fqp1Z/BwLvHZ8FGKqoujjj5/LtXHOuRHgK/7d\na4q5b5F8C86Nfz7Bw+vnHTh0kiVptoau/Ca3r/QNjbD/TC8AFSr+IGm8Co7h6cBJdfRcP90D3mhq\nc10VS1vqIm5RtMouh8Q5d8MsXr4TuBwvTyOUg2FmVcAaYATYN4t9ALT7t6kpW865XjM7CiwzsyWT\n5JFs8G/Py28RicpWzY0H4MjZiQNHS301SxJ+4JDzXbi0me8+dRRIdrLuiye6GZ+Fs6a1kbrqjNcb\nloS4YGkzP959GvD6yo0XLYm4RdEIVuTbskTFH8pxhGQ27vdvXz3Jc9cADcCjzrnBWe7nCv82PbCZ\nbv+vSfsdkcgFS/8m+SQrPUk36QcOOZ+mN3o0kigzCVZwTPKFruDUzgsSPl0LkheQ3AWcBm4xs8vH\nHzSzOuAT/t0vBF9gZi1mttnMlqQ9vs3Mzvv8zOwG4Pf9u+n5K1/0bz9iZvMCr1kNvB8YBP4xy/ck\nUjBrWudQ71/hPNU9yKnugYhbFI3QgWPJVLMuJcmCJxS7T3UzODIaYWuiEwxIdJIlkwlNbzzamdjE\ndgXvYYkKSJxzXcC7gUrgQTP7ipn9NfA0cCVewHJn2svegFcC+K/SHv80cNjMvmVmn/F/fgT8J94C\nhx9zzj2atv9H/detA3b4r/k88DgwH/hDrdIupaSywkInFUldj0RlTGUmLfXVrFrQAMDwqGP3yZ6I\nWxQNVdiSmaya38CcWi9j4EzvECe7ZjsppTy9cCIQvKuvJCsgAXDO3Y1Xnvdh4I3AB4Bh4A+AW1zm\nofrXgaeAX8ILcn4XLw/km8A1zrlPTPYi59yH8VZjPwG8B/gt4Dngtc65z+X4tkQKZqtWbA8dOHSS\nJVMJTUVJYF8ZG3O8eFwnWTK9igoLfTeS2Fd6Bkc4eKYP8C78rV80J+IWRa/sktrzwTn3CHBjhr97\nG3DbJI9/FfhqjvufdJsipSjpc+M7+4dTB46qCmNDmw4cMrkLljbz/We8eiVJHE3cf6aX3iFvqtqC\nxhoWNdVG3CIpVRcua+bnBzoAr6/88gVtEbeouIIX99YtVPEHSOAIiYhk58JlyV5Z95kjE+9585Im\naqt04JDJJb2c6Y4jE1XrL1reouIPMqVwYnsS+8rEe754udbDBgUkIjKDDYuaqKn0/lQcOdvPub6h\niFtUXNsDJ1mX6MAh0whWpXvheBcjo2MRtqb4th+eOMlSX5HpBC90JXEqcOi4skJ9BRSQiMgMaqoq\nQoubPZ+wqSg7FJBIhlrn1KbWqBkYHmPf6d6IW1Rcob6yQtXoZGrrF86htso7BT3WOUBHb7IudAVH\nSC5Zrr4CCkhEJAOh9UgSNrwevOp7sU6yZAYXhqrSJaevDI+OhfJmNA1FplNVWcHmJcnsKx29Qxzq\n8PISayor2LxYxR9AAYmIZODCZclMbD/VNcCJLm/tlfrqStYvVEK7TC+pRSB2nuhmcMSborZsbj2t\nc5TQLtMLL7ybnL4SHEncsqSJmiqdioMCEhHJwNaEjpBsDwyrb13WTFWl/mTK9EKJ7QmaGx9O0tVI\noswsqYntoelayh9J0dFVRGa0ZUkzlRVexZz9p3vpHRyJuEXFofwRydbWQLLu88e6GBtLxirUO5Sk\nK1namtDE9mBf0dTGCQpIRGRGddWVrFvYCIBz4ZXL4+zpw4EDh06yJAOLm+uY31gDQPfgCIfP9kXc\nouLYrhESydLGtqbUha4DZ/roHhiOuEWF55zj6cNKaJ+MAhIRyUjSVqF2zvHMUR04JDtmlri58f1D\no+w62Q2AGVy0TH1FZlZXXcmGwArlSajgeLxzgNM9gwA01lSyVnmJKQpIRCQjocT2BBw4DnX0ca7P\nu2I3t6GalfMbIm6RlIukLZD43LFORv2paWtbG2mqq464RVIutibsuJK+eOj4CJEoIBGRDIXLmcb/\nwLE9bSVdrTotmUpyX1H+iGRja8LKZIf6ivJHQhSQiEhGLggcOHaf7GZgeDTC1hTe9sPBhHZNQZHM\nBac3Pne0E+findiu4g+Sq+DI+3MJmN6ohPapKSARkYw011WzeoE3bWlkzKXmjMeVDhySq5XzG2iq\nrQLgTO9Qai2buFLJX8nVliXNjA8+7z7VTf9QfC90jY059ZVpKCARkYwlZYHEkdGx0PvTCIlko6LC\nQiOKce4rnX3D7D/dC0BVhbFliVadlszNqa1iTatXwXHMwYsn4ttX9p/ppXvAK5m/oLGG5fPqI25R\naVFAIiIZC05FCY4gxM2e9h76/Slpi5vrWNRcF3GLpNwEk3Xj3Fd2HJ14b5uXNFFXXRlha6QchY8r\n8c0jCY+6tygvMY0CEhHJ2KWBhNUnD52NsCWFFcofWaHREcleUvrKDiXpyiwlpa9sPxwulCJhCkhE\nJGOXrJgoU7j7VA+d/fFcyCq9wpZIti5bNS/176cPnUuVxY2bcPEH9RXJXrCvPHEwvgFJqPiDLnSd\nRwGJiGSsoaaKLUuaAG/F9uBK5nGiqkEyW0vn1rPYn+rXOzTKzhPxLAIRStLVSZbkYMuSZmqrvNPR\nI2f7ORXDIhDDo2OhEuC60HU+BSQikpXLVsb7atbA8CgvHp84ebxICe2So9CV3xhORTnZNZCqIFZf\nXcl6rTotOaipqghd+InjtK2dJ7oZHBkDYNncelrn1EbcotKjgEREsrItcJL1ZAwDkuePdzHiT69Z\n09pIS71WnZbcxL2vBKdrbV3WTFWlTikkN9tiPm0rlGulkcRJ6a+HiGQleNX3qUNnYzc3focWRJQ8\nifvceCW0S77Ev69oXauZKCARkawsm1tPW7M33Nw7NBq7BRJ3KKFd8uSCwNz4Qx19tHcPRtyi/Noe\nPMlaob4iudu2cuL78+zRLgZH4rVA4nYF7zNSQCIiWTEztsU4j2S7KqFIntRUVYRWY47T3HjnXNoI\nifqK5G7BnNrUAolDaQvTlrv+wIU7M+UlTkUBiYhk7bKYzo3vGhhmb7u36nRlhXHBEh04ZHbimkdy\n8Exfquz33IZqVs5viLhFUu5eEhgliVNfee5YZ2pq87qFc5hTWxVxi0qTAhIRydq2mFYPejZwxXdT\nWxP1NVp1WmYnrlXptqfNideq0zJbcc0jCa9rpYtcU1FAIiJZu3BpMzX+3PiDZ/o43ROPufHbVQlF\n8iwYvO842hmbufGariX5ll4m27l4FEwJJrRfqlyrKSkgEZGs1VZVctGywNz4mFzNUiUUybfWObWs\nWuBNZxoaCS+OVs7UVyTfNixqosmfztTePciRs/0Rtyg/VCglMwpIRCQncVz0bYeG1qUAgtO24hC8\nj4yO8cxRjZBIflVWGJcG8kjiMG2rs2+Y/ae9vMTqSmPLkqaIW1S6FJCISE62xewk61TXAEfPeVfk\naqsq2NimA4fkRyixPQbB+66TPQwMe6tOL26uY1FzXcQtkri4LGZ9JZhrtXlxM7VVykucigISEcnJ\ntlUTV7K2H+lkaGQswtbM3mP7O1L/vmTFXKq16rTkSXqybrnPjX9s/5nUv4PvTWS24lZSXn0lczri\nikhOFjXVpUp9enPjO2d4RWn72b6JA8eVaxdE2BKJm41tTalSnye7BlMjceUq2FeuWKe+Ivlz6cq5\njBdse+F4F72DI9E2aJZ+tm/iQtcVOq5MSwGJiOQsuLruk4fOTfObpS94kvWytfMjbInETWWFharr\nlPOV37ExFxpNvFJ9RfKoua6aTf502TEH2w+X73Glb2gk1P6XrlFfmY4CEhHJWVwWSDzVPZBaELGm\nsiI0bUAkH+KyQOLOk92c6/MWRGydU8O6hXMibpHEzbaYrEfyxMGzjPgLIm5e3MT8xpqIW1TaFJCI\nSM6CB47HD3aU7dz4xwLD6peunEtdtRIPJb/iUpUuNJK4ZoEWRJS8Cy0mGpO+oulaM1NAIiI529TW\nRKO/mvnJrkGOdQ5E3KLc6MAhhXbpiuDc+G76hspzbny4r2gKiuRfMHh/6tA5xsbK80JXOH9EfWUm\niQxIzOwqM7vHzDrMrN/MdpjZh8ws48uiZnabmbkZfn6U9pp3zPD7783/uxUpnKrKilDd+HKdiqKT\nLCm0lvpqNi7y5saPjjm2Hy6/IhDp+SMK3qUQVi1oSE1v6uwfZt/pnohblL3z80fUV2ZSFXUDis3M\nXgd8GxgA7gQ6gNcCnwGuBt6U4abuBg5M8dytwFrg3ime/x7w9CSPP57hvkVKxraV83hkj3dC/8TB\ns7z2kqURtyg7yh+RYtm2ai47T3YD3hoLV5ZZhapg/siCxhrWL1L+iOSfmbFt5Tz+84WTgHdcWb+o\nvNaFUv5I9hIVkJhZM/BlYBS4zjn3uP/4x4D7gZvN7Bbn3B0zbcs5dzdeUJK+j7nAHwNDwG1TvPxu\n59xUz4mUlXJf9E35I1Is21bO419/fhgoz2Td9KmNyh+RQrlsVTggecsvrYy4RdnRNODsJW3K1s3A\nQuCO8WAEwDk3AHzUv/u+We7jVqAe+I5z7vQstyVS8ratmAhInjvWVXZz43XgkGJJX4W63ObGa2qj\nFEv6YqLlRvkj2UtaQPJK//a+SZ57GOgDrjKz2lns493+7T9M8zuX+jkr/83MbjWz5bPYn0ikWhqq\n2eBP3Rgdc+w4Ul5z40Nz4lUnXgpoTWsj8xqqATjXN8y+070RtyhzY2OOnyt/RIrk4uUtVFV4I3B7\n23s51zcUcYsy1zc0wo4jyh/JVtICkk3+7a70J5xzI8B+vGlsa3PZuJldCVwE7HLOPTDNr34QL2fl\nr4B/Bg6Y2RfNrC6LfT0x2Q+wOZe2i8xG+pXfctHePcieU17CZE1lBS9R/ogUkJmVbV/Zdaqbs8of\nkSKpq67kwqXNqftPldHCu08ePMfwqDf6ualN+SOZSlpA0uLfTnUJd/zxuVM8P5P3+LdfnuL5/cAH\n8AKjRmAp8Ga85PjfAb6W435FIhVMBA9eRS11j+2fmIJy6Yq51Ncof0QK6yVl2ld+tlf5I1JcwfzE\nx8qpr2hqY07KLiAxswMZlNsN/txepHa14AUXUyazO+cecs59zjm3yznX55w77pz7FnA9cBZ4q5ld\nksn+nHOXTfYDvJifdySSueD0jcf2dTAwPBphazKnA4cUW7Cv/Hh3e9ksJqo58VJs6X2lXCgvMTdl\nF5AAe4GdWfwcC7x2fASkhcmNP57L2ODbgAZySGZ3zh0G7vHvXpPDvkUitXJBA2taGwHoHx7l8QPl\nMRUlfJKlA4cU3iXLW2ip9/JITnYNpsoAlzJv/RGdZElxXbVuQSqP5LljXZzqLv2Fd/uGRtgeyh9R\n8J6psgtInHM3OOc2Z/Hzx4GX7/RvN6Zv18yqgDXACLAvh6aNJ7N/KYfXAoyH/405vl4kUtduXJj6\n94M7T0XYkswof0SiUFVZwcs3tKbuP7iz9K/8Kn9EotBUVx3KuXp4V+kXLk3PH1kwZzY1kpKl7AKS\nWbrfv331JM9dgzfC8ahzbjCbjZrZy4BL8JLZH8yxbS/zb3MJhkQiFwxIHtpV+idZyh+RqIT6ShkE\nJMH8kZetna/8ESmaazeV13FF04Bzl7SA5C7gNHCLmV0+/qBf3eoT/t0vBF9gZi1mttnMlkyz3fFk\n9ulK/RLcZ+CxCjP778CVftsmK0ksUvKuWLuAmirvT8ruUz0cPdcfcYumpwOHROW6QEDy+MEOegZL\ne+0eTW2UqFy3cVHq3z/e3c5oia/do/yR3CUqIHHOdeFNraoEHjSzr5jZXwNP4wUEdwF3pr3sDcAL\neCV6z+Ov/v4WYBD4pxma8Asze8bMbjez/2NmXwS2A/8Lbw2U3/TbKFJ26msqeVlgvuzDJX41K3iS\n9TIdOKSIFjXXsWWJV9J0eNTx08AIRKlR/ohEacuSJhY2edOezvUNh9b3KDXKH5mdRAUkAM65u4Fr\n8RZCfCNeGd5h4A+AW1z2JU9+Ey/v47sZJLN/CujAW6Dxg8BvAdXA54GLnHM/yHLfIiWlXKaiBPNH\nqistVLZYpBjCUxxLN+cqmD8yv7EmtQiqSDGYWdlMBw7mj2xsm6P8kSwlLiABcM494py70Tk3zzlX\n75y7yDn3GefcebVKnXO3OefMOfeOKbb1Bf/5t2aw3z9yzl3rnFvqnKtzzjX4ife/55xT7oiUvesC\n830f2XOa4dGxCFszteD6D8ofkSiEi0CUbvnfx9LK/Sp/RIqtXAISjSTOTiIDEhEpjHUL57Bsbj0A\n3YMjJbu6rub5StQuWzWPRj8QPnK2n/2neyNu0eTUVyRqL1/fil/9l+2Hz3G2dyjaBk1BfWV2FJCI\nSN6YGdeUwVQUHTgkajVVFVy1fqL8byle+fXyR5TQLtGa11jDJSvmAjDm4Cd7Sq/8b//QKE8fVv7I\nbCggEZG8Sp+KUmpO9wyyW/kjUgJKva/sPtVDh381WvkjEqVS7ytPHjobyh9pVf5I1hSQiEheXb2+\ntFfXfeDFiVEb5Y9IlIInWT/bd4aB4fPSGCN1f6CvKH9EonTdponyvw/tamesxMr/hvuKRhJzoYBE\nRPIqfXXdH5fY6rr3Pnsi9e9f3tIWYUsk6VbMb2DdwkYABkfGQtOjSsG9zx5P/Vt9RaJ00bIW5jVU\nA94o9wsnSmeFBOcc9+m4MmsKSEQk70p1dd2ugWF+snsiQHrN1unWOxUpvGsDC7+VUqnsI2f72HGk\nE/CmNt6gkyyJUGWF8YoNpXlc2XGkM7UQcEt9NVeu0whJLhSQiEjeBaeilNLquve/cIohvxTxhUub\nWbmgIeIWSdKFg/fSKQIRvOJ79fpWWuqrI2yNSOmuc3VPYCTxVy5oo7pSp9a50KcmInl3wZLm1Oq6\nZ/uGeeZoZ8Qt8tzzzMSB48aLNDoi0XvZmvnUVnmH4r3tvRzu6Iu4RZ5QX9FIopSAV2ycqEr3xMGz\ndA8MR9gaj3OOe5+ZCN5vvGhxhK0pbwpIRCTvzIxrNpTW1azewZHQMP9rturAIdGrq64MJcE+vDv6\nvnKic4An/TWEKiuMX7lA07Ukeoua6rhwaTMAI2OOR/eemeEVhff88S4O+RcRmmqruDpQyluyo4BE\nRAqi1KaiPLDzFIMj3nStTW1NrF2oEqZSGkptKsp9gSkoV65dwLzGmghbIzKh1FZtD46O3LBlEbVV\nqtqYKwUkIlIQrwisrvv04XOc64t2dd3ggeM1GlaXEnJdIHh/dO8ZhvzAOSr3PKu+IqUpVP53ZzvO\nRZef6JwL5Y+8RtOAZ0UBiYgURPrquj/eHV353/6hUR7YOTFKo/wRKSVrWhtZMb8egJ7BEZ44eDay\ntrR3D/KLA175YTN41QUKSKR0vGTlXJpqqwA4eq6fve09kbVl96ke9rX3AtBQUxkavZHsKSARkYIp\nleH1h3a10zfkLTq3bmGjVpyWkmJmJdNX/uO5E4xfdH7p6vmp4hQipaC6siKUpxHlqu3Bwg/Xb15E\nXbWma82GAhIRKZjgSdZ/vnAyspWogwu8vWbrEq04LSUnuB7Jvc8ej2wl6mBf0UiilKJgfmIwKCi2\nUHUtVaKbNQUkIlIwlyyfy/J53lSUc33D/OD5k0Vvw+DIKD96YWK6lubESyl6xYZWmuq8qSgHz/Tx\ns/3FryDU0TvEz/ZNrBb/Xy5UX5HS46314V1UevLQOXad7C56G/a297DT329tVUUoD0xyo4BERAqm\nosJ4y+UrUvfv+PmhorfhJ7tP0zM4AsCqBQ1csKS56G0QmUlddSVveMmy1P07fn646G2j09lWAAAZ\nTElEQVT44fMnUouYXrZqHotb6oreBpGZtM6pDZWijqKvBBcOvW7TQhr9vBbJnQISESmomy9fnqq2\n9ejeMxw801vU/d8TGFZ/9dbFmq4lJestvzQRvN/37AnO9ha3Ml2wr2idHillb/mllal/f+epI0Wf\nDqxFdvNPAYmIFNSSlnquD5RqvOMXxbuaNTQyxg+f1zxfKQ8XLm3h4uUtAAyNjvGdp44Wbd+dfcM8\nuneiEt6rFZBICXvF+laWzY1mOvChM308d6wLgJrKCl65edEMr5BMKCARkYK75aUTV7PueuIIw6PF\nWWfhp/vO0DXgTddaNrc+dbInUqpuCVz5vfMXh4q2zsJ/vnCS4VFvX5csb2H5vIai7FckFxUVFhpR\nLOZ04GDhBy/3q7po+44zBSQiUnDXb1rIIr98aHv3IPe/WJyV2+8NDKtrupaUg5suXUpDjVc+dNfJ\nHp48dK4o+71XC7xJmXlTRNOBwwuHqq/kiwISESm4qsoK3nT58tT9YlzNGhkdCw3j36jqWlIG5tRW\n8WsXT5zkFKOvdA8M83Bg4VLlj0g5WNJSH1q5/c4iTAc+eq6f7Ye9iwRVFcavbGmb4RWSKQUkIlIU\nb7l8YirKQ7vaOXauv6D7e3TvGTr8pOC25lpesmJeQfcnki/BKY7/vuM43QPDBd3fD58/ydCIN43y\ngiXNrFrQWND9ieTLLYFpW98qwnTg7+84lvr3VetbaWnQdK18UUAiIkWxckEDL/dX2B1z8K3HjxR0\nf198aG/q36/ZuoSKCk3XkvLwkhVz2dTWBED/8Cj/d/uxGV6Ru7Exx5ce2pe6/6sXawqKlI9Xbl5U\ntOnAA8OjfO0nB1L3f1Wj7nmlgEREiiaYhPjNxw+n1jzIt8f2neHRvd7CcpUVxjuvXl2Q/YgUgll6\nwm7hpqLc99yJ1AJvDTWVvDUwOiNS6qoqK7j5sonpwIWctvXNxw9zomsAgIVNtbzu0mUzvEKyoYBE\nRIrmVRe2Mc8f4j56rp8f724vyH4++6PdqX//+kuWaQqKlJ1f37aMmirvEP3M0U6ePdqZ932MjTk+\n+58TfeXtV61mfmNN3vcjUkjB4P3Bnac43pn/6cADw6P8/QMTo+7vu3YdddWVed9PkikgEZGiqa2q\n5I3bgsnt+b+alT468nuvXJ/3fYgU2tyGmlBy+R2/yH9ye/royLtfsTbv+xAptFULGrl6/QLAmw78\nzV/kfzpw+ujIb7xMI4n5poBERIrqlpdOXM36zxdO0t49mNfta3RE4iK4Jsn3njpG/1D+VqPW6IjE\nSbCv5Hs6sEZHikMBiYgU1fpFTVy+yqt4NTLm+PaT+buapdERiZMr1s5n9QJvgcLuwRG+H1hXZ7Y0\nOiJxkj4d+Cd7Ts/wisxpdKQ4FJCISNEFy5p+47GDDAzn58qvRkckTrzk9om+ctuj+/Ny5VejIxI3\ntVWV/HpgOvDXfrIf52bfVzQ6UjwKSESk6H71oiU011UBcLijn7++b+est/nz/R0aHZHYufmy5VRX\neiWrnz3axZce3jvDK2am0RGJo7cGpgM/tKudu56Y/ei7RkeKRwGJiBRdfU0lf/Kazan7X3tkP4/M\ncoj9sz/alfq3RkckLhY21fJ7129I3f/MD3fx3LHcK25pdETiav2iJm69YlXq/p//2/Mc7ujLeXsa\nHSkuBSQiEonfeOlKrt+0MHX/D7+1nc7+3Fak/vn+Dh7Zo9ERiaf3X7+OS1bMBWB41PH7dz6d8zRH\njY5InP33GzezttW7GNUzOMKHv7k952mOGh0pLgUkIhIJM+P/3HxxKhHxeOcAf/a9Z3PalkZHJM6q\nKiv4zJsvoa7aO2TvOtnDp/4j+2mOGh2RuGuoqeLTb7mUygpvmuPPD3TwlR/vy3o7Gh0pPgUkIhKZ\nRU11/NWvX5S6f/fTx/j+juwqCf3w+ZMaHZHYW7twDh+5cUvq/lcf2c9P/ZypTN3xi8MaHZHYu3TF\nXN5//cRx4P//wS5eON6V1Tb+4eF9Gh0pskQFJGZWbWYfNLN/NLOnzWzIzJyZvWsW27zKzO4xsw4z\n6zezHWb2ITObMpQ2s7eb2c/NrMfMOs3sQTP7tVzbIFLOXr11Cb++bVnq/kfufoaT/oFgJt98/DDv\nu/2J1H2Njkicve2KVVyz0Zvm6Jw3zbFrYOZpjs45vvjQXv7Hd59JPabREYmzD7xyPRcvbwFgaHSM\n37/zaQZHZp7mODbm+Kt7XuDTP5wYddfoSHEkKiABGoG/Ad4BLAZOzGZjZvY64GHgGuC7wOeAGuAz\nwB1TvOZTwG3AEuDLwO3ARcC/mdnvzaY9IuXq4zddyLK59QCc6xvmj+7aMW3JRuccn/7BTv74rh2M\n+PODl7TU8Qev2liU9opEwcz45M0XMzew3sLH/+9z075mZHSMj979LP/73hdTj61b2Mh7r11X0LaK\nRKm6soJPv/lSaqu809wXT3Tz6R/smvY1A8OjfOCOp/jSwxNTvC5dMVejI0WStICkD7gRWOqcWwx8\nLdcNmVkzXkAxClznnPtt59wfAZcCPwVuNrNb0l5zFfBhYC9wsXPu951z7wcuAzqAT5nZ6lzbJFKu\nmuuq+dSbLsG8ab88vKudv39w76SJu0MjY3z4m9v52/v3pB7bsqSZ7/7u1SxpqS9Wk0Ui0dZcx/98\n/cQ0x+88eZQ7fn6I4dGx8363d3CE93z9Cb7x2KHUYy9dM59vv+8qWuqri9JekaisXzSH/xGY5vgP\nP97Hfc8enzTJ/WzvEG/7ymOhKcO/vGUR//Lul2l0pEgSFZA454acc/c65/Kx3O3NwELgDufc44F9\nDAAf9e++L+017/Vv/6dz7mzgNQeAzwO1wDvz0DaRsnPlugW86+VrUvc/+R87eclf/JB3/dMv+MZj\nBzl2rp/O/mHe/rWf852njqZ+79qNC/nWe69kcUtdFM0WKbpfvXgJr790aer+f/vOM2z7ix/yu994\ngm89fphT3QOc6hrgLf/wU+5/8VTq9266ZClf/+2XMrdBU7UkGW69YhWv2NAKeNMc33v7k1z+iR/y\noTue4ntPH+Vc3xAHz/Tyxi88yuMHU6dlvP3KVXzp1stpqKmKqumJY/lYybJcmdnHgT8D3u2c+0qW\nr70d+E3gN5xz/5r2XBXQiTd9a45zbtB//AiwDG+E5njaa64EHgV+4px7RW7vCMzsiW3btm174okn\nZv5lkRIzMDzK6z//CC+e6J70+abaKroHR1L33/rSFfzF67ZSXZmoaysidPYP85q/eZhjnZPnW82p\nraIn0Fd+97p1/OGrNlHhVx8SSYoTnQO8+rMPc67v/HyrCoO66kr6hrzReDP4yI1b+O2Xr8FMfWUm\nl112GU8++eSTzrnLZrstHcVzt8m/PW9SonNuBNgPVAFrAcysES8Y6ZlihGa8FmNGk+DN7InJfoDN\nM75YpETVVVdyx3uu4F0vX8Oa1vOT04PByB/9l038rzdcpGBEEqmlvprvvv9qbr1iVSr/Kmg8GKms\nMP7XGy7ij1+9WcGIJNLiljq+9/6refPly1nYVBt6bsyRCkZqqyr4+9/YxrtesVbBSAQ0FpW7Fv92\nqiVzxx+fm+PviyTS3IYaPvprF/DRX7uA/ad7eeDFUzyw8xSP7etgaHSMmsoKPvmmi3ndpctm3phI\njLU11/GXr9/KXzjH7lM93P/iKR548RSPHzzL6JijsaaSz/3mNq7ftCjqpopEatWCRv765ksYG3M8\nf7zL6ys7T/H04XM4B/Mba/jyb13OZavmRd3UxCq7gMTMDgCrsnjJN5xzbytQcyIz1fCYP0qyrcjN\nESmINa2NrHn5Gv6/l6+hd3CE7YfPsWJ+AyvmN0TdNJGSYWZsbGtiY1sT7712HZ39w+w4co6NbU20\nNSu3SmRcRYWxdVkLW5e18F9v2EBH7xDPHO3k4mUtzFMZ7EiVXUCCV6Eqs0UKPMcK1I7xEY2WKZ4f\nf/xcjr8vIgGNtVVctb416maIlLyW+mpesWFh1M0QKXnzG2u4dqP6Sikou4DEOXdD1G3w7QQux8v5\nCGWQ+0nta4ARYB+Ac67XzI4Cy8xsySR5JBv82+kLZYuIiIiIxIiyQXN3v3/76kmeuwZoAB4dr7CV\nwWtek/Y7IiIiIiKxp4BkBmbWYmabzWxJ2lN3AaeBW8zs8sDv1wGf8O9+Ie01X/RvP2Jm8wKvWQ28\nHxgE/jF/rRcRERERKW1lN2VrtszsvzFRGvdS//adZvZy/98/SVuT5A14QcI/Ae8Yf9A512Vm78YL\nTB40szvwVlu/Ca8k8F3AncF9O+ceNbNPA38A7DCzu/DWKnkLMB/4gL9IooiIiIhIIiQuIMGbLnVt\n2mNX+T/jMlok0Tl3t5ldC3wEeCNQB+zBCzj+1k2y6qRz7sNm9gzeiMh7gDHgSeCTzrl/z/K9iIiI\niIiUtcQFJM6567L8/duA26Z5/hHgxnxuU0REREQkKZRDIiIiIiIikVFAIiIiIiIikVFAIiIiIiIi\nkVFAIiIiIiIikVFAIiIiIiIikVFAIiIiIiIikVFAIiIiIiIikVFAIiIiIiIikVFAIiIiIiIikVFA\nIiIiIiIikTHnXNRtkDwyszP19fXzt2zZEnVTRERERCSmXnjhBfr7+zuccwtmuy0FJDFjZvuBZuBA\nkXe92b99scj7jRN9hrOnz3B29PnNnj7D2dNnODv6/GZPn2FmVgNdzrk1s92QAhLJCzN7AsA5d1nU\nbSlX+gxnT5/h7Ojzmz19hrOnz3B29PnNnj7D4lMOiYiIiIiIREYBiYiIiIiIREYBiYiIiIiIREYB\niYiIiIiIREYBiYiIiIiIREZVtkREREREJDIaIRERERERkcgoIBERERERkcgoIBERERERkcgoIBER\nERERkcgoIBERERERkcgoIBERERERkcgoIBERERERkcgoIJEpmdlyM/uamR0zs0EzO2Bmf2Nm86LY\nTrkwswVm9i4z+66Z7TGzfjPrNLOfmNlvm1nG/c7/rNwUPycK+T6ils/3nrTvIICZvWOaz2/8ZzTD\nbcX6e2hmN5vZ35nZj82sy39ft8/wmqvM7B4z6/D7+A4z+5CZVeaw/7xtKyrZfIZmtsHM/sTM7jez\nw2Y2ZGYnzex7ZnZ9lvtdPcN3/I78vMPCyvLzy/t7TuB38LYM/j7+KMP9xuI7GLWqqBsgpcnM1gGP\nAouA7wEvAi8FPgi82syuds6dKdZ2ysybgC8Ax4EHgENAG/DrwFeA15jZm1zmq5J2An8zyeM9eWhr\nqZv1e0/odxDgaeDPp3juFcArgXuz2F6cv4cfBS7Bey9HgM3T/bKZvQ74NjAA3Al0AK8FPgNcjfc3\nICP53FbEsvkM/xJ4C/A8cA/ee94E3ATcZGYfdM79bZb73w7cPcnjz2a5nahk9R305eU9J/Q7eDdw\nYIrnbgXWkt3fRyj/72C0nHP60c95P8B/AA74QNrjn/Yf/2Ixt1NOP3gneq8FKtIeX4wXnDjgjRlu\n6wBwIOr3FNHnmJf3nsTvYAafyU/9935TMf8vSvUHuB7YABhwnf/Z3D7F7zYDp4BB4PLA43V4ga8D\nbslwv3nbVtQ/WX6G7wBeMsnj1wJD/uexJMP9rvb3dVvUn0ERP7+8veekfgen2cZcoM//PFozfE0s\nvoNR/2jKlpzHv6L8KryTkM+nPf1nQC9wq5k1FmM75cY5d79z7t+cc2Npj58Avujfva7oDUugpH4H\np2NmFwFXAEeB70fcnJLgnHvAObfb+WcXM7gZWAjc4Zx7PLCNAbwrtADvy3DX+dxWpLL5DJ1ztznn\nnprk8YeAB4Ea4Kr8t7J0ZfkdzKdEfgencStQD3zHOXc6T02TDGjKlkxmfA7vDyY5qe42s0fwTvKu\nAKabY5mv7cTJsH87ksVras3sbcBKvBPoHcDDzrmM5v+Xudm+d30Hz/ce//arWX6Hkvw9DHqlf3vf\nJM89jHd19Sozq3XODRZxW3GRy99IgKVm9jvAAuAM8FPn3I68tqz05OM96zsY9m7/9h9yeG0Sv4N5\no4BEJrPJv901xfO78U7iNjL9SVy+thMLZlYF/JZ/d7I//lNZDHw97bH9ZvZO/4pinM32ves7GGBm\n9cDbgFG8fKZsJPl7GDTld8o5N2Jm+4EL8eagv1DEbZU9M1sF3IB3Evxwli//Ff8nuL0Hgbc75w7l\npYGlJx/vWd9Bn5ldCVwE7HLOPZDDJpL4HcwbTdmSybT4t51TPD/++NwibScu/jewFbjHOfcfGb7m\nH/EO0IuBRrw/ll/Cm7N6r5ldUoB2lop8vHd9B8PejPde73POHc7idUn+HqbL53dK30+fmdUC3wBq\ngY87585m+NI+vCT5y4B5/s+1eAVFrgN+FMMpmfl8z/oOThgfPf5ylq9L4ncw7xSQiBSBmf1X4MN4\nFZ5uzfR1zrk/93NSTjrn+pxzzzrn3ouXkF0PfLwgDS4BSX7vBTR+wP1SNi/S/4UUkl9a9ut4FZ3u\nBD6V6Wudc6ecc3/qnHvSOXfO/3kYb+TzMWA98K5CtDsqSXzPhWZmLXgXbIaA27J5rf4/8kMBiUxm\n/IpIyxTPjz9+rkjbKWtm9nvAZ/FKXF7vnOvIw2bHk+OvycO2yk02713fQZ+ZXYiXKHwEr9RqPiTx\ne5jP71Tiv59+MHI7XmnZbwJvy0dit3NuhIlpiYn4fub4nhP/HfS9DWggj8nsSfwOzoYCEpnMTv92\n4xTPb/Bvp5qXn+/tlC0z+xDwd3h1yK/3K23lQ7t/m8Rh4Gzee+K/gwG5JrNPJ4nfwym/U36e2Bq8\nhOx9Rd5W2TGzauBfgVuAfwF+wz+Jy5ckfj+zfc+J/g4GjCezZzV6nIEkfgdzooBEJjOezPUqS1tV\n3Mya8IbV+4CfFWk7ZcnM/gRvYamn8YKRU3nc/BX+bdwPEpPJ5r0n+js4zszq8KYKjgJfzeOmk/g9\nvN+/ffUkz12Dd5X10QwrEuVzW2XFzGqAb+GNjPwzcGsBKrYl8fuZ7XtO7HdwnJm9DG9BxV3OuQfz\nvPkkfgdzooBEzuOc2wv8AC9h9f1pT/85XqT/dedcL3hXucxss7/mQ87biRMz+xheEvsTwA3TDQFP\n9fmZ2ZbJEuHMbDXwOf/u7XlrdAnJ9r3rOzijN+ElWt47VTK7vocZuws4DdxiZpePP+gHfZ/w734h\n+AIza/E/2yWz3VYc+Ans3wVehxcgvzO9LPckr5n0MzSzbekXG/zHbwB+378bq+9nLu9Z38FpjY8e\nT1vqV9/BwrLir8Ej5cA/KXkUWAR8D6/c38vw1nXYBVzlnDvj/+5qYD9w0Dm3OtftxIWZvR0vKW4U\nb7rWZNVLDjjnbvN/fzWTfH5m9nG8RPiHgYNAN7AO+FW8VXTvAd7gnBsqxPuIUrbvXd/B6ZnZj4GX\n463M/m9T/M5qEvo9NLPXA6/37y4G/gveFc0f+4+dds79Ydrv3wUMAHcAHcBNeCVU7wLeHMyDMLN3\n4FUq+yfn3Dsm2XfG2ypV2XyGZvaPeKu1nwb+Hm+V63QPBq9WT/UZ+mVVN+D18SP+wxczsb7Gx5xz\n4yfWJSvLz+9BsnzP+g4Caf3Yf00zcAxvGYzlM1w8fAcx/g5GzpXAcvH6Kc0fYAVe5zuOV3niIPA3\nwLy031uNd0A5MJvtxOUHr+KQm+HnwZk+P7yygf+KV5nrHN6CYe3AD/HWM7Go32sBP8Os3ru+g9N+\nllv8z+YwUDnN7yX2e5hBnz3ve4U33e8e4CzQDzyDdzX0vM8Y7+TbAbdNsf+Mt1WqP9l8hnirsc/0\nN/LjmXyGwG8D/w4cAHqAQeAQXrWuV0T9uRTo88v6Pes7OGU/fp//3L9msP1Yfwej/tEIiYiIiIiI\nREY5JCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkF\nJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIi\nIiIiEhkFJCIiIiIiEhkFJCIiIiIiEhkFJCIikjhmdreZOTP7r5M895f+c1+Nom0iIkljzrmo2yAi\nIlJUZjYfeApoA650zj3lP34D8APgReCXnHN90bVSRCQZFJCIiEgimdlVwEPAfmAb0Ag8zf9r5w5Z\nuwqjOI7/jghGq0Xb4sAVk9kqC0PwDaztHYhREIPVbBiWsSiYNxDBtip7GWMKx3AXxBfwP+H5fOJz\ny6nfe+5zk4fZYuRqcDyAZfhkC4AldfdlkjdJ9pJ8SvI5yaMkJ2IEYHdsSABYVlVVkq9JXtwdnXb3\n68GRAJZjQwLAsnp7K3f2z9HHqVkAVmVDAsCyqmovyc8kv7PdHblK8qy7b0YHA1iIDQkAS6qqB0m+\nZLvM/irJuyT7sSUB2ClBAsCqPiQ5SPK+u78leZvkIslxVR2NTgawEJ9sAbCcqjrMdnfke5Ln3f3n\n7vxxtl//3k9y0N2/5qYEWIMgAWApVfUkW3TcS/K0u6//e/4yyXmSH9li5XbnQwIsRJAAAABj3CEB\nAADGCBIAAGCMIAEAAMYIEgAAYIwgAQAAxggSAABgjCABAADGCBIAAGCMIAEAAMYIEgAAYIwgAQAA\nxggSAABgjCABAADGCBIAAGCMIAEAAMYIEgAAYIwgAQAAxvwFkvswRoYilLcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1134bcc10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 402
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,6*np.pi,100)\n",
    "#print(x)\n",
    "y = np.sin(x)\n",
    "\n",
    "plt.figure(1)\n",
    "plt.plot(x, y,label='sin'.format(i=1))\n",
    "plt.legend(loc='best')\n",
    "plt.title('Sin plotting')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<br>\n",
    "## 5. Control statements\n",
    "<hr>\n",
    "### 5.1 Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    }
   ],
   "source": [
    "x = 3\n",
    "y = f(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def g(x,y):\n",
    "    return x**2, y**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 125)\n"
     ]
    }
   ],
   "source": [
    "x = 3\n",
    "y = 5\n",
    "u,v = g(x,y)\n",
    "print(u,v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 5.2 Logical control statements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "i = 0\n",
    "while (i<10):\n",
    "    i += 1\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "i = True\n",
    "if i==True:\n",
    "    print(True)\n",
    "    \n",
    "i = False  \n",
    "if i==True:\n",
    "    print(True)\n",
    "elif i==False:\n",
    "    print(False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<br>\n",
    "## 6. Vectorization and efficient linear algebra computations\n",
    "<hr>\n",
    "### 6.1 No vectorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n = 10**7\n",
    "x = np.linspace(0,1,n)\n",
    "y = np.linspace(0,2,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6666667.0\n",
      "('Time=', 4.040402173995972)\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "z = 0\n",
    "for i in range(len(x)):\n",
    "    z += x[i]*y[i]\n",
    "end = time.time() - start\n",
    "print(z)\n",
    "print('Time=',end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### 6.2 Vectorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6666667.0\n",
      "('Time=', 0.01205897331237793)\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "z = x.T.dot(y)\n",
    "end = time.time() - start\n",
    "print(z)\n",
    "print('Time=',end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Speed of vectorized codes maybe 2-3 orders of magnitude faster than unvectorized codes.\n",
    "\n",
    "Vectorized codes (with vectors, matrices) benefit from fast linear algebra libraries (BLAS, LAPACK) and adapted architectures for CPUs, multi-core CPUs, and GPUs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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