{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Libraries for data analysis and plots\n",
    "\n",
    "**NumPy**: for numerical data, NumPy arrays are the more efficient way of storing and manipulating data, ndarray\n",
    "\n",
    "**matplotlib**:  most popular Python library for producing plots\n",
    "\n",
    "**SciPy**: a collection of packages addressing a number of different standard problem domains in scientific computing.\n",
    "\n",
    "**pandas**: flexible data manipulation capabilities of spreadsheets and relational databases, dataFrame\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy\n",
    "\n",
    "* a powerful N-dimensional array object\n",
    "* sophisticated (broadcasting) functions\n",
    "* tools for integrating C/C++ and Fortran code\n",
    "* useful linear algebra, Fourier transform, and random number capabilities\n",
    "\n",
    "Besides its obvious scientific uses, **NumPy** can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows **NumPy** to seamlessly and speedily integrate with a wide variety of databases.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3] [4 5 6]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "#generation of an array\n",
    "#vectors\n",
    "vector1 = np.array([1,2,3])\n",
    "vector2 = np.array([4,5,6])\n",
    "print(vector1,vector2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.]\n",
      " [ 1.  4.  5.]\n",
      " [ 5.  6.  7.]]\n"
     ]
    }
   ],
   "source": [
    "#matrix\n",
    "matrix=np.array([[1,2,3.0],[1,4,5],[5,6,7]])\n",
    "print(matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elements of an array are all of the same type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arrays enable you to perform mathematical operations on whole blocks of data using similar syntax to the equivalent operations between scalar elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.ndim   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.shape   # a tuple indicating the size of each dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.dtype    # an object describing the data type of the array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a number of other functions for **creating** new arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ident = np.identity(3)\n",
    "ident"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)   # an array-valued version of the built-in Python range function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1, 2, 3], dtype=np.float)  # you can specify the datatype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([b'1.25', b'-9.6', b'42'], \n",
       "      dtype='|S4')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings = np.array(['1.25', '-9.6', '42'], dtype=np.string_)\n",
    "numeric_strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.25,  -9.6 ,  42.  ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings.astype(float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Operations between Arrays and Scalars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 2, 3]), array([4, 5, 6]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1, vector2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 7 9]\n"
     ]
    }
   ],
   "source": [
    "# somma tra vettori\n",
    "print(vector1+vector2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4 10 18]\n"
     ]
    }
   ],
   "source": [
    "# prodotto tra vettori/matrici (elemento per elemento!!)\n",
    "print(vector1*vector2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32\n"
     ]
    }
   ],
   "source": [
    "#prodotto scalare\n",
    "print(vector1.dot(vector2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  5.]\n",
      " [ 2.  4.  6.]\n",
      " [ 3.  5.  7.]]\n"
     ]
    }
   ],
   "source": [
    "#trasposta di una matrice\n",
    "print(matrix.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.25, -0.5 ,  0.25],\n",
       "       [-2.25,  1.  ,  0.25],\n",
       "       [ 1.75, -0.5 , -0.25]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#inversa di una matrice\n",
    "from numpy.linalg import inv\n",
    "inv(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.00000000e+00,   2.22044605e-16,   5.55111512e-17],\n",
       "       [  0.00000000e+00,   1.00000000e+00,  -1.11022302e-16],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# prodotto matrici\n",
    "matrix.dot(inv(matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [0, 1, 0],\n",
       "       [0, 0, 1]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.dot(inv(matrix)).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basic Indexing and Slicing (creating sub-arrays)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "subArray = arr[5:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 12, 666,  12])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subArray[1]= 666\n",
    "subArray                     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   2,   3,   4,  12, 666,  12,   8,   9])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr              # Important distinction from lists: subarrays are views on the original array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 666, 7]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lista = [  0,   1,   2,   3,   4,  5,  6,  7,   8,   9]\n",
    "sublist = lista[5:8]\n",
    "sublist[1]= 666\n",
    "sublist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lista"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [1, 4, 5],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix[0, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.,  5.],\n",
       "       [ 6.,  7.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix[1:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.76272564,  0.7954443 ,  0.69589486,  0.10098095],\n",
       "       [ 0.5480459 ,  0.06034182,  0.72958103,  0.2511865 ],\n",
       "       [-0.59294382, -0.74146416,  0.76937381,  0.07666637],\n",
       "       [-0.42471613, -1.39515152, -0.03012301,  0.11994199],\n",
       "       [-0.45952758,  0.1234292 , -0.69791327, -0.96443499],\n",
       "       [ 0.27059413, -1.01364169,  0.23803428, -1.01708924],\n",
       "       [ 0.98327203, -0.44501003, -1.11012779,  0.14849479]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = arr = np.random.randn(7, 4)    # generation of some random normally distributed data\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "bollArr = names == 'Bob'\n",
    "bollArr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.76272564,  0.7954443 ,  0.69589486,  0.10098095],\n",
       "       [-0.42471613, -1.39515152, -0.03012301,  0.11994199]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[bollArr]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.7954443 ,  0.69589486,  0.10098095],\n",
       "       [ 0.5480459 ,  0.06034182,  0.72958103,  0.2511865 ],\n",
       "       [ 0.        ,  0.        ,  0.76937381,  0.07666637],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.11994199],\n",
       "       [ 0.        ,  0.1234292 ,  0.        ,  0.        ],\n",
       "       [ 0.27059413,  0.        ,  0.23803428,  0.        ],\n",
       "       [ 0.98327203,  0.        ,  0.        ,  0.14849479]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data<0]=0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sin(0)= 0.0\n",
      "cos(0)= 6.12323399574e-17\n",
      "Pi greco= 3.141592653589793\n",
      "Nepero's number = 2.718281828459045\n"
     ]
    }
   ],
   "source": [
    "#funzioni\n",
    "print('sin(0)=',np.sin(0))\n",
    "print('cos(0)=',np.cos(np.pi/2))\n",
    "#costanti\n",
    "print('Pi greco=',np.pi)\n",
    "print(\"Nepero's number =\",np.e)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -1.00000000e+00,  -9.00000000e-01,  -8.00000000e-01,\n",
       "        -7.00000000e-01,  -6.00000000e-01,  -5.00000000e-01,\n",
       "        -4.00000000e-01,  -3.00000000e-01,  -2.00000000e-01,\n",
       "        -1.00000000e-01,  -2.22044605e-16,   1.00000000e-01,\n",
       "         2.00000000e-01,   3.00000000e-01,   4.00000000e-01,\n",
       "         5.00000000e-01,   6.00000000e-01,   7.00000000e-01,\n",
       "         8.00000000e-01,   9.00000000e-01])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#array equispaziati\n",
    "np.arange(-1, 1, 0.1) # 20 equally spaced points with step 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.        , -0.89473684, -0.78947368, -0.68421053, -0.57894737,\n",
       "       -0.47368421, -0.36842105, -0.26315789, -0.15789474, -0.05263158,\n",
       "        0.05263158,  0.15789474,  0.26315789,  0.36842105,  0.47368421,\n",
       "        0.57894737,  0.68421053,  0.78947368,  0.89473684,  1.        ])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-1,1,20) # here wix fix the number of interval, not the step\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mathematical and Statistical Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.32405277,  1.05552548,  2.40570979,  1.40748301, -1.46633919])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5) # normally-distributed data\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.287758987649 1.43879493824\n"
     ]
    }
   ],
   "source": [
    "print( arr.mean(),arr.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2877589876489331"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2485150507560063"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.69586742,  0.22304061,  0.22611136,  1.15068924,  1.53482114])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Example: Random Walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QBq+aQiEVCQ0/+UM4+fj0bw/Gt51U94VhUmGXhv8nAOdbtN+nLXto07UYDYFQFF63Q10u\nBL2RzKN/iMhS+85UJw2EIknHo9Vsi6XhZ4ryQMpkkpXROmRcN94HduIyuWKLwBdCvAOAa9YWgWA4\niuGyk69QKXWzdQb7LSYl9WaglSqJ4NTxhI2abeLBY3dqBbsx2vCtyOS+uhxkekvguHwmVwptw7+J\niFbIJp8B6XdnsmFTZxDzN+7DkAYPAKnMXiESbmWrUVoVJvnBsytNNnkjSiK4liavfN2EoNt+QJ+i\nIV2UTLHxuJyocTnSpIiQxicMt0V7+6JxgYfe2qTbbqevhqkuCvmreRjAEQAmAugA8BurnYjoeiJa\nTESLOzs5b0g2fOuvUr517SzXJZ8ctP06mQqYH188HgDQNqgeE0c1odbt1G1Xin8nv44kHJWwRG0E\n0vc16YYvP2lE2iiZUsDvcZnu3aD6GnVZ8bkYTWY/+cxxuPeKE3HXpcdbnpdNOkyuFEzgCyH2CCFi\nQog4gEcBTEmy3ywhRLsQor25ublQ3alIIrI2X1eTEKx2xG8IIeB0EL41/Ug4KLUdOiQLq1vPOxpf\nmzYGgJQt8t83nI4Xbjxdt2+66BIlEdzwRknD15ouonFprM1+D+69YmKWIyoOSooJ7f38wQXHqNu1\nk8yOGupTUzsMb6rF5SeNxFVTR+vO9//OGivtXwLOeaY8KZjAJ6IWzeplAFYl25fJD4dG243G8hf5\nvZEYYnGBBjk7ZEo7tCx8rFMKuy33TYai0Q9vkjR87XVJjlwxvjWUMj6vC8FwFKFIHLG4gN/r1vk3\nFO0/GI5mlBuoRb0vbNJhcsOWUAciegrAdACDiWgHgJ8AmE5EEyEpnVsBfMOOazEJInGzvT5oQ94V\nRdD6vS74ve60qYqVfY0Y29IJfEWjVwSb1VjKwJKj4ve4EQhFVAHt97p0ufKDqoYfxUCNqScZLRZv\nPgyTDbYIfCHEDIvmx+04N5Mcqx++1u69cW8AXrcTIwfUZXXeZdsOAZBmzPq9Lrz28W7cEzsBbos8\n8UofrGa+ak1NgHYWbQTrdgfQ3RdDfY0TRw3zY+7qPfjnkh0AgCF+yQn9yqrd+GJ7KzbvCyJchtWf\nfF4Xth/owbLt0v00PgC1mU5bB6b/jIb4vXAQ2/CZ3CntYGYmJYN8HhzsieDzk0fiQHcfNu/r1gmD\n7/z9I4wcUIuHr5qc1Xm/+dclAKTQx3V7AhAC+O3c9bj1vGNM+wZSJDMzOlaVvt345DK8naKwR4Oc\nnnjZtkM48af/AQBMaRsIALjqlNFJjys1FBv+N/6yRF0fN8SvbtcWe0lm0rloQgvmrJAKyzTUumQT\nG5t0mNwo7dg2JiV1NU6ceVQzrpzSite+cyYAvda/PxjG/u6+nM/v87rUkMENe4KW+3SpGr617rD5\nZxfio5+cq+vbsm2pI4mszhUMR9E+egCuO2NMRn0vBRoMWUN9HjdGDazDpp9diBFNtZrc/5GkE8ke\nnDFJXfZ73JKJjZ22TI6wwC9jAqGoWqzD7XSgrsZpSpecz+u/3+tCjRzvnsx2nsheaa2hOhwEv8cF\nosTbQLqQSiuB33G4F4217rIIx1TweVw6ga8IdadDmo0cDEXRF40jHI1bTlYD9PfK53XlVVyGYVjg\nlzGBkL7Un1bAxOMCwb5o1k5cIbTpC9zwppnglMqko+BwkGSKyFAztZq4dbAnUrT8Obni97qSpoNQ\nBHeqKCcj2gcFw+QCC/wyJhCK6PLCa7W/7r4ohMjewadNX+DzuNJq1KrTNl1BkDThnZlQ6vlzjBjv\niV/j2FaKxCTuX2apIqQHJ9vwmdxggV+mqKYAjVDxyfbdtplzcMIdkrNTmfiTKVqTkM/jwrEtkpMx\nLoAnF25D28w5uOyh9wAAJ9zxGn7z+noAsIzg0bI3EMY/l+xA28w5ONybm8Cyu45toTH2V/sAUJyv\n2VbwqqtxYdXOLt19PNDdh5PufB1L0/hGSo3fzd2Atplzsvp+MvnBAr9MUUwBWpNOg9eFLoMwjcUF\nQpHMQxoVjfPLp7TC6SA8cpWU+10I4LF3NwNIhG1mo7FHM8jhfs2po/HSTdMAAO9+/1Om7ckcw6WK\n1i4/Y0qrzlSlvI2p8xhSjO3N701X74vQzKXuONwLANhxsAcHuvuwfnfy4uilyH1zJWUhk1q/jD2U\n1y+IUUnYzhNapM/jwqa95miaQCiC2prMZqgqUTefHj8UANBY58aUMQOl6xXQXzqswYufXpLIHTPK\nIi69WGUNc0WrtZ973FDdNp9X8mkkbPjJ317GDE5UCiOYZ1Vr4/nLkUAoivoye5iXK6zhlykBC9u5\n3+vCnkDYvG8WYXxWAshviDYpBJmYNMrPaZu4h8aHVYPXjb5oHPuD0ueVy9i0cfxA+ebYsWN2OJMZ\nLPDLFKuUBn6v2zJBWTaan1XUjWJ+CGtMQ3bbXTMReP4i1bHNFe2YjBqscn87Dod069mgTb6m/V9u\ndJXpm0k5wgK/TFF+3A0Gk44Vl/7+Pay0qCl77+vr0TZzjvr31rq9lg8SJQmYVqC8sWavLeNQyMQh\nW3ZROjWJ/joM0U7KZ/W7NzYAyG1swXAEc1fvwWPvbgEgPQC27uvG3XNWp609UEyEEPjNf9ap65c/\ntAAfyeknAMnvdOdLq001ENLxysoOPCun52CsYYFfplg5bVMJjUvlyBot98vCRuErf/xQkxtH/+YQ\nCEVw5BCf2nbdnxeryw9+KTEbNBn/+OapuvWLJ7Tg4gktGCEnSrNyWhrzwZebSaeh1oWT2wZg7BAf\njtDY4QHzA87jyszHcvtFx6rLgVAU1/15MdbtkZy1wVAUNzy5FI++uwUbO61nRpcCwXAUD8zbqGu7\n5PeJ7+fKnYfx+PwtuOUfH2V13ife34rH5m+xo4sVS3n9ghgVa5NO8o/TaOpJZpIJhCIgAuo12qnP\n40IkJizDKe+fMQkXTxietr8ntw3E1nsuMrW/+NEu3PTUMsu+XzV1NK6aOhrn//YdrN0dKPmyhkaI\nCP/45mmW23KNOBreVIu1d56PY/73VXOt23AE4ahkdktXe6CYpPMHKX3vi2aXME+KeipPs1Z/wRp+\nmaJq+AYbfqYkK0weCEuzd7VpfBWH465Dvab9U4UTZoLS/1QC0J/BPuVGPuYpr9uJGqe5fKJ2Bm5P\nBjWEi0W6mcLZCnr1vJqoJ8YaFvhlSlcoghqXQ2cKyEYgJnPkBkJRkxBXHiShSBzGrAf52tWVh0mq\nh5WyrdxMOqnI975JfhW9Nqv9TEvZEZqub7lq6cq8Bp7IlRwW+GVKIBQ1hfopQiRZNoQVOxKOseQC\nP2KeIepJ/haRrxBWzpdKAPq9LtS6nWln85YT+c4a9ntdmGdwnB/qjWCjPA9j2bZD2CeHfAoh8MHm\n/WkF4dvrOws+W/fDrQewcMt+y21KP5Xv5vLthyydz4FQBKt2moMQgqEoYnGBt9d3YtXOwznP6K5k\nKucXVGUEDYnTAI0mXOPCyAG1JiH62QffQ3dYH8pnOm84as4Bo1k/Y9xgy2vmylC/F3U1Toxprk+6\nz5jB9brJR5WA9rNrlgu+ZMMn+3uwSw7pVDigSYV9/xsb8Ol73wYAvLiiA1fO+gDPLt2Z9HybOoO4\ndvYiXP7QgoLZ/z/afghf+MP7+OWr6yy3K/3844KE43X2e2Yn7HVPLMbFD8zX9TMUiaFPLpLzlT9+\niIsfmI9rHl9o8wjKn8p5R64yrDRx1dbtdeGt700HIOXA+c4zy9UiGsGwNKtRsXU+8bUpmDx6AB6Y\ntwGPvL0ZB7sjGNKgF0DaB8ApRwzCYJ8Hf1qwVdqWp129sc6Npf/7aXhSZOW86axx+Nb0sXldp9So\n0YzXKo2EHRzskR7qW/d1AwC27EseuXNQ87AIhqJorLPfQb6nK2Rq+92VEzF3zV58uOWA2s9VO7vU\n7ev3mNNFLNxywNRPqzfWjyxCkasdWzR8IppNRHuJaJWmbSARvU5EG+T/A+y4FiMRDFtp+C71v8vp\ngMvpQI3LoZYMBMzT8Ic2eODzuDDUL9VL3d0VMj1IGgwzRrUaqR2OVK/bmTIrp9NBOgFZaXhLoDC7\nVlvuz2ycA+tr0Ozz5GS31/aTnbWZYdev6E8Azje0zQTwhhBiHIA35HXGJqSyeHphW+t2winnntei\ndcIqPyxjvL2ixR/o7jMdb8y5r6zX1zgtc9czpQWp/5N/Vt2aqJ5C5eSJxMymIqVucndfDHELH0Oq\nPmv7yeGYmWGLwBdCvAPggKH5EgBPyMtPALjUjmsxElZ1UIlI/gEZTT1u3XEANGl5pW1aB7DRGWwM\n/fRnEFnDlA6K8q7NtGlEKzwLpS1bCeXaGqf6fbIK18y4zyUclVRKFPI9eagQokNe3g1gaKqdmeSM\nve1lNf2BQrI6qE11bjTVJY+kuWb2Ihzo7sNdc9ZI2xQN35M8RYPb6UCtbHbwexMafrmlOqgkxmlm\nPQNATZIIptv+tVJNQxxOkSZbKzy/8If38+/f7S/j7jmr1fVv/W0JZj630rRfrTsh8K0S/xmV/ueW\nJlInXPFIop/JQj3bZs5BOJpZ+uVrZy/CrHc2ZbRvudIvhlEhxYNZPqqJ6HoiWkxEizs7O/ujO2WH\nMZe8EALBsNmkAwD3XnEivn3OUbo2434bNI4wxSSTbsaudoJUJcbFF4PXvn2mmuc+W57876nq8q3n\nHY0/fvVk6/0WblOXU5lq7DTjCCEQiQk8+m4iwubllbt1+/y/s8fhkasnY/SgevX71GExsc84QfAP\nb1sL5FRvJYd7MjP3LN12ECsq3NFbyF/sHiJqEUJ0EFELAMtsW0KIWQBmAUB7ezvPmEiDVNAkhriw\ndphOHj3Q1GY0vVgVnDBm3bTa3hkIo8Hrht9rzsXPZM/Rw/w5H6t1nF82aURGs1NTCUXjJK5oLA5X\njvMeMim485kJLRg3VBq/8j3uMISZThjZmNa8FInF4XY6UtrwuzMosKIoUZXu/C2khv8CgGvl5WsB\nPF/Aa1UsxskyUtbK9EUztBgfDJ0Wr85abd0qakRx/NZ7Eq/g+aZVYOzB53Vl9LbVlUIoBkJRXSRU\nPoIvEweqrt6CkrrjcELDdztJV6M5GUFD1Fmu/enui+VUA7rcsCss8ykA7wM4moh2ENHXAdwD4NNE\ntAHAOfI6kyVhg+YWCEUsc9anwrjfTotX53SJyfxeN+pqnHA5HRnNjmX6D1+NK6PPIpUwC4aiaPaZ\nw3dzIZO0DlZvlFrdxuVwwOdxmZyxxjcZpZ/BcBRet7U4y2Qs5V5TIFPsitKZIYRoEUK4hRAjhRCP\nCyH2CyHOFkKME0KcI4QwRvEwadgfDGPyna/r2q55fBE+fd87ADK3oRtDJ39nSIsMIOXEJ0Afjmn8\nzxQXh4MySq+8fPshnf9GS5chzFeZWJctmzqDOEee4QsAp98zD794da1pvzpNyc1kDyslLXc0Fsfd\nc1Zj/Z4Atu7X58hXYvEDoYgu8EDLlx9biM89vAB90Ti6QhH89MXVCBl8A8qDpdKjfSp3NksFcNec\nNSb742Z5NiKQeY3X0QPrcOEJw0wC+vYLE7nViQhnHtUMAJh+dLPpHBdOaMGVJ48CIM0S/dIprTjr\nmCGZDYQpCH+46iR89fQ2df3qqaPx6DXtePK6U0wpMBRmPGqdbiAYjqDB68b4lgYAwOM55pX/6h8/\n1K3vPNSLh9/SO1pnTGnVTbSzEvh/+urJqknn3Q378Oi7W3CurOgAkskH0E8kbPC68L1zj8KZRzWb\nxr/kk4N47ePd+P2bGzH7vS14ZvF23fauDExDlQCraCWMVgu58VNj8eCb+qIRyTQaIy6nAw99eTLW\n7wnofjRfnzZGt9+fvzYl6Tk+e6I+5/3PLjsho2szheP841tw/vEt6vqdmoIxp40djCseeR+L5DQE\nF01owZwVHWouJSOBUBRDG7z40cXH4rMPmovlZEqy8yuMHFCLn1+u/+7UanxGZx8zBI9/RYo4em/j\nPgT7omqOHC3P/s9p+OyD7+ls+H6vCzeeNU7d51BPHyb+NPGGHIsLNTTVOAlM8VkE+6KIx4UuPXgl\nwRp+mTBcrgylJVsbulHDr9QvNSNBFstWs1mBhMDM10yXLszOKoOGVtvXbvd73RDC+iGi2P0Vk45V\n0j9jHeFwL92VAAAeiElEQVQU2TtU270Q+lnHlQYL/BJG+9tsafKatmcr8NnJWl0Ii2VjEICCMq9D\nGz2TSyGSdIVX0qWq125XBPheQ1SZx+VQH0zaQu7GIvfGdNra8Rij3/RpGljgM0VmcL05ha62DGEm\nZLs/U7l0BsJqkXAhhOr01CoFuYRmZhKDnylKX6wmZCnb1u8JoONwLwIhs4ZvZO3ugBqSvHirPu+/\n1llbybH4LPDLhJEDzCadbE0ybMKpLi6ekLDvf/pYKbOJEh1z8t1zccYv3wQgaf2RmIDf69JFa+US\nojjYV5Ny++dOGply+3nHDVOXFS3emPd/xpRWeFwOuJ2Ev36wDaf+fB6CFskEjTw+fwvmrJSyvbz6\n8W6s3Z1Iw6wdayWHZrLKV8L0xeI4YnA9nr/xdN2r9rxb/gstjeYHQDYUKgc7UzpcPXU0Lp4wHPUe\nJzwuJ/69fCe2Hegx7ZeYyOcCEeF3V07EzU8vz8m0Majeg3FD/Pjq6W24/i9L1PaLTmjBLz8/Qeeg\n1bLurvPRHY5hYH3igaGmXDis1/B/fPF4EBH8Xrda9CXYZ04mCABr7zwfgVAUJ98917StMxDGMfLz\nJRBmkw5TZAKhCIY2eE1f5NGD6lFbk18Ode0Pi6lMiAgD62vUGP2WRq+lMFNMGIqGrKRtyEXwBUIR\njBhQiyENep+Tz+NCvceV9C3T43KavpMNqklHr+E7LPI/CWE989vrdqLZ78FgX+qqYmzDZ4qOVc57\nwDyRKhfq8nxgMOWHz+MymSvicZGYuS07PZX/ORUlCSnOX/33NlWa46T9lc+xX1ONS7c9SQEgK6y2\naXNKBUIR9QHDAp8pCpk4onIlVYUppjLxe90IReKIaOLag33RRDEcTcU0IHvnZTwuJNOKx2VLnqV0\nuaKMYZepfisuCyXJ6KhVQp+NieQqCRb4JciMWR+gbeYc7DzUmzbHDcNkiqIR/+hfaiVS/GzOGnzp\nMWn2rd8g8LPVdLv7opJpxes2CeuhDeaw4nTUuZ2m2HmtD8Bp2JjqAWGl3+gdtVHVDPWzl9dif1CK\n5lF+i20z55hCOTMlFImhbeYc/HPJjvQ7Fxh22pYg72/ery5rX1tf+/aZeWsfc7/7X9gXNGfLZCof\nRZD/XZNW4OkPE8uKKceXo4av9QXU1jjxyNWTMam1CW+v68RnJw5Pc7QZh1yuMxCK4tiWBpx6xCBd\nKgkjmc4zOW54Az7e1aUbXzAURevAOnV9TUcA08Z5dL/Fnr6Y6a0iE5RQ0PteX4/PT04dpVRoWOCX\nOFp7fT750xXGDvFhrKFaElMdpDORKALT43KixuVImU7ZioDBNKSEWH6hfVS2XU30SRb4Rw/14cef\nGZ9230w4fngjNuwN6t5gjMnjrAiEojkJfGOitmLCJp0ShyvCMHaRTqDpahd70ueiNxII2V8YJ1V1\nNaMjONV1tdYYAYEGr0uXxjkYjuhnGcfMQjrXt+tM0kX3FyzwS4xc7YQMk450Al+bisDvNeeiT4eq\n4duYNjvhV0j/EMkmwMHncakmnUgsjlAkruu31cMuV8FdSjN3WeCXEIFQRJdLHNAnwGKYfMhGEPu8\nLizcsh/n3vc2VmrqvL63cR+eX77T8hhFSGaatjvTfgDWfSfDr6M+Raix1mlLINTVuPDiR7vQftdc\nLNgk2em1D8RAKGpSvi5/aIFudm4q7njhY9z89DIIIfCAXH9i56Fe1RlcLFjglxD3v7EBmzq7dW1f\nPqW1SL1hKo1sTC1+jxt7usJYvyeIzzw4X22fPX8LfjfXXEAH0Dpt7TfpWD1EfvyZ8ThhRCMA4NiW\nhpShxr/8/Ik4YUQjThzZiBs+NRarOyTBvS8YxrWzF6nX+sH5x6hjMRZQB4CL759vajPSHY7iTwu2\n4vnlu7BuTwCLP0nk7fnxCx+nPb6QsNO2hDB+wc47bqhpxiLD5IpWg/1i+yj8Y8l2xJNYEJOZRwKh\naFLThmLDt3PuiFpdzeKcx7Y04MWbpmV0nomjmnT7Ogimsfs8LnzupBH49X/WyaVEpXFqa1FEk90w\nDVoTzuEevd2/N4OC6oWk4AKfiLYCCACIAYgKIdoLfc1yhc33TCHRJkYjkgRcMuGdzN7fpampbCQQ\nioIotWklWxTN3pj6OF+sxt4g5xJSQkGVcVqlJk+F9v7sMaR2LraPrr80/E8JIfb107UYhrHAaPLw\ne91JBX6yCX/BcBThaBx90ThqDHWQA6EofB6XrbO4U2n4+eBymq3ZWn9BMBRVNfxhWb5lax2+Vqmd\niwnb8EuEjsO9auY/hukPUkXtGJ2kHYd7sS8YVoWZ1mzR0xfFps6gXFfWXk3cOPu3kCj+Ar/XhTfX\n7cUK2VndWJvdmHQC35Da+b1N+/H2+s6imXb6Q+ALAHOJaAkRXW/cSETXE9FiIlrc2dnZD90pTU79\n+Ty8smq3ru1TR3ORcKYwnD52sE6IGgvSGwXsqT+fh/a75iZqv2qE2v/8dSnO/s3bONwbsV0wtw6q\nQ43TkVNqhlRcNmmEqU3p+/YDPTjYE8FPZAdrtk5o7cNwl0HD74vGce3sRbj56WXZdtkW+sOkM00I\nsZOIhgB4nYjWCiHUStpCiFkAZgFAe3t71VuxB/s8eOXmM+ByEJrqOI8OYy+rf3oeunqjGNboxXNL\npdwu98+YhAuOH6bbT2tCaax143CvZJeOyU5L7Szct9dLitqerpCtMfiApPQsvO1sDLA5nfdtFx6L\nr08bgztfWq0qWkrfuw3at8/rwqr/Ow83PrkUazsCac+tteErGv6/vnUaLntogdr+zobiKLcF1/CF\nEDvl/3sB/AvAlEJfs5wZMaAWzX4PBtTXcEZLxnbqalwY1ihpy4rmOrzRa6r/qtVqrSYOWU1M2nWo\n13YNn4hsF/aAlLJkeFMtjmyW0ozUOB3wyonZjKnDleLuRwz2ZZQyWm/SkTR8Y8GiDIJ9CkJBBT4R\n1RORX1kGcC6AVamPqj60nns70soyTCaoTkoLIV2jeQDELKST1UNgf3cffGWW3dVvcQ+8hqpcSi1o\nv9eF7r6Y5f3Qop1xvC/Yp7uOQi4F4u2g0NJlKIB/yZqqC8CTQohXC3zNskP7CtkfzimGAVKnLUj3\ncplM0y2376+xBgBgnt3uNFTYCoajKR25SrRSY60bwXAUDiqdgkMF1fCFEJuFECfKf8cJIe4u5PXK\nFa0DzG4bKMMkQxFaVrNYle9hsjfO7z7zkaWWWm4CXxuZozBKkyZZv29maaOD4Qh8nkTVLyVU1fiQ\nmLt6T879zhUOyywBtNqSMbaZYQrFFyaPwv0zJllq+KcdOQj3XH4C7vnchKTHH+o1hxGXm0lS6a9W\n0Xr0mnYcP6LBvK83s9KPxjKPynEv3TRNFx30wDzrFBWFhKVLCRAooWx6TPXQ7PfgsydaFyYhIlw5\npRVDG5IX/+4Om2PJa2vKTOBbmLWa/R48OOMk077KQyFd2mhF4KtvSfI1Rg2sw31fnKjWoyiG35YF\nfglQyUWTmfIm1QxXq/TJ5RZXppp0MqiPq5p00gn8cBQ+TZlHo5nLWJqxP2GBXwJov0AcicmUEqkm\nHQVCkaJFm9iFldPWal3blq4SWCAkTUBLltpZ+Y0XI60OC/wSIJPYXoYpBqmCCALhqMmBWW4KS7JI\nJY/LHFWj7PPn9z/BMf/7Cv7+4Tbd9lhc4Ia/LcXmzm74PWYbvpHuvv5/s2eBXwIoJp0RTbW4btoR\nRe4NwyTwe1y6usrHtjTgwhOkWbmBUNRk3rh4QvbFyouJr8aFC44fhtOOHGTadt5xQ/GbL5yorisC\nfMknBxGKxPGDZ1fq9p+/cR/mrOxQ9/UnSfx216XHAwCafcn9I4WivDwsFYritH33+5+Cw1FmKhJT\n0TgchE0/u1DXdqC7Dy+v3I1AKKKaNx65erJatLyccDgID1812XLbI1frM7nXup1wOijpxCutecvl\ndCS14be3DcQZ4wYXpfQha/glQCAkxe2ysGfKAa3zUnk7LbdwzFwgIlOuf63wN+a6TzWXwe/Nvki8\nHbDALwGCchgXw5QDbqcDXrdDZ8O3s6xhKWPMOaQ1aRkr1qWy4fs97qL47ljglwDKVGyGKRd8Hjd2\nHerFvLXSbNFqVVgC4YTQNppokpl0AMmuny68sxBU56dUYgTDrOEz5UWD14WXVnSo63ZXpCoXtGYZ\n7fLk1gEY3uQFkRSMYUSbiM3Zj6bc6vyUSoxAKIKmOvtTwDJMoTAK+GpRWBQr/VnHDMG8tXt1Ql7R\n2N++dTpGD6oHACz84dkYYlG8RXmjT5eIzW7YpFMCSDPzquMHw1QGRgFvFbdeyShhnEGNSScQiqDB\n61KFPQBLYQ8kagb3tx2fBX4JINUCZYHPlA/V6nNSjC9KQROdSScczdh5nWnmTbthgV8CKGGZDFMu\nVEtUTjJamiTN3WjDz9S0pbzR93doJgv8IvDwW5vw4+elwl8/f3kNQpF41f+AmPKiWhWU4bIDdohf\nmiVrtOFnKvAzTbVsN9X5qRWZBZv2YduBHgDAI+9sBlA9Ti+mMtCaIJ/871OK2JP+5bFr2/Huhn0Y\n0VQLp4N0AjsQjmCI39pmbyTTVMt2U3ANn4jOJ6J1RLSRiGYW+nrlgFUOkmrVmJjyRJmA9K3pR+K0\nIwcXuTf9x9AGLz4/eSSICH6vS2eDz2Y+TUMlmnSIyAng9wAuADAewAwiGl/Ia5YDgVDE9EHXlVnh\nCIapdozpEbIx6fgq1Gk7BcBGubZtH4CnAVxS4GuWPMFwFH2xOMLRxFTscksryzDVjs/jNjltMw2v\nVhKxVVpY5ggA2zXrO+Q2W/lkfzdmPrsC63YH7D51QVC+JFzpimHKF0nDlwT2gk370BeLq/H16VBN\nQpVk0skEIrqeiBYT0eLOzs6czhEIRfH0h9uxdX+3zb2zn2gsjp4+SbPXCnyrfNwMU6pcPnkkhjd6\nceXJrcXuStHwexImnS89ulBqyyL4wufp/4yZhRb4OwGM0qyPlNtUhBCzhBDtQoj25ubmnC7iL5ID\nJBe0hZ8PdIcBAN879yhOrcCUFSOaarHgh2ejdVBdsbtSNIxOWyC74Au/142uChP4HwIYR0RjiKgG\nwJUAXrD7IsWKac0FbT3MjsMhADyJhWHKEZ/GpKOQzW/Z73HpUjP0BwUNDRFCRInoRgCvAXACmC2E\n+Nju66iJiMpAw9dqBB2HFIHPEToMU274vW4Ew1Fd4ROvO3Md2u91YXdXqBBdS0rBJY0Q4mUALxfy\nGjUuBzwuB3Yd7sX+YBiDilArMlO0Zqddh3sBcAw+w5QjPo8LkZhAWFPakJB5uJ3f68LGzsoy6fQb\nfq8bTy3ajsl3zS12V1KifQVMaPhs0mGYckOZPKU10w5vymymLaCYhFjg50S5mEV0Jh1Zwy+XvjMM\nk0BR1PYF+gAAV01txRHNvqyOr7qwTLsoF6Gp9crvZBs+w5QtiilWUdyOHtaQ9fF9sThChlq4haRi\nBL7WDm6sHl9KKE90v8eFfUEpLJNNOgxTfiiK2i452i7bmhbFyKdTMQJfqyUbq8eXEoFQBC4HYbA/\n4Vhmpy3DlB9KGoWOQ7kFXxQjn07FCHyfJ6El/+GtTbj09+8VsTfJUYokKA8oj8uBGlfFfAwMUzUo\naRQeemsTgOzf1P2e/p8/VDGqpVZo3j9vIwDJtEMllpUsKNevVbQBtt8zTHli1Oiz1fDVMods0rGH\nUjTtBEIR+D1u9cNm+z3DlCfGzJjZKm8+NayTBb4tlOLM24RJRxL0bL9nmPJEKQKjkGmmTOP+/WnS\nqRiBb2W56e/ERJmgCHw26TBMZVHvcWa1v5oShp222WMVifnvZTvNjUnYdagXz3yYSN3/1rq9WLrt\noB1dAyD5E3764mqs7uiC3+tWQ7JY4DNMZeByZidOFZPO/724Gh9s3l+ILpmoGIF/7WmjTW0Pvrkx\n4+OfXbID3392hfq0/cofP8TlDy2wrX8f7TiM2e9tAQDU1jjVD1sbXcQwTHkxZcxAAEBdTXbaPaA3\nCV056wPb+pSKilEvjxnWgE0/uxBH3pZbnjYlH0YgFCmIXT2scSA7KOGsZQ2fYcqXZ75xarG7kBUV\no+EDgNNBJmGd6axbRbMvlKM3Ftf3w88mHYZh+pmKEviAOeqluy+z0EzFwdsVipqEsx0EklTGYYHP\nMEx/UXEC3yhAM9XYE4XFI7qiBHYlNtL2QwitSYdt+AzD9E8OsIoT+MbJEJnGuAbl/YLhKE6/Z57a\nfsUj79vSL20/Jo5qwtAGD4iAYY2Z589mGKZy6cnQGpEPFSfwFY35guOHATCbUpKR0PD1+6/YcdiW\nfik+gn9881R8fvJIjBxQh3m3TMf0o3Ir3M4wTPnz0U/OxRcmjwTQP1kzCybwiegOItpJRMvlvwsL\ndS0tiknnpNYBADK/iYV22gZCUXhcDpzcNlDN7zNmcH3J5fphGKb/aKx14wxZ6euPguaF9hjeJ4T4\ndYGvocMvO0Nb5FJjmZp0tDb8QtAlz7BlGIbR4u/HnDoVaNKRBX5jLYDMNPZYXKgafqFuejAcZQct\nwzAmFCW1rE06MjcR0Qoimk1EAwp8LQAJG/5wVcNPfxO7+xL7/GnBVtP2v37wCdpmzsHkO1/Puj//\nWLwdVz22sGATuhiGKW8UmdUfyR7zkkBENBfAMItNtwN4GMCdAIT8/zcAvmZxjusBXA8Ara2t+XQH\nAHDZpBForHVjqN8LosyctlYPhWENXjU880f/XgUA2N/dl3WO/Vv/uQIAMHn0ADbpMAxjwqeWOixx\nG74Q4pxM9iOiRwG8lOQcswDMAoD29va8A1FHDazDtae1AQB8Na6MbqLVk/WWc4/Csu2H8OTCbbr2\nUCSO2hzyZnQGwjhmmD/r4xiGqWz8/VjqsJBROi2a1csArCrUtZLh87oyek2yeigks7fn+hTuONzL\nNnyGYUzU1/Sf07aQNoZfEtFESCadrQC+UcBrWeL3ujKy4Vvt4/e6LFMud4WiGNKQfV8iMcEmHYZh\nTCg5wErepJMKIcTVhTp3pvg8LgQMsa2RWBx/++ATfHnqaDU96VOLtpmOTSacg+Eo3tu4D3sDIQgh\nmXhmTBmVkV2fBT7DMFb4PJlZI/KloiWQ3+vGoZ4+XdvCzQdwx4urMW6oH6ePHYxoLI7/rN4DALhu\n2hg8Nl/KWe/zuPDlU1pND4NAKIKrH1+kaztueANOHNWUQX8q+nYzDJMjA+trEONcOvlhZdJR8t53\n9Ur/u8OJ/BXf+fRRmmPdOH5EIya16gW51VM40wRrXOyEYRgrXr75DNx7xcSCX6fyBb7B8x1QC50o\nE60SJh9t1RpFG3caTDVW9v5k6ZSN2e+Mid0YhmH6kwoX+G6TI0RNoRA2J0vT2uE9LunWGEX5od4+\nGEkW62/MxW98eDAMw/QnFa1y+jwuhCJxBEIRxOIC9R6XKWdOstjXZE7YVTu7TG3BUBSdgTCcDkKD\n16UWM+4PJwzDMEymVLTAV8wyJ989F6FIHJdMHI5B9R4ACWFsfAMYVF+D/d0JLf6UMQOx5JOD6voL\nH+0yXefllR245R8fAQCumtqKuy49wfLcowbW5jskhmGYnKlwgS85SUOROADg+eW7cEW7Pve0ouE/\n+d+nAADm3TIdPZGEZn7LuUdj2rjBOHqoH5Pvmmt5nbfWd6rLzy/blRD48rnvvOQ4HDeiERNGpo/k\nYRiGKRQVLfCtkpUlbPhytI68PrbZBwBorHOjEYloGqeDcNqRg1NeR+e01ViClGuNH96g5udnGIYp\nFhXutDUL/KDBWauYXWxLe6CR/cq5ORyTYZhSoKIFvtNhdrx2hfQCPxiKwukgeN323wrFT8ATrhiG\nKQUqWhIpqRO0aKNz9gfDeOitTQCSR+VkSyAcxUsrduHGJ5epbRx/zzBMKVDRGv6kUU2ocemHqI3O\neXllR1bn+/v1U9Xlr50+BreedzSa/R7TflphD0hpmhmGYYpNRQt8h4PwwwuO0bVpTTnZZq445YhB\n6vL/XnwsbvjUWExKk0PH53HBYWFaYhiG6W8qWuADgMNgqumNxOByELr7YklTImSCYgJK5+xl+z3D\nMKVCxQt8K4Y2ZF7vNh3pBLrHVZW3mGGYEqQqpdGIJmnG672vr8/7XOkEvl3OYIZhmHypeIH/qaOH\nmNpamry69f+ZfmTG57vohBb811HN6rrV5C6GYZhSpOIFfuugOmy95yI8cvVkta2lUZ/T5gfnH2M8\nLCm///JJeOJrU9R1xYb/ldPasPWeizD1iIF59phhGKYw5CXwiegLRPQxEcWJqN2w7YdEtJGI1hHR\nefl1M3+0ppfhBg3fjvMm/uuduMac+AzDMMUiXw1/FYDLAbyjbSSi8QCuBHAcgPMBPERETvPh/Ydf\nk97AqOHngzKpSjHt+OX/g+prbLsGwzCMHeQl8IUQa4QQ6yw2XQLgaSFEWAixBcBGAFMs9us3tBp+\nS6N9Gn6DQbNXrqNMyGKnLcMwpUKhbPgjAGzXrO+Q24qGT2fSsU/Db/ZJD48hsoBXrqNEAk1pY5s+\nwzClQdoQEyKaC2CYxabbhRDP59sBIroewPUA0Nramu/pkqJo3i4HYUCdGy/dNA3bDvRgypj8BHLr\noDq8dNM0jG9pkK8jafpHNNfj1vPPwJjB9fl1nGEYxibSCnwhxDk5nHcngFGa9ZFym9X5ZwGYBQDt\n7e0F83B6XE7UuByor3GCiHD8iEYcP6LRlnNrz6N13h4zrMGW8zMMw9hBoUw6LwC4kog8RDQGwDgA\niwp0rYzxe1wFz1ypOG85Pp9hmFIj37DMy4hoB4BTAcwhotcAQAjxMYBnAKwG8CqAG4QQsXw7my9+\nr0sXrVMIGgzOW4ZhmFIhL6kkhPgXgH8l2XY3gLvzOb/d+Lwu1BU4VbHPEJfPMAxTKlSVVLph+ljL\noih2MmFkI64/8wicNjZ1HVyGYZj+pqoE/gUntBT8Gh6XE7ddeGzBr8MwDJMtFZ9Lh2EYhpFggc8w\nDFMlsMBnGIapEljgMwzDVAks8BmGYaoEFvgMwzBVAgt8hmGYKoEFPsMwTJVApVSCj4g6AXySxykG\nA9hnU3fKgWobL8BjrhZ4zNkxWgjRnG6nkhL4+UJEi4UQ7en3rAyqbbwAj7la4DEXBjbpMAzDVAks\n8BmGYaqEShP4s4rdgX6m2sYL8JirBR5zAagoGz7DMAyTnErT8BmGYZgkVITAJ6LziWgdEW0kopnF\n7o9dENEoInqTiFYT0cdEdLPcPpCIXieiDfL/AZpjfijfh3VEdF7xep87ROQkomVE9JK8XunjbSKi\nfxLRWiJaQ0SnVsGYvyN/p1cR0VNE5K20MRPRbCLaS0SrNG1Zj5GIJhPRSnnb/UREOXdKCFHWfwCc\nADYBOAJADYCPAIwvdr9sGlsLgJPkZT+A9QDGA/glgJly+0wAv5CXx8vj9wAYI98XZ7HHkcO4vwvg\nSQAvyeuVPt4nAFwnL9cAaKrkMQMYAWALgFp5/RkAX6m0MQM4E8BJAFZp2rIeI4BFAKYCIACvALgg\n1z5VgoY/BcBGIcRmIUQfgKcBXFLkPtmCEKJDCLFUXg4AWAPpx3IJJCEB+f+l8vIlAJ4WQoSFEFsA\nbIR0f8oGIhoJ4CIAj2maK3m8jZAEw+MAIIToE0IcQgWPWcYFoJaIXADqAOxChY1ZCPEOgAOG5qzG\nSEQtABqEEB8ISfr/WXNM1lSCwB8BYLtmfYfcVlEQURuASQAWAhgqhOiQN+0GMFReroR78VsA3wcQ\n17RV8njHAOgE8EfZjPUYEdWjgscshNgJ4NcAtgHoAHBYCPEfVPCYNWQ7xhHysrE9JypB4Fc8ROQD\n8CyAbwshurTb5Kd+RYRaEdHFAPYKIZYk26eSxivjgvTa/7AQYhKAbkiv+iqVNmbZbn0JpIfdcAD1\nRHSVdp9KG7MVxRhjJQj8nQBGadZHym0VARG5IQn7vwkhnpOb98ivepD/75Xby/1enA7gs0S0FZJp\n7iwi+isqd7yApLHtEEIslNf/CekBUMljPgfAFiFEpxAiAuA5AKehsseskO0Yd8rLxvacqASB/yGA\ncUQ0hohqAFwJ4IUi98kWZG/84wDWCCHu1Wx6AcC18vK1AJ7XtF9JRB4iGgNgHCSHT1kghPihEGKk\nEKIN0uc4TwhxFSp0vAAghNgNYDsRHS03nQ1gNSp4zJBMOVOJqE7+jp8NyT9VyWNWyGqMsvmni4im\nyvfqGs0x2VNsT7ZN3vALIUWwbAJwe7H7Y+O4pkF65VsBYLn8dyGAQQDeALABwFwAAzXH3C7fh3XI\nw5tf7D8A05GI0qno8QKYCGCx/Dn/G8CAKhjz/wFYC2AVgL9Aik6pqDEDeAqSjyIC6U3u67mMEUC7\nfJ82AXgQ8oTZXP54pi3DMEyVUAkmHYZhGCYDWOAzDMNUCSzwGYZhqgQW+AzDMFUCC3yGYZgqgQU+\nwzBMlcACn2EYpkpggc8wDFMl/H/mJeNVn8IHpgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113da7748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random \n",
    "import matplotlib.pyplot as plt\n",
    "position = 0\n",
    "walk = [position] \n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0, 1) else -1 \n",
    "    position += step\n",
    "    walk.append(position)\n",
    "plt.plot(walk)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib\n",
    "It is a (primarily 2D) desktop plotting package designed for creating publication-quality plots. The project was started by John Hunter in 2002 to enable a MATLAB-like plotting interface in Python. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G86YXUlPpY950H2NSNDtWKrIAYEwS6+x22bFW+UfU3NHksmNN843kxkunsKDc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\nUtT/BxA+8FMZRCBuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114c8b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(np.arange(10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143f1dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.linspace(0,1,10), np.arange(10), 'r--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IBYVcZNPRK4hOYUEEGmOMwYqPomvq1F1zSVdWuoBgvY+NMRn4LT6KXFAQkZVA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\ngoIxxph6/x9faN+L7myo/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1144ad438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(2,1, 1) \n",
    "ax2 = fig.add_subplot(2,1, 2)\n",
    "\n",
    "ax1.plot(np.random.randn(30).cumsum(), 'ro--',label='first')\n",
    "ax2.scatter(np.arange(30), np.arange(30) + 3 * np.random.randn(30),label='second')\n",
    "\n",
    "ax1.set_title('My first matplotlib plot')\n",
    "ax1.set_ylabel('Steps')\n",
    "\n",
    "# legend\n",
    "ax1.legend(loc='best')\n",
    "ax2.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}