001-Loading-Data-MNIST-v1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST Dataset\n",
    "\n",
    "ชุดข้อมูล MNIST เป็นชุดข้อมูลลายมือตัวเลขอารบิก (0-9) โดยรูปภาพมีขนาด 28x28 พิกเซล และมีข้อมูลในชุดเรียนรู้จำนวน 60000 รูปภาพ และข้อมูลชุดทดสอบจำนวน 10000 รูปภาพ แต่ใน scikit-learn นั้นเป็นชุดตัวอย่างของ MNSIT ที่กำหนดให้รูปภาพตัวอักษรลายมือตัวเลขอารบิก แต่ละรูปมีขนาด 8x8 พิกเซล และมีจำนวน 5620 ชุด\n",
    "\n",
    "![alt text](https://raw.githubusercontent.com/yashk2810/yashk2810.github.io/master/images/mnist.png \"MNIST dataset\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "digits = datasets.load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Keys of digits: \n",
      "['images', 'data', 'target_names', 'DESCR', 'target']\n"
     ]
    }
   ],
   "source": [
    "print(\"Keys of digits: \\n{}\".format(digits.keys()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optical Recognition of Handwritten Digits Data Set\n",
      "===================================================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 5620\n",
      "    :Number of Attributes: 64\n",
      "    :Attribute Information: 8x8 image of integer pixels in the range 0..16.\n",
      "    :Missing Attribute Values: None\n",
      "    :Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)\n",
      "    :Date: July; 1998\n",
      "\n",
      "This is a copy of the test set of the UCI ML hand-written digits datasets\n",
      "http://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits\n",
      "\n",
      "The data set contains images of hand-written digits: 10 classes where\n",
      "each class refers to a digit.\n",
      "\n",
      "Preprocessing programs made available by NIST were used to extract\n",
      "normalized bitmaps of handwritten digits from a preprinted form. From a\n",
      "total of 43 people, 30 contributed to the training set and different 13\n",
      "to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of\n",
      "4x4 and the number of on pixels are counted in each block. This generates\n",
      "an input matrix of 8x8 where each element is an integer in the range\n",
      "0..16. This reduces dimensionality and gives invariance to small\n",
      "distortions.\n",
      "\n",
      "For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.\n",
      "T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.\n",
      "L. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,\n",
      "1994.\n",
      "\n",
      "References\n",
      "----------\n",
      "  - C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their\n",
      "    Applications to Handwritten Digit Recognition, MSc Thesis, Institute of\n",
      "    Graduate Studies in Science and Engineering, Bogazici University.\n",
      "  - E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.\n",
      "  - Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.\n",
      "    Linear dimensionalityreduction using relevance weighted LDA. School of\n",
      "    Electrical and Electronic Engineering Nanyang Technological University.\n",
      "    2005.\n",
      "  - Claudio Gentile. A New Approximate Maximal Margin Classification\n",
      "    Algorithm. NIPS. 2000.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(digits['DESCR'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('size of the MNIST dataset', (1797, 8, 8))\n"
     ]
    }
   ],
   "source": [
    "print(\"size of the MNIST dataset\", digits.images.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('target name', array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n"
     ]
    }
   ],
   "source": [
    "print(\"target name\", digits.target_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Shape of each image', (8, 8))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
       "       [ 0.,  0., 13., 15., 10., 15.,  5.,  0.],\n",
       "       [ 0.,  3., 15.,  2.,  0., 11.,  8.,  0.],\n",
       "       [ 0.,  4., 12.,  0.,  0.,  8.,  8.,  0.],\n",
       "       [ 0.,  5.,  8.,  0.,  0.,  9.,  8.,  0.],\n",
       "       [ 0.,  4., 11.,  0.,  1., 12.,  7.,  0.],\n",
       "       [ 0.,  2., 14.,  5., 10., 12.,  0.,  0.],\n",
       "       [ 0.,  0.,  6., 13., 10.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Shape of each image\", digits.images[0].shape)\n",
    "\n",
    "digits.images[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target (y / label / class) from 0 to 20\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"target (y / label / class) from 0 to 20\") \n",
    "digits.target[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample image 0 to 3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
       "        [ 0.,  0., 13., 15., 10., 15.,  5.,  0.],\n",
       "        [ 0.,  3., 15.,  2.,  0., 11.,  8.,  0.],\n",
       "        [ 0.,  4., 12.,  0.,  0.,  8.,  8.,  0.],\n",
       "        [ 0.,  5.,  8.,  0.,  0.,  9.,  8.,  0.],\n",
       "        [ 0.,  4., 11.,  0.,  1., 12.,  7.,  0.],\n",
       "        [ 0.,  2., 14.,  5., 10., 12.,  0.,  0.],\n",
       "        [ 0.,  0.,  6., 13., 10.,  0.,  0.,  0.]],\n",
       "\n",
       "       [[ 0.,  0.,  0., 12., 13.,  5.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., 11., 16.,  9.,  0.,  0.],\n",
       "        [ 0.,  0.,  3., 15., 16.,  6.,  0.,  0.],\n",
       "        [ 0.,  7., 15., 16., 16.,  2.,  0.,  0.],\n",
       "        [ 0.,  0.,  1., 16., 16.,  3.,  0.,  0.],\n",
       "        [ 0.,  0.,  1., 16., 16.,  6.,  0.,  0.],\n",
       "        [ 0.,  0.,  1., 16., 16.,  6.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., 11., 16., 10.,  0.,  0.]],\n",
       "\n",
       "       [[ 0.,  0.,  0.,  4., 15., 12.,  0.,  0.],\n",
       "        [ 0.,  0.,  3., 16., 15., 14.,  0.,  0.],\n",
       "        [ 0.,  0.,  8., 13.,  8., 16.,  0.,  0.],\n",
       "        [ 0.,  0.,  1.,  6., 15., 11.,  0.,  0.],\n",
       "        [ 0.,  1.,  8., 13., 15.,  1.,  0.,  0.],\n",
       "        [ 0.,  9., 16., 16.,  5.,  0.,  0.,  0.],\n",
       "        [ 0.,  3., 13., 16., 16., 11.,  5.,  0.],\n",
       "        [ 0.,  0.,  0.,  3., 11., 16.,  9.,  0.]]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#แสดงตัวอย่างข้อมูลจำนวน 3 ชุด ตั้งแต่ชุดที่ 0 ถึง 3\n",
    "print(\"Sample image 0 to 3\")\n",
    "digits.images[0:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3b11faa10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "\n",
    "pylab.imshow(digits.images[0], cmap=pylab.cm.gray_r) \n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fb3aca48850>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cEP9mF0Gugcx/jN9KGxpu6QZ7cLc8R+8ZeXABh3NuDXJqa6tOVt0sK631j9ZNlj+2JgW3N/INAbR8YB64Weucsd6avPm2tMgc5vPz84NjHtZc1VaYW/IQcPK++HPTnqM1IPL5NW00r5eWm9elZb6d6Vc0aHXtbxnAoz7SV5OBOwJai2u1nB7AEcxZsGVZ2r1Rh9Ng0lxyDjHBzSGXwHuQWq+Sdjv9V0yi69A9eq+6rOcm24r/KyeHm2Bfr9cAYA5gFtTegppWNwKb7s+y2lnAo37uxffRJOC2Rnd53NJRrGMP6q4wew9cux9A/4SatTpO29nZ2QHccstYbhmXhVo7j4Dj96U9R+3Z8TaWYHOgaVU+ehXWB3KrH2luuNU/LLAz/WEMTQJuLg1qHpbHEchDAd4Vcqlozi2h1gDmkMswh1vORb15atc07UcEM1Zba18ONsHN9zSQeJ5E9nWc1p/4+gFt1nTOMybWvWv9e0xNCm7txrtYbG8eHC2SRFC3Ai/vC4ittuaKE8RnZ2fXNh5H+TU4LWCjcJTO4dbm29pgnRlspUtObVNK7tdYeH0yawBaXyK4tT7iPXPPglv9fAxNCm6SNfrxcDR6ZubO1qjspXkd0xvFWwHX3HJuoa1Ns9wetH3TpFtuPSvZLvRLphrMcqMFNQ3uPgtqVp/iYGv9wQLce+4e4GNpknBzZa12BLlnuSPAsyBrx1rnanHLpWsuYb579+61Y7mgNvZews1lubA0l+auON9ofq1BzuG2BiHNgmf7FQebW+4M0C0W+xjK/EDig7j8K6GXArgA8J9qrb84VAW8kS1Ks8CORtzIKmvHXh4PdF5vwP/Kp/YpNWuVnIPN99wt9/ZD5fF+l92DO7LW1sdqS9F/S82y2C1ga4B7FrsF8my/9jyNVmUs9xbAv661fq6U8iIAny6lPF5r/eJgtRDiMGQst9WJNOg9WDMAZ+OsBwr4f2MTWW5pve/evXttI7gjWLMwZ+Lks7OegYRF+08wC+rILed1423M29zrY1r/AQ5/CtsbyC2YtT7Aw2Mp8+unXwfw9X34m6WUpwG8DMDgcGsNboU90Fvm2F3A90Zubc6ttOmBWx7Nt+lVmOaWS7gjmLV5qjV/zQwM8plZgyoPa3+LTC46/+sg3jZkubNWm7e11d80oOk8q0+1WGur72p9fmg1zblLKd8D4LUAnhijMvsyDo67WO8hwPXcykz8anX4u1qeWy4tN3fNNcvN3fG7d+/i29/+9oFbHsGcOdYAknB7z0R7DvL/wLbbrWm5OeTUptZmQW71NatvccutPd8s7LIcr68PrTTc5dIlfwzAo7XWbw5ZCQtozZJbca3Q9xmBtbIjadZFc8k1wK1PrGnAc7c8AjOKy+QFcA1WgpT2HrARyNoe0D9brk11sqCXov+Nk9WHMjDza2l9fWywgSTcpZQNLsH+1Vrrb45bpYOy1TgvPjNYeNI6hdZZMmBonVCbL1rzR+04U7a3afdp3b/WNl67yTyZ+rSszgMI28S65+g4ur9TU9Zy/zKAp2qt7xmzMpYsKD1gM6C3wK7FadbXcxczIGegHgLwFqB5eratJERaWhZ4vgGHn8mP2ku7P+3+56ZVlKGU8giAnwTwD0opny2lfKaU8sbxq3ZQDzdNc4usdC3NU9QBrbQM6C2dtNVadQVdu+9I3jW8NrTazQpLa97aLlqdsvdyasqslv8+APuTCgMpY0U9gOV1vLlyRlqHyHZMrbO1gt0K+FDWvAXo1rbz2tGrfzSt6XO/VCe+n4sm/wk1TRHA1jmZhQ7Adtky1sayMl0A7nKe1smt+xpalhXMDpAa4PL+AJhAt1ptbz8HTQruviuILSuZmfKsTpGBPOOK9wW/a6fuauEy0spsKdfyfvic22qHTHvItpD1nJMmBTfgA6rla70238swkF/xtayGB3jLHNyD3YM+6tRdAe4CuVUmxVuehga1BXc2HIHuhU9Vk4PbU+Z9c+u7yEjaA5cd1AI8A2+UZuXPduAIbHmvEeytgGv5MwOltcnzs20h6yPrNgeYpU4K7qEUAa5B7G0RiBlrnoW4izuq3QO/1wh2q32itsnk0YBuae+WQc6rm3V/p6yThbuLxe5quTMW0JojakB7sLZYaStPVG/tWN6vjOuiFtg82C3LHbn0mcFGq/NcdHJwd5lry3O9lXKS1/GjDulB3meftVKyrt6xlkZx8t5bZIHTOlDKdoyeQ3aa4tVrLpo03NGiWst50XtxS0NanSEseHYA4HXPhulYC0dpsr20tsu0pzY48uOuz6QF9rlo0nBHykKcXYH35HXSrvD2BTjqsF44Spd5s23U2nYa2JYHtEDdpsnCnflQipfWF2CvI0igvc7aZ+s6KGRAjtK0fDKcbcuobbW6Z+bc0aCWeY5zhn6ScGfAteK9z5V3AZ6UsQStoEaAtqTxeKpvtI/yyPuP2sfKG0EXueI8Xl5Hu65VlpW39V5PRZOD25sbe+Bm473rSWWA1jqkjLNA72KdNaBlHNV9yH1WGkTWdb17sNolKqPlmMfNUZODW5NlqbW4CHTtQzCaNEvUCnoGasu6Z8DOuuPaPpOnL+DZNvNA19xyft1MOMqn3eMcgJ8U3C0Qy2PrU2vWeZ7VjgDIdkgvLoI5C7ZWvlVv656i/Fq7aPGWRezTdtYAZl07KjuTdy6aFNxSEdiZd9aZD69kPqlmdSzLimatdheYI8gti+RBnUn34qy0yKJGsMs21eoZQR2lZe/t1DRpuLkid9qy3tpx5lNqkXXjHS9ave4CeF/IZZ2HDEfSAG+13labWM9nqP2cNBm4W1zoFoit+Xbfuba3+JPdMlB3AV67F+ve+qZ558jBpks7yjbVnk1LXDZtDpoM3Fm1QM/DrQtqJMu9izpqdiEtSrOua8GRhTRzbMV5beVZ/ky7aWka3Nr1ZThKz+Q9ZU0ebg9YHtbSPJC9V2FWJ/U6aAS1F+9ZsShdO5b1lvc2ZFzUfpk28wY42QYtA1iXfHNS5r/C7gfwPwDct8//WK3158esVMuHTKJ5tRafvX5rx7TgjIDO5smArVki7b6GiM+2n5eWteKWW+7Vs/XYijtVZX4g8W4p5Ydrrd8qpawB/H4p5b/XWv9g7MpFVjuT3gVqTZG1sdzIDNDRtTJx0qpFnTTTift0dGkZWzavDbN1PNYANmWl3PJa67f2wfv35xy1JbqCbaVnP4aquYFaWmTJI7c8At+C2rLgXTRE59baqxXsqE2HvJc5As2V/ceRFYBPA/hbAH6p1vrkWBVqta4e2BnLrcVrQLdYGwu+rPuehTqacx9T1gDIw9k29AY/7bks0hX+KQEA1Fovaq2vA/AggIdLKT8wbrXuKYK3NS2y2BmoLahkh5R/P9virrfCfpOdPAO2d65m7WWatS2ylYKbVGt9HsDvAhj0H0eyHzG1ji2wvffaWpmapeFhz1pbYMv/mM7MyU+tM2c+Seida6Vnp0+LdGX+Tui7SikP7MMvAPCjGOG/ubOyIM0C3vJBFs9qW6vbGYhbgT412DVFgEZTKLlW4m2LLpWZc383gF/Zz7tXAD5ca/34GJXJgmule+dFQJM42LT3LLdmxel/pCOL7Q0GWZhPCfTsGojML8+L7jXyym6LMq/CPg/g9Ueoy5Uyo3wU7wEelSHB5mEPas89j8DOWulTAdmTBbCMs86LPK6ozFNvv6wm/wk1qVY3XEvLuG7RnFtCalnv1sW0LNga5DfZaTPrJplreJabp2v3qr318Oo6d8gnD7c3WnddPdeuAXR7T+u519ZquXaeNae3IOf1m4qsZ+TFt5zjleXBflshnzzcXFmIM5Y76kCetW7ZNMClJbc8Act7oGNe16nIG0StdrfSogUzft+e252BfEptOJQmC3c0P84sxmh7S5qLm90sqEspoVveMu/m9dLqPBX1XbWOBgK671bQ526ppZrecx9DLVBblrzPnLvFLW+x1llLbYW1evH9qcmyyhkX3rP+2rld405dk4PbUjRn1h623EcDhwY1j9fm2n1cdmu+HVntUwc7kge+5bbLOO16Mm7umgzcmQWvCNRMfOaheqvT0SJa1oJrg0IEuayHVucpqcU6d72ujLOOKa7l+NQ1Gbi5so1sWWLLhcvMwz1rra1mW++tsx8/1ax/BLhV51NSZJ1brTc/luV4x3PWJOGWyj68TFrGgkeAt1rwVve8dbuN8qBuAX7OsJ8E3ED+4XmLLxHYrQtpGuDSFc+ulLcAfsry5sTac2ux3FG/yNZvLpos3K1zpii/Nd+Tx9pcts9quQd5NHB4K+VThzxa1PLm3976SyvIreE5aVLvuTMPurXTeKO9Z8FbtouLiwPLstvtAGAwq83rJes5NUWDrneeZ7nl9WutKOX6e++u4TlqUnBbioDW8mj5WjoaKQOyt2V+sKF1lVyDfCpqtYgevFY+CWcr7FY9ptSOQ2iybnlGmbkbj9fOIVkQ8fTIurZaaWvFPQJd1vmUZD0jnq7l1a6h5bfirDLmrMlZ7sx8KxOvpWUB58ct7jgvk44ji61Z7owFj+p+E4qg8dKj+bRsV26lLWvuxfFrZ+JOUZODG4g7gZbHswhamldG5A5zsDngvCzSkD+xpLnip9IJWwdtLY275dae8kUwzwVgT5OEmxS5bpmO4c3PtXMjqDWwaa9dMzPfzn54RTs+BXmDrRVvTavouBXwDMxzA36yc+5o3iTzRlbZm+dJSXgk2NY++2osAryrFb9JZQfQlqmVN92J9l5dMufMQZO23FzW/FnLx/NnLAHJcns9Cy7LpDhSF7fcsuJafacAtqUs2DysQaxdx7Pct8n19pS23KWUVSnlM6WUj41ZoUQ9zNGc54nOtSQBt6CWC2FdLbZ2jVbLPTVlILbivHNaLPdts9KaWtzyRwE8NVZF+soa8aO5t2XBM1sWcu+9tgW0B/mpqQVsz3J3Bdyr05xhT8FdSnkQwJsBvG/c6oyvlrk3VwZyy3rzreuKuVeXU5ZnvaMBgMe3zLmjesxF2Tn3LwD4OQAPjFiXA3nW10qLtkhZi529TutcW4uX9bLKmoKygFppGctN82mg7X03LytKm4My/zjy4wCeq7V+DkDZbzeqMUZZD5DIilp5ojjtOFO3qXU+y9WOXOuWbbVapQZuy6pn3XBr8LTiWtO8aw6tjOV+BMBbSilvBvACAH+tlPLBWutPjVu1S3luauTCZuerNIpbDz7T6Var1UEHXK0ux04rrUvnpfpodbwJWSB1AddqE9nG/Flq1lqqJS/PP4TnZBmDYyi03LXWd9VaX15rfSWAtwL4xDHB7pqWtcKaW9Znow4YbTK/B7KVxtPHUN+28KyvBq7Vhl66NzjKe+D3JWWta8gwz5sF96Y8rZN5z51RV8udVRe4uVfgdfbIWlv1GEpdrqVZbblvvW/LWss25XXIWk6qVzTwW+dL4LVzMi65du0x1AR3rfX3APzeSHXJ1sGd08o83vkZZaypZkkovtYaWu/WbQi1XMfL64FsxUfW29tzt7z1WWbzWtM/eR1rHSRKP5ZOxnJ3WVTKzMctRUBnLLcHfh+g+wCeObclTwvMXUHXLHfmjYVUF8AsyLMA3yTgJwF3X5BlnlbJjsvDlrtJHZHntcDPQG1B1OU+WtOy52Yg9xYSLbBlGMCBBfdg54toWryW3zMmkevuXTtKG1KThdtrpMwKpkyP5k5cXTqrZWkAHMRZnbrFesu6RupyfuacPpbagthKp2MNavpHVSla86CwvI/Im/Mst9WPMvBbx0NqknBnwdbSLOC7zNFIWYut7fmcuwvMVtmyflH9s/Fd82YGQs9aZ8GWbjmHWgIuwbYg19QF3haoj6FJwm2pdZHMA926Hu+gtM902mjO6IVlJ+d10erB69dVWbCjgcQajDygW2DX2uzi4uIa5BxqrY0IbO6et7jWnuW2ztGum4kfUpP7PndLY2QttGbRM6Nqq2WyXPOMtWq13rJ+lrLARnFenqzF9mCPFiGjtpTX4/fZ0l5ZsGV+K+9N6iQstzcPaomLFkpIWqe3NRN1AAAYi0lEQVTOWiPZ8QB9zt26yXp1VcYStxzz+NYtaj9roKRnpn2f3gObW3DNepMyYEfrNtZ1jqlJWW5vjp3NEy2gRdciaZaKx1tWR7M8lsWxrE7G+nSxSn1Atiy5VW8tjwWz137W9KVlcdK6P6nICnuW+6YA9jQpuCNlLLOVLl3z7ENosT5ap/Tm4F0tdxZoL70VZC9Nu5bXXtb9Z9JaFidlXaz74bKMQtaa900bUpN1yz1wPcucdb1b1QpjtlNmrI4HeEv9tbCXlgWiS/tEA6G3cdGPU1I8/zXaUu654DLOU7RYNnTfGkuThduS56YPZbkzViDTUfmcW7NOWQvOy6awrG9X9QG764DXBXrNqnPQJdQZmCnNmzNnrWzGZT+2Jgl3Zp4t473G9h6IjPOskjzOdNBaq9o5tY4aAa7VbygLHoWPCbjXnrxsD+jMZq3VSAPQdS91bMgnA3crwBmXPVogiaRZzkwn5MfcLfQskAZzBHkWbGvA8sIt6bJOfeBtsdYArrVvNDB2UReL7cUfU5OBO1IXyGkfzZW0B2B1aBnOrIRbC0XR4pqmbIeNgI7uMxPH62PFWTBn7t+CXQ6YJAm6V8dIkQXP9Ct5Pe94DJ0M3KQuMGtzb3k+4Hd+z5p6r2qAw/fcXVfM+1qhzH169+7FyTpmwI5g1uIjoKN2i9pR8+yiqZ0W1o6PrcnB3WVBIrOY0eqOy31m0157ZTtfC9wtsHt5soNZ1C5WG2XbznK/NQ+IrkvtarWxVr9WyT5jTf9a02QZY2lycJO0m46sc580qYyF8iy2taDWxYJr9ZJ1iuR1cgvoPoBH7aVB7b0S4+cD158fb2drMNXqKmUZAsvzk+fJsJV2LIs+Wbgz8kBtAdxSttNqnTVaLfc6fWSpu1gh7968vcxv5W2x1FEbWIBTnAZ01oK3yINazrspbkqa/CfUspaW5/fAlteVsixj1DGjzmnljSy2BXZk0YeSVU4fwK3Xgl3is+3o1R2wjYBnxa24lv42plKWu5TyJwD+CsAFgPNa60NjVqoPwPIaXebeHihZi0PHdE4EueyovCyrXq1AZ611FmAtLmOZtXhvcJRx0lJnrLY1KGqypoQZF7sF7LGBz7rlFwDeUGv9yzErEzVCC8DePlN2xiJElkm65VlrY5XP43k9I7XkifZWWtd20sD2ACe4OeDeoqWsn9cmltvtzb+1eOuax1YW7oIbcOEzjdUCtrdFaoVawh115qhz8r0Me3WO0rQ8HuDZQSACOgO7tfjInxs/l/+IgwZ0pl08t9uy3BnrnUkbWllgK4DfLqU8WUr56TErZFbAaEAtrosrrska8S2osx02A7UHuAdm5p6suIx19tL6WO3s3hpMW8rOyBr4LcsdpVlxYypruR+ptT5bSnkJgN8ppTxda/3kUJXIjnAZeL0FkRaLLTuB7Nxep+UbYH+IJdrkwGFZfJ7OrRa/D63+UTiTd71eY71eY7VaHey73Gu0l/Xwnpn1zOWW/etl7U8cW/5XXfZjWc+hlYK71vrsfv+NUspHADwEYDC4RVluXAS29wClSyfPt8r0OrdljYaAm8MiNyveq2fLcTbvZrPBnTt3cOfOnavwZrM52Nbr9dU+gr/VO/FAlXHyL5Xltt1uD4751vKXzC1/0zyGQrhLKS8EsKq1frOU8h0AfgzAz49Sm72iBYvsPDq7yetrijq/ZV0BG27L4nnWUAPagtsbjLS4lrwUR2BzwCXUEmw5SHmutWxz2U/48+PwWP+V7kFO8HKIJdwa4BbwlpEZG2pSxnK/FMBHSil1n/9DtdbHh66INn+hvQZ5xuW23C/LvdfqwZVxy6XlrjX+hJoGvAe/B3umfpk82Xzccnuge1BbltuCWusfGkAa2BxADWhtL6HWBgE5cEQWW/bnMRTCXWv9vwBeO0rpDfLmLV1Az1pu2bkybrnmokvoPagj6+656FbdxtqkW2655FZ9Nagl4FpfkPsM4JbVliB7cHtgW266ZrGnYrmPJs16e3FDueWW10CKrJnsmHIBqIuljqy0N+e2XNyMx9EHbstia5BnLTe1t9VXPO+sxS33XHFrPq6BLQGXA41mVLQ+N4QmBTfgfzrIc8+teG0hzRogrPK5LNBlp+y6oCah9oDXIO8Kr5UWxfNFNG9RzfM4tPWKLODRFCyy2t7imTbHzgDearlvzC2/CXkuSxZq+aABqJDLa1uyOpwGNN+AQ7il5bLAzSyibTYb7HY7FW5twBn6OLLcnvXW3HIP8KgveGB3gdpaQPMAb10lH9M1nyTcpEyDtLjeQzZy1s2lvJl5tuaueuB7ltuaww4dHnpBTXo9Xr+QxxpIrRa8y+p4FvRjQU2aNNyeWufU0UbX1GRZ6shyW1BHbrkGQbSQZsGtAdk3zYLbWlCz3HINcq99rT6g9YcIagm4XDTbbrc4Pz833e+s1dbqZE0Jh9Zk4dZc5iE26z2jBbg254vmpryzXlxcuFY7WlyyQLeA98C0AO6zX6/X1+balsW2PsDCjy23XOsXFtT8GVsLai0uugW2F9YW9TIe6NCaFNz8puX82Jp3aed2tdz8WpYiKy7BAuIFNQ9gy0W3LGEEYwR7No7PuWnrsqAWWW7Z5taAbIEtIbestmW9vRXxzGq5tqAm6z6WJgN3X4Dp3K6ueMY90jqbB1EW7laAvS2C2atrNABoYQlx66fUrOtG7rjXJ7zXYZbl1sCmzXqVZsVlX4WNDfhk4LbkWe9WyDPukSZpRaJ5twXPUFsGbqv8lvTMMV8Jj7as1dYAzzx7C/JoAS1aUPPel3uvwDKvwsZ0zScBtwcuj9dAjqwyf9Cr1SrMF7nkkdWWnb/W+OOnXSy0t0DlDSpDp8nXXK0LatGiWqbvaDB7W/ZVGC2oedfJlukBnTEwXTQJuKUsqDWrbAEu8/Fja1HNU7SgprmVEdzUuXe7XRPwXjqV19dryJ7P3W3vvXb2dZg237Zcc889j1bKs5BnAM4OLK0eY19NDm4NbAm1duzBbVnt1oaOXHLNclur5V02DgYNCBbcx9ok3N4+WjS0XHJqe94neNiafmUtt3TPPbjldTPH0bRwLE0ObpIGsge1BJzn42G5aqmVya/puYdZ0FusoGedNaD5p9MycFsWs2seWUfPWmfn3Rxwamevj1hgc9Csle4Wy61d14vT5tta/xsL8EnBLa22jI+gprxWWDZsywhqLfBo1ppvWUsq3XPt2No44Fp5GkgyzoItOter11gfXrGec2S5LbCj7297A4e2j9JuteXWLHYG6gh0Hte1gT3r7C2oeQOABrKEh1ttDaqLi4sDuD2Ah0yz1gQ2m004AGRB9/qKZcG1hS/rQynaVzstuLXjTFjzLPl9DK1Jwk3SwNYAz4JOe6uhM9abhyPQPcvtWUpuiaXbTccyPoKbQ9eanjnHC2tp1mZBrS2mZraWVXPLelvX7Ruf7XdddeNwewBHew1c2tNCltx3GUE1Nzw7v7bgllZZhq10DWgJtwdodt/n3Oy1Zbz2xsGz2vyZdQHZ+ybY+fn51auw1gGlZRtTNw53izLAUz5rP4TljsDWLLjnhluWm7viGuAR3No+A2ALrEO59xbUfebd2ty75XPl5KJHfSYTH50zhiYJtwVtBmgvTXu/rTWwZb1pH1lxDrhnuSPYLVdcA96COxPum9e7r+jeM4DLdufPyHOBowU1OefWAOdwy/Jk/+mSz+qDQyj7X2EPAHgfgL+Dy78W+he11ieGrgxBycNenASa8vC9DEeAy0a2OpgFtXQvM3BrVtuy3LQnmOWe4G6dA1tpGeg1OPsAHS2oeR5Z5h139K5bAm6VqdWha94xlLXc7wHw8VrrPymlbAC8cLQaKbIABxBCDuBqvk3xlltkNbTsXFFH5J02glsDV3slJt1w7RwJtwVqBuAW0DWoZTt0OY5ccut5Wi655ZpHr8K0MseKG1KZ3y1/MYAfqrX+831FtgCeH6U20EGm8L4+apjnkWF+rHWGjFsUAd0CfBdLTp1Sm3PzvYQ7C3ZLuszjrTl4eytNm3dbfcXbNKAtyL3FNa0fjXU8pDKW+3sB/EUp5QMAXgPgUwAerbX+v7EqZUEtj3nDeKDz41aoPWXABXDQkVvccgk2d9W7wj3kxoHUwhJYLd4KtwLurZZnFtTkRqvlnrL9Z0yILWXg3gB4PYCfqbV+qpTy7wD8GwDvHqoSHGYrzoKc4qIR8eLC/hVU2QEiiyDndxlvQNbHmr9bg4AEn+q62Wyu9lRGxvK2wCt/RcWC24Iz62Lz50TPiq5H/UFa2hZYWzdq41NVBu6vAnim1vqp/fFjAN45XpXuSQLN43i8NipaI+XQozt1Mg0Kstzab3FR5/EGBMu153BLsLnlzsy3owUuHpZ1strXgpof83zavVrx2+0Wd+/exdnZ2dVG76Rpy/zIYWZAP3Vl/nHkuVLKM6WUV9VavwzgRwA8NXRFNOvN07g8qCndSstY7uiDDxKW7XZrutkAUp3M6lAR2Np5HGC5j8KWO83rEj0fitPcau1aLXEEtwTcg1wumvFVc77wFnlbp6bsavk7AHyolHIHwFcAvH2MymhWOcrXmq4B7S2+aGDLY4LbstxaJ/OsBm8Dy1Vfr9fXrDUXz+PtZVhbvc7OfyUUfIDl+fuGNcudsd7aoKoNrnOx2kD+L3z/EMDfH7kuskw3vSv8fJTOvAe1Xp1wq83h1iDxfk1TQi7vUVu0I7CtzqjVxQO6C+DaM8haPe/ZRedst1ucnZ2ZgPOPjnrWW2t/7TMQp6xJfkIto66NL90wC+zM3JuglnBLy60tAFmutbR2EeAkDp63Gu+t1ntzbwlkl/WOlngrL8GtWW0OuPYtrwzQc4CadDJw92107ip6ltuy4NwFl664NefmlttyCbX5ngb4arW6Wizz5ubAvT8CbAU5Wun2FtO0KYKM65tWa8Vut7sGtdy3uOXRAHvqmiTcVufN5NPy8A7ZZRHNmmNnrV10Xc9ycLBpo4U6Ei+bnyPd6z7HWbAlJH3StLzkdmsWO5p7awtrc7bgk4ObYLTSuKJVc03ag2xdLZeubmS5NXc/Wqml+5NuueaK02slStfmzBLaTJxc0IsW1Mba+PXlnNrbsq/E5gY1aVJwa2DLzizjKD77UDygW95vW7BrLqzn9luAyzk3WWV53zR4UDkATDA9cCOoJdj8OWlAagOod5zNw+H2QLeg9qZic4N8UnBLSdhlx5fgZ910z1pnoI/ccmkJvddu2pyP35O03FYaXVemSUC1ASiTJ7Lcsm3H2u92u2tgy72Msz7FZgE9B6hJk4FbA1lCrB23AM7BanHJV6vVAdQe5BZ43p67n/x+ONRWGr8WpbUsjmlbBDhvU9rL+9IGNK3NvXR5TO3O4c2Eo0W16FmcoiYDN5cE24O6xSWna0SdbbfbXfuwCsGsQR255TQPzrih2n3QvRPEVEatVb02nWNZXG/L5rHatItX1Lrx14pys+bZmffbi1t+BHlgW1BnYOfne+4xB1vuOeQENQFsWTq+0k310DqRFidh4hacb9KyS1B5eMg0rY09yDlYGmSZdPmZAQtkb5U8cs3noknALV1yGcfBbLHa1nWtjheBTGGCloeteakEz9rLML9f7V6961B+WZeWfTYvb9MIavnZga5pHFYJs5WmvQbTXPM5AT4JuEke5BHgHuj8utGcmwCnsDXHJrC9+SkA80Mnsn6aJNiWxbTaTwtH6a3n8bI1wDUw5bEXb+XVrDE/9tI8sPm9nLomBTfJAzoDs3ddPk/15nVykYxbcel2yzhSKfdeT9ExlwaJlceDK3PdbHktcYC+oGZ5RS2vF1vPad3mPNcmTRJurhbQM8B3XfzRgNfA1ubckZtrWeism6wNAMeUnC5obWsB3Nf6Zo+tPHOGfHJwS1i9NM+dtdK0B5qBOPqgima5AVz9xpi2KKWdZ8GbKZOHvSmK1/at5/A8Htjegljr3Dmaq2fSrX4wB6hJk4E7ghnQ59dZ95yfJzug505aYHvzbKoXcO+XVz2L7n36TCvLO5b33DXMj2Uba/lawNZgzq5+awD3PZb1txYpT02TgZtLWynnYa3TtUAeWW0ONQ9nLTYPU53lazOa/1NeAlxeR4PY+3w4L7fvXmtTz2vyFtUsl7zL++rsVKp1W9zyI8kDHOgONuWN5ta0z7rDWlm11qt/upQQcsBJFKcBnvm4q4TbWgFuCfO29YD31jA0uDOfLJOQ8//usqZW3uAdpc0FatKk4JYd24JaHkfzSHlNzxWXgBNYFuy8TrJc2q9W934oQdZVThV4vLTatHm/qqJdT3M7ozR+Has9vetYgGtWW8J8dnZmfnacw833Wpy1j9LmAnjmTwleBeDDACqAAuCVAP5trfUXx6iQBuO+HteOKc6Cxbu+N4Lzztg6v7bK41aavost78taCNNcb7qO9tto3DMBDv8+qWXz7ilqW9rLObIHtvXtLn5McMuyusRZUM8F8Myvn34ZwOsAoJSywuVPHX9kzEpJwCmO5IEQPRTPwkigtXgNZM8tr/Xer6fIH1ng19Q6lGa5o98Zl2UP0fm1e/PaVGtXyzXXwNZ+dMH7S12rDq0D2VygJrW65f8QwP+ptT4zRmW4NJi1NJ7uWRS+ep3ZJNDZxTStbMsaSni7As7/NIBbbgkthWng4vGllIM44N4XVnj79p13W665BzmFd7vdQXn8uE94bpC3wv1PAfzXMSriSWtozXXPXINbya5wR+VYVkHWn6DSvlxCeawFNQ42wb3ZbK6uq80pOdR8EKBzqGyel7e1XOCU9fUsN+2jObf1+2ga3LJdM3HZtDkoDXe5/M3yt+Dyr4RuXF0fBO943PXWwPZccs8V52HNasvBgtfHApuHJdh8k/co1xXonglODraEHLj3DyKULsGW9y6tv2W5ozm39gunZ2dnV3BH/WCo+FNWi+V+E4BP11q/MVZljiFrzsU7Ioeew6dBL+GnY+AQUDmIWO66psxrMD7nloMHD5PoXvmxfAvA1wQoLqpv5KJ7Lrv1/pug19YAFuk6/GiUrbfhBlzyRYsWdVMK7lLKC3G5mPbfxq3OokWLhlL274S+BeAlI9dl0aJFA6rFLV+0aNEJaYF70aKZaoF70aKZaoF70aKZaoF70aKZaoF70aKZaoF7RH3ta187anlPPPHEUcv7whe+cNTy5vgR0TG1wD2inn322aOWt8C9iGuBe9GimWqBe9GimaoM5eqUUhafadGiG1Kt9eA7yIPBvWjRomlpccsXLZqpFrgXLZqpbgzuUsobSylfLKV8uZTyzpHLen8p5blSyh+NWQ4r78FSyidKKV8opXy+lPKOkcu7v5TyRCnls/vy3j1mefsyV6WUz5RSPjZ2Wfvy/qSU8of7e/yDkct6oJTyG6WUp/fP8OERy3rV/p4+s9//1WD9xfrZoTE3XA4q/xvAKwDcAfA5AN8/Ynk/COC1AP7oSPf3NwC8dh9+EYAvjXl/+3JeuN+vAfxPAA+NXN6/AvBfAHzsSG36FQB//Uhl/WcAb9+HNwBefKRyVwC+BuBvDnG9m7LcDwH441rrn9ZazwH8OoCfGKuwWusnAfzlWNdXyvt6rfVz+/A3ATwN4GUjl/mtffB+XHbI0VZKSykPAngzgPeNVYZWLI7gaZZSXgzgh2qtHwCAWuu21vr82OXuNehPh98U3C8DwG/gqxi589+USinfg0uvYdSPj+3d5M8C+DqA36m1Pjlicb8A4Ocw4gCiqAL47VLKk6WUnx6xnO8F8BellA/sXeX/WEp5wYjlcQ360+HLgtqIKqW8CMBjAB7dW/DRVGu9qLW+DsCDAB4upfzAGOWUUn4cwHN7z6Tst2PokVrr38Olx/AzpZQfHKmcDYDXA/ilWuvrAXwLR/g5b/bT4b8x1DVvCu4/B/BydvzgPm42KqVscAn2r9Zaf/NY5e5dyN8F8MaRingEwFtKKV/BpZX54VLKB0cq60q11mf3+2/g8u+sHhqpqK8CeKbW+qn98WO4hH1sDf7T4TcF95MAvq+U8opSyn0A3gpg7FXXY1oZAPhlAE/VWt8zdkGllO8qpTywD78AwI8C+OIYZdVa31VrfXmt9ZW4fG6fqLX+1BhlkUopL9x7QSilfAeAHwPwv8Yoq9b6HIBnyuUfYALAjwB4aoyyhAb/6fAb+QvfWuuulPKzAB7H5QDz/lrr02OVV0r5NQBvAPCdpZQ/A/BuWjAZqbxHAPwkgM/v58EVwLtqrb81UpHfDeBXyuUfNa4AfLjW+vGRyroJvRTAR/Yfcd4A+FCt9fERy3sHgA/tXeWvAHj7iGXxnw7/l4Ned78Ev2jRoplpWVBbtGimWuBetGimWuBetGimWuBetGimWuBetGimWuBetGimWuBetGimWuBetGim+v+yZzqNNwpBbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3acafd290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.imshow(digits.images[0], cmap=plt.get_cmap('gray'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fb3ac996790>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fxc6qN+C75Rxe+d0r+f0r71tZrZB6S3QMn+iy1DMLlwUMr1NAV+5svlY5LDA91bbStKj4mDY5uC3rCnXUWOS6i1JHKk7lJ5MgaIBziOV3sbzwLgD3WTS3PGOyrqJOl+ABnodbe+JgzdZrY36rY4nKkIHaa8O7ssnC3RfgDOAWzH2Blkqj3dCMW24tR0dHZtzQcHM3WCsvh7vlPnr3yIMLuKjcmZl6WSarbJZKa4rdusj8x7ZJwe31fEMALW+YB3or9FnVBnKuuQScgD46OjoHt9zW4Nag9GBuSUfAyWvj9027j1anyMfXtNCfJkjljlzy7MSe1V5K0f9VpQ/kVr5j2GTgjoDWwqKGkoHcgjQTr+VljbVpW7qLmnJrSi3h1sIovQep9ShpudT/xSQ6D8HtPeqy7pu8L/yrnBxugn2z2QCAOqGmAU7mjfm1shHYdH2WcmcBj9q5F97HJgG31bvL/ZaGYu17qu2pdSvYtK1dnwa2NzMuIb927doFyGmRyp0BNgu1dhwBx69Nu7faveP1KcHmQNOsfOZRWFfIPYW25gcygHvtd2ybBNzcNKj5ttyPQM4Art3IKL13Y3m4vCbAdsu1MbeE99q1a+fglttS1TJA94njfyJI60wnrHWyHGyCm6+pI8m65bLOZbuS94jPH9BitQ9PTKw60Nr3mDYpuLUL76LYntpGkyTe2Luls+CNhV+P55ZnFJsvMoxcc2sWOYK3y3Ea3Pweap11VH+aS071Umvu31h4HWfmALS2RHB7nl3U0VvAW+UZ0iYFN5nV+/HtqPf0xtHazWqBuutNJcuAbQGuQc4XDrcH6FBx0i237pWsJ/onUw1mudCEmga3Nd7OTKhZbYqDbXXekVuu1YW2HtMmCTe3rGpHkGfccA9qT228DoVfA5nnllMjzoJ9/fr1C3B7MHZda5NXGtzcLBeWxtJWh0vjaw1yDrdXRqng2XbFwebKnQG6RbF3YZk/SLwHp58SehGAEwD/udb680MVwOvZojgL7KjH9cZR1n6k1la8vE7NLae1NplmzZJzsPnaU26pckOkIeAyHW1Wqb3XamvV/0vNUuwWsDXAI3HIQn4Zap5R7jWAf1Nr/Xwp5QUAPltKebDW+sVBS8JMg6JFrS3YonF2Rpmj47yem0wDx5pQ8ybVCGi+ENwRrFmYozD66AK/X9Y9kLBo3wSzoI7ccl42Xse8zr02prUfAC7gXvvzxEprE2NY5t9Pvwbga9vtb5RSHgfwEgCDw61VuLXtgR6NnaNxdwZgT5XkDdZMuuTRY7DVaqWOsTW4I5i1cao1fs10DPKeWZ0q35Zf6txsNmez5fzTQbxuSLlbVNsbd1tAl1LcNtWi1lbb1dr80NY05i6lfA+AVwH41BiFAfxn3i3q3RdcS5G9cC2MGiRdQ2a8LSfVLOXm7vj169dx2223XXDLI5gz+xpAEm7vnmj3QX4PbLVamcrNIac69RYPaKu9aZAD+l9heyruQR219aEtDffWJf8IgLfVWr+hpenyrTDAfzyRDWuFvk8PrOWdqD93vE2NVwPce2tNAs/d8gjMKCyTFsA5WAlSWnvARiBra0B/tzxzLVq7I5Wm+EwbysDMz6W19T5gD/qtsFLKCqdg/3Kt9detdGN8K8zq8bzwTGfhWcbFy4JhjQ+9mehoP5O3t2jXaV2/Vjdevck0mfK0zNoDCOvEuuZoP7q+qZgUzr7fCvtFAI/VWt/bu2QdzILSAzYDegvscj8CuRXsFoiHALwFaB6frSsJkRbnlVurMw53S/1p16dd/6HZIkpQSrkPwE8A+PullEdLKZ8rpdw/ftHOmwei5RZZ8VqcZxnV8WC39mXalgbbFegM6Np1R+adw6pDLTyqC6v+svWilSl7Lftmmdny3wOwHLsgGRX1AJbn8cbKmfyjRqg1JGscaLnaWXhbt4eCv6tZdWfVY1R+b6iiwd56jXJ9KDb5N9Q0iwC2jolmL8nkTeb7mcaZcdFlw7S2WwHXGrl1XUObpYIR2NnOUnPLWzo0XsZofQg2Kbj7PhpomcnM5pdpmBFsmspkYR7LFe2icBnT8rTy1codeT90Lk+xvfqQdSHLKe/7Ptuk4AZ8QLV0refma7kN6H+irzUOr7FqSh0puRWmnbsP4F0B7gK5lScP98qt1RUd22Wo4oEutw/BJge3Z5nnza3PIi3Lqo8FnzcR5I0XI5VvbcAR2PKaI9hbAbdUUYPYg1rC3QVmrT66XNe+2F7BPZR1AdyCxHOlM6qchdiC3ypLBm4tXF6/BadM43UcGeA0yKOONHPt1rV613gooO813F1UOwO21aNnGlt2zJ0FuxV0Td20fR4mr32oxp6F2oI8Uu7Ipc90Nt6933fbO7hbX0DJHKudy4NaC/PcSg3kLmB7oEcwW/tanLx+bT8yCxyvDjOwR8dlhyleuQ7FJg93lzfKMhNyPK1lGXCsRuipkAX5EOsIYG+b9rXtKE7WmVZPXt15nSTfz5yjdTlUmzTcLS+2ZN5CywLvWavaDAludsIoA3QUL9Nm6yaqM68OLW8mOxafoT5vk4W75aUUK64rwECbOnhjRG/pCnirevPrkWFWnJZObmfrL1OfsuwW4NG5MvHRPT4UmyTcmffIrXDvvfIM9NYNblWFDMRZ0COVk+FU3mgdpZHX75nXAUTQRa44D5fn0c5r5WWlbb3WfbHJwR2psRbWEp7Ji1vUYKzxtRYWTbJZ0LbAnoG6yzprWl1Z5/Wuwersojxa9uX9PTSbHNyaWUqthUWgay/BkFmKw7db1KcV5gzYVroMTN41ZY/JmAZP62J5OPK8me0onXaNhwD8pOBugVjuW2+tWcd5r6ACdgOV+xaMfWHWwI7ypDUvfwbqKL1WJ1q4pYhRx+jVi1cH2rmjvDNpD8UmBbe0COys6229vOKNu63tLmpjhbU26ghy2fCta8mGyW0vzIqLFDWqS1lHWpkjqKO47LXtm00abmkemJZ6a/vZGfSoYUTuswVqxl3PgO9BLq9hyO1svfH9VvW2rlu7N0OuD8kmA3fkQnsutQexNd6OQG9RmUi5M0oega9tW2nkNWj7Q8V5x8jOJlLoCGwP7mxYNu4QbDJwZy1Sb2vbmlDzLGqwFnQtypuBN5NHpNpd9q0wr7485c/Unxanwa2dX25H8Zm0+2yThzs7CabFtSg+WasCWeppKbKlzh78EcwyzrqWMcI0i9Tag1irv64dWJd0h2SZb4VdB/C7AK5t03+k1nprzEK1vFUWud1eGstkA9LiIpXxGm0EeEbJPQWncnrXN0R4ZF3q0eq8LLfcK2frvhW2r5b5g8TnSik/VGt9tpSyBPB7pZTfqLV+euzCRaqdie/ijpNlVScCvVWZI7WO4qns0bVlrr+rSWXsW3eaW+6VcVcd2JQt5ZbXWp/dbl7fHtPvz84arSvYVnzL66hkXRujp9IZZW5Rb9rvYkM0bq2DGWqx4O56LYcIs7TsF0cWAD4L4K8D+IVa6yNjFahVXT2wh1Ruud/SKC2gW5Rbc1ctF/YyLOMpZAHWOkzr+q4CpF0tq9wnAF5dSrkTwH8vpXx/rfUxma7rt8KCvC9se+ocxXUZc3uAe5NA8jtXmSULsLfs2rQ8Zf15x2r1LeMuu/Oakg36rTCyWuvXSym/A+B+AC7cjecNw7Kz43JtPc+W+7xB8TAe7k2UScDpi5QR2JF6TQliyzJvEnrHWvHZzviqmRRO61thmc8JfVcp5a7t9u0AfhgjfJs7axakWcA94LPqYbnRUrG7LBnF3keLAI2GUN5cydwJ6JZR7rsB/FI5HXcvAHy41vrxMQoTgWulzwAfnYtb5BZmXPIWyFtd7X2FPjMH4k1+ZvPQbB/qZ2jLPAr7AoDX7KAsPE83PIrX0soGEjUCb5wtwdYA5265Bbml/hq0+wRxZBbAMkw7zoPcqxt+3CHUYcYm/4aatFY3XIuLIM9MoHmKrSl3y9i7ZRJNlvuyLDNvkjmHp9w8XrtWb5ilpTt0yCcPt6fWXWfPLcu6v96jqi6Aa+f0YNbmBqZgLWrrudsZNzwDcgTxoUM+ebi5ZSHOKLfVgLKKaYEszx+pttY5WOpN5ePrqZk3ZLLq3YqLJs14HXhudwbyqdZnH5ss3JHrnJmM0dZdLAI7M6km19Y5WtzxqYLed+Y6O5EWgd4K+aFZt3cVR7QWqC0lbxlza+ZNaHlj5C6PvTSwI9Xm2/vaUC1Vjlz4SP2jMArPhO27TQ5uyzx3T4v33HUtvQVQi1seqXYEeIt6H7J54FtuuwyT59PyOHSbDNwRvHzbAjUTngVcblsQWu55y6un2Qk1WdapTqyRtahz1/PKsOw+hXn7+26TgZtbtpItUCOYs+f3FFuD3ZspzwDeot6ynPtmEfit6s33ZT7e/iHbJOGWlr15nmtujcOlReqdGWdrUGsvs1jHX3UXPQOgB3UEfGte+2qTnS2Xlr15lgLwdNEN9cBeLBY4OTk52661nq35o7DlcgkAqTG313kcGsjexFdWuYHnO2G+r8VF21r5DqGegQkrd+sYKUpvjff4vjWutSbSshNrXWbRLaj3BXQLYLnfMtllddrymD7bh2STgrvlRvP4rHJbabhl3GALai3Me7c8O+aW5ZJlnZpFna53nKfcVjor32j70G0v3PJWBZZpveOy5gEu3XRu1jjcmpDLjK+nPKHWCpIFr5dOutfSNc+64llXfV9tL+C2LDN24+HaMZpFai3z4WEyz5ZXT6NJNCobL+O+mXWPeLyWVktjwdwC9SHb5OD2xltWeDbOc9Wj8W0WdH5+Aj/7nDszoWZBPYXGmhlCeXHeeFrWMYc4C/hVA31SY+7IPAX2FCFSC2nWWNdSWAta671yC2wLdM0dt1z0qdpQnbO8/97Y2/MMoo7mEGxyyg34CpuJ53GeW6cdq0FtKTZXbj7e5uft8qZa5DHsO9itnbC2rym3p9YZhT40FZ8k3EDbxIzmFndJI80DXQJunTMDdosrbg0fLtuyHah3b7xwfv88sD3Xu+WYQ7DJwi3NGj9r6Xh6Swk8s2DiUEvArfNmJ9RaJtVkWadqWbD5duZ+ZWE9VGizlh5zl1IWpZTPlVI+NmaBIrN6c5kmOlYzTREt1ZbjbW3s3fLPK12UfKoNNwOxFSaPse513/VVsBblfhtO/6v8zpHK0su0m++pN08jLXKHCTx+Hr7PrVW1u6j31K0FbOs+yu2+yn0V1D2l3KWUewC8AcD7xi3O+GaB7lmknt54mt5Qy7ypllXofYedW+R+W9stypxR7UNU9Kxy/xyAnwVw14hluWDRuLnLElkEslTt6DyZGXLPNfcm0mReU7AsoFZcRrlJcYG25908r6nU15iW+T73jwJ4qtb6+VLKDQBmrYzxrTBpraqbNQIk46bzNJbbTg0ogjSjwNpcgGWXoUCWq+0B2rqcnJyk5kws6GUYlSUDudWhdonzzpm1Ib8Vdh+AN5ZS3gDgdgB/pZTygVrrT8qEXb8VZlnkpkYubHa8SjfdajiZRndycnKuAVIYADPO24+8Fq2M/Fp2ZZpb3BVcXge8zmQd83uZgbUlLU8/hOekDan6mhTOzt8Kq7W+s9b60lrrywH8OIBPaGDv2lqUTouzblZXZZGNMlq0RmyBbMXxNNr2ENa3PqKO0ALYqksZ7nWOsvxeHVnzGnKbp816VJc1BNib59wZ66rcWesCN/cKrMaeUWuvHENYl/Noqi3XXeC3oKe1VN+MVybDrLRemATeSqOdKzr3GNb6Cd+HATw8UllS5rnlWhrv+Ixl1FRTEt4QI/VuXYawlvN4aT2QrXALYE/VZYfZch9b7rc3/JPnawV817Y3yt0yqSSPae0AAP2NuFbl9sDvA3QfwDPHtqbJwpwFXAOah/H7mXlyIa0L7Nq2PFdG+XdpewF3X5BlmlaTDZdve24lTah54GehthSxy3W0xnnxVpla1drqCLU4DjSH3QJdm1fRwnl6T0w8lzuj2rsCfrJwe5WUmcGU8ZmxE1mfxioVB4CpQtINbVFvWdbIuhyfOaZVoSPAtTqpSAJBAAAaAElEQVTU6k5Tbwk+cHHMze93rRdnzLMTa5rr7p3DihvTJgl3FmwtzoO5j3JnFNua/MnM7FowW3m3lj8b3jVtpiPMQB/NmhOQFtQSZKnSGtA8Pd9uhXcqUJNNEm7LWifJvHBtDdgzvnw701i9RqopNt/mZdHKwcsnt7OWBTsLdRewNag9Fecd5mKxOAc1bVugc8gjxbbaR+skm7YfhQ9pk4O7pTI0eLPKnancFmWylIbSe423i3rL8mWuwQrrk6YFbEulozqUYRxiDWa59u61BD0Ltkxvpb1MmxzcmnnjoJawaKKEzFImr7FaDRjQx9ytiyxXV4ugbd3n4VmV9lQ7CqM61QDX4Cal5tuWepNlwM4Ihech7sIm9R9qngudTeMpdyY/Mg6VFh65ldbkmaVSEdDZtWd9QJb1ke2MWjpFrx694U2Uv7atWaTCnnJfFsCe7YVyk2WU2YqXrnn2JrQokdYYSSW6zI5nQffKno2T4LbEaR1h6/VZoGtwk1oDOFNsuS+hzkyoAbpQ8PAM9H3ihrTJwu2B6ylz1vVutaEaquwUovE3z5u2+bql/Nq2F5fZ7lpHHsAR3ADOAU77Xt1JyCkuM5eTUe4p2mThtsxz04dS7sjNa2moAJrd8SzgvLxdrQ/YfdS5T2dJpgFtgSyvOVJwIK/AWrwVtkubJNyZcbYMt47xJj40yDVQOFh8PwN7KeWC8mhgZ2bNtfINpeDR9pCAe5NlmcUyPnnWBXo6hxSAyH3Oute7hnwycLcCnHHZowmSyDKqrTVSvs8bnDVjHrnjFuRZsK0OK7sdhckyZcDOPj0Y4klDVE+eN9cKdhS+S5sM3JF1gZzW0VhJuwFWg5bbmZlwq2FGDVazLNQR0NF1ZsJ4eTKdoHet3hhbG3OTyc5TU2+tnBnzFDzTruS5vP0xbHJwZ8ZB3rZ3M6x4Mq/xe43XmijjY26r4Q6pQFlrBT8DexbwLPTeUAZ4HmqqY8sl5+XxrpVbNGEr02rb2v6ubXJwc8u6NpnJjFZ3XK5bGilfZ8eBLXC3wO6lyXZmUb1oZcrWl/Uo0Qrj8xjAecgpnMK0Mkb1YkHN4zQ3PnOc3Nb2h7TJwh2Nf7zJji5x0iKFihTbmlDrouBauWSZItOux4obAvCorjLDGLlsNhvUWs/du0wHGl0/mSUEnnLLsIyy70rRJwt3xjxQWwC3rFWVtEYq4Y4afkapMzBH1gK03O8KeAZ6Lc6aqNTUugXwqB6t4Rzfz4y3L8smD3dWaXl6D2x5XmmWMmYbqAW5pVqZBplRoCGAz9aHtc50glEHp7nhst6A5+8zB1uDnJcjU0+a6+253FpYS3sb01Jwl1L+GMBfAjgBcFxrvXfMQvUBWJ6jy9jbawDZRklhdEwEuWz0PC+rXK1AZ9U6AlgL82CKOkXviYMGOofaA9urP1l3EYhZgFvAHhv4rHKfALhRa/2LMQsTVUILwN46k3dGWb1Gq7nlnnJlVI+H83JG1pImWkdpWurIWlthHG4JtafYXeoso9xTANizLNwFl/ALsmjygu9n1t4SWSvUEm5PoTKg87Xc9socxWlpWpVbS5MB2wv3oJf3rrXztcxqC9742nLT+TobN7Rlga0AfquU8kgp5aeGLkTmQq0K5Nt9XHHNrF7fgrpVoTKNMANY6zVZYZE6Z4H26smrG1mXLU8VtPiuFqm250lmwN6VZZX7vlrrV0sp3w3gt0spj9daPykTDfmtMM/1ycZpNyOr2LJxRA1Xa4w05o4ehWUWS9kkJFzJ+HVo5Y+2M2k3mw02m83Zoypvnb1O7/qs+s+Y57lFH2y0Pruc/UprZkyftSG/FYZa61e362dKKR8FcC8AF+6uFl14q7vNb5506fjxVt5A7pGPNRkEdIebwyEXK9wrp7ffNe16vcbx8fG5hcLW6zXW6zU2m83ZWl6D1oFpk4tee8kAKz+fzD+rvFqtzP3VanVuafkkc8tnmlss+62wzFc+7wCwqLV+o5TyHQB+BIB+toHMUmYPbLnfssi8tP1ItTWVieD2lC6KsxatjNmwlrQUJqHmC0Etwc4otwRbQu7dd0tZOdTat9Ml1BrcGuAe8FrZukLdahnlfhGAj5ZS6jb9B2utDw5dEAsub9zTCjavcJmHVQ6tgUXqLd3kLmodubcW7Fq5smB3Sacpt1TtaMmMq712k3WzLaglzBbcVloJNW3LNme56GNBHsJda/2/AF41Su4N5o1b+iq4dn5pHtjW+DADtwduVrl5uCzb2IuEW6q3VHLPJZd1aYFtDamkMmrqnQXcgtsD23LTNcWeinLvzDT19sK6uuGtlRwptga4hLyLantge2NuTwG9pctxHG451o7U23LLeTl4vWfbQTTujdxxyw23XHLZaVhgay65NSwcwiYFN+AD7bnnVrg2kRa5RpGCZ+HgY24OumzYlmpb43ANflq6wmvFRcdoym1NptHaulZPuS3XPDsU86C0oNbG2BnAW5X70tzyyzLrgrNQyxsMoBlybi1A8wWACW0G1mgSbb1eY7lcqnBrZRt6P5ot18bfHHJvzM3rPWoHGcWW6m2539EEmgd46yz5mK75ZOEGfGAzabSbP2Qla6BbcHdxzVtB53Bb49iht7tMqGmdmwe41i6idhK541K1M255y5IBfGybNNyedRlXd4VaqoimLJo7abnlHswawFa455Zrbq4M6xpnwe1NpmUeh0VDgWwbkBNp3jNub0Lt6OjIdeUzqq11ONwdHxP2ycKd6Z27LNakhlXJ2pjPc821MWRGrb3nvxrMFvAemBbAfdabzSY9oea9yCLLaEEtx6nyHmqTWNqEV+ZRmDUjHm1rz9l37ZIDE4ObX7QcH1sumnZsi2K3VLKm2BHkVPYWyL1Z5cg9j2CMYM+G8TE3LS1vp2VcctmxUpuI7rn3Aov3IovnknsdhDdbrk2oUdn5egybDNx9AaZjh4BcU28Pagvyk5PnP1TXZ4nG2R7cmgehpcl0ANq2Brf1pprXWWmuv+eOR+0i+xhMU2kJuObeazBHYFvj7rEAnwzclnnq3Qp5a+XK/DKqLcEEur1b3gK0BrdVnpb4zD6B2zLe9tTb6zSje98yW2655tpieQAe1NlHYdITGdImAbcHLg/XQM6oMVUuucke4FEFeyquAQD475ZnG33Lcd4wYOg4DncG9Ow1Ut1l2o7nnmcVW4OaJtS8ziHbkXhAtwwNW2wScEuzoNZU2QJcppP7WQXXQJb7FuQW3H0B9pZSigtjdmmZJ9B+JBKpNh3bRbX5vdTuqzahpYFO29GvwDLgdgF8LHecbHJwa2BLqLV9D26p2q0VrbnnFsxeXAYUa1yqxXlw72qRcHtrD3BrvO2Nub2hlwZe9DjLep/cAzmz37Xd9bXJwU2mgexBLQHn6fg2VXCrZSbSNJgzsFFjXy6XKrhReAvcGXe4JQ3PW0LsPQaLvAYJtjXZGoHeMqkWKbfXeVgdioSab8trGNomBbdUbRkeQU1prW1vUqOlN20BPAMbh1eDSwItFZCHaflpMHmz1i3HekOE1jfU5OTkGG65p97WGFzzCrx1FHellVtT7AzUEeg8rEvlampiTajRvoRNKq4GtlRkua9BtVgsLsDtATxkXGaRabPKbSk2byuW22tBLcGOHoV552/Z1jxLfh1D2yThJtPA1gDXoKZ1BLcM0ywzkSahpn0g/yjMAl9TaKngEdzaJFY2PnOMB7HXKWWg5vuRxxVNalmvnnqPwqx8+obLNjq0XTrcHsDRWgNXrmkyzXsU5lWuNu6LXHIOOIAL6qxBbbncHFy+vV6v1fBSigtodt3nWMv1tmAfSrkzkGfH2kdHR2ePwqIOpc8ypl063C2WAZ7SWevIRdJcJiD3TywSbM0t1xp6i5tOHYCn3BnY+qbR4M0ovxWu1WMEuHVfvfG2B7g1oea1mWx4dMwYNkm4LWgzQHuQS9eI4iygyTywvXG3B3fkkmdccb5vwZ3Z7pvWu6aWcA1s7T5o91YDmwNuvReeebc8ajPedpRO2x/Kst8KuwvA+wD8LZx+Wuhf1lo/NXRhCFi+7YV5QGthgA64TOOZbHjWDG+k3BmllmpNEHPACGoJdzTezcZljs0u0qux0liLvFeWQkYvlmiAe2+ryTytdSaNlXYMyyr3ewF8vNb6T0spKwB3jFYixSzAAYSQAzgDgsI918jqRbWGZqm2dMujRq2521Y4rSXUGtwamF54l7AI4C77LS45v2dylrrlMZin3jJPTRSGChvSMv9bfieAH6y1/gsAqLWuAXx9lNJAB5m2t/mr2zyN3Ob7FtytrpGnMBnos266Nc624iTcWbBb4mUab96hT5wcDmltRVNt740x7/m29k+nHG6vXQ21P6RllPt7Afx5KeUBAH8HwGcAvK3W+s2xCmVBLfd5xXig8/0uMPeBGPAfhVmgyjip0JZ6Z+AectHGytp2S7wGtgZ41FFnwPYUnGbLo7aasTEhtiwD9wrAawD8dK31M6WUfw/g3wJ4t0x4s+O3wjjMVpgFOYVFPeJiof8LKu/howaSaUyeu8/Lyy2r9FK9F4sF1uv1OZcUeP4PGYeCV/4WW4PbAjRys61hFKUt5flvcdda1ZdOxlqoM5iaZb8VViyX5yxBKS8C8Pu11pdv918H4O211n8i0tXoXJplGoYV1+WY4+NjPPfcc/jWt76F5557Llwy6bw0AM6emR4dHZ17hnrt2rVB4nh8ZswdTZi1HOcprgd3pgPQwlerFa5fv55erl27huvXr+O22247t589VrrlU7Rtx3fBNch8ceSpUsqTpZRX1Fq/BOD1AB4bo4Db/Mw4ViY1nMdbcd6ES+sbTdyFs5QPwIVxHFcG680lug7NjeUuOD+G1hxEuY62LTeZl8e7f9aciXWe1njq3Ag+raOjzi76B1NtfO4N7fbNst3SWwF8sJRyBODLAN4yVoE8yGWaLvFZuLvCzCGhMXcEtmxYGhSai27NHXCgLchlnLV442CvvrX7qG1H8TItwS0B56CTF+MBboHdOrE6Zct+wvcPAPy9kctyzqIK7gq/hMl69um96EBjXw1yCQ2AC2C3KrcEXIJNnQF5LBLYCGYtzBveWPdAGz9H96o13Wq1ugC0NUyxVDsC+1AAn/6AwrCulR+94BC96CDB5oBbgGjKbQHOLQJbpiXzJuSimXtPubX8oo60JTxzDKlyK+CWay7bwiHZ3sDdtycldePK3eUVRYLUGstqj8LksVI9PMUgsOlFHJo9pvE8T0fAybFz6xJNdkXzIpqCZ8Iy6TncHHINar5tDYuuvFu+a9MqNzPRZp2LN8hozG2BzZXaGstymDgIlquvNTB+vVK5qewEtqbsgP6FE28/kzYDtpw30PYz217ccrk8B7O2bY29rUddcqh2KIBPDm4+maTFccu4htJkT90ymcbdck3BrfGq5hFYs7SWa05wa9fP09C+nPXWZsIzcXKb5yvvTWZpSast/JGgtVjKrXWqGtiHYpOCWwNbqpkMo/DsTYmUO4KdK3dmLFtrveAVaIsGuASb4OXXTec/OTk5e+HCA9SCNoqXYGv3SS4SGk0dW8Pk76050PRcWkJuzXd4k5qHAPmk4JYmYeeNnu9TWNZNtwDPPNP2xt7WeNXrTKJGJVWZG43FadGUW7ruUVg05ub1L++LBNFaZ9JYx0hVli/4eGNta8wt8zkUmwzcGsgSYm2/BXAJdaTgEdSklrQvx798MizbgLnR9WhuN4/jefD4liU7kRaB7dWxrO+WfQm35nq3POPOTGruO+iTgZubBNuDusUlBy4+CvMUnI+vJdjSPfcgaXVF6br4mlxzcsPpvHyijcLpuEh9+8TL+5UZ7vB47TFUZtF+wRUtmlue8aT23SYHtwe2BXUGdn68p9oSalJnDWwOuOf2WqqQGeNx2Cgd35bnorQSUr7txUXpeJm0Oo5A52BpkMkwua/9JJP26VdcEdgtjyL32SYBt3TJZRhv0C2qbZ23BXDpeq9Wq3Mge5NOAM5eOqG8vbXclmBLD8Zay3JoZRtqzevUgtp6fyATL9casBJ2bZwdva12SO442STgJvMgjwD3QOfnjdxx+lEGgU1w83UGcloWi4tvPbU0Hg2m6DyWyo6xzcuiAW493/f2tXDaloBqkEdxltdwaAo+KbjJPKAzMHvnJTc5Umv+mIvCONAW5FLFKZybBkeUpss5rLAhw4GLnocG+FCL9UirdTlkqMkmCTe3FtAzwGtjXW8CR8LOgY4mmgCce5uM1p6Lq0HsucbeucYy6QlRWKYu+ygu7WeUX6q+PC6aTDsEyCcHt4TVi/PcUisumsW1gNZeTokWyi9KR9djwWudO9vBeMOVLmlb3HINvGhsHK2tcXqX9SHOkpNNBu4IZkAfX2fdcznL7E2m0XNjDXIOkgW5lq91jHTb5XbmWL7P8+2ybcXLa5L7mXq1INdmv71Z8a6z75FiH9rE2mTg5qbNlPNtDewWyCPF5tsccA0qyttSzsViceGFFn4+Op72NRXn8fLRmzahl52d1xoyX2t16nlNGuQe0NaivYRiwT3kMrvlOzIPcKA72JQ2GmNLoCy3mK95+WjNYaaFGg8pLQ/TlDsaIvBFlkEC3BqXATwzf6EBLiHW3jCT28vl+ZdfZJ594g4FarJJwS0btwW13PduiHZO7eZqgC+Xy86Qky0Wiwv/hKI1Ijlk4OEa5Na/q8jzaGrUGs/rTta5dYzmGsuxc/Y9cb5NcMv76K1b0x4K4JmPErwCwIcBVAAFwMsB/Lta68+PUSANRiD/Y5EM7F4PzhtkdmztTWTR+ekPHUop6h8tLBaLC+fRxtcEs/VHhzzfLstiEf8biabk8npprc1mW6649fNNvs/hlvkNEcavY98t8++nXwLwagAopSwAfAXAR8cslAScwliZLoRRuHZTpAfgKQwfG2ugWwDK/PjC1dr6BxWuuNKkcnt/zsjzlw23tXFbwFt17NWrNfbWgLb+0VTCreXbugAXH+cdirW65f8AwP+ptT45RmG4aTBrcTw+c2MyEysS5mjJXEsErUwTueMcaP7RAPICNBXlL/DQms9BaAos6586Sk29NbCtMbfmmnuQ0/ZyubxQp57ydt0+BMhb4f5nAD40RkE8s8Dw4q1zcIXsCniUj6cSvPwEHK3ltXiAc7AJ7vV6fXYObUxJ23xWnkPMGzgvm5zYlIBrYFhjbs015+43/080bc3hlvdWrvvEHYKl4S6n/1n+Rpx+SujSreuN4A1Put8Sas8l1yCP3EVu3P3XlJuns9xyApsvQPyzVg4trWmb1y3F8fSRckuvQSq39dhLU20JOodb5p0J6xK+z9ai3P8IwGdrrc9YCW52+FbYrivVUlXe8Pk+NXoOOt+W8NM+cN7tlp2IBEHrBDSvQT7jlopOxxGEHFpeB9w44BxkPhfAyxPds8hF91x2qwPgY+6rbtlvhbXA/WYELjmHe7arYX08qNm6mRTOW7duqelS/8JeSrkDp5Np/22Ass12QJaZUBzyuNnylv2c0LMAvnvkssy2hzYr93TtsL6fMtvObVbu6doM92y9bFbu6doM92y9bFbu6doM92yzHajNcM/Wy2a3fLo2wz1bL5vd8unapcOdedNmH/MCgCeeeGKn+X3zm9/caX5PP/30TpV71/dv3/Ob4R7RDh3uZ555ZqfK/fDDD3fKq6vNcM92pW0ec0/XZrhn62XzmHu6Voaq5FLKfLdmm+2SrNZ6wRUaDO7ZZpttWja75bPNdqA2wz3bbAdqlwZ3KeX+UsoXSylfKqW8feS83l9KeaqU8odj5sPyu6eU8olSyv8qpXyhlPLWkfO7Xkr5VCnl0W1+7x4zv22ei1LK50opHxs7r21+f1xK+YPtNX565LzuKqX8Winl8e09/IER83rF9po+t13/5WDtpeVfPodacNqp/G8ALwNwBODzAL5vxPxeB+BVAP5wR9f3VwG8arv9AgBPjHl923zu2K6XAP4HgHtHzu9fA/ivAD62ozr9MoAX7iiv/wLgLdvtFYA7d5TvAsD/A/DXhjjfZSn3vQD+qNb6J7XWYwC/CuDHxsqs1vpJAH8x1vmV/L5Wa/38dvsbAB4H8JKR83x2u3kdpw1ytJnSUso9AN4A4H1j5aFlix14mqWUOwH8YK31AQCota5rrV8fO9+tDfrX4ZcF90sA8Av4CkZu/JdlpZTvwanX8KmR81mUUh4F8DUAv11rfWTE7H4OwM9ixA5EsQrgt0opj5RSfmrEfL4XwJ+XUh7Yusr/qZRy+4j5cRv0r8PnCbURrZTyAgAfAfC2rYKPZrXWk1rrqwHcA+AHSinfP0Y+pZQfBfDU1jMp22UXdl+t9e/i1GP46VLK60bKZwXgNQB+odb6GgDPYgd/583+OvzXhjrnZcH9ZwBeyvbv2YYdjJVSVjgF+5drrb++q3y3LuTvALh/pCzuA/DGUsqXcaoyP1RK+cBIeZ1ZrfWr2/UzOP2c1b0jZfUVAE/WWj+z3f8ITmEf28K/Dm+1y4L7EQB/o5TyslLKNQA/DmDsWdddqgwA/CKAx2qt7x07o1LKd5VS7tpu3w7ghwF8cYy8aq3vrLW+tNb6cpzet0/UWn9yjLzISil3bL0glFK+A8CPAPifY+RVa30KwJPl9AOYAPB6AI+NkZew8K/DW+1SPuFba92UUn4GwIM47WDeX2t9fKz8Sim/AuAGgO8spfwpgHfThMlI+d0H4CcAfGE7Dq4A3llr/c2RsrwbwC+V0w81LgB8uNb68ZHyugx7EYCPbl9xXgH4YK31wRHzeyuAD25d5S8DeMuIefG/Dv9Xg553OwU/22yzHZjNE2qzzXagNsM922wHajPcs812oDbDPdtsB2oz3LPNdqA2wz3bbAdqM9yzzXagNsM922wHav8ffWWIzAcsEaMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3aca67c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.imshow(digits.images[0], cmap=plt.cm.gray_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('size of the data', (1797, 64))\n"
     ]
    }
   ],
   "source": [
    "# ข้อมูลที่จะนำไปใช้ใน scikit-learn จะต้องแปลงให้เป็นเว็กเตอร์ ดังนั้น รูปภาพขนาด 8x8 เมื่อแปลงเป็นเว็กเตอร์จึงมีขนาด 64\n",
    "data = digits.images.reshape((digits.images.shape[0], -1))\n",
    "\n",
    "print(\"size of the data\", data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('size of each row', (64,))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.,  0.,  0., 13., 15., 10.,\n",
       "       15.,  5.,  0.,  0.,  3., 15.,  2.,  0., 11.,  8.,  0.,  0.,  4.,\n",
       "       12.,  0.,  0.,  8.,  8.,  0.,  0.,  5.,  8.,  0.,  0.,  9.,  8.,\n",
       "        0.,  0.,  4., 11.,  0.,  1., 12.,  7.,  0.,  0.,  2., 14.,  5.,\n",
       "       10., 12.,  0.,  0.,  0.,  0.,  6., 13., 10.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"size of each row\", data[0].shape)\n",
    "data[0]"
   ]
  }
 ],
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