(原創) 如何产生Yokoi Connectivity Number? (.NET) (C++/CLI) (C/C++) (Image Processing)
本范例先将leng.jpg轉成binary image，然後从512*512 downsampling成64*64，downsampling的规则为以8*8为unit，取topmost-left为downsampled data，最后产生Yokoi Connectivity Number。
1
/*
2
(C) OOMusou 2006 http://oomusou.cnblogs.com
3
4Filename : memset1.cpp
5Compiler : Visual C++ 8.0
6Description : Demo how to produce Yokoi connectivity number
7Release : 12/06/2006
8
*/
9
10#include "stdafx.h"
11#include <fstream>
12#include <iostream>
13
14using namespace System::Drawing;
15using namespace System::Drawing::Imaging;
16
17// enum for q,r,s
18// only support in C++/CLI
19enum class hType {
20 q,
21 r,
22 s
23};
24
25// Binarize image
26void binarize(Bitmap^ , Bitmap^);
27// Downsampling image by factor
28void downSampleing(Bitmap^ , Bitmap^, int, int);
29// h func for Yokoi
30hType h(Color, Color, Color, Color);
31// h func for Yokoi
32int f(hType, hType, hType, hType);
33// Process Yokoi connectivity number
34void yokoi(Bitmap^ , const char*);
35
36int main() {
37 // Read lena.jpg
38 Bitmap^ oriImg = gcnew Bitmap("lena.jpg");
39 // Declare binary image for lena.jpg
40 Bitmap^ binImg = gcnew Bitmap(oriImg->Width, oriImg->Height);
41 // Binarize lena.jpg
42 binarize(oriImg, binImg);
43
44 // Declare down-sampling image for binarized image
45 Bitmap^ dsImg = gcnew Bitmap(64, 64);
46 // Downsampling image by factor 8*8
47 downSampleing(binImg, dsImg, 8, 8);
48 // Process Yokoi connectivity number
49 yokoi(dsImg, "YokoiMatrix.txt");
50
51 return 0;
52}
53
54// Binarize image
55void binarize(Bitmap^ oriImg, Bitmap^ binImg) {
56
for (int y = 0; y != oriImg->Height; ++y) {
57 for (int x = 0; x != oriImg->Width; ++x) {
58 int gray = (oriImg->GetPixel(x, y).R +
59 oriImg->GetPixel(x, y).G +
60 oriImg->GetPixel(x, y).B) / 3;
61
62 // If intensity >= 128, set the pixel to black.
63 // If intensity < 128, set the pixel to white.
64 if (gray >= 128) {
65 binImg->SetPixel(x, y, Color::White);
66
}
67 else {
68 binImg->SetPixel(x, y, Color::Black);
69 }
70 }
71 }
72}
73
74// Downsampling image by factor
75void downSampleing(Bitmap^ oriImg, Bitmap^ dsImg, int unitX, int unitY) {
76 for (int x = 0, i = 0; x != oriImg->Width; x += unitX, ++i) {
77 for (int y = 0, j = 0; y != oriImg->Height; y += unitY, ++j) {
78 dsImg->SetPixel(i, j,oriImg->GetPixel(x, y));
79 }
80 }
81}
82
83// h func for Yokoi
84// Computer and Robot Vision P.274, Robert M. Haralick
85hType h(Color b, Color c, Color d, Color e) {
86 if (b == c && (d != b || e != b)) {
87 //return q;
88 return hType::q;
89 }
90 else if (b == c && (d == b && e == b)) {
91 //return r;
92 return hType::r;
93 }
94 else {
95 //return s;
96 return hType::s;
97 }
98}
99
100// f func for Yokoi
101// Computer and Robot Vision P.274, Robert M. Haralick
102int f(hType a1, hType a2, hType a3, hType a4) {
103 if ((a1 == a2) && (a2 == a3) && (a3 == a4) && (a4 == hType::r)) {
104 return 5;
105 }
106 else {
107 // Count the number of q
108 int n = 0;
109
110 if (a1 == hType::q) ++n;
111 if (a2 == hType::q) ++n;
112 if (a3 == hType::q) ++n;
113 if (a4 == hType::q) ++n;
114
115 return n;
116 }
117}
118
119// Process Yokoi connectivity number
120void yokoi(Bitmap^ oriImg, const char* fileName) {
121 std::ofstream output(fileName);
122
123 for (int y = 0; y != oriImg->Height; ++y) {
124 for (int x = 0; x != oriImg->Width; ++x) {
125 Color x0 = oriImg->GetPixel(x, y);
126
127 // Only process 1 in binary image (White)
128 if (x0 == Color::FromArgb(255,255,255)) {
129 Color x1 = Color::Black;
130 if (x+1 < oriImg->Width) { // Check for the boundary
131 x1 = oriImg->GetPixel(x+1, y);
132 }
133
134 Color x2 = Color::Black;
135 if (y-1 >= 0) {
136 x2 = oriImg->GetPixel(x, y-1);
137 }
138
139 Color x3 = Color::Black;
140 if (x-1 >= 0) {
141 x3 = oriImg->GetPixel(x-1, y);
142 }
143
144 Color x4 = Color::Black;
145 if (y+1 < oriImg->Height) {
146 x4 = oriImg->GetPixel(x, y+1);
147 }
148
149 Color x5 = Color::Black;
150 if (x+1 < oriImg->Width && y+1 < oriImg->Height) {
151 x5 = oriImg->GetPixel(x+1, y+1);
152 }
153
154 Color x6 = Color::Black;
155 if (x+1 < oriImg->Width && y-1 >= 0) {
156 x6 = oriImg->GetPixel(x+1, y-1);
157 }
158
159 Color x7 = Color::Black;
160 if (x-1 >= 0 && y-1 >= 0) {
161 x7 = oriImg->GetPixel(x-1, y-1);
162 }
163
164 Color x8 = Color::Black;
165 if (x-1 >= 0 && y+1 < oriImg->Height) {
166 x8 = oriImg->GetPixel(x-1, y+1);
167 }
168
169 // Computer and Robot Vision P.274, Robert M. Haralick
170 int n = f(h(x0, x1, x6, x2),
171 h(x0, x2, x7, x3),
172 h(x0, x3, x8, x4),
173 h(x0, x4, x5, x1));
174
175 // Write to file
176 output << n << " ";
177
178 }
179 else { // 0 in binary image (Black)
180 output << " " << " ";
181 }
182 }
183 // New line
184 output << std::endl;
185 }
186}
/* 
2
(C) OOMusou 2006 http://oomusou.cnblogs.com3
4
Filename : memset1.cpp5
Compiler : Visual C++ 8.06
Description : Demo how to produce Yokoi connectivity number7
Release : 12/06/20068
*/9
10
#include "stdafx.h"11
#include <fstream>12
#include <iostream>13
14
using namespace System::Drawing;15
using namespace System::Drawing::Imaging;16
17
// enum for q,r,s 18
// only support in C++/CLI19
enum class hType {
20
q,21
r,22
s23
};24
25
// Binarize image26
void binarize(Bitmap^ , Bitmap^);27
// Downsampling image by factor28
void downSampleing(Bitmap^ , Bitmap^, int, int);29
// h func for Yokoi30
hType h(Color, Color, Color, Color);31
// h func for Yokoi32
int f(hType, hType, hType, hType);33
// Process Yokoi connectivity number34
void yokoi(Bitmap^ , const char*);35
36
int main() {37
// Read lena.jpg38
Bitmap^ oriImg = gcnew Bitmap("lena.jpg");39
// Declare binary image for lena.jpg40
Bitmap^ binImg = gcnew Bitmap(oriImg->Width, oriImg->Height);41
// Binarize lena.jpg42
binarize(oriImg, binImg);43
44
// Declare down-sampling image for binarized image45
Bitmap^ dsImg = gcnew Bitmap(64, 64);46
// Downsampling image by factor 8*847
downSampleing(binImg, dsImg, 8, 8);48
// Process Yokoi connectivity number49
yokoi(dsImg, "YokoiMatrix.txt");50
51
return 0;52
}53
54
// Binarize image55
void binarize(Bitmap^ oriImg, Bitmap^ binImg) {56
for (int y = 0; y != oriImg->Height; ++y) {
57
for (int x = 0; x != oriImg->Width; ++x) {58
int gray = (oriImg->GetPixel(x, y).R +59
oriImg->GetPixel(x, y).G +60
oriImg->GetPixel(x, y).B) / 3;61
62
// If intensity >= 128, set the pixel to black.63
// If intensity < 128, set the pixel to white.64
if (gray >= 128) {65
binImg->SetPixel(x, y, Color::White);66
}67
else {68
binImg->SetPixel(x, y, Color::Black);69
}70
}71
}72
}73
74
// Downsampling image by factor75
void downSampleing(Bitmap^ oriImg, Bitmap^ dsImg, int unitX, int unitY) {76
for (int x = 0, i = 0; x != oriImg->Width; x += unitX, ++i) {77
for (int y = 0, j = 0; y != oriImg->Height; y += unitY, ++j) {78
dsImg->SetPixel(i, j,oriImg->GetPixel(x, y));79
}80
}81
}82
83
// h func for Yokoi84
// Computer and Robot Vision P.274, Robert M. Haralick85
hType h(Color b, Color c, Color d, Color e) {86
if (b == c && (d != b || e != b)) {87
//return q;88
return hType::q;89
}90
else if (b == c && (d == b && e == b)) {91
//return r;92
return hType::r;93
}94
else {95
//return s;96
return hType::s;97
}98
}99
100
// f func for Yokoi101
// Computer and Robot Vision P.274, Robert M. Haralick102
int f(hType a1, hType a2, hType a3, hType a4) {103
if ((a1 == a2) && (a2 == a3) && (a3 == a4) && (a4 == hType::r)) {104
return 5;105
}106
else {107
// Count the number of q108
int n = 0;109
110
if (a1 == hType::q) ++n;111
if (a2 == hType::q) ++n;112
if (a3 == hType::q) ++n;113
if (a4 == hType::q) ++n;114
115
return n;116
}117
}118
119
// Process Yokoi connectivity number120
void yokoi(Bitmap^ oriImg, const char* fileName) {121
std::ofstream output(fileName);122
123
for (int y = 0; y != oriImg->Height; ++y) {124
for (int x = 0; x != oriImg->Width; ++x) {125
Color x0 = oriImg->GetPixel(x, y);126
127
// Only process 1 in binary image (White)128
if (x0 == Color::FromArgb(255,255,255)) {129
Color x1 = Color::Black;130
if (x+1 < oriImg->Width) { // Check for the boundary131
x1 = oriImg->GetPixel(x+1, y);132
}133
134
Color x2 = Color::Black;135
if (y-1 >= 0) {136
x2 = oriImg->GetPixel(x, y-1);137
}138
139
Color x3 = Color::Black;140
if (x-1 >= 0) {141
x3 = oriImg->GetPixel(x-1, y);142
}143
144
Color x4 = Color::Black;145
if (y+1 < oriImg->Height) {146
x4 = oriImg->GetPixel(x, y+1);147
}148
149
Color x5 = Color::Black;150
if (x+1 < oriImg->Width && y+1 < oriImg->Height) {151
x5 = oriImg->GetPixel(x+1, y+1);152
}153
154
Color x6 = Color::Black;155
if (x+1 < oriImg->Width && y-1 >= 0) {156
x6 = oriImg->GetPixel(x+1, y-1);157
}158
159
Color x7 = Color::Black;160
if (x-1 >= 0 && y-1 >= 0) {161
x7 = oriImg->GetPixel(x-1, y-1);162
}163
164
Color x8 = Color::Black;165
if (x-1 >= 0 && y+1 < oriImg->Height) {166
x8 = oriImg->GetPixel(x-1, y+1);167
}168
169
// Computer and Robot Vision P.274, Robert M. Haralick170
int n = f(h(x0, x1, x6, x2),171
h(x0, x2, x7, x3),172
h(x0, x3, x8, x4),173
h(x0, x4, x5, x1));174
175
// Write to file176
output << n << " ";177
178
}179
else { // 0 in binary image (Black)180
output << " " << " ";181
}182
}183
// New line184
output << std::endl;185
}186
}
原图
Downsampling
Yokoi Connectivity Number
11 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
21 5 5 5 5 5 5 1 1 5 5 5 5 5 5 5 5 5 5 1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1
31 5 5 5 5 5 5 1 1 3 1 1 2 1 1 5 5 1 1 1 3 2 2 1 1 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 1 2 1
41 5 5 5 5 5 5 1 2 2 1 1 1 1 2 1 1 0 2 1 1 5 5 5 5 5 5 5 5 5 5 1 1 1
51 5 5 5 5 5 5 1 1 3 1 3 1 1 1 1 1 2 1 2 2 1 5 5 5 5 5 5 5 5 5 5 5 1 0
61 5 5 5 5 5 5 1 1 1 1 2 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1 1
71 5 1 1 1 5 5 1 1 1 1 3 2 1 1 1 1 1 2 1 3 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1
81 5 1 1 5 5 1 1 1 1 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1
91 1 1 1 5 5 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1
101 1 1 5 5 1 0 1 2 5 1 1 1 5 5 5 5 5 1 1 1 1 5 5 1 1 1 5 5 5 5 5 5 1 1
112 1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 5 5 5 5 1 1
121 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 5 5 5 1 1
13 1 5 5 1 0 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 5 5 1 1 1 2
14 1 5 5 1 1 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 1 1 1 1 1
15 1 5 5 1 1 2 2 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 1 1 1 1 1 5 1
16 1 5 5 1 2 1 2 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 2 2 1 5 1 1 1 1 1 1 1 1 5 5 1
17 1 5 5 1 2 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 1 1 1 5 5 5 1 1 5 5 5 1
18 1 5 5 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 1 1 1 5 5 5 1 1 1 1 5 5 5 1
19 1 5 5 1 1 2 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 5 1
20 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 1
21 1 5 5 1 1 1 1 2 2 1 5 1 1 1 5 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 5 5 5 5 5 1
22 1 5 5 1 1 5 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 1
23 1 5 5 1 1 5 5 1 0 1 2 2 1 2 2 1 5 5 5 5 5 5 5 1 1 1 0 1 1 5 5 5 5 5 5 1
24 1 5 5 1 1 1 5 1 0 0 2 2 0 1 1 1 1 5 5 5 5 5 1 1 2 0 1 5 5 5 5 5 5 5 1
25 1 5 5 1 1 5 1 0 1 2 1 1 5 5 5 5 1 1 1 2 1 2 1 1 5 5 5 5 5 5 5 1
26 1 5 5 1 1 2 2 1 0 0 1 5 5 5 5 5 1 1 1 1 1 2 5 5 5 5 5 5 5 1
27 1 5 5 1 2 0 1 1 5 5 5 5 5 1 1 2 1 1 5 5 5 5 5 5 5 1
28 1 5 5 1 2 0 0 1 1 5 5 5 5 5 5 5 1 1 1 1 1 5 5 5 5 5 5 5 1
29 1 5 5 1 0 2 1 1 5 5 5 5 5 5 5 5 1 1 5 5 5 5 5 5 5 5 5 1
30 1 5 5 1 1 0 1 1 5 5 5 5 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 5 5 5 1
31 1 5 5 1 1 1 5 5 1 1 1 1 5 5 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1
32 1 5 5 1 1 1 0 1 1 1 1 1 1 1 1 5 5 5 1 1 2 1 5 5 5 5 5 5 5 5 5 1
33 1 5 5 1 1 1 2 1 1 5 1 1 1 5 1 1 1 2 1 1 1 5 5 5 5 5 5 5 5 5 1
34 1 5 5 1 2 1 1 0 1 1 1 1 1 1 5 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1
35 1 5 5 1 1 1 1 1 1 1 2 1 1 1 5 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1
36 1 5 5 1 1 0 2 1 1 2 1 1 5 5 5 5 5 1 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1
37 1 5 5 1 2 1 1 3 2 1 5 5 5 5 5 5 5 5 5 5 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 1
38 1 5 5 1 1 1 1 5 5 5 5 5 1 1 1 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1
39 1 5 5 1 1 1 1 1 5 5 5 5 1 1 1 1 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1
40 1 5 5 1 1 1 1 5 5 5 5 1 1 5 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1
41 1 5 5 1 0 0 1 1 1 5 5 5 5 1 1 1 5 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1
42 1 5 5 1 1 1 5 5 5 5 5 1 1 1 5 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1
43 1 5 5 1 1 1 0 1 2 5 5 5 5 5 5 1 1 2 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1
44 1 5 5 1 2 2 1 1 5 1 1 1 1 1 5 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1
45 1 5 5 1 0 1 2 1 1 1 1 5 2 1 1 5 5 5 5 5 5 5 1 1 1 5 5 5 5 5 1
46 1 5 5 1 0 0 0 1 1 1 1 1 5 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 5 1
47 1 5 5 1 0 1 1 1 1 1 5 1 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 5 1
48 1 5 5 1 0 1 1 5 5 5 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 1 1
49 1 5 5 1 1 1 1 5 5 5 1 2 1 1 1 1 1 1 1 1 1 5 5 5 1 1
50 1 1 5 2 1 0 1 0 1 1 5 5 5 1 1 1 2 1 1 1 1 5 5 1 1
510 1 5 1 0 2 1 5 5 5 5 5 5 1 1 1 2 1 1 1 1 5 5 1 1
52 1 1 5 1 1 2 3 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 1 5 1 1
53 2 2 1 5 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 1 1 1 1 5 1
54 2 1 5 1 0 1 1 1 1 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 1 1 2 1 5 1 1
55 2 1 5 2 1 0 0 1 3 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 1 2 2 1 5 1
56 2 1 5 1 1 1 1 0 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 2 1 1 5 1 1
57 2 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 5 1 1 5 1
58 2 1 1 5 1 1 0 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 2 2 1 1 5 1
59 1 1 1 5 1 0 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 1 1
60 1 1 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 1
61 1 1 1 5 1 0 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 2 1 1
62 1 1 1 5 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1
63 1 1 1 5 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1
64 1 1 1 1 1 0 0 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2
1 5 5 5 5 5 5 1 1 5 5 5 5 5 5 5 5 5 5 1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 3
1 5 5 5 5 5 5 1 1 3 1 1 2 1 1 5 5 1 1 1 3 2 2 1 1 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 1 2 1 4
1 5 5 5 5 5 5 1 2 2 1 1 1 1 2 1 1 0 2 1 1 5 5 5 5 5 5 5 5 5 5 1 1 1 5
1 5 5 5 5 5 5 1 1 3 1 3 1 1 1 1 1 2 1 2 2 1 5 5 5 5 5 5 5 5 5 5 5 1 0 6
1 5 5 5 5 5 5 1 1 1 1 2 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1 1 7
1 5 1 1 1 5 5 1 1 1 1 3 2 1 1 1 1 1 2 1 3 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 8
1 5 1 1 5 5 1 1 1 1 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 9
1 1 1 1 5 5 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 10
1 1 1 5 5 1 0 1 2 5 1 1 1 5 5 5 5 5 1 1 1 1 5 5 1 1 1 5 5 5 5 5 5 1 1 11
2 1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 5 5 5 5 1 1 12
1 1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 5 5 5 1 1 13
1 5 5 1 0 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 5 5 1 1 1 2 14
1 5 5 1 1 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 1 1 1 1 1 15
1 5 5 1 1 2 2 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 1 1 1 1 1 5 1 16
1 5 5 1 2 1 2 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 2 2 1 5 1 1 1 1 1 1 1 1 5 5 1 17
1 5 5 1 2 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 1 1 1 5 5 5 1 1 5 5 5 1 18
1 5 5 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 1 1 1 5 5 5 1 1 1 1 5 5 5 1 19
1 5 5 1 1 2 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 5 1 20
1 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 1 21
1 5 5 1 1 1 1 2 2 1 5 1 1 1 5 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 5 5 5 5 5 1 22
1 5 5 1 1 5 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 1 23
1 5 5 1 1 5 5 1 0 1 2 2 1 2 2 1 5 5 5 5 5 5 5 1 1 1 0 1 1 5 5 5 5 5 5 1 24
1 5 5 1 1 1 5 1 0 0 2 2 0 1 1 1 1 5 5 5 5 5 1 1 2 0 1 5 5 5 5 5 5 5 1 25
1 5 5 1 1 5 1 0 1 2 1 1 5 5 5 5 1 1 1 2 1 2 1 1 5 5 5 5 5 5 5 1 26
1 5 5 1 1 2 2 1 0 0 1 5 5 5 5 5 1 1 1 1 1 2 5 5 5 5 5 5 5 1 27
1 5 5 1 2 0 1 1 5 5 5 5 5 1 1 2 1 1 5 5 5 5 5 5 5 1 28
1 5 5 1 2 0 0 1 1 5 5 5 5 5 5 5 1 1 1 1 1 5 5 5 5 5 5 5 1 29
1 5 5 1 0 2 1 1 5 5 5 5 5 5 5 5 1 1 5 5 5 5 5 5 5 5 5 1 30
1 5 5 1 1 0 1 1 5 5 5 5 5 5 5 5 5 1 1 1 1 5 5 5 5 5 5 5 5 5 1 31
1 5 5 1 1 1 5 5 1 1 1 1 5 5 5 5 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 32
1 5 5 1 1 1 0 1 1 1 1 1 1 1 1 5 5 5 1 1 2 1 5 5 5 5 5 5 5 5 5 1 33
1 5 5 1 1 1 2 1 1 5 1 1 1 5 1 1 1 2 1 1 1 5 5 5 5 5 5 5 5 5 1 34
1 5 5 1 2 1 1 0 1 1 1 1 1 1 5 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1 35
1 5 5 1 1 1 1 1 1 1 2 1 1 1 5 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1 36
1 5 5 1 1 0 2 1 1 2 1 1 5 5 5 5 5 1 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 1 37
1 5 5 1 2 1 1 3 2 1 5 5 5 5 5 5 5 5 5 5 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 1 38
1 5 5 1 1 1 1 5 5 5 5 5 1 1 1 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 39
1 5 5 1 1 1 1 1 5 5 5 5 1 1 1 1 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 40
1 5 5 1 1 1 1 5 5 5 5 1 1 5 1 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 1 41
1 5 5 1 0 0 1 1 1 5 5 5 5 1 1 1 5 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 42
1 5 5 1 1 1 5 5 5 5 5 1 1 1 5 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 43
1 5 5 1 1 1 0 1 2 5 5 5 5 5 5 1 1 2 1 1 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 44
1 5 5 1 2 2 1 1 5 1 1 1 1 1 5 1 2 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 45
1 5 5 1 0 1 2 1 1 1 1 5 2 1 1 5 5 5 5 5 5 5 1 1 1 5 5 5 5 5 1 46
1 5 5 1 0 0 0 1 1 1 1 1 5 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 5 1 47
1 5 5 1 0 1 1 1 1 1 5 1 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 5 1 48
1 5 5 1 0 1 1 5 5 5 1 1 5 5 5 5 5 5 5 1 1 5 5 5 5 1 1 49
1 5 5 1 1 1 1 5 5 5 1 2 1 1 1 1 1 1 1 1 1 5 5 5 1 1 50
1 1 5 2 1 0 1 0 1 1 5 5 5 1 1 1 2 1 1 1 1 5 5 1 1 51
0 1 5 1 0 2 1 5 5 5 5 5 5 1 1 1 2 1 1 1 1 5 5 1 1 52
1 1 5 1 1 2 3 1 1 5 5 5 5 5 5 5 5 1 1 1 5 5 1 1 1 1 5 1 1 53
2 2 1 5 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 5 1 1 1 1 5 1 54
2 1 5 1 0 1 1 1 1 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 1 1 2 1 5 1 1 55
2 1 5 2 1 0 0 1 3 1 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5 5 1 2 2 1 5 1 56
2 1 5 1 1 1 1 0 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 5 5 2 1 1 5 1 1 57
2 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 5 1 1 5 1 58
2 1 1 5 1 1 0 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 2 2 1 1 5 1 59
1 1 1 5 1 0 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 1 1 60
1 1 1 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 5 1 61
1 1 1 5 1 0 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 2 1 1 62
1 1 1 5 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 63
1 1 1 5 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 64
1 1 1 1 1 0 0 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Reference
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