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How to produce a perfect (Nasik) magic 15x15x15 cube?
Use Frost's method to produce a perfect (nasik) magic 15x15x15 cube.
You need a 15x15 magic square, which is panmagic, symmetric, but not compact.
Use the horizontal shifted versions of the 15x15 magic square: 2-4-6-8-10-12-14-[1]-3-5-7-9-11-13-15 and
use the grids with the row- or the column coördinates in reversed order (15 up to 1 in stead of 1 up to 15).
Take 1x digit from the shifted versions of the 15x15 magic square and add 225x digit from row- or column grid.
|
1x digit [1st level] + 225x digit [1st level]
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
1x digit [2nd level] + 225x digit [2nd level]
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
1x digit [3rd level] + 225x digit [3rd level]
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
1x digit [4th level] + 225x digit [4th level]
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
1x digit [5th level] + 225x digit [5th level]
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
1x digit [6th level] + 225x digit [6th level]
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
1x digit [7th level] + 225x digit [7th level]
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
1x digit [8th level] + 225x digit [8th level]
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
1x digit [9th level] + 225x digit [9th level]
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
1x digit [10th level] + 225x digit [10th level]
|
|
87
|
213
|
209
|
152
|
118
|
64
|
26
|
1
|
142
|
171
|
188
|
100
|
129
|
45
|
50
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
115
|
69
|
30
|
5
|
147
|
168
|
194
|
92
|
133
|
34
|
56
|
76
|
217
|
201
|
158
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
|
21
|
8
|
145
|
174
|
195
|
95
|
132
|
33
|
59
|
77
|
223
|
199
|
161
|
106
|
67
|
|
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
|
184
|
101
|
121
|
37
|
51
|
83
|
220
|
204
|
165
|
110
|
72
|
18
|
14
|
137
|
178
|
|
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
|
48
|
89
|
212
|
208
|
154
|
116
|
61
|
22
|
6
|
143
|
175
|
189
|
105
|
125
|
42
|
|
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
|
159
|
120
|
65
|
27
|
3
|
149
|
167
|
193
|
94
|
131
|
31
|
52
|
81
|
218
|
205
|
|
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
|
7
|
141
|
173
|
190
|
99
|
135
|
35
|
57
|
78
|
224
|
197
|
163
|
109
|
71
|
16
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
103
|
124
|
41
|
46
|
82
|
216
|
203
|
160
|
114
|
75
|
20
|
12
|
138
|
179
|
182
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
1x digit [11th level] + 225x digit [11th level]
|
|
136
|
172
|
186
|
98
|
130
|
39
|
60
|
80
|
222
|
198
|
164
|
107
|
73
|
19
|
11
|
|
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
|
122
|
43
|
49
|
86
|
211
|
202
|
156
|
113
|
70
|
24
|
15
|
140
|
177
|
183
|
104
|
|
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
|
215
|
207
|
153
|
119
|
62
|
28
|
4
|
146
|
166
|
187
|
96
|
128
|
40
|
54
|
90
|
|
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
|
68
|
25
|
9
|
150
|
170
|
192
|
93
|
134
|
32
|
58
|
79
|
221
|
196
|
157
|
111
|
|
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
|
176
|
181
|
97
|
126
|
38
|
55
|
84
|
225
|
200
|
162
|
108
|
74
|
17
|
13
|
139
|
|
|
1
|
0
|
9
|
11
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
|
44
|
47
|
88
|
214
|
206
|
151
|
112
|
66
|
23
|
10
|
144
|
180
|
185
|
102
|
123
|
|
|
12
|
6
|
8
|
2
|
3
|
5
|
14
|
13
|
10
|
7
|
4
|
1
|
0
|
9
|
11
|
|
210
|
155
|
117
|
63
|
29
|
2
|
148
|
169
|
191
|
91
|
127
|
36
|
53
|
85
|
219
|
|
|
3
|
5
|
14
|
13
|
10
|
|
|
|
