Coverage Report

Created: 2025-11-11 06:57

next uncovered line (L), next uncovered region (R), next uncovered branch (B)
/src/igraph/src/isomorphism/isoclasses.c
Line
Count
Source
1
/*
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   igraph library.
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   Copyright (C) 2006-2021 The igraph development team
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   This program is free software; you can redistribute it and/or modify
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   it under the terms of the GNU General Public License as published by
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   the Free Software Foundation; either version 2 of the License, or
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   (at your option) any later version.
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   This program is distributed in the hope that it will be useful,
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   but WITHOUT ANY WARRANTY; without even the implied warranty of
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   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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   GNU General Public License for more details.
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   You should have received a copy of the GNU General Public License
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   along with this program; if not, write to the Free Software
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   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
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   02110-1301 USA
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*/
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#include "igraph_isomorphism.h"
22
23
#include "igraph_constructors.h"
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#include "igraph_interface.h"
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26
#include "isomorphism/isoclasses.h"
27
28
/*
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 * Small labelled graphs are encoded into a compact representation, a "code",
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 * that fits into a single integer value. Each non-loop edge corresponds to
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 * a specific bit of the integer. The edge-to-bit mappings are stored in
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 * the "isoclass_idx" arrays while the bit-to-edge mappings are in the "classedges"
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 * arrays.
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 *
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 * The "isoclass2" array is a mapping from the code of each possible labelled
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 * graph to its isomorphism class. A canonical representative of each isomorphism
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 * class is stored in "isographs".
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 *
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 * In the names of arrays, the number refers to the vertex count, while "u"
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 * indicates undirected graphs (the other arrays store directed ones).
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 *
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 * Description of each array for graphs of size n:
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 *
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 * isosclass_idx represents an n-by-n matrix stored in column-major order.
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 * Element i,j of the matrix is an integer with a single bit set. This bit,
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 * if set, represents edge i-j in the graph code.
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 *
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 * isoclass2[code] gives the isomorphism class of the graph represented by code.
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 * Classes are labelled by integers starting at 0, after ordering them by the
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 * graph code of their smallest-code representative.
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 *
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 * isographs[class] is the code of a graph belonging to the given class. For each
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 * class, the representative with the smallest code is chosen.
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 *
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 * classedges[2*i] - classedges[2*i+1] are the endpoints of the edge represented
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 * by bit i in the code. Bits are numbered from most to least significant, thus
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 * the most significant one has index i=0.
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 */
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const unsigned int igraph_i_isoclass_3_idx[] = { 0, 4, 16, 1, 0, 32, 2, 8, 0 };
61
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const unsigned int igraph_i_isoclass_4_idx[] = {
63
    0, 8, 64, 512, 1, 0, 128, 1024, 2, 16, 0, 2048, 4, 32, 256, 0
64
};
65
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const unsigned int igraph_i_isoclass_3u_idx[] = { 0, 1, 2, 1, 0, 4, 2, 4, 0 };
67
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const unsigned int igraph_i_isoclass_4u_idx[] = {
69
    0, 1, 2, 8, 1, 0, 4, 16, 2, 4, 0, 32, 8, 16, 32, 0
70
};
71
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const unsigned int igraph_i_isoclass_5u_idx[] = {
73
    0, 1, 2, 8, 64, 1, 0, 4, 16, 128, 2, 4, 0, 32, 256, 8, 16, 32, 0, 512, 64, 128, 256, 512, 0
74
};
75
76
const unsigned int igraph_i_isoclass_6u_idx[] = {
77
    0, 1, 2, 8, 64, 1024, 1, 0, 4, 16, 128, 2048, 2, 4, 0, 32, 256, 4096,
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    8, 16, 32, 0, 512, 8192, 64, 128, 256, 512, 0, 16384, 1024, 2048,
79
    4096, 8192, 16384, 0
80
};
81
82
const unsigned int igraph_i_isoclass2_3[] = {
83
    0, 1, 1, 2, 1, 3, 4, 5, 1, 4, 6, 7, 2, 5, 7, 8, 1, 4, 3, 5, 6, 9, 9, 10, 4, 11,
84
    9, 12, 7, 12, 13, 14, 1, 6, 4, 7, 4, 9, 11, 12, 3, 9, 9, 13, 5, 10, 12, 14, 2, 7, 5, 8,
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    7, 13, 12, 14, 5, 12, 10, 14, 8, 14, 14, 15
86
};
87
88
const unsigned int igraph_i_isoclass2_3u[] = {
89
    0, 1, 1, 2, 1, 2, 2, 3
90
};
91
92
const unsigned int igraph_i_isoclass2_4u[] = {
93
    0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 4, 5, 6, 6, 7, 1, 2, 5, 6, 2, 4, 6, 7, 2, 3,
94
    6, 7, 6, 7, 8, 9, 1, 5, 2, 6, 2, 6, 4, 7, 2, 6, 3, 7, 6, 8, 7, 9, 2, 6, 6, 8,
95
    3, 7, 7, 9, 4, 7, 7, 9, 7, 9, 9, 10
96
};
97
98
const unsigned int igraph_i_isoclass2_4[] = {
99
    0,  1,  1,  2,  1,  2,  2,  3,  1,  4,  5,  6,  5,  6,  7,  8,  1,  5,  9, 10,
100
    11, 12, 13, 14,  2,  6, 10, 15, 12, 16, 17, 18,  1,  5, 11, 12,  9, 10, 13, 14,
101
    2,  6, 12, 16, 10, 15, 17, 18,  2,  7, 13, 17, 13, 17, 19, 20,  3,  8, 14, 18,
102
    14, 18, 20, 21,  1,  5,  4,  6,  5,  7,  6,  8,  9, 22, 22, 23, 24, 25, 25, 26,
103
    5, 27, 22, 28, 29, 30, 31, 32, 10, 28, 33, 34, 35, 36, 37, 38, 11, 29, 39, 40,
104
    41, 42, 43, 44, 13, 31, 45, 46, 47, 48, 49, 50, 12, 30, 45, 51, 52, 53, 54, 55,
105
    14, 32, 56, 57, 58, 59, 60, 61,  1,  9,  5, 10, 11, 13, 12, 14,  5, 22, 27, 28,
106
    29, 31, 30, 32,  4, 22, 22, 33, 39, 45, 45, 56,  6, 23, 28, 34, 40, 46, 51, 57,
107
    5, 24, 29, 35, 41, 47, 52, 58,  7, 25, 30, 36, 42, 48, 53, 59,  6, 25, 31, 37,
108
    43, 49, 54, 60,  8, 26, 32, 38, 44, 50, 55, 61,  2, 10,  6, 15, 12, 17, 16, 18,
109
    10, 33, 28, 34, 35, 37, 36, 38,  6, 28, 23, 34, 40, 51, 46, 57, 15, 34, 34, 62,
110
    63, 64, 64, 65, 12, 35, 40, 63, 66, 67, 68, 69, 17, 37, 51, 64, 67, 70, 71, 72,
111
    16, 36, 46, 64, 68, 71, 73, 74, 18, 38, 57, 65, 69, 72, 74, 75,  1, 11,  5, 12,
112
    9, 13, 10, 14, 11, 39, 29, 40, 41, 43, 42, 44,  5, 29, 24, 35, 41, 52, 47, 58,
113
    12, 40, 35, 63, 66, 68, 67, 69,  9, 41, 41, 66, 76, 77, 77, 78, 13, 43, 52, 68,
114
    77, 79, 80, 81, 10, 42, 47, 67, 77, 80, 82, 83, 14, 44, 58, 69, 78, 81, 83, 84,
115
    2, 12,  6, 16, 10, 17, 15, 18, 13, 45, 31, 46, 47, 49, 48, 50,  7, 30, 25, 36,
116
    42, 53, 48, 59, 17, 51, 37, 64, 67, 71, 70, 72, 13, 52, 43, 68, 77, 80, 79, 81,
117
    19, 54, 54, 73, 82, 85, 85, 86, 17, 53, 49, 71, 80, 87, 85, 88, 20, 55, 60, 74,
118
    83, 88, 89, 90,  2, 13,  7, 17, 13, 19, 17, 20, 12, 45, 30, 51, 52, 54, 53, 55,
119
    6, 31, 25, 37, 43, 54, 49, 60, 16, 46, 36, 64, 68, 73, 71, 74, 10, 47, 42, 67,
120
    77, 82, 80, 83, 17, 49, 53, 71, 80, 85, 87, 88, 15, 48, 48, 70, 79, 85, 85, 89,
121
    18, 50, 59, 72, 81, 86, 88, 90,  3, 14,  8, 18, 14, 20, 18, 21, 14, 56, 32, 57,
122
    58, 60, 59, 61,  8, 32, 26, 38, 44, 55, 50, 61, 18, 57, 38, 65, 69, 74, 72, 75,
123
    14, 58, 44, 69, 78, 83, 81, 84, 20, 60, 55, 74, 83, 89, 88, 90, 18, 59, 50, 72,
124
    81, 88, 86, 90, 21, 61, 61, 75, 84, 90, 90, 91,  1,  5,  5,  7,  4,  6,  6,  8,
125
    9, 22, 24, 25, 22, 23, 25, 26, 11, 29, 41, 42, 39, 40, 43, 44, 13, 31, 47, 48,
126
    45, 46, 49, 50,  5, 27, 29, 30, 22, 28, 31, 32, 10, 28, 35, 36, 33, 34, 37, 38,
127
    12, 30, 52, 53, 45, 51, 54, 55, 14, 32, 58, 59, 56, 57, 60, 61,  9, 24, 22, 25,
128
    22, 25, 23, 26, 76, 92, 92, 93, 92, 93, 93, 94, 41, 95, 96, 97, 98, 99, 100, 101,
129
    77, 102, 103, 104, 105, 106, 107, 108, 41, 95, 98, 99, 96, 97, 100, 101, 77, 102, 105, 106,
130
    103, 104, 107, 108, 66, 109, 110, 111, 110, 111, 112, 113, 78, 114, 115, 116, 115, 116, 117, 118,
131
    11, 41, 29, 42, 39, 43, 40, 44, 41, 96, 95, 97, 98, 100, 99, 101, 39, 98, 98, 119,
132
    120, 121, 121, 122, 43, 100, 123, 124, 121, 125, 126, 127, 29, 95, 128, 129, 98, 123, 130, 131,
133
    42, 97, 129, 132, 119, 124, 133, 134, 40, 99, 130, 133, 121, 126, 135, 136, 44, 101, 131, 134,
134
    122, 127, 136, 137, 13, 47, 31, 48, 45, 49, 46, 50, 77, 103, 102, 104, 105, 107, 106, 108,
135
    43, 123, 100, 124, 121, 126, 125, 127, 79, 138, 138, 139, 140, 141, 141, 142, 52, 143, 130, 144,
136
    110, 145, 146, 147, 80, 148, 149, 150, 151, 152, 153, 154, 68, 155, 146, 156, 157, 158, 159, 160,
137
    81, 161, 162, 163, 164, 165, 166, 167,  5, 29, 27, 30, 22, 31, 28, 32, 41, 98, 95, 99,
138
    96, 100, 97, 101, 29, 128, 95, 129, 98, 130, 123, 131, 52, 130, 143, 144, 110, 146, 145, 147,
139
    24, 95, 95, 109, 92, 102, 102, 114, 47, 123, 143, 155, 103, 138, 148, 161, 35, 129, 143, 168,
140
    105, 149, 169, 170, 58, 131, 171, 172, 115, 162, 173, 174, 10, 35, 28, 36, 33, 37, 34, 38,
141
    77, 105, 102, 106, 103, 107, 104, 108, 42, 129, 97, 132, 119, 133, 124, 134, 80, 149, 148, 150,
142
    151, 153, 152, 154, 47, 143, 123, 155, 103, 148, 138, 161, 82, 169, 169, 175, 176, 177, 177, 178,
143
    67, 168, 145, 179, 151, 180, 181, 182, 83, 170, 173, 183, 184, 185, 186, 187, 12, 52, 30, 53,
144
    45, 54, 51, 55, 66, 110, 109, 111, 110, 112, 111, 113, 40, 130, 99, 133, 121, 135, 126, 136,
145
    68, 146, 155, 156, 157, 159, 158, 160, 35, 143, 129, 168, 105, 169, 149, 170, 67, 145, 168, 179,
146
    151, 181, 180, 182, 63, 144, 144, 188, 140, 189, 189, 190, 69, 147, 172, 191, 164, 192, 193, 194,
147
    14, 58, 32, 59, 56, 60, 57, 61, 78, 115, 114, 116, 115, 117, 116, 118, 44, 131, 101, 134,
148
    122, 136, 127, 137, 81, 162, 161, 163, 164, 166, 165, 167, 58, 171, 131, 172, 115, 173, 162, 174,
149
    83, 173, 170, 183, 184, 186, 185, 187, 69, 172, 147, 191, 164, 193, 192, 194, 84, 174, 174, 195,
150
    196, 197, 197, 198,  1,  9, 11, 13,  5, 10, 12, 14,  5, 22, 29, 31, 27, 28, 30, 32,
151
    5, 24, 41, 47, 29, 35, 52, 58,  7, 25, 42, 48, 30, 36, 53, 59,  4, 22, 39, 45,
152
    22, 33, 45, 56,  6, 23, 40, 46, 28, 34, 51, 57,  6, 25, 43, 49, 31, 37, 54, 60,
153
    8, 26, 44, 50, 32, 38, 55, 61, 11, 41, 39, 43, 29, 42, 40, 44, 41, 96, 98, 100,
154
    95, 97, 99, 101, 29, 95, 98, 123, 128, 129, 130, 131, 42, 97, 119, 124, 129, 132, 133, 134,
155
    39, 98, 120, 121, 98, 119, 121, 122, 43, 100, 121, 125, 123, 124, 126, 127, 40, 99, 121, 126,
156
    130, 133, 135, 136, 44, 101, 122, 127, 131, 134, 136, 137,  9, 76, 41, 77, 41, 77, 66, 78,
157
    24, 92, 95, 102, 95, 102, 109, 114, 22, 92, 96, 103, 98, 105, 110, 115, 25, 93, 97, 104,
158
    99, 106, 111, 116, 22, 92, 98, 105, 96, 103, 110, 115, 25, 93, 99, 106, 97, 104, 111, 116,
159
    23, 93, 100, 107, 100, 107, 112, 117, 26, 94, 101, 108, 101, 108, 113, 118, 13, 77, 43, 79,
160
    52, 80, 68, 81, 47, 103, 123, 138, 143, 148, 155, 161, 31, 102, 100, 138, 130, 149, 146, 162,
161
    48, 104, 124, 139, 144, 150, 156, 163, 45, 105, 121, 140, 110, 151, 157, 164, 49, 107, 126, 141,
162
    145, 152, 158, 165, 46, 106, 125, 141, 146, 153, 159, 166, 50, 108, 127, 142, 147, 154, 160, 167,
163
    5, 41, 29, 52, 24, 47, 35, 58, 29, 98, 128, 130, 95, 123, 129, 131, 27, 95, 95, 143,
164
    95, 143, 143, 171, 30, 99, 129, 144, 109, 155, 168, 172, 22, 96, 98, 110, 92, 103, 105, 115,
165
    31, 100, 130, 146, 102, 138, 149, 162, 28, 97, 123, 145, 102, 148, 169, 173, 32, 101, 131, 147,
166
    114, 161, 170, 174, 12, 66, 40, 68, 35, 67, 63, 69, 52, 110, 130, 146, 143, 145, 144, 147,
167
    30, 109, 99, 155, 129, 168, 144, 172, 53, 111, 133, 156, 168, 179, 188, 191, 45, 110, 121, 157,
168
    105, 151, 140, 164, 54, 112, 135, 159, 169, 181, 189, 192, 51, 111, 126, 158, 149, 180, 189, 193,
169
    55, 113, 136, 160, 170, 182, 190, 194, 10, 77, 42, 80, 47, 82, 67, 83, 35, 105, 129, 149,
170
    143, 169, 168, 170, 28, 102, 97, 148, 123, 169, 145, 173, 36, 106, 132, 150, 155, 175, 179, 183,
171
    33, 103, 119, 151, 103, 176, 151, 184, 37, 107, 133, 153, 148, 177, 180, 185, 34, 104, 124, 152,
172
    138, 177, 181, 186, 38, 108, 134, 154, 161, 178, 182, 187, 14, 78, 44, 81, 58, 83, 69, 84,
173
    58, 115, 131, 162, 171, 173, 172, 174, 32, 114, 101, 161, 131, 170, 147, 174, 59, 116, 134, 163,
174
    172, 183, 191, 195, 56, 115, 122, 164, 115, 184, 164, 196, 60, 117, 136, 166, 173, 186, 193, 197,
175
    57, 116, 127, 165, 162, 185, 192, 197, 61, 118, 137, 167, 174, 187, 194, 198,  2, 10, 12, 17,
176
    6, 15, 16, 18, 10, 33, 35, 37, 28, 34, 36, 38, 12, 35, 66, 67, 40, 63, 68, 69,
177
    17, 37, 67, 70, 51, 64, 71, 72,  6, 28, 40, 51, 23, 34, 46, 57, 15, 34, 63, 64,
178
    34, 62, 64, 65, 16, 36, 68, 71, 46, 64, 73, 74, 18, 38, 69, 72, 57, 65, 74, 75,
179
    13, 47, 45, 49, 31, 48, 46, 50, 77, 103, 105, 107, 102, 104, 106, 108, 52, 143, 110, 145,
180
    130, 144, 146, 147, 80, 148, 151, 152, 149, 150, 153, 154, 43, 123, 121, 126, 100, 124, 125, 127,
181
    79, 138, 140, 141, 138, 139, 141, 142, 68, 155, 157, 158, 146, 156, 159, 160, 81, 161, 164, 165,
182
    162, 163, 166, 167, 13, 77, 52, 80, 43, 79, 68, 81, 47, 103, 143, 148, 123, 138, 155, 161,
183
    45, 105, 110, 151, 121, 140, 157, 164, 49, 107, 145, 152, 126, 141, 158, 165, 31, 102, 130, 149,
184
    100, 138, 146, 162, 48, 104, 144, 150, 124, 139, 156, 163, 46, 106, 146, 153, 125, 141, 159, 166,
185
    50, 108, 147, 154, 127, 142, 160, 167, 19, 82, 54, 85, 54, 85, 73, 86, 82, 176, 169, 177,
186
    169, 177, 175, 178, 54, 169, 112, 181, 135, 189, 159, 192, 85, 177, 181, 199, 189, 200, 201, 202,
187
    54, 169, 135, 189, 112, 181, 159, 192, 85, 177, 189, 200, 181, 199, 201, 202, 73, 175, 159, 201,
188
    159, 201, 203, 204, 86, 178, 192, 202, 192, 202, 204, 205,  7, 42, 30, 53, 25, 48, 36, 59,
189
    42, 119, 129, 133, 97, 124, 132, 134, 30, 129, 109, 168, 99, 144, 155, 172, 53, 133, 168, 188,
190
    111, 156, 179, 191, 25, 97, 99, 111, 93, 104, 106, 116, 48, 124, 144, 156, 104, 139, 150, 163,
191
    36, 132, 155, 179, 106, 150, 175, 183, 59, 134, 172, 191, 116, 163, 183, 195, 17, 67, 51, 71,
192
    37, 70, 64, 72, 80, 151, 149, 153, 148, 152, 150, 154, 53, 168, 111, 179, 133, 188, 156, 191,
193
    87, 180, 180, 206, 180, 206, 206, 207, 49, 145, 126, 158, 107, 152, 141, 165, 85, 181, 189, 201,
194
    177, 199, 200, 202, 71, 179, 158, 208, 153, 206, 201, 209, 88, 182, 193, 209, 185, 210, 211, 212,
195
    17, 80, 53, 87, 49, 85, 71, 88, 67, 151, 168, 180, 145, 181, 179, 182, 51, 149, 111, 180,
196
    126, 189, 158, 193, 71, 153, 179, 206, 158, 201, 208, 209, 37, 148, 133, 180, 107, 177, 153, 185,
197
    70, 152, 188, 206, 152, 199, 206, 210, 64, 150, 156, 206, 141, 200, 201, 211, 72, 154, 191, 207,
198
    165, 202, 209, 212, 20, 83, 55, 88, 60, 89, 74, 90, 83, 184, 170, 185, 173, 186, 183, 187,
199
    55, 170, 113, 182, 136, 190, 160, 194, 88, 185, 182, 210, 193, 211, 209, 212, 60, 173, 136, 193,
200
    117, 186, 166, 197, 89, 186, 190, 211, 186, 213, 211, 214, 74, 183, 160, 209, 166, 211, 204, 215,
201
    90, 187, 194, 212, 197, 214, 215, 216,  1, 11,  9, 13,  5, 12, 10, 14, 11, 39, 41, 43,
202
    29, 40, 42, 44,  9, 41, 76, 77, 41, 66, 77, 78, 13, 43, 77, 79, 52, 68, 80, 81,
203
    5, 29, 41, 52, 24, 35, 47, 58, 12, 40, 66, 68, 35, 63, 67, 69, 10, 42, 77, 80,
204
    47, 67, 82, 83, 14, 44, 78, 81, 58, 69, 83, 84,  5, 29, 22, 31, 27, 30, 28, 32,
205
    41, 98, 96, 100, 95, 99, 97, 101, 24, 95, 92, 102, 95, 109, 102, 114, 47, 123, 103, 138,
206
    143, 155, 148, 161, 29, 128, 98, 130, 95, 129, 123, 131, 52, 130, 110, 146, 143, 144, 145, 147,
207
    35, 129, 105, 149, 143, 168, 169, 170, 58, 131, 115, 162, 171, 172, 173, 174,  5, 41, 24, 47,
208
    29, 52, 35, 58, 29, 98, 95, 123, 128, 130, 129, 131, 22, 96, 92, 103, 98, 110, 105, 115,
209
    31, 100, 102, 138, 130, 146, 149, 162, 27, 95, 95, 143, 95, 143, 143, 171, 30, 99, 109, 155,
210
    129, 144, 168, 172, 28, 97, 102, 148, 123, 145, 169, 173, 32, 101, 114, 161, 131, 147, 170, 174,
211
    7, 42, 25, 48, 30, 53, 36, 59, 42, 119, 97, 124, 129, 133, 132, 134, 25, 97, 93, 104,
212
    99, 111, 106, 116, 48, 124, 104, 139, 144, 156, 150, 163, 30, 129, 99, 144, 109, 168, 155, 172,
213
    53, 133, 111, 156, 168, 188, 179, 191, 36, 132, 106, 150, 155, 179, 175, 183, 59, 134, 116, 163,
214
    172, 191, 183, 195,  4, 39, 22, 45, 22, 45, 33, 56, 39, 120, 98, 121, 98, 121, 119, 122,
215
    22, 98, 92, 105, 96, 110, 103, 115, 45, 121, 105, 140, 110, 157, 151, 164, 22, 98, 96, 110,
216
    92, 105, 103, 115, 45, 121, 110, 157, 105, 140, 151, 164, 33, 119, 103, 151, 103, 151, 176, 184,
217
    56, 122, 115, 164, 115, 164, 184, 196,  6, 40, 23, 46, 28, 51, 34, 57, 43, 121, 100, 125,
218
    123, 126, 124, 127, 25, 99, 93, 106, 97, 111, 104, 116, 49, 126, 107, 141, 145, 158, 152, 165,
219
    31, 130, 100, 146, 102, 149, 138, 162, 54, 135, 112, 159, 169, 189, 181, 192, 37, 133, 107, 153,
220
    148, 180, 177, 185, 60, 136, 117, 166, 173, 193, 186, 197,  6, 43, 25, 49, 31, 54, 37, 60,
221
    40, 121, 99, 126, 130, 135, 133, 136, 23, 100, 93, 107, 100, 112, 107, 117, 46, 125, 106, 141,
222
    146, 159, 153, 166, 28, 123, 97, 145, 102, 169, 148, 173, 51, 126, 111, 158, 149, 189, 180, 193,
223
    34, 124, 104, 152, 138, 181, 177, 186, 57, 127, 116, 165, 162, 192, 185, 197,  8, 44, 26, 50,
224
    32, 55, 38, 61, 44, 122, 101, 127, 131, 136, 134, 137, 26, 101, 94, 108, 101, 113, 108, 118,
225
    50, 127, 108, 142, 147, 160, 154, 167, 32, 131, 101, 147, 114, 170, 161, 174, 55, 136, 113, 160,
226
    170, 190, 182, 194, 38, 134, 108, 154, 161, 182, 178, 187, 61, 137, 118, 167, 174, 194, 187, 198,
227
    2, 12, 10, 17,  6, 16, 15, 18, 13, 45, 47, 49, 31, 46, 48, 50, 13, 52, 77, 80,
228
    43, 68, 79, 81, 19, 54, 82, 85, 54, 73, 85, 86,  7, 30, 42, 53, 25, 36, 48, 59,
229
    17, 51, 67, 71, 37, 64, 70, 72, 17, 53, 80, 87, 49, 71, 85, 88, 20, 55, 83, 88,
230
    60, 74, 89, 90, 10, 35, 33, 37, 28, 36, 34, 38, 77, 105, 103, 107, 102, 106, 104, 108,
231
    47, 143, 103, 148, 123, 155, 138, 161, 82, 169, 176, 177, 169, 175, 177, 178, 42, 129, 119, 133,
232
    97, 132, 124, 134, 80, 149, 151, 153, 148, 150, 152, 154, 67, 168, 151, 180, 145, 179, 181, 182,
233
    83, 170, 184, 185, 173, 183, 186, 187, 12, 66, 35, 67, 40, 68, 63, 69, 52, 110, 143, 145,
234
    130, 146, 144, 147, 45, 110, 105, 151, 121, 157, 140, 164, 54, 112, 169, 181, 135, 159, 189, 192,
235
    30, 109, 129, 168, 99, 155, 144, 172, 53, 111, 168, 179, 133, 156, 188, 191, 51, 111, 149, 180,
236
    126, 158, 189, 193, 55, 113, 170, 182, 136, 160, 190, 194, 17, 67, 37, 70, 51, 71, 64, 72,
237
    80, 151, 148, 152, 149, 153, 150, 154, 49, 145, 107, 152, 126, 158, 141, 165, 85, 181, 177, 199,
238
    189, 201, 200, 202, 53, 168, 133, 188, 111, 179, 156, 191, 87, 180, 180, 206, 180, 206, 206, 207,
239
    71, 179, 153, 206, 158, 208, 201, 209, 88, 182, 185, 210, 193, 209, 211, 212,  6, 40, 28, 51,
240
    23, 46, 34, 57, 43, 121, 123, 126, 100, 125, 124, 127, 31, 130, 102, 149, 100, 146, 138, 162,
241
    54, 135, 169, 189, 112, 159, 181, 192, 25, 99, 97, 111, 93, 106, 104, 116, 49, 126, 145, 158,
242
    107, 141, 152, 165, 37, 133, 148, 180, 107, 153, 177, 185, 60, 136, 173, 193, 117, 166, 186, 197,
243
    15, 63, 34, 64, 34, 64, 62, 65, 79, 140, 138, 141, 138, 141, 139, 142, 48, 144, 104, 150,
244
    124, 156, 139, 163, 85, 189, 177, 200, 181, 201, 199, 202, 48, 144, 124, 156, 104, 150, 139, 163,
245
    85, 189, 181, 201, 177, 200, 199, 202, 70, 188, 152, 206, 152, 206, 199, 210, 89, 190, 186, 211,
246
    186, 211, 213, 214, 16, 68, 36, 71, 46, 73, 64, 74, 68, 157, 155, 158, 146, 159, 156, 160,
247
    46, 146, 106, 153, 125, 159, 141, 166, 73, 159, 175, 201, 159, 203, 201, 204, 36, 155, 132, 179,
248
    106, 175, 150, 183, 71, 158, 179, 208, 153, 201, 206, 209, 64, 156, 150, 206, 141, 201, 200, 211,
249
    74, 160, 183, 209, 166, 204, 211, 215, 18, 69, 38, 72, 57, 74, 65, 75, 81, 164, 161, 165,
250
    162, 166, 163, 167, 50, 147, 108, 154, 127, 160, 142, 167, 86, 192, 178, 202, 192, 204, 202, 205,
251
    59, 172, 134, 191, 116, 183, 163, 195, 88, 193, 182, 209, 185, 211, 210, 212, 72, 191, 154, 207,
252
    165, 209, 202, 212, 90, 194, 187, 212, 197, 215, 214, 216,  2, 13, 13, 19,  7, 17, 17, 20,
253
    12, 45, 52, 54, 30, 51, 53, 55, 10, 47, 77, 82, 42, 67, 80, 83, 17, 49, 80, 85,
254
    53, 71, 87, 88,  6, 31, 43, 54, 25, 37, 49, 60, 16, 46, 68, 73, 36, 64, 71, 74,
255
    15, 48, 79, 85, 48, 70, 85, 89, 18, 50, 81, 86, 59, 72, 88, 90, 12, 52, 45, 54,
256
    30, 53, 51, 55, 66, 110, 110, 112, 109, 111, 111, 113, 35, 143, 105, 169, 129, 168, 149, 170,
257
    67, 145, 151, 181, 168, 179, 180, 182, 40, 130, 121, 135, 99, 133, 126, 136, 68, 146, 157, 159,
258
    155, 156, 158, 160, 63, 144, 140, 189, 144, 188, 189, 190, 69, 147, 164, 192, 172, 191, 193, 194,
259
    10, 77, 47, 82, 42, 80, 67, 83, 35, 105, 143, 169, 129, 149, 168, 170, 33, 103, 103, 176,
260
    119, 151, 151, 184, 37, 107, 148, 177, 133, 153, 180, 185, 28, 102, 123, 169, 97, 148, 145, 173,
261
    36, 106, 155, 175, 132, 150, 179, 183, 34, 104, 138, 177, 124, 152, 181, 186, 38, 108, 161, 178,
262
    134, 154, 182, 187, 17, 80, 49, 85, 53, 87, 71, 88, 67, 151, 145, 181, 168, 180, 179, 182,
263
    37, 148, 107, 177, 133, 180, 153, 185, 70, 152, 152, 199, 188, 206, 206, 210, 51, 149, 126, 189,
264
    111, 180, 158, 193, 71, 153, 158, 201, 179, 206, 208, 209, 64, 150, 141, 200, 156, 206, 201, 211,
265
    72, 154, 165, 202, 191, 207, 209, 212,  6, 43, 31, 54, 25, 49, 37, 60, 40, 121, 130, 135,
266
    99, 126, 133, 136, 28, 123, 102, 169, 97, 145, 148, 173, 51, 126, 149, 189, 111, 158, 180, 193,
267
    23, 100, 100, 112, 93, 107, 107, 117, 46, 125, 146, 159, 106, 141, 153, 166, 34, 124, 138, 181,
268
    104, 152, 177, 186, 57, 127, 162, 192, 116, 165, 185, 197, 16, 68, 46, 73, 36, 71, 64, 74,
269
    68, 157, 146, 159, 155, 158, 156, 160, 36, 155, 106, 175, 132, 179, 150, 183, 71, 158, 153, 201,
270
    179, 208, 206, 209, 46, 146, 125, 159, 106, 153, 141, 166, 73, 159, 159, 203, 175, 201, 201, 204,
271
    64, 156, 141, 201, 150, 206, 200, 211, 74, 160, 166, 204, 183, 209, 211, 215, 15, 79, 48, 85,
272
    48, 85, 70, 89, 63, 140, 144, 189, 144, 189, 188, 190, 34, 138, 104, 177, 124, 181, 152, 186,
273
    64, 141, 150, 200, 156, 201, 206, 211, 34, 138, 124, 181, 104, 177, 152, 186, 64, 141, 156, 201,
274
    150, 200, 206, 211, 62, 139, 139, 199, 139, 199, 199, 213, 65, 142, 163, 202, 163, 202, 210, 214,
275
    18, 81, 50, 86, 59, 88, 72, 90, 69, 164, 147, 192, 172, 193, 191, 194, 38, 161, 108, 178,
276
    134, 182, 154, 187, 72, 165, 154, 202, 191, 209, 207, 212, 57, 162, 127, 192, 116, 185, 165, 197,
277
    74, 166, 160, 204, 183, 211, 209, 215, 65, 163, 142, 202, 163, 210, 202, 214, 75, 167, 167, 205,
278
    195, 212, 212, 216,  3, 14, 14, 20,  8, 18, 18, 21, 14, 56, 58, 60, 32, 57, 59, 61,
279
    14, 58, 78, 83, 44, 69, 81, 84, 20, 60, 83, 89, 55, 74, 88, 90,  8, 32, 44, 55,
280
    26, 38, 50, 61, 18, 57, 69, 74, 38, 65, 72, 75, 18, 59, 81, 88, 50, 72, 86, 90,
281
    21, 61, 84, 90, 61, 75, 90, 91, 14, 58, 56, 60, 32, 59, 57, 61, 78, 115, 115, 117,
282
    114, 116, 116, 118, 58, 171, 115, 173, 131, 172, 162, 174, 83, 173, 184, 186, 170, 183, 185, 187,
283
    44, 131, 122, 136, 101, 134, 127, 137, 81, 162, 164, 166, 161, 163, 165, 167, 69, 172, 164, 193,
284
    147, 191, 192, 194, 84, 174, 196, 197, 174, 195, 197, 198, 14, 78, 58, 83, 44, 81, 69, 84,
285
    58, 115, 171, 173, 131, 162, 172, 174, 56, 115, 115, 184, 122, 164, 164, 196, 60, 117, 173, 186,
286
    136, 166, 193, 197, 32, 114, 131, 170, 101, 161, 147, 174, 59, 116, 172, 183, 134, 163, 191, 195,
287
    57, 116, 162, 185, 127, 165, 192, 197, 61, 118, 174, 187, 137, 167, 194, 198, 20, 83, 60, 89,
288
    55, 88, 74, 90, 83, 184, 173, 186, 170, 185, 183, 187, 60, 173, 117, 186, 136, 193, 166, 197,
289
    89, 186, 186, 213, 190, 211, 211, 214, 55, 170, 136, 190, 113, 182, 160, 194, 88, 185, 193, 211,
290
    182, 210, 209, 212, 74, 183, 166, 211, 160, 209, 204, 215, 90, 187, 197, 214, 194, 212, 215, 216,
291
    8, 44, 32, 55, 26, 50, 38, 61, 44, 122, 131, 136, 101, 127, 134, 137, 32, 131, 114, 170,
292
    101, 147, 161, 174, 55, 136, 170, 190, 113, 160, 182, 194, 26, 101, 101, 113, 94, 108, 108, 118,
293
    50, 127, 147, 160, 108, 142, 154, 167, 38, 134, 161, 182, 108, 154, 178, 187, 61, 137, 174, 194,
294
    118, 167, 187, 198, 18, 69, 57, 74, 38, 72, 65, 75, 81, 164, 162, 166, 161, 165, 163, 167,
295
    59, 172, 116, 183, 134, 191, 163, 195, 88, 193, 185, 211, 182, 209, 210, 212, 50, 147, 127, 160,
296
    108, 154, 142, 167, 86, 192, 192, 204, 178, 202, 202, 205, 72, 191, 165, 209, 154, 207, 202, 212,
297
    90, 194, 197, 215, 187, 212, 214, 216, 18, 81, 59, 88, 50, 86, 72, 90, 69, 164, 172, 193,
298
    147, 192, 191, 194, 57, 162, 116, 185, 127, 192, 165, 197, 74, 166, 183, 211, 160, 204, 209, 215,
299
    38, 161, 134, 182, 108, 178, 154, 187, 72, 165, 191, 209, 154, 202, 207, 212, 65, 163, 163, 210,
300
    142, 202, 202, 214, 75, 167, 195, 212, 167, 205, 212, 216, 21, 84, 61, 90, 61, 90, 75, 91,
301
    84, 196, 174, 197, 174, 197, 195, 198, 61, 174, 118, 187, 137, 194, 167, 198, 90, 197, 187, 214,
302
    194, 215, 212, 216, 61, 174, 137, 194, 118, 187, 167, 198, 90, 197, 194, 215, 187, 214, 212, 216,
303
    75, 195, 167, 212, 167, 212, 205, 216, 91, 198, 198, 216, 198, 216, 216, 217
304
};
305
306
const unsigned int igraph_i_isoclass2_5u[] = {
307
    0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 4, 5, 6, 6, 7, 1, 2, 5, 6, 2, 4, 6,
308
    7, 2, 3, 6, 7, 6, 7, 8, 9, 1, 5, 2, 6, 2, 6, 4, 7, 2, 6, 3, 7, 6, 8,
309
    7, 9, 2, 6, 6, 8, 3, 7, 7, 9, 4, 7, 7, 9, 7, 9, 9, 10, 1, 2, 2, 4, 5,
310
    6, 6, 7, 2, 4, 4, 11, 12, 13, 13, 14, 5, 6, 12, 13, 12, 13, 15, 16,
311
    6, 7, 13, 14, 15, 16, 17, 18, 5, 12, 6, 13, 12, 15, 13, 16, 6, 13, 7,
312
    14, 15, 17, 16, 18, 12, 15, 15, 17, 19, 20, 20, 21, 13, 16, 16, 18,
313
    20, 21, 21, 22, 1, 2, 5, 6, 2, 4, 6, 7, 5, 6, 12, 13, 12, 13, 15, 16,
314
    2, 4, 12, 13, 4, 11, 13, 14, 6, 7, 15, 16, 13, 14, 17, 18, 5, 12, 12,
315
    15, 6, 13, 13, 16, 12, 15, 19, 20, 15, 17, 20, 21, 6, 13, 15, 17, 7,
316
    14, 16, 18, 13, 16, 20, 21, 16, 18, 21, 22, 2, 3, 6, 7, 6, 7, 8, 9,
317
    6, 7, 13, 14, 15, 16, 17, 18, 6, 7, 15, 16, 13, 14, 17, 18, 8, 9, 17,
318
    18, 17, 18, 23, 24, 12, 19, 15, 20, 15, 20, 17, 21, 15, 20, 20, 25,
319
    26, 27, 27, 28, 15, 20, 26, 27, 20, 25, 27, 28, 17, 21, 27, 28, 27,
320
    28, 29, 30, 1, 5, 2, 6, 2, 6, 4, 7, 5, 12, 6, 13, 12, 15, 13, 16, 5,
321
    12, 12, 15, 6, 13, 13, 16, 12, 19, 15, 20, 15, 20, 17, 21, 2, 12, 4,
322
    13, 4, 13, 11, 14, 6, 15, 7, 16, 13, 17, 14, 18, 6, 15, 13, 17, 7,
323
    16, 14, 18, 13, 20, 16, 21, 16, 21, 18, 22, 2, 6, 3, 7, 6, 8, 7, 9,
324
    6, 13, 7, 14, 15, 17, 16, 18, 12, 15, 19, 20, 15, 17, 20, 21, 15, 20,
325
    20, 25, 26, 27, 27, 28, 6, 15, 7, 16, 13, 17, 14, 18, 8, 17, 9, 18,
326
    17, 23, 18, 24, 15, 26, 20, 27, 20, 27, 25, 28, 17, 27, 21, 28, 27,
327
    29, 28, 30, 2, 6, 6, 8, 3, 7, 7, 9, 12, 15, 15, 17, 19, 20, 20, 21,
328
    6, 13, 15, 17, 7, 14, 16, 18, 15, 20, 26, 27, 20, 25, 27, 28, 6, 15,
329
    13, 17, 7, 16, 14, 18, 15, 26, 20, 27, 20, 27, 25, 28, 8, 17, 17, 23,
330
    9, 18, 18, 24, 17, 27, 27, 29, 21, 28, 28, 30, 4, 7, 7, 9, 7, 9, 9,
331
    10, 13, 16, 16, 18, 20, 21, 21, 22, 13, 16, 20, 21, 16, 18, 21, 22,
332
    17, 21, 27, 28, 27, 28, 29, 30, 13, 20, 16, 21, 16, 21, 18, 22, 17,
333
    27, 21, 28, 27, 29, 28, 30, 17, 27, 27, 29, 21, 28, 28, 30, 23, 29,
334
    29, 31, 29, 31, 31, 32, 1, 5, 5, 12, 5, 12, 12, 19, 2, 6, 6, 13, 12,
335
    15, 15, 20, 2, 6, 12, 15, 6, 13, 15, 20, 4, 7, 13, 16, 13, 16, 17,
336
    21, 2, 12, 6, 15, 6, 15, 13, 20, 4, 13, 7, 16, 13, 17, 16, 21, 4, 13,
337
    13, 17, 7, 16, 16, 21, 11, 14, 14, 18, 14, 18, 18, 22, 2, 6, 6, 13,
338
    12, 15, 15, 20, 3, 7, 7, 14, 19, 20, 20, 25, 6, 8, 15, 17, 15, 17,
339
    26, 27, 7, 9, 16, 18, 20, 21, 27, 28, 6, 15, 8, 17, 15, 26, 17, 27,
340
    7, 16, 9, 18, 20, 27, 21, 28, 13, 17, 17, 23, 20, 27, 27, 29, 14, 18,
341
    18, 24, 25, 28, 28, 30, 2, 6, 12, 15, 6, 13, 15, 20, 6, 8, 15, 17,
342
    15, 17, 26, 27, 3, 7, 19, 20, 7, 14, 20, 25, 7, 9, 20, 21, 16, 18,
343
    27, 28, 6, 15, 15, 26, 8, 17, 17, 27, 13, 17, 20, 27, 17, 23, 27, 29,
344
    7, 16, 20, 27, 9, 18, 21, 28, 14, 18, 25, 28, 18, 24, 28, 30, 4, 7,
345
    13, 16, 13, 16, 17, 21, 7, 9, 16, 18, 20, 21, 27, 28, 7, 9, 20, 21,
346
    16, 18, 27, 28, 9, 10, 21, 22, 21, 22, 29, 30, 13, 20, 17, 27, 17,
347
    27, 23, 29, 16, 21, 21, 28, 27, 29, 29, 31, 16, 21, 27, 29, 21, 28,
348
    29, 31, 18, 22, 28, 30, 28, 30, 31, 32, 2, 12, 6, 15, 6, 15, 13, 20,
349
    6, 15, 8, 17, 15, 26, 17, 27, 6, 15, 15, 26, 8, 17, 17, 27, 13, 20,
350
    17, 27, 17, 27, 23, 29, 3, 19, 7, 20, 7, 20, 14, 25, 7, 20, 9, 21,
351
    16, 27, 18, 28, 7, 20, 16, 27, 9, 21, 18, 28, 14, 25, 18, 28, 18, 28,
352
    24, 30, 4, 13, 7, 16, 13, 17, 16, 21, 7, 16, 9, 18, 20, 27, 21, 28,
353
    13, 17, 20, 27, 17, 23, 27, 29, 16, 21, 21, 28, 27, 29, 29, 31, 7,
354
    20, 9, 21, 16, 27, 18, 28, 9, 21, 10, 22, 21, 29, 22, 30, 16, 27, 21,
355
    29, 21, 29, 28, 31, 18, 28, 22, 30, 28, 31, 30, 32, 4, 13, 13, 17, 7,
356
    16, 16, 21, 13, 17, 17, 23, 20, 27, 27, 29, 7, 16, 20, 27, 9, 18, 21,
357
    28, 16, 21, 27, 29, 21, 28, 29, 31, 7, 20, 16, 27, 9, 21, 18, 28, 16,
358
    27, 21, 29, 21, 29, 28, 31, 9, 21, 21, 29, 10, 22, 22, 30, 18, 28,
359
    28, 31, 22, 30, 30, 32, 11, 14, 14, 18, 14, 18, 18, 22, 14, 18, 18,
360
    24, 25, 28, 28, 30, 14, 18, 25, 28, 18, 24, 28, 30, 18, 22, 28, 30,
361
    28, 30, 31, 32, 14, 25, 18, 28, 18, 28, 24, 30, 18, 28, 22, 30, 28,
362
    31, 30, 32, 18, 28, 28, 31, 22, 30, 30, 32, 24, 30, 30, 32, 30, 32,
363
    32, 33
364
};
365
366
const unsigned int igraph_i_isoclass2_6u[] = {
367
    0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 4, 5, 6, 6, 7, 1, 2, 5, 6, 2, 4, 6,
368
    7, 2, 3, 6, 7, 6, 7, 8, 9, 1, 5, 2, 6, 2, 6, 4, 7, 2, 6, 3, 7, 6, 8,
369
    7, 9, 2, 6, 6, 8, 3, 7, 7, 9, 4, 7, 7, 9, 7, 9, 9, 10, 1, 2, 2, 4, 5,
370
    6, 6, 7, 2, 4, 4, 11, 12, 13, 13, 14, 5, 6, 12, 13, 12, 13, 15, 16,
371
    6, 7, 13, 14, 15, 16, 17, 18, 5, 12, 6, 13, 12, 15, 13, 16, 6, 13, 7,
372
    14, 15, 17, 16, 18, 12, 15, 15, 17, 19, 20, 20, 21, 13, 16, 16, 18,
373
    20, 21, 21, 22, 1, 2, 5, 6, 2, 4, 6, 7, 5, 6, 12, 13, 12, 13, 15, 16,
374
    2, 4, 12, 13, 4, 11, 13, 14, 6, 7, 15, 16, 13, 14, 17, 18, 5, 12, 12,
375
    15, 6, 13, 13, 16, 12, 15, 19, 20, 15, 17, 20, 21, 6, 13, 15, 17, 7,
376
    14, 16, 18, 13, 16, 20, 21, 16, 18, 21, 22, 2, 3, 6, 7, 6, 7, 8, 9,
377
    6, 7, 13, 14, 15, 16, 17, 18, 6, 7, 15, 16, 13, 14, 17, 18, 8, 9, 17,
378
    18, 17, 18, 23, 24, 12, 19, 15, 20, 15, 20, 17, 21, 15, 20, 20, 25,
379
    26, 27, 27, 28, 15, 20, 26, 27, 20, 25, 27, 28, 17, 21, 27, 28, 27,
380
    28, 29, 30, 1, 5, 2, 6, 2, 6, 4, 7, 5, 12, 6, 13, 12, 15, 13, 16, 5,
381
    12, 12, 15, 6, 13, 13, 16, 12, 19, 15, 20, 15, 20, 17, 21, 2, 12, 4,
382
    13, 4, 13, 11, 14, 6, 15, 7, 16, 13, 17, 14, 18, 6, 15, 13, 17, 7,
383
    16, 14, 18, 13, 20, 16, 21, 16, 21, 18, 22, 2, 6, 3, 7, 6, 8, 7, 9,
384
    6, 13, 7, 14, 15, 17, 16, 18, 12, 15, 19, 20, 15, 17, 20, 21, 15, 20,
385
    20, 25, 26, 27, 27, 28, 6, 15, 7, 16, 13, 17, 14, 18, 8, 17, 9, 18,
386
    17, 23, 18, 24, 15, 26, 20, 27, 20, 27, 25, 28, 17, 27, 21, 28, 27,
387
    29, 28, 30, 2, 6, 6, 8, 3, 7, 7, 9, 12, 15, 15, 17, 19, 20, 20, 21,
388
    6, 13, 15, 17, 7, 14, 16, 18, 15, 20, 26, 27, 20, 25, 27, 28, 6, 15,
389
    13, 17, 7, 16, 14, 18, 15, 26, 20, 27, 20, 27, 25, 28, 8, 17, 17, 23,
390
    9, 18, 18, 24, 17, 27, 27, 29, 21, 28, 28, 30, 4, 7, 7, 9, 7, 9, 9,
391
    10, 13, 16, 16, 18, 20, 21, 21, 22, 13, 16, 20, 21, 16, 18, 21, 22,
392
    17, 21, 27, 28, 27, 28, 29, 30, 13, 20, 16, 21, 16, 21, 18, 22, 17,
393
    27, 21, 28, 27, 29, 28, 30, 17, 27, 27, 29, 21, 28, 28, 30, 23, 29,
394
    29, 31, 29, 31, 31, 32, 1, 5, 5, 12, 5, 12, 12, 19, 2, 6, 6, 13, 12,
395
    15, 15, 20, 2, 6, 12, 15, 6, 13, 15, 20, 4, 7, 13, 16, 13, 16, 17,
396
    21, 2, 12, 6, 15, 6, 15, 13, 20, 4, 13, 7, 16, 13, 17, 16, 21, 4, 13,
397
    13, 17, 7, 16, 16, 21, 11, 14, 14, 18, 14, 18, 18, 22, 2, 6, 6, 13,
398
    12, 15, 15, 20, 3, 7, 7, 14, 19, 20, 20, 25, 6, 8, 15, 17, 15, 17,
399
    26, 27, 7, 9, 16, 18, 20, 21, 27, 28, 6, 15, 8, 17, 15, 26, 17, 27,
400
    7, 16, 9, 18, 20, 27, 21, 28, 13, 17, 17, 23, 20, 27, 27, 29, 14, 18,
401
    18, 24, 25, 28, 28, 30, 2, 6, 12, 15, 6, 13, 15, 20, 6, 8, 15, 17,
402
    15, 17, 26, 27, 3, 7, 19, 20, 7, 14, 20, 25, 7, 9, 20, 21, 16, 18,
403
    27, 28, 6, 15, 15, 26, 8, 17, 17, 27, 13, 17, 20, 27, 17, 23, 27, 29,
404
    7, 16, 20, 27, 9, 18, 21, 28, 14, 18, 25, 28, 18, 24, 28, 30, 4, 7,
405
    13, 16, 13, 16, 17, 21, 7, 9, 16, 18, 20, 21, 27, 28, 7, 9, 20, 21,
406
    16, 18, 27, 28, 9, 10, 21, 22, 21, 22, 29, 30, 13, 20, 17, 27, 17,
407
    27, 23, 29, 16, 21, 21, 28, 27, 29, 29, 31, 16, 21, 27, 29, 21, 28,
408
    29, 31, 18, 22, 28, 30, 28, 30, 31, 32, 2, 12, 6, 15, 6, 15, 13, 20,
409
    6, 15, 8, 17, 15, 26, 17, 27, 6, 15, 15, 26, 8, 17, 17, 27, 13, 20,
410
    17, 27, 17, 27, 23, 29, 3, 19, 7, 20, 7, 20, 14, 25, 7, 20, 9, 21,
411
    16, 27, 18, 28, 7, 20, 16, 27, 9, 21, 18, 28, 14, 25, 18, 28, 18, 28,
412
    24, 30, 4, 13, 7, 16, 13, 17, 16, 21, 7, 16, 9, 18, 20, 27, 21, 28,
413
    13, 17, 20, 27, 17, 23, 27, 29, 16, 21, 21, 28, 27, 29, 29, 31, 7,
414
    20, 9, 21, 16, 27, 18, 28, 9, 21, 10, 22, 21, 29, 22, 30, 16, 27, 21,
415
    29, 21, 29, 28, 31, 18, 28, 22, 30, 28, 31, 30, 32, 4, 13, 13, 17, 7,
416
    16, 16, 21, 13, 17, 17, 23, 20, 27, 27, 29, 7, 16, 20, 27, 9, 18, 21,
417
    28, 16, 21, 27, 29, 21, 28, 29, 31, 7, 20, 16, 27, 9, 21, 18, 28, 16,
418
    27, 21, 29, 21, 29, 28, 31, 9, 21, 21, 29, 10, 22, 22, 30, 18, 28,
419
    28, 31, 22, 30, 30, 32, 11, 14, 14, 18, 14, 18, 18, 22, 14, 18, 18,
420
    24, 25, 28, 28, 30, 14, 18, 25, 28, 18, 24, 28, 30, 18, 22, 28, 30,
421
    28, 30, 31, 32, 14, 25, 18, 28, 18, 28, 24, 30, 18, 28, 22, 30, 28,
422
    31, 30, 32, 18, 28, 28, 31, 22, 30, 30, 32, 24, 30, 30, 32, 30, 32,
423
    32, 33, 1, 2, 2, 4, 5, 6, 6, 7, 2, 4, 4, 11, 12, 13, 13, 14, 5, 6,
424
    12, 13, 12, 13, 15, 16, 6, 7, 13, 14, 15, 16, 17, 18, 5, 12, 6, 13,
425
    12, 15, 13, 16, 6, 13, 7, 14, 15, 17, 16, 18, 12, 15, 15, 17, 19, 20,
426
    20, 21, 13, 16, 16, 18, 20, 21, 21, 22, 2, 4, 4, 11, 12, 13, 13, 14,
427
    4, 11, 11, 34, 35, 36, 36, 37, 12, 13, 35, 36, 38, 39, 40, 41, 13,
428
    14, 36, 37, 40, 41, 42, 43, 12, 35, 13, 36, 38, 40, 39, 41, 13, 36,
429
    14, 37, 40, 42, 41, 43, 38, 40, 40, 42, 44, 45, 45, 46, 39, 41, 41,
430
    43, 45, 46, 46, 47, 5, 6, 12, 13, 12, 13, 15, 16, 12, 13, 35, 36, 38,
431
    39, 40, 41, 12, 13, 38, 39, 35, 36, 40, 41, 15, 16, 40, 41, 40, 41,
432
    48, 49, 50, 51, 51, 52, 51, 52, 52, 53, 51, 52, 54, 55, 56, 57, 58,
433
    59, 51, 52, 56, 57, 54, 55, 58, 59, 52, 53, 58, 59, 58, 59, 60, 61,
434
    6, 7, 13, 14, 15, 16, 17, 18, 13, 14, 36, 37, 40, 41, 42, 43, 15, 16,
435
    40, 41, 40, 41, 48, 49, 17, 18, 42, 43, 48, 49, 62, 63, 51, 54, 52,
436
    55, 56, 58, 57, 59, 52, 55, 55, 64, 65, 66, 66, 67, 56, 58, 65, 66,
437
    68, 69, 70, 71, 57, 59, 66, 67, 70, 71, 72, 73, 5, 12, 6, 13, 12, 15,
438
    13, 16, 12, 35, 13, 36, 38, 40, 39, 41, 50, 51, 51, 52, 51, 52, 52,
439
    53, 51, 54, 52, 55, 56, 58, 57, 59, 12, 38, 13, 39, 35, 40, 36, 41,
440
    15, 40, 16, 41, 40, 48, 41, 49, 51, 56, 52, 57, 54, 58, 55, 59, 52,
441
    58, 53, 59, 58, 60, 59, 61, 6, 13, 7, 14, 15, 17, 16, 18, 13, 36, 14,
442
    37, 40, 42, 41, 43, 51, 52, 54, 55, 56, 57, 58, 59, 52, 55, 55, 64,
443
    65, 66, 66, 67, 15, 40, 16, 41, 40, 48, 41, 49, 17, 42, 18, 43, 48,
444
    62, 49, 63, 56, 65, 58, 66, 68, 70, 69, 71, 57, 66, 59, 67, 70, 72,
445
    71, 73, 12, 15, 15, 17, 19, 20, 20, 21, 38, 40, 40, 42, 44, 45, 45,
446
    46, 51, 52, 56, 57, 54, 55, 58, 59, 56, 58, 65, 66, 68, 69, 70, 71,
447
    51, 56, 52, 57, 54, 58, 55, 59, 56, 65, 58, 66, 68, 70, 69, 71, 74,
448
    75, 75, 76, 77, 78, 78, 79, 75, 80, 80, 81, 82, 83, 83, 84, 13, 16,
449
    16, 18, 20, 21, 21, 22, 39, 41, 41, 43, 45, 46, 46, 47, 52, 53, 58,
450
    59, 58, 59, 60, 61, 57, 59, 66, 67, 70, 71, 72, 73, 52, 58, 53, 59,
451
    58, 60, 59, 61, 57, 66, 59, 67, 70, 72, 71, 73, 75, 80, 80, 81, 82,
452
    83, 83, 84, 76, 81, 81, 85, 86, 87, 87, 88, 5, 12, 12, 35, 50, 51,
453
    51, 54, 6, 13, 13, 36, 51, 52, 52, 55, 12, 15, 38, 40, 51, 52, 56,
454
    58, 13, 16, 39, 41, 52, 53, 57, 59, 12, 38, 15, 40, 51, 56, 52, 58,
455
    13, 39, 16, 41, 52, 57, 53, 59, 35, 40, 40, 48, 54, 58, 58, 60, 36,
456
    41, 41, 49, 55, 59, 59, 61, 6, 13, 13, 36, 51, 52, 52, 55, 7, 14, 14,
457
    37, 54, 55, 55, 64, 15, 17, 40, 42, 56, 57, 65, 66, 16, 18, 41, 43,
458
    58, 59, 66, 67, 15, 40, 17, 42, 56, 65, 57, 66, 16, 41, 18, 43, 58,
459
    66, 59, 67, 40, 48, 48, 62, 68, 70, 70, 72, 41, 49, 49, 63, 69, 71,
460
    71, 73, 12, 15, 38, 40, 51, 52, 56, 58, 15, 17, 40, 42, 56, 57, 65,
461
    66, 19, 20, 44, 45, 54, 55, 68, 69, 20, 21, 45, 46, 58, 59, 70, 71,
462
    51, 56, 56, 65, 74, 75, 75, 80, 52, 57, 58, 66, 75, 76, 80, 81, 54,
463
    58, 68, 70, 77, 78, 82, 83, 55, 59, 69, 71, 78, 79, 83, 84, 13, 16,
464
    39, 41, 52, 53, 57, 59, 16, 18, 41, 43, 58, 59, 66, 67, 20, 21, 45,
465
    46, 58, 59, 70, 71, 21, 22, 46, 47, 60, 61, 72, 73, 52, 58, 57, 66,
466
    75, 80, 76, 81, 53, 59, 59, 67, 80, 81, 81, 85, 58, 60, 70, 72, 82,
467
    83, 86, 87, 59, 61, 71, 73, 83, 84, 87, 88, 12, 38, 15, 40, 51, 56,
468
    52, 58, 15, 40, 17, 42, 56, 65, 57, 66, 51, 56, 56, 65, 74, 75, 75,
469
    80, 52, 58, 57, 66, 75, 80, 76, 81, 19, 44, 20, 45, 54, 68, 55, 69,
470
    20, 45, 21, 46, 58, 70, 59, 71, 54, 68, 58, 70, 77, 82, 78, 83, 55,
471
    69, 59, 71, 78, 83, 79, 84, 13, 39, 16, 41, 52, 57, 53, 59, 16, 41,
472
    18, 43, 58, 66, 59, 67, 52, 57, 58, 66, 75, 76, 80, 81, 53, 59, 59,
473
    67, 80, 81, 81, 85, 20, 45, 21, 46, 58, 70, 59, 71, 21, 46, 22, 47,
474
    60, 72, 61, 73, 58, 70, 60, 72, 82, 86, 83, 87, 59, 71, 61, 73, 83,
475
    87, 84, 88, 35, 40, 40, 48, 54, 58, 58, 60, 40, 48, 48, 62, 68, 70,
476
    70, 72, 54, 58, 68, 70, 77, 78, 82, 83, 58, 60, 70, 72, 82, 83, 86,
477
    87, 54, 68, 58, 70, 77, 82, 78, 83, 58, 70, 60, 72, 82, 86, 83, 87,
478
    77, 82, 82, 86, 89, 90, 90, 91, 78, 83, 83, 87, 90, 91, 91, 92, 36,
479
    41, 41, 49, 55, 59, 59, 61, 41, 49, 49, 63, 69, 71, 71, 73, 55, 59,
480
    69, 71, 78, 79, 83, 84, 59, 61, 71, 73, 83, 84, 87, 88, 55, 69, 59,
481
    71, 78, 83, 79, 84, 59, 71, 61, 73, 83, 87, 84, 88, 78, 83, 83, 87,
482
    90, 91, 91, 92, 79, 84, 84, 88, 91, 92, 92, 93, 1, 2, 5, 6, 2, 4, 6,
483
    7, 5, 6, 12, 13, 12, 13, 15, 16, 2, 4, 12, 13, 4, 11, 13, 14, 6, 7,
484
    15, 16, 13, 14, 17, 18, 5, 12, 12, 15, 6, 13, 13, 16, 12, 15, 19, 20,
485
    15, 17, 20, 21, 6, 13, 15, 17, 7, 14, 16, 18, 13, 16, 20, 21, 16, 18,
486
    21, 22, 5, 6, 12, 13, 12, 13, 15, 16, 12, 13, 35, 36, 38, 39, 40, 41,
487
    12, 13, 38, 39, 35, 36, 40, 41, 15, 16, 40, 41, 40, 41, 48, 49, 50,
488
    51, 51, 52, 51, 52, 52, 53, 51, 52, 54, 55, 56, 57, 58, 59, 51, 52,
489
    56, 57, 54, 55, 58, 59, 52, 53, 58, 59, 58, 59, 60, 61, 2, 4, 12, 13,
490
    4, 11, 13, 14, 12, 13, 38, 39, 35, 36, 40, 41, 4, 11, 35, 36, 11, 34,
491
    36, 37, 13, 14, 40, 41, 36, 37, 42, 43, 12, 35, 38, 40, 13, 36, 39,
492
    41, 38, 40, 44, 45, 40, 42, 45, 46, 13, 36, 40, 42, 14, 37, 41, 43,
493
    39, 41, 45, 46, 41, 43, 46, 47, 6, 7, 15, 16, 13, 14, 17, 18, 15, 16,
494
    40, 41, 40, 41, 48, 49, 13, 14, 40, 41, 36, 37, 42, 43, 17, 18, 48,
495
    49, 42, 43, 62, 63, 51, 54, 56, 58, 52, 55, 57, 59, 56, 58, 68, 69,
496
    65, 66, 70, 71, 52, 55, 65, 66, 55, 64, 66, 67, 57, 59, 70, 71, 66,
497
    67, 72, 73, 5, 12, 12, 15, 6, 13, 13, 16, 50, 51, 51, 52, 51, 52, 52,
498
    53, 12, 35, 38, 40, 13, 36, 39, 41, 51, 54, 56, 58, 52, 55, 57, 59,
499
    12, 38, 35, 40, 13, 39, 36, 41, 51, 56, 54, 58, 52, 57, 55, 59, 15,
500
    40, 40, 48, 16, 41, 41, 49, 52, 58, 58, 60, 53, 59, 59, 61, 12, 15,
501
    19, 20, 15, 17, 20, 21, 51, 52, 54, 55, 56, 57, 58, 59, 38, 40, 44,
502
    45, 40, 42, 45, 46, 56, 58, 68, 69, 65, 66, 70, 71, 51, 56, 54, 58,
503
    52, 57, 55, 59, 74, 75, 77, 78, 75, 76, 78, 79, 56, 65, 68, 70, 58,
504
    66, 69, 71, 75, 80, 82, 83, 80, 81, 83, 84, 6, 13, 15, 17, 7, 14, 16,
505
    18, 51, 52, 56, 57, 54, 55, 58, 59, 13, 36, 40, 42, 14, 37, 41, 43,
506
    52, 55, 65, 66, 55, 64, 66, 67, 15, 40, 40, 48, 16, 41, 41, 49, 56,
507
    65, 68, 70, 58, 66, 69, 71, 17, 42, 48, 62, 18, 43, 49, 63, 57, 66,
508
    70, 72, 59, 67, 71, 73, 13, 16, 20, 21, 16, 18, 21, 22, 52, 53, 58,
509
    59, 58, 59, 60, 61, 39, 41, 45, 46, 41, 43, 46, 47, 57, 59, 70, 71,
510
    66, 67, 72, 73, 52, 58, 58, 60, 53, 59, 59, 61, 75, 80, 82, 83, 80,
511
    81, 83, 84, 57, 66, 70, 72, 59, 67, 71, 73, 76, 81, 86, 87, 81, 85,
512
    87, 88, 5, 12, 50, 51, 12, 35, 51, 54, 12, 15, 51, 52, 38, 40, 56,
513
    58, 6, 13, 51, 52, 13, 36, 52, 55, 13, 16, 52, 53, 39, 41, 57, 59,
514
    12, 38, 51, 56, 15, 40, 52, 58, 35, 40, 54, 58, 40, 48, 58, 60, 13,
515
    39, 52, 57, 16, 41, 53, 59, 36, 41, 55, 59, 41, 49, 59, 61, 12, 15,
516
    51, 52, 38, 40, 56, 58, 19, 20, 54, 55, 44, 45, 68, 69, 15, 17, 56,
517
    57, 40, 42, 65, 66, 20, 21, 58, 59, 45, 46, 70, 71, 51, 56, 74, 75,
518
    56, 65, 75, 80, 54, 58, 77, 78, 68, 70, 82, 83, 52, 57, 75, 76, 58,
519
    66, 80, 81, 55, 59, 78, 79, 69, 71, 83, 84, 6, 13, 51, 52, 13, 36,
520
    52, 55, 15, 17, 56, 57, 40, 42, 65, 66, 7, 14, 54, 55, 14, 37, 55,
521
    64, 16, 18, 58, 59, 41, 43, 66, 67, 15, 40, 56, 65, 17, 42, 57, 66,
522
    40, 48, 68, 70, 48, 62, 70, 72, 16, 41, 58, 66, 18, 43, 59, 67, 41,
523
    49, 69, 71, 49, 63, 71, 73, 13, 16, 52, 53, 39, 41, 57, 59, 20, 21,
524
    58, 59, 45, 46, 70, 71, 16, 18, 58, 59, 41, 43, 66, 67, 21, 22, 60,
525
    61, 46, 47, 72, 73, 52, 58, 75, 80, 57, 66, 76, 81, 58, 60, 82, 83,
526
    70, 72, 86, 87, 53, 59, 80, 81, 59, 67, 81, 85, 59, 61, 83, 84, 71,
527
    73, 87, 88, 12, 38, 51, 56, 15, 40, 52, 58, 51, 56, 74, 75, 56, 65,
528
    75, 80, 15, 40, 56, 65, 17, 42, 57, 66, 52, 58, 75, 80, 57, 66, 76,
529
    81, 19, 44, 54, 68, 20, 45, 55, 69, 54, 68, 77, 82, 58, 70, 78, 83,
530
    20, 45, 58, 70, 21, 46, 59, 71, 55, 69, 78, 83, 59, 71, 79, 84, 35,
531
    40, 54, 58, 40, 48, 58, 60, 54, 58, 77, 78, 68, 70, 82, 83, 40, 48,
532
    68, 70, 48, 62, 70, 72, 58, 60, 82, 83, 70, 72, 86, 87, 54, 68, 77,
533
    82, 58, 70, 78, 83, 77, 82, 89, 90, 82, 86, 90, 91, 58, 70, 82, 86,
534
    60, 72, 83, 87, 78, 83, 90, 91, 83, 87, 91, 92, 13, 39, 52, 57, 16,
535
    41, 53, 59, 52, 57, 75, 76, 58, 66, 80, 81, 16, 41, 58, 66, 18, 43,
536
    59, 67, 53, 59, 80, 81, 59, 67, 81, 85, 20, 45, 58, 70, 21, 46, 59,
537
    71, 58, 70, 82, 86, 60, 72, 83, 87, 21, 46, 60, 72, 22, 47, 61, 73,
538
    59, 71, 83, 87, 61, 73, 84, 88, 36, 41, 55, 59, 41, 49, 59, 61, 55,
539
    59, 78, 79, 69, 71, 83, 84, 41, 49, 69, 71, 49, 63, 71, 73, 59, 61,
540
    83, 84, 71, 73, 87, 88, 55, 69, 78, 83, 59, 71, 79, 84, 78, 83, 90,
541
    91, 83, 87, 91, 92, 59, 71, 83, 87, 61, 73, 84, 88, 79, 84, 91, 92,
542
    84, 88, 92, 93, 2, 3, 6, 7, 6, 7, 8, 9, 6, 7, 13, 14, 15, 16, 17, 18,
543
    6, 7, 15, 16, 13, 14, 17, 18, 8, 9, 17, 18, 17, 18, 23, 24, 12, 19,
544
    15, 20, 15, 20, 17, 21, 15, 20, 20, 25, 26, 27, 27, 28, 15, 20, 26,
545
    27, 20, 25, 27, 28, 17, 21, 27, 28, 27, 28, 29, 30, 6, 7, 13, 14, 15,
546
    16, 17, 18, 13, 14, 36, 37, 40, 41, 42, 43, 15, 16, 40, 41, 40, 41,
547
    48, 49, 17, 18, 42, 43, 48, 49, 62, 63, 51, 54, 52, 55, 56, 58, 57,
548
    59, 52, 55, 55, 64, 65, 66, 66, 67, 56, 58, 65, 66, 68, 69, 70, 71,
549
    57, 59, 66, 67, 70, 71, 72, 73, 6, 7, 15, 16, 13, 14, 17, 18, 15, 16,
550
    40, 41, 40, 41, 48, 49, 13, 14, 40, 41, 36, 37, 42, 43, 17, 18, 48,
551
    49, 42, 43, 62, 63, 51, 54, 56, 58, 52, 55, 57, 59, 56, 58, 68, 69,
552
    65, 66, 70, 71, 52, 55, 65, 66, 55, 64, 66, 67, 57, 59, 70, 71, 66,
553
    67, 72, 73, 8, 9, 17, 18, 17, 18, 23, 24, 17, 18, 42, 43, 48, 49, 62,
554
    63, 17, 18, 48, 49, 42, 43, 62, 63, 23, 24, 62, 63, 62, 63, 94, 95,
555
    74, 77, 75, 78, 75, 78, 76, 79, 75, 78, 96, 97, 98, 99, 100, 101, 75,
556
    78, 98, 99, 96, 97, 100, 101, 76, 79, 100, 101, 100, 101, 102, 103,
557
    12, 19, 15, 20, 15, 20, 17, 21, 51, 54, 52, 55, 56, 58, 57, 59, 51,
558
    54, 56, 58, 52, 55, 57, 59, 74, 77, 75, 78, 75, 78, 76, 79, 38, 44,
559
    40, 45, 40, 45, 42, 46, 56, 68, 58, 69, 65, 70, 66, 71, 56, 68, 65,
560
    70, 58, 69, 66, 71, 75, 82, 80, 83, 80, 83, 81, 84, 15, 20, 20, 25,
561
    26, 27, 27, 28, 52, 55, 55, 64, 65, 66, 66, 67, 56, 58, 68, 69, 65,
562
    66, 70, 71, 75, 78, 96, 97, 98, 99, 100, 101, 56, 68, 58, 69, 65, 70,
563
    66, 71, 75, 96, 78, 97, 98, 100, 99, 101, 104, 105, 105, 106, 105,
564
    106, 106, 107, 108, 109, 109, 110, 111, 112, 112, 113, 15, 20, 26,
565
    27, 20, 25, 27, 28, 56, 58, 65, 66, 68, 69, 70, 71, 52, 55, 65, 66,
566
    55, 64, 66, 67, 75, 78, 98, 99, 96, 97, 100, 101, 56, 68, 65, 70, 58,
567
    69, 66, 71, 104, 105, 105, 106, 105, 106, 106, 107, 75, 96, 98, 100,
568
    78, 97, 99, 101, 108, 109, 111, 112, 109, 110, 112, 113, 17, 21, 27,
569
    28, 27, 28, 29, 30, 57, 59, 66, 67, 70, 71, 72, 73, 57, 59, 70, 71,
570
    66, 67, 72, 73, 76, 79, 100, 101, 100, 101, 102, 103, 75, 82, 80, 83,
571
    80, 83, 81, 84, 108, 109, 109, 110, 111, 112, 112, 113, 108, 109,
572
    111, 112, 109, 110, 112, 113, 114, 115, 116, 117, 116, 117, 118, 119,
573
    12, 19, 51, 54, 51, 54, 74, 77, 15, 20, 52, 55, 56, 58, 75, 78, 15,
574
    20, 56, 58, 52, 55, 75, 78, 17, 21, 57, 59, 57, 59, 76, 79, 38, 44,
575
    56, 68, 56, 68, 75, 82, 40, 45, 58, 69, 65, 70, 80, 83, 40, 45, 65,
576
    70, 58, 69, 80, 83, 42, 46, 66, 71, 66, 71, 81, 84, 15, 20, 52, 55,
577
    56, 58, 75, 78, 20, 25, 55, 64, 68, 69, 96, 97, 26, 27, 65, 66, 65,
578
    66, 98, 99, 27, 28, 66, 67, 70, 71, 100, 101, 56, 68, 75, 96, 104,
579
    105, 108, 109, 58, 69, 78, 97, 105, 106, 109, 110, 65, 70, 98, 100,
580
    105, 106, 111, 112, 66, 71, 99, 101, 106, 107, 112, 113, 15, 20, 56,
581
    58, 52, 55, 75, 78, 26, 27, 65, 66, 65, 66, 98, 99, 20, 25, 68, 69,
582
    55, 64, 96, 97, 27, 28, 70, 71, 66, 67, 100, 101, 56, 68, 104, 105,
583
    75, 96, 108, 109, 65, 70, 105, 106, 98, 100, 111, 112, 58, 69, 105,
584
    106, 78, 97, 109, 110, 66, 71, 106, 107, 99, 101, 112, 113, 17, 21,
585
    57, 59, 57, 59, 76, 79, 27, 28, 66, 67, 70, 71, 100, 101, 27, 28, 70,
586
    71, 66, 67, 100, 101, 29, 30, 72, 73, 72, 73, 102, 103, 75, 82, 108,
587
    109, 108, 109, 114, 115, 80, 83, 109, 110, 111, 112, 116, 117, 80,
588
    83, 111, 112, 109, 110, 116, 117, 81, 84, 112, 113, 112, 113, 118,
589
    119, 38, 44, 56, 68, 56, 68, 75, 82, 56, 68, 75, 96, 104, 105, 108,
590
    109, 56, 68, 104, 105, 75, 96, 108, 109, 75, 82, 108, 109, 108, 109,
591
    114, 115, 44, 120, 68, 121, 68, 121, 96, 122, 68, 121, 82, 122, 105,
592
    123, 109, 124, 68, 121, 105, 123, 82, 122, 109, 124, 96, 122, 109,
593
    124, 109, 124, 115, 125, 40, 45, 58, 69, 65, 70, 80, 83, 58, 69, 78,
594
    97, 105, 106, 109, 110, 65, 70, 105, 106, 98, 100, 111, 112, 80, 83,
595
    109, 110, 111, 112, 116, 117, 68, 121, 82, 122, 105, 123, 109, 124,
596
    82, 122, 90, 126, 127, 128, 129, 130, 105, 123, 127, 128, 127, 128,
597
    131, 132, 109, 124, 129, 130, 131, 132, 133, 134, 40, 45, 65, 70, 58,
598
    69, 80, 83, 65, 70, 98, 100, 105, 106, 111, 112, 58, 69, 105, 106,
599
    78, 97, 109, 110, 80, 83, 111, 112, 109, 110, 116, 117, 68, 121, 105,
600
    123, 82, 122, 109, 124, 105, 123, 127, 128, 127, 128, 131, 132, 82,
601
    122, 127, 128, 90, 126, 129, 130, 109, 124, 131, 132, 129, 130, 133,
602
    134, 42, 46, 66, 71, 66, 71, 81, 84, 66, 71, 99, 101, 106, 107, 112,
603
    113, 66, 71, 106, 107, 99, 101, 112, 113, 81, 84, 112, 113, 112, 113,
604
    118, 119, 96, 122, 109, 124, 109, 124, 115, 125, 109, 124, 129, 130,
605
    131, 132, 133, 134, 109, 124, 131, 132, 129, 130, 133, 134, 115, 125,
606
    133, 134, 133, 134, 135, 136, 1, 5, 2, 6, 2, 6, 4, 7, 5, 12, 6, 13,
607
    12, 15, 13, 16, 5, 12, 12, 15, 6, 13, 13, 16, 12, 19, 15, 20, 15, 20,
608
    17, 21, 2, 12, 4, 13, 4, 13, 11, 14, 6, 15, 7, 16, 13, 17, 14, 18, 6,
609
    15, 13, 17, 7, 16, 14, 18, 13, 20, 16, 21, 16, 21, 18, 22, 5, 12, 6,
610
    13, 12, 15, 13, 16, 12, 35, 13, 36, 38, 40, 39, 41, 50, 51, 51, 52,
611
    51, 52, 52, 53, 51, 54, 52, 55, 56, 58, 57, 59, 12, 38, 13, 39, 35,
612
    40, 36, 41, 15, 40, 16, 41, 40, 48, 41, 49, 51, 56, 52, 57, 54, 58,
613
    55, 59, 52, 58, 53, 59, 58, 60, 59, 61, 5, 12, 12, 15, 6, 13, 13, 16,
614
    50, 51, 51, 52, 51, 52, 52, 53, 12, 35, 38, 40, 13, 36, 39, 41, 51,
615
    54, 56, 58, 52, 55, 57, 59, 12, 38, 35, 40, 13, 39, 36, 41, 51, 56,
616
    54, 58, 52, 57, 55, 59, 15, 40, 40, 48, 16, 41, 41, 49, 52, 58, 58,
617
    60, 53, 59, 59, 61, 12, 19, 15, 20, 15, 20, 17, 21, 51, 54, 52, 55,
618
    56, 58, 57, 59, 51, 54, 56, 58, 52, 55, 57, 59, 74, 77, 75, 78, 75,
619
    78, 76, 79, 38, 44, 40, 45, 40, 45, 42, 46, 56, 68, 58, 69, 65, 70,
620
    66, 71, 56, 68, 65, 70, 58, 69, 66, 71, 75, 82, 80, 83, 80, 83, 81,
621
    84, 2, 12, 4, 13, 4, 13, 11, 14, 12, 38, 13, 39, 35, 40, 36, 41, 12,
622
    38, 35, 40, 13, 39, 36, 41, 38, 44, 40, 45, 40, 45, 42, 46, 4, 35,
623
    11, 36, 11, 36, 34, 37, 13, 40, 14, 41, 36, 42, 37, 43, 13, 40, 36,
624
    42, 14, 41, 37, 43, 39, 45, 41, 46, 41, 46, 43, 47, 6, 15, 7, 16, 13,
625
    17, 14, 18, 15, 40, 16, 41, 40, 48, 41, 49, 51, 56, 54, 58, 52, 57,
626
    55, 59, 56, 68, 58, 69, 65, 70, 66, 71, 13, 40, 14, 41, 36, 42, 37,
627
    43, 17, 48, 18, 49, 42, 62, 43, 63, 52, 65, 55, 66, 55, 66, 64, 67,
628
    57, 70, 59, 71, 66, 72, 67, 73, 6, 15, 13, 17, 7, 16, 14, 18, 51, 56,
629
    52, 57, 54, 58, 55, 59, 15, 40, 40, 48, 16, 41, 41, 49, 56, 68, 65,
630
    70, 58, 69, 66, 71, 13, 40, 36, 42, 14, 41, 37, 43, 52, 65, 55, 66,
631
    55, 66, 64, 67, 17, 48, 42, 62, 18, 49, 43, 63, 57, 70, 66, 72, 59,
632
    71, 67, 73, 13, 20, 16, 21, 16, 21, 18, 22, 52, 58, 53, 59, 58, 60,
633
    59, 61, 52, 58, 58, 60, 53, 59, 59, 61, 75, 82, 80, 83, 80, 83, 81,
634
    84, 39, 45, 41, 46, 41, 46, 43, 47, 57, 70, 59, 71, 66, 72, 67, 73,
635
    57, 70, 66, 72, 59, 71, 67, 73, 76, 86, 81, 87, 81, 87, 85, 88, 5,
636
    50, 12, 51, 12, 51, 35, 54, 12, 51, 15, 52, 38, 56, 40, 58, 12, 51,
637
    38, 56, 15, 52, 40, 58, 35, 54, 40, 58, 40, 58, 48, 60, 6, 51, 13,
638
    52, 13, 52, 36, 55, 13, 52, 16, 53, 39, 57, 41, 59, 13, 52, 39, 57,
639
    16, 53, 41, 59, 36, 55, 41, 59, 41, 59, 49, 61, 12, 51, 15, 52, 38,
640
    56, 40, 58, 19, 54, 20, 55, 44, 68, 45, 69, 51, 74, 56, 75, 56, 75,
641
    65, 80, 54, 77, 58, 78, 68, 82, 70, 83, 15, 56, 17, 57, 40, 65, 42,
642
    66, 20, 58, 21, 59, 45, 70, 46, 71, 52, 75, 57, 76, 58, 80, 66, 81,
643
    55, 78, 59, 79, 69, 83, 71, 84, 12, 51, 38, 56, 15, 52, 40, 58, 51,
644
    74, 56, 75, 56, 75, 65, 80, 19, 54, 44, 68, 20, 55, 45, 69, 54, 77,
645
    68, 82, 58, 78, 70, 83, 15, 56, 40, 65, 17, 57, 42, 66, 52, 75, 58,
646
    80, 57, 76, 66, 81, 20, 58, 45, 70, 21, 59, 46, 71, 55, 78, 69, 83,
647
    59, 79, 71, 84, 35, 54, 40, 58, 40, 58, 48, 60, 54, 77, 58, 78, 68,
648
    82, 70, 83, 54, 77, 68, 82, 58, 78, 70, 83, 77, 89, 82, 90, 82, 90,
649
    86, 91, 40, 68, 48, 70, 48, 70, 62, 72, 58, 82, 60, 83, 70, 86, 72,
650
    87, 58, 82, 70, 86, 60, 83, 72, 87, 78, 90, 83, 91, 83, 91, 87, 92,
651
    6, 51, 13, 52, 13, 52, 36, 55, 15, 56, 17, 57, 40, 65, 42, 66, 15,
652
    56, 40, 65, 17, 57, 42, 66, 40, 68, 48, 70, 48, 70, 62, 72, 7, 54,
653
    14, 55, 14, 55, 37, 64, 16, 58, 18, 59, 41, 66, 43, 67, 16, 58, 41,
654
    66, 18, 59, 43, 67, 41, 69, 49, 71, 49, 71, 63, 73, 13, 52, 16, 53,
655
    39, 57, 41, 59, 20, 58, 21, 59, 45, 70, 46, 71, 52, 75, 58, 80, 57,
656
    76, 66, 81, 58, 82, 60, 83, 70, 86, 72, 87, 16, 58, 18, 59, 41, 66,
657
    43, 67, 21, 60, 22, 61, 46, 72, 47, 73, 53, 80, 59, 81, 59, 81, 67,
658
    85, 59, 83, 61, 84, 71, 87, 73, 88, 13, 52, 39, 57, 16, 53, 41, 59,
659
    52, 75, 57, 76, 58, 80, 66, 81, 20, 58, 45, 70, 21, 59, 46, 71, 58,
660
    82, 70, 86, 60, 83, 72, 87, 16, 58, 41, 66, 18, 59, 43, 67, 53, 80,
661
    59, 81, 59, 81, 67, 85, 21, 60, 46, 72, 22, 61, 47, 73, 59, 83, 71,
662
    87, 61, 84, 73, 88, 36, 55, 41, 59, 41, 59, 49, 61, 55, 78, 59, 79,
663
    69, 83, 71, 84, 55, 78, 69, 83, 59, 79, 71, 84, 78, 90, 83, 91, 83,
664
    91, 87, 92, 41, 69, 49, 71, 49, 71, 63, 73, 59, 83, 61, 84, 71, 87,
665
    73, 88, 59, 83, 71, 87, 61, 84, 73, 88, 79, 91, 84, 92, 84, 92, 88,
666
    93, 2, 6, 3, 7, 6, 8, 7, 9, 6, 13, 7, 14, 15, 17, 16, 18, 12, 15, 19,
667
    20, 15, 17, 20, 21, 15, 20, 20, 25, 26, 27, 27, 28, 6, 15, 7, 16, 13,
668
    17, 14, 18, 8, 17, 9, 18, 17, 23, 18, 24, 15, 26, 20, 27, 20, 27, 25,
669
    28, 17, 27, 21, 28, 27, 29, 28, 30, 6, 13, 7, 14, 15, 17, 16, 18, 13,
670
    36, 14, 37, 40, 42, 41, 43, 51, 52, 54, 55, 56, 57, 58, 59, 52, 55,
671
    55, 64, 65, 66, 66, 67, 15, 40, 16, 41, 40, 48, 41, 49, 17, 42, 18,
672
    43, 48, 62, 49, 63, 56, 65, 58, 66, 68, 70, 69, 71, 57, 66, 59, 67,
673
    70, 72, 71, 73, 12, 15, 19, 20, 15, 17, 20, 21, 51, 52, 54, 55, 56,
674
    57, 58, 59, 38, 40, 44, 45, 40, 42, 45, 46, 56, 58, 68, 69, 65, 66,
675
    70, 71, 51, 56, 54, 58, 52, 57, 55, 59, 74, 75, 77, 78, 75, 76, 78,
676
    79, 56, 65, 68, 70, 58, 66, 69, 71, 75, 80, 82, 83, 80, 81, 83, 84,
677
    15, 20, 20, 25, 26, 27, 27, 28, 52, 55, 55, 64, 65, 66, 66, 67, 56,
678
    58, 68, 69, 65, 66, 70, 71, 75, 78, 96, 97, 98, 99, 100, 101, 56, 68,
679
    58, 69, 65, 70, 66, 71, 75, 96, 78, 97, 98, 100, 99, 101, 104, 105,
680
    105, 106, 105, 106, 106, 107, 108, 109, 109, 110, 111, 112, 112, 113,
681
    6, 15, 7, 16, 13, 17, 14, 18, 15, 40, 16, 41, 40, 48, 41, 49, 51, 56,
682
    54, 58, 52, 57, 55, 59, 56, 68, 58, 69, 65, 70, 66, 71, 13, 40, 14,
683
    41, 36, 42, 37, 43, 17, 48, 18, 49, 42, 62, 43, 63, 52, 65, 55, 66,
684
    55, 66, 64, 67, 57, 70, 59, 71, 66, 72, 67, 73, 8, 17, 9, 18, 17, 23,
685
    18, 24, 17, 42, 18, 43, 48, 62, 49, 63, 74, 75, 77, 78, 75, 76, 78,
686
    79, 75, 96, 78, 97, 98, 100, 99, 101, 17, 48, 18, 49, 42, 62, 43, 63,
687
    23, 62, 24, 63, 62, 94, 63, 95, 75, 98, 78, 99, 96, 100, 97, 101, 76,
688
    100, 79, 101, 100, 102, 101, 103, 15, 26, 20, 27, 20, 27, 25, 28, 56,
689
    65, 58, 66, 68, 70, 69, 71, 56, 65, 68, 70, 58, 66, 69, 71, 104, 105,
690
    105, 106, 105, 106, 106, 107, 52, 65, 55, 66, 55, 66, 64, 67, 75, 98,
691
    78, 99, 96, 100, 97, 101, 75, 98, 96, 100, 78, 99, 97, 101, 108, 111,
692
    109, 112, 109, 112, 110, 113, 17, 27, 21, 28, 27, 29, 28, 30, 57, 66,
693
    59, 67, 70, 72, 71, 73, 75, 80, 82, 83, 80, 81, 83, 84, 108, 109,
694
    109, 110, 111, 112, 112, 113, 57, 70, 59, 71, 66, 72, 67, 73, 76,
695
    100, 79, 101, 100, 102, 101, 103, 108, 111, 109, 112, 109, 112, 110,
696
    113, 114, 116, 115, 117, 116, 118, 117, 119, 12, 51, 19, 54, 51, 74,
697
    54, 77, 15, 52, 20, 55, 56, 75, 58, 78, 38, 56, 44, 68, 56, 75, 68,
698
    82, 40, 58, 45, 69, 65, 80, 70, 83, 15, 56, 20, 58, 52, 75, 55, 78,
699
    17, 57, 21, 59, 57, 76, 59, 79, 40, 65, 45, 70, 58, 80, 69, 83, 42,
700
    66, 46, 71, 66, 81, 71, 84, 15, 52, 20, 55, 56, 75, 58, 78, 20, 55,
701
    25, 64, 68, 96, 69, 97, 56, 75, 68, 96, 104, 108, 105, 109, 58, 78,
702
    69, 97, 105, 109, 106, 110, 26, 65, 27, 66, 65, 98, 66, 99, 27, 66,
703
    28, 67, 70, 100, 71, 101, 65, 98, 70, 100, 105, 111, 106, 112, 66,
704
    99, 71, 101, 106, 112, 107, 113, 38, 56, 44, 68, 56, 75, 68, 82, 56,
705
    75, 68, 96, 104, 108, 105, 109, 44, 68, 120, 121, 68, 96, 121, 122,
706
    68, 82, 121, 122, 105, 109, 123, 124, 56, 104, 68, 105, 75, 108, 96,
707
    109, 75, 108, 82, 109, 108, 114, 109, 115, 68, 105, 121, 123, 82,
708
    109, 122, 124, 96, 109, 122, 124, 109, 115, 124, 125, 40, 58, 45, 69,
709
    65, 80, 70, 83, 58, 78, 69, 97, 105, 109, 106, 110, 68, 82, 121, 122,
710
    105, 109, 123, 124, 82, 90, 122, 126, 127, 129, 128, 130, 65, 105,
711
    70, 106, 98, 111, 100, 112, 80, 109, 83, 110, 111, 116, 112, 117,
712
    105, 127, 123, 128, 127, 131, 128, 132, 109, 129, 124, 130, 131, 133,
713
    132, 134, 15, 56, 20, 58, 52, 75, 55, 78, 26, 65, 27, 66, 65, 98, 66,
714
    99, 56, 104, 68, 105, 75, 108, 96, 109, 65, 105, 70, 106, 98, 111,
715
    100, 112, 20, 68, 25, 69, 55, 96, 64, 97, 27, 70, 28, 71, 66, 100,
716
    67, 101, 58, 105, 69, 106, 78, 109, 97, 110, 66, 106, 71, 107, 99,
717
    112, 101, 113, 17, 57, 21, 59, 57, 76, 59, 79, 27, 66, 28, 67, 70,
718
    100, 71, 101, 75, 108, 82, 109, 108, 114, 109, 115, 80, 109, 83, 110,
719
    111, 116, 112, 117, 27, 70, 28, 71, 66, 100, 67, 101, 29, 72, 30, 73,
720
    72, 102, 73, 103, 80, 111, 83, 112, 109, 116, 110, 117, 81, 112, 84,
721
    113, 112, 118, 113, 119, 40, 65, 45, 70, 58, 80, 69, 83, 65, 98, 70,
722
    100, 105, 111, 106, 112, 68, 105, 121, 123, 82, 109, 122, 124, 105,
723
    127, 123, 128, 127, 131, 128, 132, 58, 105, 69, 106, 78, 109, 97,
724
    110, 80, 111, 83, 112, 109, 116, 110, 117, 82, 127, 122, 128, 90,
725
    129, 126, 130, 109, 131, 124, 132, 129, 133, 130, 134, 42, 66, 46,
726
    71, 66, 81, 71, 84, 66, 99, 71, 101, 106, 112, 107, 113, 96, 109,
727
    122, 124, 109, 115, 124, 125, 109, 129, 124, 130, 131, 133, 132, 134,
728
    66, 106, 71, 107, 99, 112, 101, 113, 81, 112, 84, 113, 112, 118, 113,
729
    119, 109, 131, 124, 132, 129, 133, 130, 134, 115, 133, 125, 134, 133,
730
    135, 134, 136, 2, 6, 6, 8, 3, 7, 7, 9, 12, 15, 15, 17, 19, 20, 20,
731
    21, 6, 13, 15, 17, 7, 14, 16, 18, 15, 20, 26, 27, 20, 25, 27, 28, 6,
732
    15, 13, 17, 7, 16, 14, 18, 15, 26, 20, 27, 20, 27, 25, 28, 8, 17, 17,
733
    23, 9, 18, 18, 24, 17, 27, 27, 29, 21, 28, 28, 30, 12, 15, 15, 17,
734
    19, 20, 20, 21, 38, 40, 40, 42, 44, 45, 45, 46, 51, 52, 56, 57, 54,
735
    55, 58, 59, 56, 58, 65, 66, 68, 69, 70, 71, 51, 56, 52, 57, 54, 58,
736
    55, 59, 56, 65, 58, 66, 68, 70, 69, 71, 74, 75, 75, 76, 77, 78, 78,
737
    79, 75, 80, 80, 81, 82, 83, 83, 84, 6, 13, 15, 17, 7, 14, 16, 18, 51,
738
    52, 56, 57, 54, 55, 58, 59, 13, 36, 40, 42, 14, 37, 41, 43, 52, 55,
739
    65, 66, 55, 64, 66, 67, 15, 40, 40, 48, 16, 41, 41, 49, 56, 65, 68,
740
    70, 58, 66, 69, 71, 17, 42, 48, 62, 18, 43, 49, 63, 57, 66, 70, 72,
741
    59, 67, 71, 73, 15, 20, 26, 27, 20, 25, 27, 28, 56, 58, 65, 66, 68,
742
    69, 70, 71, 52, 55, 65, 66, 55, 64, 66, 67, 75, 78, 98, 99, 96, 97,
743
    100, 101, 56, 68, 65, 70, 58, 69, 66, 71, 104, 105, 105, 106, 105,
744
    106, 106, 107, 75, 96, 98, 100, 78, 97, 99, 101, 108, 109, 111, 112,
745
    109, 110, 112, 113, 6, 15, 13, 17, 7, 16, 14, 18, 51, 56, 52, 57, 54,
746
    58, 55, 59, 15, 40, 40, 48, 16, 41, 41, 49, 56, 68, 65, 70, 58, 69,
747
    66, 71, 13, 40, 36, 42, 14, 41, 37, 43, 52, 65, 55, 66, 55, 66, 64,
748
    67, 17, 48, 42, 62, 18, 49, 43, 63, 57, 70, 66, 72, 59, 71, 67, 73,
749
    15, 26, 20, 27, 20, 27, 25, 28, 56, 65, 58, 66, 68, 70, 69, 71, 56,
750
    65, 68, 70, 58, 66, 69, 71, 104, 105, 105, 106, 105, 106, 106, 107,
751
    52, 65, 55, 66, 55, 66, 64, 67, 75, 98, 78, 99, 96, 100, 97, 101, 75,
752
    98, 96, 100, 78, 99, 97, 101, 108, 111, 109, 112, 109, 112, 110, 113,
753
    8, 17, 17, 23, 9, 18, 18, 24, 74, 75, 75, 76, 77, 78, 78, 79, 17, 42,
754
    48, 62, 18, 43, 49, 63, 75, 96, 98, 100, 78, 97, 99, 101, 17, 48, 42,
755
    62, 18, 49, 43, 63, 75, 98, 96, 100, 78, 99, 97, 101, 23, 62, 62, 94,
756
    24, 63, 63, 95, 76, 100, 100, 102, 79, 101, 101, 103, 17, 27, 27, 29,
757
    21, 28, 28, 30, 75, 80, 80, 81, 82, 83, 83, 84, 57, 66, 70, 72, 59,
758
    67, 71, 73, 108, 109, 111, 112, 109, 110, 112, 113, 57, 70, 66, 72,
759
    59, 71, 67, 73, 108, 111, 109, 112, 109, 112, 110, 113, 76, 100, 100,
760
    102, 79, 101, 101, 103, 114, 116, 116, 118, 115, 117, 117, 119, 12,
761
    51, 51, 74, 19, 54, 54, 77, 38, 56, 56, 75, 44, 68, 68, 82, 15, 52,
762
    56, 75, 20, 55, 58, 78, 40, 58, 65, 80, 45, 69, 70, 83, 15, 56, 52,
763
    75, 20, 58, 55, 78, 40, 65, 58, 80, 45, 70, 69, 83, 17, 57, 57, 76,
764
    21, 59, 59, 79, 42, 66, 66, 81, 46, 71, 71, 84, 38, 56, 56, 75, 44,
765
    68, 68, 82, 44, 68, 68, 96, 120, 121, 121, 122, 56, 75, 104, 108, 68,
766
    96, 105, 109, 68, 82, 105, 109, 121, 122, 123, 124, 56, 104, 75, 108,
767
    68, 105, 96, 109, 68, 105, 82, 109, 121, 123, 122, 124, 75, 108, 108,
768
    114, 82, 109, 109, 115, 96, 109, 109, 115, 122, 124, 124, 125, 15,
769
    52, 56, 75, 20, 55, 58, 78, 56, 75, 104, 108, 68, 96, 105, 109, 20,
770
    55, 68, 96, 25, 64, 69, 97, 58, 78, 105, 109, 69, 97, 106, 110, 26,
771
    65, 65, 98, 27, 66, 66, 99, 65, 98, 105, 111, 70, 100, 106, 112, 27,
772
    66, 70, 100, 28, 67, 71, 101, 66, 99, 106, 112, 71, 101, 107, 113,
773
    40, 58, 65, 80, 45, 69, 70, 83, 68, 82, 105, 109, 121, 122, 123, 124,
774
    58, 78, 105, 109, 69, 97, 106, 110, 82, 90, 127, 129, 122, 126, 128,
775
    130, 65, 105, 98, 111, 70, 106, 100, 112, 105, 127, 127, 131, 123,
776
    128, 128, 132, 80, 109, 111, 116, 83, 110, 112, 117, 109, 129, 131,
777
    133, 124, 130, 132, 134, 15, 56, 52, 75, 20, 58, 55, 78, 56, 104, 75,
778
    108, 68, 105, 96, 109, 26, 65, 65, 98, 27, 66, 66, 99, 65, 105, 98,
779
    111, 70, 106, 100, 112, 20, 68, 55, 96, 25, 69, 64, 97, 58, 105, 78,
780
    109, 69, 106, 97, 110, 27, 70, 66, 100, 28, 71, 67, 101, 66, 106, 99,
781
    112, 71, 107, 101, 113, 40, 65, 58, 80, 45, 70, 69, 83, 68, 105, 82,
782
    109, 121, 123, 122, 124, 65, 98, 105, 111, 70, 100, 106, 112, 105,
783
    127, 127, 131, 123, 128, 128, 132, 58, 105, 78, 109, 69, 106, 97,
784
    110, 82, 127, 90, 129, 122, 128, 126, 130, 80, 111, 109, 116, 83,
785
    112, 110, 117, 109, 131, 129, 133, 124, 132, 130, 134, 17, 57, 57,
786
    76, 21, 59, 59, 79, 75, 108, 108, 114, 82, 109, 109, 115, 27, 66, 70,
787
    100, 28, 67, 71, 101, 80, 109, 111, 116, 83, 110, 112, 117, 27, 70,
788
    66, 100, 28, 71, 67, 101, 80, 111, 109, 116, 83, 112, 110, 117, 29,
789
    72, 72, 102, 30, 73, 73, 103, 81, 112, 112, 118, 84, 113, 113, 119,
790
    42, 66, 66, 81, 46, 71, 71, 84, 96, 109, 109, 115, 122, 124, 124,
791
    125, 66, 99, 106, 112, 71, 101, 107, 113, 109, 129, 131, 133, 124,
792
    130, 132, 134, 66, 106, 99, 112, 71, 107, 101, 113, 109, 131, 129,
793
    133, 124, 132, 130, 134, 81, 112, 112, 118, 84, 113, 113, 119, 115,
794
    133, 133, 135, 125, 134, 134, 136, 4, 7, 7, 9, 7, 9, 9, 10, 13, 16,
795
    16, 18, 20, 21, 21, 22, 13, 16, 20, 21, 16, 18, 21, 22, 17, 21, 27,
796
    28, 27, 28, 29, 30, 13, 20, 16, 21, 16, 21, 18, 22, 17, 27, 21, 28,
797
    27, 29, 28, 30, 17, 27, 27, 29, 21, 28, 28, 30, 23, 29, 29, 31, 29,
798
    31, 31, 32, 13, 16, 16, 18, 20, 21, 21, 22, 39, 41, 41, 43, 45, 46,
799
    46, 47, 52, 53, 58, 59, 58, 59, 60, 61, 57, 59, 66, 67, 70, 71, 72,
800
    73, 52, 58, 53, 59, 58, 60, 59, 61, 57, 66, 59, 67, 70, 72, 71, 73,
801
    75, 80, 80, 81, 82, 83, 83, 84, 76, 81, 81, 85, 86, 87, 87, 88, 13,
802
    16, 20, 21, 16, 18, 21, 22, 52, 53, 58, 59, 58, 59, 60, 61, 39, 41,
803
    45, 46, 41, 43, 46, 47, 57, 59, 70, 71, 66, 67, 72, 73, 52, 58, 58,
804
    60, 53, 59, 59, 61, 75, 80, 82, 83, 80, 81, 83, 84, 57, 66, 70, 72,
805
    59, 67, 71, 73, 76, 81, 86, 87, 81, 85, 87, 88, 17, 21, 27, 28, 27,
806
    28, 29, 30, 57, 59, 66, 67, 70, 71, 72, 73, 57, 59, 70, 71, 66, 67,
807
    72, 73, 76, 79, 100, 101, 100, 101, 102, 103, 75, 82, 80, 83, 80, 83,
808
    81, 84, 108, 109, 109, 110, 111, 112, 112, 113, 108, 109, 111, 112,
809
    109, 110, 112, 113, 114, 115, 116, 117, 116, 117, 118, 119, 13, 20,
810
    16, 21, 16, 21, 18, 22, 52, 58, 53, 59, 58, 60, 59, 61, 52, 58, 58,
811
    60, 53, 59, 59, 61, 75, 82, 80, 83, 80, 83, 81, 84, 39, 45, 41, 46,
812
    41, 46, 43, 47, 57, 70, 59, 71, 66, 72, 67, 73, 57, 70, 66, 72, 59,
813
    71, 67, 73, 76, 86, 81, 87, 81, 87, 85, 88, 17, 27, 21, 28, 27, 29,
814
    28, 30, 57, 66, 59, 67, 70, 72, 71, 73, 75, 80, 82, 83, 80, 81, 83,
815
    84, 108, 109, 109, 110, 111, 112, 112, 113, 57, 70, 59, 71, 66, 72,
816
    67, 73, 76, 100, 79, 101, 100, 102, 101, 103, 108, 111, 109, 112,
817
    109, 112, 110, 113, 114, 116, 115, 117, 116, 118, 117, 119, 17, 27,
818
    27, 29, 21, 28, 28, 30, 75, 80, 80, 81, 82, 83, 83, 84, 57, 66, 70,
819
    72, 59, 67, 71, 73, 108, 109, 111, 112, 109, 110, 112, 113, 57, 70,
820
    66, 72, 59, 71, 67, 73, 108, 111, 109, 112, 109, 112, 110, 113, 76,
821
    100, 100, 102, 79, 101, 101, 103, 114, 116, 116, 118, 115, 117, 117,
822
    119, 23, 29, 29, 31, 29, 31, 31, 32, 76, 81, 81, 85, 86, 87, 87, 88,
823
    76, 81, 86, 87, 81, 85, 87, 88, 114, 115, 116, 117, 116, 117, 118,
824
    119, 76, 86, 81, 87, 81, 87, 85, 88, 114, 116, 115, 117, 116, 118,
825
    117, 119, 114, 116, 116, 118, 115, 117, 117, 119, 137, 138, 138, 139,
826
    138, 139, 139, 140, 35, 54, 54, 77, 54, 77, 77, 89, 40, 58, 58, 78,
827
    68, 82, 82, 90, 40, 58, 68, 82, 58, 78, 82, 90, 48, 60, 70, 83, 70,
828
    83, 86, 91, 40, 68, 58, 82, 58, 82, 78, 90, 48, 70, 60, 83, 70, 86,
829
    83, 91, 48, 70, 70, 86, 60, 83, 83, 91, 62, 72, 72, 87, 72, 87, 87,
830
    92, 40, 58, 58, 78, 68, 82, 82, 90, 45, 69, 69, 97, 121, 122, 122,
831
    126, 65, 80, 105, 109, 105, 109, 127, 129, 70, 83, 106, 110, 123,
832
    124, 128, 130, 65, 105, 80, 109, 105, 127, 109, 129, 70, 106, 83,
833
    110, 123, 128, 124, 130, 98, 111, 111, 116, 127, 131, 131, 133, 100,
834
    112, 112, 117, 128, 132, 132, 134, 40, 58, 68, 82, 58, 78, 82, 90,
835
    65, 80, 105, 109, 105, 109, 127, 129, 45, 69, 121, 122, 69, 97, 122,
836
    126, 70, 83, 123, 124, 106, 110, 128, 130, 65, 105, 105, 127, 80,
837
    109, 109, 129, 98, 111, 127, 131, 111, 116, 131, 133, 70, 106, 123,
838
    128, 83, 110, 124, 130, 100, 112, 128, 132, 112, 117, 132, 134, 48,
839
    60, 70, 83, 70, 83, 86, 91, 70, 83, 106, 110, 123, 124, 128, 130, 70,
840
    83, 123, 124, 106, 110, 128, 130, 86, 91, 128, 130, 128, 130, 141,
841
    142, 98, 127, 111, 131, 111, 131, 116, 133, 111, 131, 131, 143, 144,
842
    145, 145, 146, 111, 131, 144, 145, 131, 143, 145, 146, 116, 133, 145,
843
    146, 145, 146, 147, 148, 40, 68, 58, 82, 58, 82, 78, 90, 65, 105, 80,
844
    109, 105, 127, 109, 129, 65, 105, 105, 127, 80, 109, 109, 129, 98,
845
    127, 111, 131, 111, 131, 116, 133, 45, 121, 69, 122, 69, 122, 97,
846
    126, 70, 123, 83, 124, 106, 128, 110, 130, 70, 123, 106, 128, 83,
847
    124, 110, 130, 100, 128, 112, 132, 112, 132, 117, 134, 48, 70, 60,
848
    83, 70, 86, 83, 91, 70, 106, 83, 110, 123, 128, 124, 130, 98, 111,
849
    127, 131, 111, 116, 131, 133, 111, 131, 131, 143, 144, 145, 145, 146,
850
    70, 123, 83, 124, 106, 128, 110, 130, 86, 128, 91, 130, 128, 141,
851
    130, 142, 111, 144, 131, 145, 131, 145, 143, 146, 116, 145, 133, 146,
852
    145, 147, 146, 148, 48, 70, 70, 86, 60, 83, 83, 91, 98, 111, 111,
853
    116, 127, 131, 131, 133, 70, 106, 123, 128, 83, 110, 124, 130, 111,
854
    131, 144, 145, 131, 143, 145, 146, 70, 123, 106, 128, 83, 124, 110,
855
    130, 111, 144, 131, 145, 131, 145, 143, 146, 86, 128, 128, 141, 91,
856
    130, 130, 142, 116, 145, 145, 147, 133, 146, 146, 148, 62, 72, 72,
857
    87, 72, 87, 87, 92, 100, 112, 112, 117, 128, 132, 132, 134, 100, 112,
858
    128, 132, 112, 117, 132, 134, 116, 133, 145, 146, 145, 146, 147, 148,
859
    100, 128, 112, 132, 112, 132, 117, 134, 116, 145, 133, 146, 145, 147,
860
    146, 148, 116, 145, 145, 147, 133, 146, 146, 148, 138, 149, 149, 150,
861
    149, 150, 150, 151, 1, 5, 5, 12, 5, 12, 12, 19, 2, 6, 6, 13, 12, 15,
862
    15, 20, 2, 6, 12, 15, 6, 13, 15, 20, 4, 7, 13, 16, 13, 16, 17, 21, 2,
863
    12, 6, 15, 6, 15, 13, 20, 4, 13, 7, 16, 13, 17, 16, 21, 4, 13, 13,
864
    17, 7, 16, 16, 21, 11, 14, 14, 18, 14, 18, 18, 22, 5, 12, 12, 35, 50,
865
    51, 51, 54, 6, 13, 13, 36, 51, 52, 52, 55, 12, 15, 38, 40, 51, 52,
866
    56, 58, 13, 16, 39, 41, 52, 53, 57, 59, 12, 38, 15, 40, 51, 56, 52,
867
    58, 13, 39, 16, 41, 52, 57, 53, 59, 35, 40, 40, 48, 54, 58, 58, 60,
868
    36, 41, 41, 49, 55, 59, 59, 61, 5, 12, 50, 51, 12, 35, 51, 54, 12,
869
    15, 51, 52, 38, 40, 56, 58, 6, 13, 51, 52, 13, 36, 52, 55, 13, 16,
870
    52, 53, 39, 41, 57, 59, 12, 38, 51, 56, 15, 40, 52, 58, 35, 40, 54,
871
    58, 40, 48, 58, 60, 13, 39, 52, 57, 16, 41, 53, 59, 36, 41, 55, 59,
872
    41, 49, 59, 61, 12, 19, 51, 54, 51, 54, 74, 77, 15, 20, 52, 55, 56,
873
    58, 75, 78, 15, 20, 56, 58, 52, 55, 75, 78, 17, 21, 57, 59, 57, 59,
874
    76, 79, 38, 44, 56, 68, 56, 68, 75, 82, 40, 45, 58, 69, 65, 70, 80,
875
    83, 40, 45, 65, 70, 58, 69, 80, 83, 42, 46, 66, 71, 66, 71, 81, 84,
876
    5, 50, 12, 51, 12, 51, 35, 54, 12, 51, 15, 52, 38, 56, 40, 58, 12,
877
    51, 38, 56, 15, 52, 40, 58, 35, 54, 40, 58, 40, 58, 48, 60, 6, 51,
878
    13, 52, 13, 52, 36, 55, 13, 52, 16, 53, 39, 57, 41, 59, 13, 52, 39,
879
    57, 16, 53, 41, 59, 36, 55, 41, 59, 41, 59, 49, 61, 12, 51, 19, 54,
880
    51, 74, 54, 77, 15, 52, 20, 55, 56, 75, 58, 78, 38, 56, 44, 68, 56,
881
    75, 68, 82, 40, 58, 45, 69, 65, 80, 70, 83, 15, 56, 20, 58, 52, 75,
882
    55, 78, 17, 57, 21, 59, 57, 76, 59, 79, 40, 65, 45, 70, 58, 80, 69,
883
    83, 42, 66, 46, 71, 66, 81, 71, 84, 12, 51, 51, 74, 19, 54, 54, 77,
884
    38, 56, 56, 75, 44, 68, 68, 82, 15, 52, 56, 75, 20, 55, 58, 78, 40,
885
    58, 65, 80, 45, 69, 70, 83, 15, 56, 52, 75, 20, 58, 55, 78, 40, 65,
886
    58, 80, 45, 70, 69, 83, 17, 57, 57, 76, 21, 59, 59, 79, 42, 66, 66,
887
    81, 46, 71, 71, 84, 35, 54, 54, 77, 54, 77, 77, 89, 40, 58, 58, 78,
888
    68, 82, 82, 90, 40, 58, 68, 82, 58, 78, 82, 90, 48, 60, 70, 83, 70,
889
    83, 86, 91, 40, 68, 58, 82, 58, 82, 78, 90, 48, 70, 60, 83, 70, 86,
890
    83, 91, 48, 70, 70, 86, 60, 83, 83, 91, 62, 72, 72, 87, 72, 87, 87,
891
    92, 2, 12, 12, 38, 12, 38, 38, 44, 4, 13, 13, 39, 35, 40, 40, 45, 4,
892
    13, 35, 40, 13, 39, 40, 45, 11, 14, 36, 41, 36, 41, 42, 46, 4, 35,
893
    13, 40, 13, 40, 39, 45, 11, 36, 14, 41, 36, 42, 41, 46, 11, 36, 36,
894
    42, 14, 41, 41, 46, 34, 37, 37, 43, 37, 43, 43, 47, 6, 15, 15, 40,
895
    51, 56, 56, 68, 7, 16, 16, 41, 54, 58, 58, 69, 13, 17, 40, 48, 52,
896
    57, 65, 70, 14, 18, 41, 49, 55, 59, 66, 71, 13, 40, 17, 48, 52, 65,
897
    57, 70, 14, 41, 18, 49, 55, 66, 59, 71, 36, 42, 42, 62, 55, 66, 66,
898
    72, 37, 43, 43, 63, 64, 67, 67, 73, 6, 15, 51, 56, 15, 40, 56, 68,
899
    13, 17, 52, 57, 40, 48, 65, 70, 7, 16, 54, 58, 16, 41, 58, 69, 14,
900
    18, 55, 59, 41, 49, 66, 71, 13, 40, 52, 65, 17, 48, 57, 70, 36, 42,
901
    55, 66, 42, 62, 66, 72, 14, 41, 55, 66, 18, 49, 59, 71, 37, 43, 64,
902
    67, 43, 63, 67, 73, 13, 20, 52, 58, 52, 58, 75, 82, 16, 21, 53, 59,
903
    58, 60, 80, 83, 16, 21, 58, 60, 53, 59, 80, 83, 18, 22, 59, 61, 59,
904
    61, 81, 84, 39, 45, 57, 70, 57, 70, 76, 86, 41, 46, 59, 71, 66, 72,
905
    81, 87, 41, 46, 66, 72, 59, 71, 81, 87, 43, 47, 67, 73, 67, 73, 85,
906
    88, 6, 51, 15, 56, 15, 56, 40, 68, 13, 52, 17, 57, 40, 65, 48, 70,
907
    13, 52, 40, 65, 17, 57, 48, 70, 36, 55, 42, 66, 42, 66, 62, 72, 7,
908
    54, 16, 58, 16, 58, 41, 69, 14, 55, 18, 59, 41, 66, 49, 71, 14, 55,
909
    41, 66, 18, 59, 49, 71, 37, 64, 43, 67, 43, 67, 63, 73, 13, 52, 20,
910
    58, 52, 75, 58, 82, 16, 53, 21, 59, 58, 80, 60, 83, 39, 57, 45, 70,
911
    57, 76, 70, 86, 41, 59, 46, 71, 66, 81, 72, 87, 16, 58, 21, 60, 53,
912
    80, 59, 83, 18, 59, 22, 61, 59, 81, 61, 84, 41, 66, 46, 72, 59, 81,
913
    71, 87, 43, 67, 47, 73, 67, 85, 73, 88, 13, 52, 52, 75, 20, 58, 58,
914
    82, 39, 57, 57, 76, 45, 70, 70, 86, 16, 53, 58, 80, 21, 59, 60, 83,
915
    41, 59, 66, 81, 46, 71, 72, 87, 16, 58, 53, 80, 21, 60, 59, 83, 41,
916
    66, 59, 81, 46, 72, 71, 87, 18, 59, 59, 81, 22, 61, 61, 84, 43, 67,
917
    67, 85, 47, 73, 73, 88, 36, 55, 55, 78, 55, 78, 78, 90, 41, 59, 59,
918
    79, 69, 83, 83, 91, 41, 59, 69, 83, 59, 79, 83, 91, 49, 61, 71, 84,
919
    71, 84, 87, 92, 41, 69, 59, 83, 59, 83, 79, 91, 49, 71, 61, 84, 71,
920
    87, 84, 92, 49, 71, 71, 87, 61, 84, 84, 92, 63, 73, 73, 88, 73, 88,
921
    88, 93, 2, 6, 6, 13, 12, 15, 15, 20, 3, 7, 7, 14, 19, 20, 20, 25, 6,
922
    8, 15, 17, 15, 17, 26, 27, 7, 9, 16, 18, 20, 21, 27, 28, 6, 15, 8,
923
    17, 15, 26, 17, 27, 7, 16, 9, 18, 20, 27, 21, 28, 13, 17, 17, 23, 20,
924
    27, 27, 29, 14, 18, 18, 24, 25, 28, 28, 30, 6, 13, 13, 36, 51, 52,
925
    52, 55, 7, 14, 14, 37, 54, 55, 55, 64, 15, 17, 40, 42, 56, 57, 65,
926
    66, 16, 18, 41, 43, 58, 59, 66, 67, 15, 40, 17, 42, 56, 65, 57, 66,
927
    16, 41, 18, 43, 58, 66, 59, 67, 40, 48, 48, 62, 68, 70, 70, 72, 41,
928
    49, 49, 63, 69, 71, 71, 73, 12, 15, 51, 52, 38, 40, 56, 58, 19, 20,
929
    54, 55, 44, 45, 68, 69, 15, 17, 56, 57, 40, 42, 65, 66, 20, 21, 58,
930
    59, 45, 46, 70, 71, 51, 56, 74, 75, 56, 65, 75, 80, 54, 58, 77, 78,
931
    68, 70, 82, 83, 52, 57, 75, 76, 58, 66, 80, 81, 55, 59, 78, 79, 69,
932
    71, 83, 84, 15, 20, 52, 55, 56, 58, 75, 78, 20, 25, 55, 64, 68, 69,
933
    96, 97, 26, 27, 65, 66, 65, 66, 98, 99, 27, 28, 66, 67, 70, 71, 100,
934
    101, 56, 68, 75, 96, 104, 105, 108, 109, 58, 69, 78, 97, 105, 106,
935
    109, 110, 65, 70, 98, 100, 105, 106, 111, 112, 66, 71, 99, 101, 106,
936
    107, 112, 113, 12, 51, 15, 52, 38, 56, 40, 58, 19, 54, 20, 55, 44,
937
    68, 45, 69, 51, 74, 56, 75, 56, 75, 65, 80, 54, 77, 58, 78, 68, 82,
938
    70, 83, 15, 56, 17, 57, 40, 65, 42, 66, 20, 58, 21, 59, 45, 70, 46,
939
    71, 52, 75, 57, 76, 58, 80, 66, 81, 55, 78, 59, 79, 69, 83, 71, 84,
940
    15, 52, 20, 55, 56, 75, 58, 78, 20, 55, 25, 64, 68, 96, 69, 97, 56,
941
    75, 68, 96, 104, 108, 105, 109, 58, 78, 69, 97, 105, 109, 106, 110,
942
    26, 65, 27, 66, 65, 98, 66, 99, 27, 66, 28, 67, 70, 100, 71, 101, 65,
943
    98, 70, 100, 105, 111, 106, 112, 66, 99, 71, 101, 106, 112, 107, 113,
944
    38, 56, 56, 75, 44, 68, 68, 82, 44, 68, 68, 96, 120, 121, 121, 122,
945
    56, 75, 104, 108, 68, 96, 105, 109, 68, 82, 105, 109, 121, 122, 123,
946
    124, 56, 104, 75, 108, 68, 105, 96, 109, 68, 105, 82, 109, 121, 123,
947
    122, 124, 75, 108, 108, 114, 82, 109, 109, 115, 96, 109, 109, 115,
948
    122, 124, 124, 125, 40, 58, 58, 78, 68, 82, 82, 90, 45, 69, 69, 97,
949
    121, 122, 122, 126, 65, 80, 105, 109, 105, 109, 127, 129, 70, 83,
950
    106, 110, 123, 124, 128, 130, 65, 105, 80, 109, 105, 127, 109, 129,
951
    70, 106, 83, 110, 123, 128, 124, 130, 98, 111, 111, 116, 127, 131,
952
    131, 133, 100, 112, 112, 117, 128, 132, 132, 134, 6, 15, 15, 40, 51,
953
    56, 56, 68, 7, 16, 16, 41, 54, 58, 58, 69, 13, 17, 40, 48, 52, 57,
954
    65, 70, 14, 18, 41, 49, 55, 59, 66, 71, 13, 40, 17, 48, 52, 65, 57,
955
    70, 14, 41, 18, 49, 55, 66, 59, 71, 36, 42, 42, 62, 55, 66, 66, 72,
956
    37, 43, 43, 63, 64, 67, 67, 73, 8, 17, 17, 42, 74, 75, 75, 96, 9, 18,
957
    18, 43, 77, 78, 78, 97, 17, 23, 48, 62, 75, 76, 98, 100, 18, 24, 49,
958
    63, 78, 79, 99, 101, 17, 48, 23, 62, 75, 98, 76, 100, 18, 49, 24, 63,
959
    78, 99, 79, 101, 42, 62, 62, 94, 96, 100, 100, 102, 43, 63, 63, 95,
960
    97, 101, 101, 103, 15, 26, 56, 65, 56, 65, 104, 105, 20, 27, 58, 66,
961
    68, 70, 105, 106, 20, 27, 68, 70, 58, 66, 105, 106, 25, 28, 69, 71,
962
    69, 71, 106, 107, 52, 65, 75, 98, 75, 98, 108, 111, 55, 66, 78, 99,
963
    96, 100, 109, 112, 55, 66, 96, 100, 78, 99, 109, 112, 64, 67, 97,
964
    101, 97, 101, 110, 113, 17, 27, 57, 66, 75, 80, 108, 109, 21, 28, 59,
965
    67, 82, 83, 109, 110, 27, 29, 70, 72, 80, 81, 111, 112, 28, 30, 71,
966
    73, 83, 84, 112, 113, 57, 70, 76, 100, 108, 111, 114, 116, 59, 71,
967
    79, 101, 109, 112, 115, 117, 66, 72, 100, 102, 109, 112, 116, 118,
968
    67, 73, 101, 103, 110, 113, 117, 119, 15, 56, 26, 65, 56, 104, 65,
969
    105, 20, 58, 27, 66, 68, 105, 70, 106, 52, 75, 65, 98, 75, 108, 98,
970
    111, 55, 78, 66, 99, 96, 109, 100, 112, 20, 68, 27, 70, 58, 105, 66,
971
    106, 25, 69, 28, 71, 69, 106, 71, 107, 55, 96, 66, 100, 78, 109, 99,
972
    112, 64, 97, 67, 101, 97, 110, 101, 113, 17, 57, 27, 66, 75, 108, 80,
973
    109, 21, 59, 28, 67, 82, 109, 83, 110, 57, 76, 70, 100, 108, 114,
974
    111, 116, 59, 79, 71, 101, 109, 115, 112, 117, 27, 70, 29, 72, 80,
975
    111, 81, 112, 28, 71, 30, 73, 83, 112, 84, 113, 66, 100, 72, 102,
976
    109, 116, 112, 118, 67, 101, 73, 103, 110, 117, 113, 119, 40, 65, 65,
977
    98, 68, 105, 105, 127, 45, 70, 70, 100, 121, 123, 123, 128, 58, 80,
978
    105, 111, 82, 109, 127, 131, 69, 83, 106, 112, 122, 124, 128, 132,
979
    58, 105, 80, 111, 82, 127, 109, 131, 69, 106, 83, 112, 122, 128, 124,
980
    132, 78, 109, 109, 116, 90, 129, 129, 133, 97, 110, 110, 117, 126,
981
    130, 130, 134, 42, 66, 66, 99, 96, 109, 109, 129, 46, 71, 71, 101,
982
    122, 124, 124, 130, 66, 81, 106, 112, 109, 115, 131, 133, 71, 84,
983
    107, 113, 124, 125, 132, 134, 66, 106, 81, 112, 109, 131, 115, 133,
984
    71, 107, 84, 113, 124, 132, 125, 134, 99, 112, 112, 118, 129, 133,
985
    133, 135, 101, 113, 113, 119, 130, 134, 134, 136, 2, 6, 12, 15, 6,
986
    13, 15, 20, 6, 8, 15, 17, 15, 17, 26, 27, 3, 7, 19, 20, 7, 14, 20,
987
    25, 7, 9, 20, 21, 16, 18, 27, 28, 6, 15, 15, 26, 8, 17, 17, 27, 13,
988
    17, 20, 27, 17, 23, 27, 29, 7, 16, 20, 27, 9, 18, 21, 28, 14, 18, 25,
989
    28, 18, 24, 28, 30, 12, 15, 38, 40, 51, 52, 56, 58, 15, 17, 40, 42,
990
    56, 57, 65, 66, 19, 20, 44, 45, 54, 55, 68, 69, 20, 21, 45, 46, 58,
991
    59, 70, 71, 51, 56, 56, 65, 74, 75, 75, 80, 52, 57, 58, 66, 75, 76,
992
    80, 81, 54, 58, 68, 70, 77, 78, 82, 83, 55, 59, 69, 71, 78, 79, 83,
993
    84, 6, 13, 51, 52, 13, 36, 52, 55, 15, 17, 56, 57, 40, 42, 65, 66, 7,
994
    14, 54, 55, 14, 37, 55, 64, 16, 18, 58, 59, 41, 43, 66, 67, 15, 40,
995
    56, 65, 17, 42, 57, 66, 40, 48, 68, 70, 48, 62, 70, 72, 16, 41, 58,
996
    66, 18, 43, 59, 67, 41, 49, 69, 71, 49, 63, 71, 73, 15, 20, 56, 58,
997
    52, 55, 75, 78, 26, 27, 65, 66, 65, 66, 98, 99, 20, 25, 68, 69, 55,
998
    64, 96, 97, 27, 28, 70, 71, 66, 67, 100, 101, 56, 68, 104, 105, 75,
999
    96, 108, 109, 65, 70, 105, 106, 98, 100, 111, 112, 58, 69, 105, 106,
1000
    78, 97, 109, 110, 66, 71, 106, 107, 99, 101, 112, 113, 12, 51, 38,
1001
    56, 15, 52, 40, 58, 51, 74, 56, 75, 56, 75, 65, 80, 19, 54, 44, 68,
1002
    20, 55, 45, 69, 54, 77, 68, 82, 58, 78, 70, 83, 15, 56, 40, 65, 17,
1003
    57, 42, 66, 52, 75, 58, 80, 57, 76, 66, 81, 20, 58, 45, 70, 21, 59,
1004
    46, 71, 55, 78, 69, 83, 59, 79, 71, 84, 38, 56, 44, 68, 56, 75, 68,
1005
    82, 56, 75, 68, 96, 104, 108, 105, 109, 44, 68, 120, 121, 68, 96,
1006
    121, 122, 68, 82, 121, 122, 105, 109, 123, 124, 56, 104, 68, 105, 75,
1007
    108, 96, 109, 75, 108, 82, 109, 108, 114, 109, 115, 68, 105, 121,
1008
    123, 82, 109, 122, 124, 96, 109, 122, 124, 109, 115, 124, 125, 15,
1009
    52, 56, 75, 20, 55, 58, 78, 56, 75, 104, 108, 68, 96, 105, 109, 20,
1010
    55, 68, 96, 25, 64, 69, 97, 58, 78, 105, 109, 69, 97, 106, 110, 26,
1011
    65, 65, 98, 27, 66, 66, 99, 65, 98, 105, 111, 70, 100, 106, 112, 27,
1012
    66, 70, 100, 28, 67, 71, 101, 66, 99, 106, 112, 71, 101, 107, 113,
1013
    40, 58, 68, 82, 58, 78, 82, 90, 65, 80, 105, 109, 105, 109, 127, 129,
1014
    45, 69, 121, 122, 69, 97, 122, 126, 70, 83, 123, 124, 106, 110, 128,
1015
    130, 65, 105, 105, 127, 80, 109, 109, 129, 98, 111, 127, 131, 111,
1016
    116, 131, 133, 70, 106, 123, 128, 83, 110, 124, 130, 100, 112, 128,
1017
    132, 112, 117, 132, 134, 6, 15, 51, 56, 15, 40, 56, 68, 13, 17, 52,
1018
    57, 40, 48, 65, 70, 7, 16, 54, 58, 16, 41, 58, 69, 14, 18, 55, 59,
1019
    41, 49, 66, 71, 13, 40, 52, 65, 17, 48, 57, 70, 36, 42, 55, 66, 42,
1020
    62, 66, 72, 14, 41, 55, 66, 18, 49, 59, 71, 37, 43, 64, 67, 43, 63,
1021
    67, 73, 15, 26, 56, 65, 56, 65, 104, 105, 20, 27, 58, 66, 68, 70,
1022
    105, 106, 20, 27, 68, 70, 58, 66, 105, 106, 25, 28, 69, 71, 69, 71,
1023
    106, 107, 52, 65, 75, 98, 75, 98, 108, 111, 55, 66, 78, 99, 96, 100,
1024
    109, 112, 55, 66, 96, 100, 78, 99, 109, 112, 64, 67, 97, 101, 97,
1025
    101, 110, 113, 8, 17, 74, 75, 17, 42, 75, 96, 17, 23, 75, 76, 48, 62,
1026
    98, 100, 9, 18, 77, 78, 18, 43, 78, 97, 18, 24, 78, 79, 49, 63, 99,
1027
    101, 17, 48, 75, 98, 23, 62, 76, 100, 42, 62, 96, 100, 62, 94, 100,
1028
    102, 18, 49, 78, 99, 24, 63, 79, 101, 43, 63, 97, 101, 63, 95, 101,
1029
    103, 17, 27, 75, 80, 57, 66, 108, 109, 27, 29, 80, 81, 70, 72, 111,
1030
    112, 21, 28, 82, 83, 59, 67, 109, 110, 28, 30, 83, 84, 71, 73, 112,
1031
    113, 57, 70, 108, 111, 76, 100, 114, 116, 66, 72, 109, 112, 100, 102,
1032
    116, 118, 59, 71, 109, 112, 79, 101, 115, 117, 67, 73, 110, 113, 101,
1033
    103, 117, 119, 15, 56, 56, 104, 26, 65, 65, 105, 52, 75, 75, 108, 65,
1034
    98, 98, 111, 20, 58, 68, 105, 27, 66, 70, 106, 55, 78, 96, 109, 66,
1035
    99, 100, 112, 20, 68, 58, 105, 27, 70, 66, 106, 55, 96, 78, 109, 66,
1036
    100, 99, 112, 25, 69, 69, 106, 28, 71, 71, 107, 64, 97, 97, 110, 67,
1037
    101, 101, 113, 40, 65, 68, 105, 65, 98, 105, 127, 58, 80, 82, 109,
1038
    105, 111, 127, 131, 45, 70, 121, 123, 70, 100, 123, 128, 69, 83, 122,
1039
    124, 106, 112, 128, 132, 58, 105, 82, 127, 80, 111, 109, 131, 78,
1040
    109, 90, 129, 109, 116, 129, 133, 69, 106, 122, 128, 83, 112, 124,
1041
    132, 97, 110, 126, 130, 110, 117, 130, 134, 17, 57, 75, 108, 27, 66,
1042
    80, 109, 57, 76, 108, 114, 70, 100, 111, 116, 21, 59, 82, 109, 28,
1043
    67, 83, 110, 59, 79, 109, 115, 71, 101, 112, 117, 27, 70, 80, 111,
1044
    29, 72, 81, 112, 66, 100, 109, 116, 72, 102, 112, 118, 28, 71, 83,
1045
    112, 30, 73, 84, 113, 67, 101, 110, 117, 73, 103, 113, 119, 42, 66,
1046
    96, 109, 66, 99, 109, 129, 66, 81, 109, 115, 106, 112, 131, 133, 46,
1047
    71, 122, 124, 71, 101, 124, 130, 71, 84, 124, 125, 107, 113, 132,
1048
    134, 66, 106, 109, 131, 81, 112, 115, 133, 99, 112, 129, 133, 112,
1049
    118, 133, 135, 71, 107, 124, 132, 84, 113, 125, 134, 101, 113, 130,
1050
    134, 113, 119, 134, 136, 4, 7, 13, 16, 13, 16, 17, 21, 7, 9, 16, 18,
1051
    20, 21, 27, 28, 7, 9, 20, 21, 16, 18, 27, 28, 9, 10, 21, 22, 21, 22,
1052
    29, 30, 13, 20, 17, 27, 17, 27, 23, 29, 16, 21, 21, 28, 27, 29, 29,
1053
    31, 16, 21, 27, 29, 21, 28, 29, 31, 18, 22, 28, 30, 28, 30, 31, 32,
1054
    13, 16, 39, 41, 52, 53, 57, 59, 16, 18, 41, 43, 58, 59, 66, 67, 20,
1055
    21, 45, 46, 58, 59, 70, 71, 21, 22, 46, 47, 60, 61, 72, 73, 52, 58,
1056
    57, 66, 75, 80, 76, 81, 53, 59, 59, 67, 80, 81, 81, 85, 58, 60, 70,
1057
    72, 82, 83, 86, 87, 59, 61, 71, 73, 83, 84, 87, 88, 13, 16, 52, 53,
1058
    39, 41, 57, 59, 20, 21, 58, 59, 45, 46, 70, 71, 16, 18, 58, 59, 41,
1059
    43, 66, 67, 21, 22, 60, 61, 46, 47, 72, 73, 52, 58, 75, 80, 57, 66,
1060
    76, 81, 58, 60, 82, 83, 70, 72, 86, 87, 53, 59, 80, 81, 59, 67, 81,
1061
    85, 59, 61, 83, 84, 71, 73, 87, 88, 17, 21, 57, 59, 57, 59, 76, 79,
1062
    27, 28, 66, 67, 70, 71, 100, 101, 27, 28, 70, 71, 66, 67, 100, 101,
1063
    29, 30, 72, 73, 72, 73, 102, 103, 75, 82, 108, 109, 108, 109, 114,
1064
    115, 80, 83, 109, 110, 111, 112, 116, 117, 80, 83, 111, 112, 109,
1065
    110, 116, 117, 81, 84, 112, 113, 112, 113, 118, 119, 35, 54, 40, 58,
1066
    40, 58, 48, 60, 54, 77, 58, 78, 68, 82, 70, 83, 54, 77, 68, 82, 58,
1067
    78, 70, 83, 77, 89, 82, 90, 82, 90, 86, 91, 40, 68, 48, 70, 48, 70,
1068
    62, 72, 58, 82, 60, 83, 70, 86, 72, 87, 58, 82, 70, 86, 60, 83, 72,
1069
    87, 78, 90, 83, 91, 83, 91, 87, 92, 40, 58, 45, 69, 65, 80, 70, 83,
1070
    58, 78, 69, 97, 105, 109, 106, 110, 68, 82, 121, 122, 105, 109, 123,
1071
    124, 82, 90, 122, 126, 127, 129, 128, 130, 65, 105, 70, 106, 98, 111,
1072
    100, 112, 80, 109, 83, 110, 111, 116, 112, 117, 105, 127, 123, 128,
1073
    127, 131, 128, 132, 109, 129, 124, 130, 131, 133, 132, 134, 40, 58,
1074
    65, 80, 45, 69, 70, 83, 68, 82, 105, 109, 121, 122, 123, 124, 58, 78,
1075
    105, 109, 69, 97, 106, 110, 82, 90, 127, 129, 122, 126, 128, 130, 65,
1076
    105, 98, 111, 70, 106, 100, 112, 105, 127, 127, 131, 123, 128, 128,
1077
    132, 80, 109, 111, 116, 83, 110, 112, 117, 109, 129, 131, 133, 124,
1078
    130, 132, 134, 48, 60, 70, 83, 70, 83, 86, 91, 70, 83, 106, 110, 123,
1079
    124, 128, 130, 70, 83, 123, 124, 106, 110, 128, 130, 86, 91, 128,
1080
    130, 128, 130, 141, 142, 98, 127, 111, 131, 111, 131, 116, 133, 111,
1081
    131, 131, 143, 144, 145, 145, 146, 111, 131, 144, 145, 131, 143, 145,
1082
    146, 116, 133, 145, 146, 145, 146, 147, 148, 13, 20, 52, 58, 52, 58,
1083
    75, 82, 16, 21, 53, 59, 58, 60, 80, 83, 16, 21, 58, 60, 53, 59, 80,
1084
    83, 18, 22, 59, 61, 59, 61, 81, 84, 39, 45, 57, 70, 57, 70, 76, 86,
1085
    41, 46, 59, 71, 66, 72, 81, 87, 41, 46, 66, 72, 59, 71, 81, 87, 43,
1086
    47, 67, 73, 67, 73, 85, 88, 17, 27, 57, 66, 75, 80, 108, 109, 21, 28,
1087
    59, 67, 82, 83, 109, 110, 27, 29, 70, 72, 80, 81, 111, 112, 28, 30,
1088
    71, 73, 83, 84, 112, 113, 57, 70, 76, 100, 108, 111, 114, 116, 59,
1089
    71, 79, 101, 109, 112, 115, 117, 66, 72, 100, 102, 109, 112, 116,
1090
    118, 67, 73, 101, 103, 110, 113, 117, 119, 17, 27, 75, 80, 57, 66,
1091
    108, 109, 27, 29, 80, 81, 70, 72, 111, 112, 21, 28, 82, 83, 59, 67,
1092
    109, 110, 28, 30, 83, 84, 71, 73, 112, 113, 57, 70, 108, 111, 76,
1093
    100, 114, 116, 66, 72, 109, 112, 100, 102, 116, 118, 59, 71, 109,
1094
    112, 79, 101, 115, 117, 67, 73, 110, 113, 101, 103, 117, 119, 23, 29,
1095
    76, 81, 76, 81, 114, 115, 29, 31, 81, 85, 86, 87, 116, 117, 29, 31,
1096
    86, 87, 81, 85, 116, 117, 31, 32, 87, 88, 87, 88, 118, 119, 76, 86,
1097
    114, 116, 114, 116, 137, 138, 81, 87, 115, 117, 116, 118, 138, 139,
1098
    81, 87, 116, 118, 115, 117, 138, 139, 85, 88, 117, 119, 117, 119,
1099
    139, 140, 40, 68, 65, 105, 65, 105, 98, 127, 58, 82, 80, 109, 105,
1100
    127, 111, 131, 58, 82, 105, 127, 80, 109, 111, 131, 78, 90, 109, 129,
1101
    109, 129, 116, 133, 45, 121, 70, 123, 70, 123, 100, 128, 69, 122, 83,
1102
    124, 106, 128, 112, 132, 69, 122, 106, 128, 83, 124, 112, 132, 97,
1103
    126, 110, 130, 110, 130, 117, 134, 48, 70, 70, 106, 98, 111, 111,
1104
    131, 60, 83, 83, 110, 127, 131, 131, 143, 70, 86, 123, 128, 111, 116,
1105
    144, 145, 83, 91, 124, 130, 131, 133, 145, 146, 70, 123, 86, 128,
1106
    111, 144, 116, 145, 83, 124, 91, 130, 131, 145, 133, 146, 106, 128,
1107
    128, 141, 131, 145, 145, 147, 110, 130, 130, 142, 143, 146, 146, 148,
1108
    48, 70, 98, 111, 70, 106, 111, 131, 70, 86, 111, 116, 123, 128, 144,
1109
    145, 60, 83, 127, 131, 83, 110, 131, 143, 83, 91, 131, 133, 124, 130,
1110
    145, 146, 70, 123, 111, 144, 86, 128, 116, 145, 106, 128, 131, 145,
1111
    128, 141, 145, 147, 83, 124, 131, 145, 91, 130, 133, 146, 110, 130,
1112
    143, 146, 130, 142, 146, 148, 62, 72, 100, 112, 100, 112, 116, 133,
1113
    72, 87, 112, 117, 128, 132, 145, 146, 72, 87, 128, 132, 112, 117,
1114
    145, 146, 87, 92, 132, 134, 132, 134, 147, 148, 100, 128, 116, 145,
1115
    116, 145, 138, 149, 112, 132, 133, 146, 145, 147, 149, 150, 112, 132,
1116
    145, 147, 133, 146, 149, 150, 117, 134, 146, 148, 146, 148, 150, 151,
1117
    2, 12, 6, 15, 6, 15, 13, 20, 6, 15, 8, 17, 15, 26, 17, 27, 6, 15, 15,
1118
    26, 8, 17, 17, 27, 13, 20, 17, 27, 17, 27, 23, 29, 3, 19, 7, 20, 7,
1119
    20, 14, 25, 7, 20, 9, 21, 16, 27, 18, 28, 7, 20, 16, 27, 9, 21, 18,
1120
    28, 14, 25, 18, 28, 18, 28, 24, 30, 12, 38, 15, 40, 51, 56, 52, 58,
1121
    15, 40, 17, 42, 56, 65, 57, 66, 51, 56, 56, 65, 74, 75, 75, 80, 52,
1122
    58, 57, 66, 75, 80, 76, 81, 19, 44, 20, 45, 54, 68, 55, 69, 20, 45,
1123
    21, 46, 58, 70, 59, 71, 54, 68, 58, 70, 77, 82, 78, 83, 55, 69, 59,
1124
    71, 78, 83, 79, 84, 12, 38, 51, 56, 15, 40, 52, 58, 51, 56, 74, 75,
1125
    56, 65, 75, 80, 15, 40, 56, 65, 17, 42, 57, 66, 52, 58, 75, 80, 57,
1126
    66, 76, 81, 19, 44, 54, 68, 20, 45, 55, 69, 54, 68, 77, 82, 58, 70,
1127
    78, 83, 20, 45, 58, 70, 21, 46, 59, 71, 55, 69, 78, 83, 59, 71, 79,
1128
    84, 38, 44, 56, 68, 56, 68, 75, 82, 56, 68, 75, 96, 104, 105, 108,
1129
    109, 56, 68, 104, 105, 75, 96, 108, 109, 75, 82, 108, 109, 108, 109,
1130
    114, 115, 44, 120, 68, 121, 68, 121, 96, 122, 68, 121, 82, 122, 105,
1131
    123, 109, 124, 68, 121, 105, 123, 82, 122, 109, 124, 96, 122, 109,
1132
    124, 109, 124, 115, 125, 6, 51, 13, 52, 13, 52, 36, 55, 15, 56, 17,
1133
    57, 40, 65, 42, 66, 15, 56, 40, 65, 17, 57, 42, 66, 40, 68, 48, 70,
1134
    48, 70, 62, 72, 7, 54, 14, 55, 14, 55, 37, 64, 16, 58, 18, 59, 41,
1135
    66, 43, 67, 16, 58, 41, 66, 18, 59, 43, 67, 41, 69, 49, 71, 49, 71,
1136
    63, 73, 15, 56, 20, 58, 52, 75, 55, 78, 26, 65, 27, 66, 65, 98, 66,
1137
    99, 56, 104, 68, 105, 75, 108, 96, 109, 65, 105, 70, 106, 98, 111,
1138
    100, 112, 20, 68, 25, 69, 55, 96, 64, 97, 27, 70, 28, 71, 66, 100,
1139
    67, 101, 58, 105, 69, 106, 78, 109, 97, 110, 66, 106, 71, 107, 99,
1140
    112, 101, 113, 15, 56, 52, 75, 20, 58, 55, 78, 56, 104, 75, 108, 68,
1141
    105, 96, 109, 26, 65, 65, 98, 27, 66, 66, 99, 65, 105, 98, 111, 70,
1142
    106, 100, 112, 20, 68, 55, 96, 25, 69, 64, 97, 58, 105, 78, 109, 69,
1143
    106, 97, 110, 27, 70, 66, 100, 28, 71, 67, 101, 66, 106, 99, 112, 71,
1144
    107, 101, 113, 40, 68, 58, 82, 58, 82, 78, 90, 65, 105, 80, 109, 105,
1145
    127, 109, 129, 65, 105, 105, 127, 80, 109, 109, 129, 98, 127, 111,
1146
    131, 111, 131, 116, 133, 45, 121, 69, 122, 69, 122, 97, 126, 70, 123,
1147
    83, 124, 106, 128, 110, 130, 70, 123, 106, 128, 83, 124, 110, 130,
1148
    100, 128, 112, 132, 112, 132, 117, 134, 6, 51, 15, 56, 15, 56, 40,
1149
    68, 13, 52, 17, 57, 40, 65, 48, 70, 13, 52, 40, 65, 17, 57, 48, 70,
1150
    36, 55, 42, 66, 42, 66, 62, 72, 7, 54, 16, 58, 16, 58, 41, 69, 14,
1151
    55, 18, 59, 41, 66, 49, 71, 14, 55, 41, 66, 18, 59, 49, 71, 37, 64,
1152
    43, 67, 43, 67, 63, 73, 15, 56, 26, 65, 56, 104, 65, 105, 20, 58, 27,
1153
    66, 68, 105, 70, 106, 52, 75, 65, 98, 75, 108, 98, 111, 55, 78, 66,
1154
    99, 96, 109, 100, 112, 20, 68, 27, 70, 58, 105, 66, 106, 25, 69, 28,
1155
    71, 69, 106, 71, 107, 55, 96, 66, 100, 78, 109, 99, 112, 64, 97, 67,
1156
    101, 97, 110, 101, 113, 15, 56, 56, 104, 26, 65, 65, 105, 52, 75, 75,
1157
    108, 65, 98, 98, 111, 20, 58, 68, 105, 27, 66, 70, 106, 55, 78, 96,
1158
    109, 66, 99, 100, 112, 20, 68, 58, 105, 27, 70, 66, 106, 55, 96, 78,
1159
    109, 66, 100, 99, 112, 25, 69, 69, 106, 28, 71, 71, 107, 64, 97, 97,
1160
    110, 67, 101, 101, 113, 40, 68, 65, 105, 65, 105, 98, 127, 58, 82,
1161
    80, 109, 105, 127, 111, 131, 58, 82, 105, 127, 80, 109, 111, 131, 78,
1162
    90, 109, 129, 109, 129, 116, 133, 45, 121, 70, 123, 70, 123, 100,
1163
    128, 69, 122, 83, 124, 106, 128, 112, 132, 69, 122, 106, 128, 83,
1164
    124, 112, 132, 97, 126, 110, 130, 110, 130, 117, 134, 8, 74, 17, 75,
1165
    17, 75, 42, 96, 17, 75, 23, 76, 48, 98, 62, 100, 17, 75, 48, 98, 23,
1166
    76, 62, 100, 42, 96, 62, 100, 62, 100, 94, 102, 9, 77, 18, 78, 18,
1167
    78, 43, 97, 18, 78, 24, 79, 49, 99, 63, 101, 18, 78, 49, 99, 24, 79,
1168
    63, 101, 43, 97, 63, 101, 63, 101, 95, 103, 17, 75, 27, 80, 57, 108,
1169
    66, 109, 27, 80, 29, 81, 70, 111, 72, 112, 57, 108, 70, 111, 76, 114,
1170
    100, 116, 66, 109, 72, 112, 100, 116, 102, 118, 21, 82, 28, 83, 59,
1171
    109, 67, 110, 28, 83, 30, 84, 71, 112, 73, 113, 59, 109, 71, 112, 79,
1172
    115, 101, 117, 67, 110, 73, 113, 101, 117, 103, 119, 17, 75, 57, 108,
1173
    27, 80, 66, 109, 57, 108, 76, 114, 70, 111, 100, 116, 27, 80, 70,
1174
    111, 29, 81, 72, 112, 66, 109, 100, 116, 72, 112, 102, 118, 21, 82,
1175
    59, 109, 28, 83, 67, 110, 59, 109, 79, 115, 71, 112, 101, 117, 28,
1176
    83, 71, 112, 30, 84, 73, 113, 67, 110, 101, 117, 73, 113, 103, 119,
1177
    42, 96, 66, 109, 66, 109, 99, 129, 66, 109, 81, 115, 106, 131, 112,
1178
    133, 66, 109, 106, 131, 81, 115, 112, 133, 99, 129, 112, 133, 112,
1179
    133, 118, 135, 46, 122, 71, 124, 71, 124, 101, 130, 71, 124, 84, 125,
1180
    107, 132, 113, 134, 71, 124, 107, 132, 84, 125, 113, 134, 101, 130,
1181
    113, 134, 113, 134, 119, 136, 4, 13, 7, 16, 13, 17, 16, 21, 7, 16, 9,
1182
    18, 20, 27, 21, 28, 13, 17, 20, 27, 17, 23, 27, 29, 16, 21, 21, 28,
1183
    27, 29, 29, 31, 7, 20, 9, 21, 16, 27, 18, 28, 9, 21, 10, 22, 21, 29,
1184
    22, 30, 16, 27, 21, 29, 21, 29, 28, 31, 18, 28, 22, 30, 28, 31, 30,
1185
    32, 13, 39, 16, 41, 52, 57, 53, 59, 16, 41, 18, 43, 58, 66, 59, 67,
1186
    52, 57, 58, 66, 75, 76, 80, 81, 53, 59, 59, 67, 80, 81, 81, 85, 20,
1187
    45, 21, 46, 58, 70, 59, 71, 21, 46, 22, 47, 60, 72, 61, 73, 58, 70,
1188
    60, 72, 82, 86, 83, 87, 59, 71, 61, 73, 83, 87, 84, 88, 35, 40, 54,
1189
    58, 40, 48, 58, 60, 54, 58, 77, 78, 68, 70, 82, 83, 40, 48, 68, 70,
1190
    48, 62, 70, 72, 58, 60, 82, 83, 70, 72, 86, 87, 54, 68, 77, 82, 58,
1191
    70, 78, 83, 77, 82, 89, 90, 82, 86, 90, 91, 58, 70, 82, 86, 60, 72,
1192
    83, 87, 78, 83, 90, 91, 83, 87, 91, 92, 40, 45, 58, 69, 65, 70, 80,
1193
    83, 58, 69, 78, 97, 105, 106, 109, 110, 65, 70, 105, 106, 98, 100,
1194
    111, 112, 80, 83, 109, 110, 111, 112, 116, 117, 68, 121, 82, 122,
1195
    105, 123, 109, 124, 82, 122, 90, 126, 127, 128, 129, 130, 105, 123,
1196
    127, 128, 127, 128, 131, 132, 109, 124, 129, 130, 131, 132, 133, 134,
1197
    13, 52, 16, 53, 39, 57, 41, 59, 20, 58, 21, 59, 45, 70, 46, 71, 52,
1198
    75, 58, 80, 57, 76, 66, 81, 58, 82, 60, 83, 70, 86, 72, 87, 16, 58,
1199
    18, 59, 41, 66, 43, 67, 21, 60, 22, 61, 46, 72, 47, 73, 53, 80, 59,
1200
    81, 59, 81, 67, 85, 59, 83, 61, 84, 71, 87, 73, 88, 17, 57, 21, 59,
1201
    57, 76, 59, 79, 27, 66, 28, 67, 70, 100, 71, 101, 75, 108, 82, 109,
1202
    108, 114, 109, 115, 80, 109, 83, 110, 111, 116, 112, 117, 27, 70, 28,
1203
    71, 66, 100, 67, 101, 29, 72, 30, 73, 72, 102, 73, 103, 80, 111, 83,
1204
    112, 109, 116, 110, 117, 81, 112, 84, 113, 112, 118, 113, 119, 40,
1205
    65, 58, 80, 45, 70, 69, 83, 68, 105, 82, 109, 121, 123, 122, 124, 65,
1206
    98, 105, 111, 70, 100, 106, 112, 105, 127, 127, 131, 123, 128, 128,
1207
    132, 58, 105, 78, 109, 69, 106, 97, 110, 82, 127, 90, 129, 122, 128,
1208
    126, 130, 80, 111, 109, 116, 83, 112, 110, 117, 109, 131, 129, 133,
1209
    124, 132, 130, 134, 48, 70, 60, 83, 70, 86, 83, 91, 70, 106, 83, 110,
1210
    123, 128, 124, 130, 98, 111, 127, 131, 111, 116, 131, 133, 111, 131,
1211
    131, 143, 144, 145, 145, 146, 70, 123, 83, 124, 106, 128, 110, 130,
1212
    86, 128, 91, 130, 128, 141, 130, 142, 111, 144, 131, 145, 131, 145,
1213
    143, 146, 116, 145, 133, 146, 145, 147, 146, 148, 13, 52, 20, 58, 52,
1214
    75, 58, 82, 16, 53, 21, 59, 58, 80, 60, 83, 39, 57, 45, 70, 57, 76,
1215
    70, 86, 41, 59, 46, 71, 66, 81, 72, 87, 16, 58, 21, 60, 53, 80, 59,
1216
    83, 18, 59, 22, 61, 59, 81, 61, 84, 41, 66, 46, 72, 59, 81, 71, 87,
1217
    43, 67, 47, 73, 67, 85, 73, 88, 17, 57, 27, 66, 75, 108, 80, 109, 21,
1218
    59, 28, 67, 82, 109, 83, 110, 57, 76, 70, 100, 108, 114, 111, 116,
1219
    59, 79, 71, 101, 109, 115, 112, 117, 27, 70, 29, 72, 80, 111, 81,
1220
    112, 28, 71, 30, 73, 83, 112, 84, 113, 66, 100, 72, 102, 109, 116,
1221
    112, 118, 67, 101, 73, 103, 110, 117, 113, 119, 40, 65, 68, 105, 65,
1222
    98, 105, 127, 58, 80, 82, 109, 105, 111, 127, 131, 45, 70, 121, 123,
1223
    70, 100, 123, 128, 69, 83, 122, 124, 106, 112, 128, 132, 58, 105, 82,
1224
    127, 80, 111, 109, 131, 78, 109, 90, 129, 109, 116, 129, 133, 69,
1225
    106, 122, 128, 83, 112, 124, 132, 97, 110, 126, 130, 110, 117, 130,
1226
    134, 48, 70, 70, 106, 98, 111, 111, 131, 60, 83, 83, 110, 127, 131,
1227
    131, 143, 70, 86, 123, 128, 111, 116, 144, 145, 83, 91, 124, 130,
1228
    131, 133, 145, 146, 70, 123, 86, 128, 111, 144, 116, 145, 83, 124,
1229
    91, 130, 131, 145, 133, 146, 106, 128, 128, 141, 131, 145, 145, 147,
1230
    110, 130, 130, 142, 143, 146, 146, 148, 17, 75, 27, 80, 57, 108, 66,
1231
    109, 27, 80, 29, 81, 70, 111, 72, 112, 57, 108, 70, 111, 76, 114,
1232
    100, 116, 66, 109, 72, 112, 100, 116, 102, 118, 21, 82, 28, 83, 59,
1233
    109, 67, 110, 28, 83, 30, 84, 71, 112, 73, 113, 59, 109, 71, 112, 79,
1234
    115, 101, 117, 67, 110, 73, 113, 101, 117, 103, 119, 23, 76, 29, 81,
1235
    76, 114, 81, 115, 29, 81, 31, 85, 86, 116, 87, 117, 76, 114, 86, 116,
1236
    114, 137, 116, 138, 81, 115, 87, 117, 116, 138, 118, 139, 29, 86, 31,
1237
    87, 81, 116, 85, 117, 31, 87, 32, 88, 87, 118, 88, 119, 81, 116, 87,
1238
    118, 115, 138, 117, 139, 85, 117, 88, 119, 117, 139, 119, 140, 48,
1239
    98, 70, 111, 70, 111, 106, 131, 70, 111, 86, 116, 123, 144, 128, 145,
1240
    70, 111, 123, 144, 86, 116, 128, 145, 106, 131, 128, 145, 128, 145,
1241
    141, 147, 60, 127, 83, 131, 83, 131, 110, 143, 83, 131, 91, 133, 124,
1242
    145, 130, 146, 83, 131, 124, 145, 91, 133, 130, 146, 110, 143, 130,
1243
    146, 130, 146, 142, 148, 62, 100, 72, 112, 100, 116, 112, 133, 72,
1244
    112, 87, 117, 128, 145, 132, 146, 100, 116, 128, 145, 116, 138, 145,
1245
    149, 112, 133, 132, 146, 145, 149, 147, 150, 72, 128, 87, 132, 112,
1246
    145, 117, 146, 87, 132, 92, 134, 132, 147, 134, 148, 112, 145, 132,
1247
    147, 133, 149, 146, 150, 117, 146, 134, 148, 146, 150, 148, 151, 4,
1248
    13, 13, 17, 7, 16, 16, 21, 13, 17, 17, 23, 20, 27, 27, 29, 7, 16, 20,
1249
    27, 9, 18, 21, 28, 16, 21, 27, 29, 21, 28, 29, 31, 7, 20, 16, 27, 9,
1250
    21, 18, 28, 16, 27, 21, 29, 21, 29, 28, 31, 9, 21, 21, 29, 10, 22,
1251
    22, 30, 18, 28, 28, 31, 22, 30, 30, 32, 35, 40, 40, 48, 54, 58, 58,
1252
    60, 40, 48, 48, 62, 68, 70, 70, 72, 54, 58, 68, 70, 77, 78, 82, 83,
1253
    58, 60, 70, 72, 82, 83, 86, 87, 54, 68, 58, 70, 77, 82, 78, 83, 58,
1254
    70, 60, 72, 82, 86, 83, 87, 77, 82, 82, 86, 89, 90, 90, 91, 78, 83,
1255
    83, 87, 90, 91, 91, 92, 13, 39, 52, 57, 16, 41, 53, 59, 52, 57, 75,
1256
    76, 58, 66, 80, 81, 16, 41, 58, 66, 18, 43, 59, 67, 53, 59, 80, 81,
1257
    59, 67, 81, 85, 20, 45, 58, 70, 21, 46, 59, 71, 58, 70, 82, 86, 60,
1258
    72, 83, 87, 21, 46, 60, 72, 22, 47, 61, 73, 59, 71, 83, 87, 61, 73,
1259
    84, 88, 40, 45, 65, 70, 58, 69, 80, 83, 65, 70, 98, 100, 105, 106,
1260
    111, 112, 58, 69, 105, 106, 78, 97, 109, 110, 80, 83, 111, 112, 109,
1261
    110, 116, 117, 68, 121, 105, 123, 82, 122, 109, 124, 105, 123, 127,
1262
    128, 127, 128, 131, 132, 82, 122, 127, 128, 90, 126, 129, 130, 109,
1263
    124, 131, 132, 129, 130, 133, 134, 13, 52, 39, 57, 16, 53, 41, 59,
1264
    52, 75, 57, 76, 58, 80, 66, 81, 20, 58, 45, 70, 21, 59, 46, 71, 58,
1265
    82, 70, 86, 60, 83, 72, 87, 16, 58, 41, 66, 18, 59, 43, 67, 53, 80,
1266
    59, 81, 59, 81, 67, 85, 21, 60, 46, 72, 22, 61, 47, 73, 59, 83, 71,
1267
    87, 61, 84, 73, 88, 40, 65, 45, 70, 58, 80, 69, 83, 65, 98, 70, 100,
1268
    105, 111, 106, 112, 68, 105, 121, 123, 82, 109, 122, 124, 105, 127,
1269
    123, 128, 127, 131, 128, 132, 58, 105, 69, 106, 78, 109, 97, 110, 80,
1270
    111, 83, 112, 109, 116, 110, 117, 82, 127, 122, 128, 90, 129, 126,
1271
    130, 109, 131, 124, 132, 129, 133, 130, 134, 17, 57, 57, 76, 21, 59,
1272
    59, 79, 75, 108, 108, 114, 82, 109, 109, 115, 27, 66, 70, 100, 28,
1273
    67, 71, 101, 80, 109, 111, 116, 83, 110, 112, 117, 27, 70, 66, 100,
1274
    28, 71, 67, 101, 80, 111, 109, 116, 83, 112, 110, 117, 29, 72, 72,
1275
    102, 30, 73, 73, 103, 81, 112, 112, 118, 84, 113, 113, 119, 48, 70,
1276
    70, 86, 60, 83, 83, 91, 98, 111, 111, 116, 127, 131, 131, 133, 70,
1277
    106, 123, 128, 83, 110, 124, 130, 111, 131, 144, 145, 131, 143, 145,
1278
    146, 70, 123, 106, 128, 83, 124, 110, 130, 111, 144, 131, 145, 131,
1279
    145, 143, 146, 86, 128, 128, 141, 91, 130, 130, 142, 116, 145, 145,
1280
    147, 133, 146, 146, 148, 13, 52, 52, 75, 20, 58, 58, 82, 39, 57, 57,
1281
    76, 45, 70, 70, 86, 16, 53, 58, 80, 21, 59, 60, 83, 41, 59, 66, 81,
1282
    46, 71, 72, 87, 16, 58, 53, 80, 21, 60, 59, 83, 41, 66, 59, 81, 46,
1283
    72, 71, 87, 18, 59, 59, 81, 22, 61, 61, 84, 43, 67, 67, 85, 47, 73,
1284
    73, 88, 40, 65, 65, 98, 68, 105, 105, 127, 45, 70, 70, 100, 121, 123,
1285
    123, 128, 58, 80, 105, 111, 82, 109, 127, 131, 69, 83, 106, 112, 122,
1286
    124, 128, 132, 58, 105, 80, 111, 82, 127, 109, 131, 69, 106, 83, 112,
1287
    122, 128, 124, 132, 78, 109, 109, 116, 90, 129, 129, 133, 97, 110,
1288
    110, 117, 126, 130, 130, 134, 17, 57, 75, 108, 27, 66, 80, 109, 57,
1289
    76, 108, 114, 70, 100, 111, 116, 21, 59, 82, 109, 28, 67, 83, 110,
1290
    59, 79, 109, 115, 71, 101, 112, 117, 27, 70, 80, 111, 29, 72, 81,
1291
    112, 66, 100, 109, 116, 72, 102, 112, 118, 28, 71, 83, 112, 30, 73,
1292
    84, 113, 67, 101, 110, 117, 73, 103, 113, 119, 48, 70, 98, 111, 70,
1293
    106, 111, 131, 70, 86, 111, 116, 123, 128, 144, 145, 60, 83, 127,
1294
    131, 83, 110, 131, 143, 83, 91, 131, 133, 124, 130, 145, 146, 70,
1295
    123, 111, 144, 86, 128, 116, 145, 106, 128, 131, 145, 128, 141, 145,
1296
    147, 83, 124, 131, 145, 91, 130, 133, 146, 110, 130, 143, 146, 130,
1297
    142, 146, 148, 17, 75, 57, 108, 27, 80, 66, 109, 57, 108, 76, 114,
1298
    70, 111, 100, 116, 27, 80, 70, 111, 29, 81, 72, 112, 66, 109, 100,
1299
    116, 72, 112, 102, 118, 21, 82, 59, 109, 28, 83, 67, 110, 59, 109,
1300
    79, 115, 71, 112, 101, 117, 28, 83, 71, 112, 30, 84, 73, 113, 67,
1301
    110, 101, 117, 73, 113, 103, 119, 48, 98, 70, 111, 70, 111, 106, 131,
1302
    70, 111, 86, 116, 123, 144, 128, 145, 70, 111, 123, 144, 86, 116,
1303
    128, 145, 106, 131, 128, 145, 128, 145, 141, 147, 60, 127, 83, 131,
1304
    83, 131, 110, 143, 83, 131, 91, 133, 124, 145, 130, 146, 83, 131,
1305
    124, 145, 91, 133, 130, 146, 110, 143, 130, 146, 130, 146, 142, 148,
1306
    23, 76, 76, 114, 29, 81, 81, 115, 76, 114, 114, 137, 86, 116, 116,
1307
    138, 29, 81, 86, 116, 31, 85, 87, 117, 81, 115, 116, 138, 87, 117,
1308
    118, 139, 29, 86, 81, 116, 31, 87, 85, 117, 81, 116, 115, 138, 87,
1309
    118, 117, 139, 31, 87, 87, 118, 32, 88, 88, 119, 85, 117, 117, 139,
1310
    88, 119, 119, 140, 62, 100, 100, 116, 72, 112, 112, 133, 100, 116,
1311
    116, 138, 128, 145, 145, 149, 72, 112, 128, 145, 87, 117, 132, 146,
1312
    112, 133, 145, 149, 132, 146, 147, 150, 72, 128, 112, 145, 87, 132,
1313
    117, 146, 112, 145, 133, 149, 132, 147, 146, 150, 87, 132, 132, 147,
1314
    92, 134, 134, 148, 117, 146, 146, 150, 134, 148, 148, 151, 11, 14,
1315
    14, 18, 14, 18, 18, 22, 14, 18, 18, 24, 25, 28, 28, 30, 14, 18, 25,
1316
    28, 18, 24, 28, 30, 18, 22, 28, 30, 28, 30, 31, 32, 14, 25, 18, 28,
1317
    18, 28, 24, 30, 18, 28, 22, 30, 28, 31, 30, 32, 18, 28, 28, 31, 22,
1318
    30, 30, 32, 24, 30, 30, 32, 30, 32, 32, 33, 36, 41, 41, 49, 55, 59,
1319
    59, 61, 41, 49, 49, 63, 69, 71, 71, 73, 55, 59, 69, 71, 78, 79, 83,
1320
    84, 59, 61, 71, 73, 83, 84, 87, 88, 55, 69, 59, 71, 78, 83, 79, 84,
1321
    59, 71, 61, 73, 83, 87, 84, 88, 78, 83, 83, 87, 90, 91, 91, 92, 79,
1322
    84, 84, 88, 91, 92, 92, 93, 36, 41, 55, 59, 41, 49, 59, 61, 55, 59,
1323
    78, 79, 69, 71, 83, 84, 41, 49, 69, 71, 49, 63, 71, 73, 59, 61, 83,
1324
    84, 71, 73, 87, 88, 55, 69, 78, 83, 59, 71, 79, 84, 78, 83, 90, 91,
1325
    83, 87, 91, 92, 59, 71, 83, 87, 61, 73, 84, 88, 79, 84, 91, 92, 84,
1326
    88, 92, 93, 42, 46, 66, 71, 66, 71, 81, 84, 66, 71, 99, 101, 106,
1327
    107, 112, 113, 66, 71, 106, 107, 99, 101, 112, 113, 81, 84, 112, 113,
1328
    112, 113, 118, 119, 96, 122, 109, 124, 109, 124, 115, 125, 109, 124,
1329
    129, 130, 131, 132, 133, 134, 109, 124, 131, 132, 129, 130, 133, 134,
1330
    115, 125, 133, 134, 133, 134, 135, 136, 36, 55, 41, 59, 41, 59, 49,
1331
    61, 55, 78, 59, 79, 69, 83, 71, 84, 55, 78, 69, 83, 59, 79, 71, 84,
1332
    78, 90, 83, 91, 83, 91, 87, 92, 41, 69, 49, 71, 49, 71, 63, 73, 59,
1333
    83, 61, 84, 71, 87, 73, 88, 59, 83, 71, 87, 61, 84, 73, 88, 79, 91,
1334
    84, 92, 84, 92, 88, 93, 42, 66, 46, 71, 66, 81, 71, 84, 66, 99, 71,
1335
    101, 106, 112, 107, 113, 96, 109, 122, 124, 109, 115, 124, 125, 109,
1336
    129, 124, 130, 131, 133, 132, 134, 66, 106, 71, 107, 99, 112, 101,
1337
    113, 81, 112, 84, 113, 112, 118, 113, 119, 109, 131, 124, 132, 129,
1338
    133, 130, 134, 115, 133, 125, 134, 133, 135, 134, 136, 42, 66, 66,
1339
    81, 46, 71, 71, 84, 96, 109, 109, 115, 122, 124, 124, 125, 66, 99,
1340
    106, 112, 71, 101, 107, 113, 109, 129, 131, 133, 124, 130, 132, 134,
1341
    66, 106, 99, 112, 71, 107, 101, 113, 109, 131, 129, 133, 124, 132,
1342
    130, 134, 81, 112, 112, 118, 84, 113, 113, 119, 115, 133, 133, 135,
1343
    125, 134, 134, 136, 62, 72, 72, 87, 72, 87, 87, 92, 100, 112, 112,
1344
    117, 128, 132, 132, 134, 100, 112, 128, 132, 112, 117, 132, 134, 116,
1345
    133, 145, 146, 145, 146, 147, 148, 100, 128, 112, 132, 112, 132, 117,
1346
    134, 116, 145, 133, 146, 145, 147, 146, 148, 116, 145, 145, 147, 133,
1347
    146, 146, 148, 138, 149, 149, 150, 149, 150, 150, 151, 36, 55, 55,
1348
    78, 55, 78, 78, 90, 41, 59, 59, 79, 69, 83, 83, 91, 41, 59, 69, 83,
1349
    59, 79, 83, 91, 49, 61, 71, 84, 71, 84, 87, 92, 41, 69, 59, 83, 59,
1350
    83, 79, 91, 49, 71, 61, 84, 71, 87, 84, 92, 49, 71, 71, 87, 61, 84,
1351
    84, 92, 63, 73, 73, 88, 73, 88, 88, 93, 42, 66, 66, 99, 96, 109, 109,
1352
    129, 46, 71, 71, 101, 122, 124, 124, 130, 66, 81, 106, 112, 109, 115,
1353
    131, 133, 71, 84, 107, 113, 124, 125, 132, 134, 66, 106, 81, 112,
1354
    109, 131, 115, 133, 71, 107, 84, 113, 124, 132, 125, 134, 99, 112,
1355
    112, 118, 129, 133, 133, 135, 101, 113, 113, 119, 130, 134, 134, 136,
1356
    42, 66, 96, 109, 66, 99, 109, 129, 66, 81, 109, 115, 106, 112, 131,
1357
    133, 46, 71, 122, 124, 71, 101, 124, 130, 71, 84, 124, 125, 107, 113,
1358
    132, 134, 66, 106, 109, 131, 81, 112, 115, 133, 99, 112, 129, 133,
1359
    112, 118, 133, 135, 71, 107, 124, 132, 84, 113, 125, 134, 101, 113,
1360
    130, 134, 113, 119, 134, 136, 62, 72, 100, 112, 100, 112, 116, 133,
1361
    72, 87, 112, 117, 128, 132, 145, 146, 72, 87, 128, 132, 112, 117,
1362
    145, 146, 87, 92, 132, 134, 132, 134, 147, 148, 100, 128, 116, 145,
1363
    116, 145, 138, 149, 112, 132, 133, 146, 145, 147, 149, 150, 112, 132,
1364
    145, 147, 133, 146, 149, 150, 117, 134, 146, 148, 146, 148, 150, 151,
1365
    42, 96, 66, 109, 66, 109, 99, 129, 66, 109, 81, 115, 106, 131, 112,
1366
    133, 66, 109, 106, 131, 81, 115, 112, 133, 99, 129, 112, 133, 112,
1367
    133, 118, 135, 46, 122, 71, 124, 71, 124, 101, 130, 71, 124, 84, 125,
1368
    107, 132, 113, 134, 71, 124, 107, 132, 84, 125, 113, 134, 101, 130,
1369
    113, 134, 113, 134, 119, 136, 62, 100, 72, 112, 100, 116, 112, 133,
1370
    72, 112, 87, 117, 128, 145, 132, 146, 100, 116, 128, 145, 116, 138,
1371
    145, 149, 112, 133, 132, 146, 145, 149, 147, 150, 72, 128, 87, 132,
1372
    112, 145, 117, 146, 87, 132, 92, 134, 132, 147, 134, 148, 112, 145,
1373
    132, 147, 133, 149, 146, 150, 117, 146, 134, 148, 146, 150, 148, 151,
1374
    62, 100, 100, 116, 72, 112, 112, 133, 100, 116, 116, 138, 128, 145,
1375
    145, 149, 72, 112, 128, 145, 87, 117, 132, 146, 112, 133, 145, 149,
1376
    132, 146, 147, 150, 72, 128, 112, 145, 87, 132, 117, 146, 112, 145,
1377
    133, 149, 132, 147, 146, 150, 87, 132, 132, 147, 92, 134, 134, 148,
1378
    117, 146, 146, 150, 134, 148, 148, 151, 94, 102, 102, 118, 102, 118,
1379
    118, 135, 102, 118, 118, 139, 141, 147, 147, 150, 102, 118, 141, 147,
1380
    118, 139, 147, 150, 118, 135, 147, 150, 147, 150, 152, 153, 102, 141,
1381
    118, 147, 118, 147, 139, 150, 118, 147, 135, 150, 147, 152, 150, 153,
1382
    118, 147, 147, 152, 135, 150, 150, 153, 139, 150, 150, 153, 150, 153,
1383
    153, 154, 1, 5, 5, 12, 5, 12, 12, 19, 5, 12, 12, 35, 50, 51, 51, 54,
1384
    5, 12, 50, 51, 12, 35, 51, 54, 12, 19, 51, 54, 51, 54, 74, 77, 5, 50,
1385
    12, 51, 12, 51, 35, 54, 12, 51, 19, 54, 51, 74, 54, 77, 12, 51, 51,
1386
    74, 19, 54, 54, 77, 35, 54, 54, 77, 54, 77, 77, 89, 2, 6, 6, 13, 12,
1387
    15, 15, 20, 6, 13, 13, 36, 51, 52, 52, 55, 12, 15, 51, 52, 38, 40,
1388
    56, 58, 15, 20, 52, 55, 56, 58, 75, 78, 12, 51, 15, 52, 38, 56, 40,
1389
    58, 15, 52, 20, 55, 56, 75, 58, 78, 38, 56, 56, 75, 44, 68, 68, 82,
1390
    40, 58, 58, 78, 68, 82, 82, 90, 2, 6, 12, 15, 6, 13, 15, 20, 12, 15,
1391
    38, 40, 51, 52, 56, 58, 6, 13, 51, 52, 13, 36, 52, 55, 15, 20, 56,
1392
    58, 52, 55, 75, 78, 12, 51, 38, 56, 15, 52, 40, 58, 38, 56, 44, 68,
1393
    56, 75, 68, 82, 15, 52, 56, 75, 20, 55, 58, 78, 40, 58, 68, 82, 58,
1394
    78, 82, 90, 4, 7, 13, 16, 13, 16, 17, 21, 13, 16, 39, 41, 52, 53, 57,
1395
    59, 13, 16, 52, 53, 39, 41, 57, 59, 17, 21, 57, 59, 57, 59, 76, 79,
1396
    35, 54, 40, 58, 40, 58, 48, 60, 40, 58, 45, 69, 65, 80, 70, 83, 40,
1397
    58, 65, 80, 45, 69, 70, 83, 48, 60, 70, 83, 70, 83, 86, 91, 2, 12, 6,
1398
    15, 6, 15, 13, 20, 12, 38, 15, 40, 51, 56, 52, 58, 12, 38, 51, 56,
1399
    15, 40, 52, 58, 38, 44, 56, 68, 56, 68, 75, 82, 6, 51, 13, 52, 13, 52,
1400
      36, 55, 15, 56, 20, 58, 52, 75, 55, 78, 15, 56, 52, 75, 20, 58, 55,
1401
    78, 40, 68, 58, 82, 58, 82, 78, 90, 4, 13, 7, 16, 13, 17, 16, 21, 13,
1402
    39, 16, 41, 52, 57, 53, 59, 35, 40, 54, 58, 40, 48, 58, 60, 40, 45,
1403
    58, 69, 65, 70, 80, 83, 13, 52, 16, 53, 39, 57, 41, 59, 17, 57, 21,
1404
    59, 57, 76, 59, 79, 40, 65, 58, 80, 45, 70, 69, 83, 48, 70, 60, 83,
1405
    70, 86, 83, 91, 4, 13, 13, 17, 7, 16, 16, 21, 35, 40, 40, 48, 54, 58,
1406
    58, 60, 13, 39, 52, 57, 16, 41, 53, 59, 40, 45, 65, 70, 58, 69, 80,
1407
    83, 13, 52, 39, 57, 16, 53, 41, 59, 40, 65, 45, 70, 58, 80, 69, 83,
1408
    17, 57, 57, 76, 21, 59, 59, 79, 48, 70, 70, 86, 60, 83, 83, 91, 11,
1409
    14, 14, 18, 14, 18, 18, 22, 36, 41, 41, 49, 55, 59, 59, 61, 36, 41,
1410
    55, 59, 41, 49, 59, 61, 42, 46, 66, 71, 66, 71, 81, 84, 36, 55, 41,
1411
    59, 41, 59, 49, 61, 42, 66, 46, 71, 66, 81, 71, 84, 42, 66, 66, 81,
1412
    46, 71, 71, 84, 62, 72, 72, 87, 72, 87, 87, 92, 2, 12, 12, 38, 12,
1413
    38, 38, 44, 6, 15, 15, 40, 51, 56, 56, 68, 6, 15, 51, 56, 15, 40, 56,
1414
    68, 13, 20, 52, 58, 52, 58, 75, 82, 6, 51, 15, 56, 15, 56, 40, 68,
1415
    13, 52, 20, 58, 52, 75, 58, 82, 13, 52, 52, 75, 20, 58, 58, 82, 36,
1416
    55, 55, 78, 55, 78, 78, 90, 4, 13, 13, 39, 35, 40, 40, 45, 7, 16, 16,
1417
    41, 54, 58, 58, 69, 13, 17, 52, 57, 40, 48, 65, 70, 16, 21, 53, 59,
1418
    58, 60, 80, 83, 13, 52, 17, 57, 40, 65, 48, 70, 16, 53, 21, 59, 58,
1419
    80, 60, 83, 39, 57, 57, 76, 45, 70, 70, 86, 41, 59, 59, 79, 69, 83,
1420
    83, 91, 4, 13, 35, 40, 13, 39, 40, 45, 13, 17, 40, 48, 52, 57, 65,
1421
    70, 7, 16, 54, 58, 16, 41, 58, 69, 16, 21, 58, 60, 53, 59, 80, 83,
1422
    13, 52, 40, 65, 17, 57, 48, 70, 39, 57, 45, 70, 57, 76, 70, 86, 16,
1423
    53, 58, 80, 21, 59, 60, 83, 41, 59, 69, 83, 59, 79, 83, 91, 11, 14,
1424
    36, 41, 36, 41, 42, 46, 14, 18, 41, 49, 55, 59, 66, 71, 14, 18, 55,
1425
    59, 41, 49, 66, 71, 18, 22, 59, 61, 59, 61, 81, 84, 36, 55, 42, 66,
1426
    42, 66, 62, 72, 41, 59, 46, 71, 66, 81, 72, 87, 41, 59, 66, 81, 46,
1427
    71, 72, 87, 49, 61, 71, 84, 71, 84, 87, 92, 4, 35, 13, 40, 13, 40,
1428
    39, 45, 13, 40, 17, 48, 52, 65, 57, 70, 13, 40, 52, 65, 17, 48, 57,
1429
    70, 39, 45, 57, 70, 57, 70, 76, 86, 7, 54, 16, 58, 16, 58, 41, 69,
1430
    16, 58, 21, 60, 53, 80, 59, 83, 16, 58, 53, 80, 21, 60, 59, 83, 41,
1431
    69, 59, 83, 59, 83, 79, 91, 11, 36, 14, 41, 36, 42, 41, 46, 14, 41,
1432
    18, 49, 55, 66, 59, 71, 36, 42, 55, 66, 42, 62, 66, 72, 41, 46, 59,
1433
    71, 66, 72, 81, 87, 14, 55, 18, 59, 41, 66, 49, 71, 18, 59, 22, 61,
1434
    59, 81, 61, 84, 41, 66, 59, 81, 46, 72, 71, 87, 49, 71, 61, 84, 71,
1435
    87, 84, 92, 11, 36, 36, 42, 14, 41, 41, 46, 36, 42, 42, 62, 55, 66,
1436
    66, 72, 14, 41, 55, 66, 18, 49, 59, 71, 41, 46, 66, 72, 59, 71, 81,
1437
    87, 14, 55, 41, 66, 18, 59, 49, 71, 41, 66, 46, 72, 59, 81, 71, 87,
1438
    18, 59, 59, 81, 22, 61, 61, 84, 49, 71, 71, 87, 61, 84, 84, 92, 34,
1439
    37, 37, 43, 37, 43, 43, 47, 37, 43, 43, 63, 64, 67, 67, 73, 37, 43,
1440
    64, 67, 43, 63, 67, 73, 43, 47, 67, 73, 67, 73, 85, 88, 37, 64, 43,
1441
    67, 43, 67, 63, 73, 43, 67, 47, 73, 67, 85, 73, 88, 43, 67, 67, 85,
1442
    47, 73, 73, 88, 63, 73, 73, 88, 73, 88, 88, 93, 2, 6, 6, 13, 12, 15,
1443
    15, 20, 6, 13, 13, 36, 51, 52, 52, 55, 12, 15, 51, 52, 38, 40, 56,
1444
    58, 15, 20, 52, 55, 56, 58, 75, 78, 12, 51, 15, 52, 38, 56, 40, 58,
1445
    15, 52, 20, 55, 56, 75, 58, 78, 38, 56, 56, 75, 44, 68, 68, 82, 40,
1446
    58, 58, 78, 68, 82, 82, 90, 3, 7, 7, 14, 19, 20, 20, 25, 7, 14, 14,
1447
    37, 54, 55, 55, 64, 19, 20, 54, 55, 44, 45, 68, 69, 20, 25, 55, 64,
1448
    68, 69, 96, 97, 19, 54, 20, 55, 44, 68, 45, 69, 20, 55, 25, 64, 68,
1449
    96, 69, 97, 44, 68, 68, 96, 120, 121, 121, 122, 45, 69, 69, 97, 121,
1450
    122, 122, 126, 6, 8, 15, 17, 15, 17, 26, 27, 15, 17, 40, 42, 56, 57,
1451
    65, 66, 15, 17, 56, 57, 40, 42, 65, 66, 26, 27, 65, 66, 65, 66, 98,
1452
    99, 51, 74, 56, 75, 56, 75, 65, 80, 56, 75, 68, 96, 104, 108, 105,
1453
    109, 56, 75, 104, 108, 68, 96, 105, 109, 65, 80, 105, 109, 105, 109,
1454
    127, 129, 7, 9, 16, 18, 20, 21, 27, 28, 16, 18, 41, 43, 58, 59, 66,
1455
    67, 20, 21, 58, 59, 45, 46, 70, 71, 27, 28, 66, 67, 70, 71, 100, 101,
1456
    54, 77, 58, 78, 68, 82, 70, 83, 58, 78, 69, 97, 105, 109, 106, 110,
1457
    68, 82, 105, 109, 121, 122, 123, 124, 70, 83, 106, 110, 123, 124,
1458
    128, 130, 6, 15, 8, 17, 15, 26, 17, 27, 15, 40, 17, 42, 56, 65, 57,
1459
    66, 51, 56, 74, 75, 56, 65, 75, 80, 56, 68, 75, 96, 104, 105, 108,
1460
    109, 15, 56, 17, 57, 40, 65, 42, 66, 26, 65, 27, 66, 65, 98, 66, 99,
1461
    56, 104, 75, 108, 68, 105, 96, 109, 65, 105, 80, 109, 105, 127, 109,
1462
    129, 7, 16, 9, 18, 20, 27, 21, 28, 16, 41, 18, 43, 58, 66, 59, 67,
1463
    54, 58, 77, 78, 68, 70, 82, 83, 58, 69, 78, 97, 105, 106, 109, 110,
1464
    20, 58, 21, 59, 45, 70, 46, 71, 27, 66, 28, 67, 70, 100, 71, 101, 68,
1465
    105, 82, 109, 121, 123, 122, 124, 70, 106, 83, 110, 123, 128, 124,
1466
    130, 13, 17, 17, 23, 20, 27, 27, 29, 40, 48, 48, 62, 68, 70, 70, 72,
1467
    52, 57, 75, 76, 58, 66, 80, 81, 65, 70, 98, 100, 105, 106, 111, 112,
1468
    52, 75, 57, 76, 58, 80, 66, 81, 65, 98, 70, 100, 105, 111, 106, 112,
1469
    75, 108, 108, 114, 82, 109, 109, 115, 98, 111, 111, 116, 127, 131,
1470
    131, 133, 14, 18, 18, 24, 25, 28, 28, 30, 41, 49, 49, 63, 69, 71, 71,
1471
    73, 55, 59, 78, 79, 69, 71, 83, 84, 66, 71, 99, 101, 106, 107, 112,
1472
    113, 55, 78, 59, 79, 69, 83, 71, 84, 66, 99, 71, 101, 106, 112, 107,
1473
    113, 96, 109, 109, 115, 122, 124, 124, 125, 100, 112, 112, 117, 128,
1474
    132, 132, 134, 6, 15, 15, 40, 51, 56, 56, 68, 8, 17, 17, 42, 74, 75,
1475
    75, 96, 15, 26, 56, 65, 56, 65, 104, 105, 17, 27, 57, 66, 75, 80,
1476
    108, 109, 15, 56, 26, 65, 56, 104, 65, 105, 17, 57, 27, 66, 75, 108,
1477
    80, 109, 40, 65, 65, 98, 68, 105, 105, 127, 42, 66, 66, 99, 96, 109,
1478
    109, 129, 7, 16, 16, 41, 54, 58, 58, 69, 9, 18, 18, 43, 77, 78, 78,
1479
    97, 20, 27, 58, 66, 68, 70, 105, 106, 21, 28, 59, 67, 82, 83, 109,
1480
    110, 20, 58, 27, 66, 68, 105, 70, 106, 21, 59, 28, 67, 82, 109, 83,
1481
    110, 45, 70, 70, 100, 121, 123, 123, 128, 46, 71, 71, 101, 122, 124,
1482
    124, 130, 13, 17, 40, 48, 52, 57, 65, 70, 17, 23, 48, 62, 75, 76, 98,
1483
    100, 20, 27, 68, 70, 58, 66, 105, 106, 27, 29, 70, 72, 80, 81, 111,
1484
    112, 52, 75, 65, 98, 75, 108, 98, 111, 57, 76, 70, 100, 108, 114,
1485
    111, 116, 58, 80, 105, 111, 82, 109, 127, 131, 66, 81, 106, 112, 109,
1486
    115, 131, 133, 14, 18, 41, 49, 55, 59, 66, 71, 18, 24, 49, 63, 78,
1487
    79, 99, 101, 25, 28, 69, 71, 69, 71, 106, 107, 28, 30, 71, 73, 83,
1488
    84, 112, 113, 55, 78, 66, 99, 96, 109, 100, 112, 59, 79, 71, 101,
1489
    109, 115, 112, 117, 69, 83, 106, 112, 122, 124, 128, 132, 71, 84,
1490
    107, 113, 124, 125, 132, 134, 13, 40, 17, 48, 52, 65, 57, 70, 17, 48,
1491
    23, 62, 75, 98, 76, 100, 52, 65, 75, 98, 75, 98, 108, 111, 57, 70,
1492
    76, 100, 108, 111, 114, 116, 20, 68, 27, 70, 58, 105, 66, 106, 27,
1493
    70, 29, 72, 80, 111, 81, 112, 58, 105, 80, 111, 82, 127, 109, 131,
1494
    66, 106, 81, 112, 109, 131, 115, 133, 14, 41, 18, 49, 55, 66, 59, 71,
1495
    18, 49, 24, 63, 78, 99, 79, 101, 55, 66, 78, 99, 96, 100, 109, 112,
1496
    59, 71, 79, 101, 109, 112, 115, 117, 25, 69, 28, 71, 69, 106, 71,
1497
    107, 28, 71, 30, 73, 83, 112, 84, 113, 69, 106, 83, 112, 122, 128,
1498
    124, 132, 71, 107, 84, 113, 124, 132, 125, 134, 36, 42, 42, 62, 55,
1499
    66, 66, 72, 42, 62, 62, 94, 96, 100, 100, 102, 55, 66, 96, 100, 78,
1500
    99, 109, 112, 66, 72, 100, 102, 109, 112, 116, 118, 55, 96, 66, 100,
1501
    78, 109, 99, 112, 66, 100, 72, 102, 109, 116, 112, 118, 78, 109, 109,
1502
    116, 90, 129, 129, 133, 99, 112, 112, 118, 129, 133, 133, 135, 37,
1503
    43, 43, 63, 64, 67, 67, 73, 43, 63, 63, 95, 97, 101, 101, 103, 64,
1504
    67, 97, 101, 97, 101, 110, 113, 67, 73, 101, 103, 110, 113, 117, 119,
1505
    64, 97, 67, 101, 97, 110, 101, 113, 67, 101, 73, 103, 110, 117, 113,
1506
    119, 97, 110, 110, 117, 126, 130, 130, 134, 101, 113, 113, 119, 130,
1507
    134, 134, 136, 2, 6, 12, 15, 6, 13, 15, 20, 12, 15, 38, 40, 51, 52,
1508
    56, 58, 6, 13, 51, 52, 13, 36, 52, 55, 15, 20, 56, 58, 52, 55, 75,
1509
    78, 12, 51, 38, 56, 15, 52, 40, 58, 38, 56, 44, 68, 56, 75, 68, 82,
1510
    15, 52, 56, 75, 20, 55, 58, 78, 40, 58, 68, 82, 58, 78, 82, 90, 6, 8,
1511
    15, 17, 15, 17, 26, 27, 15, 17, 40, 42, 56, 57, 65, 66, 15, 17, 56,
1512
    57, 40, 42, 65, 66, 26, 27, 65, 66, 65, 66, 98, 99, 51, 74, 56, 75,
1513
    56, 75, 65, 80, 56, 75, 68, 96, 104, 108, 105, 109, 56, 75, 104, 108,
1514
    68, 96, 105, 109, 65, 80, 105, 109, 105, 109, 127, 129, 3, 7, 19, 20,
1515
    7, 14, 20, 25, 19, 20, 44, 45, 54, 55, 68, 69, 7, 14, 54, 55, 14, 37,
1516
    55, 64, 20, 25, 68, 69, 55, 64, 96, 97, 19, 54, 44, 68, 20, 55, 45,
1517
    69, 44, 68, 120, 121, 68, 96, 121, 122, 20, 55, 68, 96, 25, 64, 69,
1518
    97, 45, 69, 121, 122, 69, 97, 122, 126, 7, 9, 20, 21, 16, 18, 27, 28,
1519
    20, 21, 45, 46, 58, 59, 70, 71, 16, 18, 58, 59, 41, 43, 66, 67, 27,
1520
    28, 70, 71, 66, 67, 100, 101, 54, 77, 68, 82, 58, 78, 70, 83, 68, 82,
1521
    121, 122, 105, 109, 123, 124, 58, 78, 105, 109, 69, 97, 106, 110, 70,
1522
    83, 123, 124, 106, 110, 128, 130, 6, 15, 15, 26, 8, 17, 17, 27, 51,
1523
    56, 56, 65, 74, 75, 75, 80, 15, 40, 56, 65, 17, 42, 57, 66, 56, 68,
1524
    104, 105, 75, 96, 108, 109, 15, 56, 40, 65, 17, 57, 42, 66, 56, 104,
1525
    68, 105, 75, 108, 96, 109, 26, 65, 65, 98, 27, 66, 66, 99, 65, 105,
1526
    105, 127, 80, 109, 109, 129, 13, 17, 20, 27, 17, 23, 27, 29, 52, 57,
1527
    58, 66, 75, 76, 80, 81, 40, 48, 68, 70, 48, 62, 70, 72, 65, 70, 105,
1528
    106, 98, 100, 111, 112, 52, 75, 58, 80, 57, 76, 66, 81, 75, 108, 82,
1529
    109, 108, 114, 109, 115, 65, 98, 105, 111, 70, 100, 106, 112, 98,
1530
    111, 127, 131, 111, 116, 131, 133, 7, 16, 20, 27, 9, 18, 21, 28, 54,
1531
    58, 68, 70, 77, 78, 82, 83, 16, 41, 58, 66, 18, 43, 59, 67, 58, 69,
1532
    105, 106, 78, 97, 109, 110, 20, 58, 45, 70, 21, 59, 46, 71, 68, 105,
1533
    121, 123, 82, 109, 122, 124, 27, 66, 70, 100, 28, 67, 71, 101, 70,
1534
    106, 123, 128, 83, 110, 124, 130, 14, 18, 25, 28, 18, 24, 28, 30, 55,
1535
    59, 69, 71, 78, 79, 83, 84, 41, 49, 69, 71, 49, 63, 71, 73, 66, 71,
1536
    106, 107, 99, 101, 112, 113, 55, 78, 69, 83, 59, 79, 71, 84, 96, 109,
1537
    122, 124, 109, 115, 124, 125, 66, 99, 106, 112, 71, 101, 107, 113,
1538
    100, 112, 128, 132, 112, 117, 132, 134, 6, 15, 51, 56, 15, 40, 56,
1539
    68, 15, 26, 56, 65, 56, 65, 104, 105, 8, 17, 74, 75, 17, 42, 75, 96,
1540
    17, 27, 75, 80, 57, 66, 108, 109, 15, 56, 56, 104, 26, 65, 65, 105,
1541
    40, 65, 68, 105, 65, 98, 105, 127, 17, 57, 75, 108, 27, 66, 80, 109,
1542
    42, 66, 96, 109, 66, 99, 109, 129, 13, 17, 52, 57, 40, 48, 65, 70,
1543
    20, 27, 58, 66, 68, 70, 105, 106, 17, 23, 75, 76, 48, 62, 98, 100,
1544
    27, 29, 80, 81, 70, 72, 111, 112, 52, 75, 75, 108, 65, 98, 98, 111,
1545
    58, 80, 82, 109, 105, 111, 127, 131, 57, 76, 108, 114, 70, 100, 111,
1546
    116, 66, 81, 109, 115, 106, 112, 131, 133, 7, 16, 54, 58, 16, 41, 58,
1547
    69, 20, 27, 68, 70, 58, 66, 105, 106, 9, 18, 77, 78, 18, 43, 78, 97,
1548
    21, 28, 82, 83, 59, 67, 109, 110, 20, 58, 68, 105, 27, 66, 70, 106,
1549
    45, 70, 121, 123, 70, 100, 123, 128, 21, 59, 82, 109, 28, 67, 83,
1550
    110, 46, 71, 122, 124, 71, 101, 124, 130, 14, 18, 55, 59, 41, 49, 66,
1551
    71, 25, 28, 69, 71, 69, 71, 106, 107, 18, 24, 78, 79, 49, 63, 99,
1552
    101, 28, 30, 83, 84, 71, 73, 112, 113, 55, 78, 96, 109, 66, 99, 100,
1553
    112, 69, 83, 122, 124, 106, 112, 128, 132, 59, 79, 109, 115, 71, 101,
1554
    112, 117, 71, 84, 124, 125, 107, 113, 132, 134, 13, 40, 52, 65, 17,
1555
    48, 57, 70, 52, 65, 75, 98, 75, 98, 108, 111, 17, 48, 75, 98, 23, 62,
1556
    76, 100, 57, 70, 108, 111, 76, 100, 114, 116, 20, 68, 58, 105, 27,
1557
    70, 66, 106, 58, 105, 82, 127, 80, 111, 109, 131, 27, 70, 80, 111,
1558
    29, 72, 81, 112, 66, 106, 109, 131, 81, 112, 115, 133, 36, 42, 55,
1559
    66, 42, 62, 66, 72, 55, 66, 78, 99, 96, 100, 109, 112, 42, 62, 96,
1560
    100, 62, 94, 100, 102, 66, 72, 109, 112, 100, 102, 116, 118, 55, 96,
1561
    78, 109, 66, 100, 99, 112, 78, 109, 90, 129, 109, 116, 129, 133, 66,
1562
    100, 109, 116, 72, 102, 112, 118, 99, 112, 129, 133, 112, 118, 133,
1563
    135, 14, 41, 55, 66, 18, 49, 59, 71, 55, 66, 96, 100, 78, 99, 109,
1564
    112, 18, 49, 78, 99, 24, 63, 79, 101, 59, 71, 109, 112, 79, 101, 115,
1565
    117, 25, 69, 69, 106, 28, 71, 71, 107, 69, 106, 122, 128, 83, 112,
1566
    124, 132, 28, 71, 83, 112, 30, 73, 84, 113, 71, 107, 124, 132, 84,
1567
    113, 125, 134, 37, 43, 64, 67, 43, 63, 67, 73, 64, 67, 97, 101, 97,
1568
    101, 110, 113, 43, 63, 97, 101, 63, 95, 101, 103, 67, 73, 110, 113,
1569
    101, 103, 117, 119, 64, 97, 97, 110, 67, 101, 101, 113, 97, 110, 126,
1570
    130, 110, 117, 130, 134, 67, 101, 110, 117, 73, 103, 113, 119, 101,
1571
    113, 130, 134, 113, 119, 134, 136, 4, 7, 13, 16, 13, 16, 17, 21, 13,
1572
    16, 39, 41, 52, 53, 57, 59, 13, 16, 52, 53, 39, 41, 57, 59, 17, 21,
1573
    57, 59, 57, 59, 76, 79, 35, 54, 40, 58, 40, 58, 48, 60, 40, 58, 45,
1574
    69, 65, 80, 70, 83, 40, 58, 65, 80, 45, 69, 70, 83, 48, 60, 70, 83,
1575
    70, 83, 86, 91, 7, 9, 16, 18, 20, 21, 27, 28, 16, 18, 41, 43, 58, 59,
1576
    66, 67, 20, 21, 58, 59, 45, 46, 70, 71, 27, 28, 66, 67, 70, 71, 100,
1577
    101, 54, 77, 58, 78, 68, 82, 70, 83, 58, 78, 69, 97, 105, 109, 106,
1578
    110, 68, 82, 105, 109, 121, 122, 123, 124, 70, 83, 106, 110, 123,
1579
    124, 128, 130, 7, 9, 20, 21, 16, 18, 27, 28, 20, 21, 45, 46, 58, 59,
1580
    70, 71, 16, 18, 58, 59, 41, 43, 66, 67, 27, 28, 70, 71, 66, 67, 100,
1581
    101, 54, 77, 68, 82, 58, 78, 70, 83, 68, 82, 121, 122, 105, 109, 123,
1582
    124, 58, 78, 105, 109, 69, 97, 106, 110, 70, 83, 123, 124, 106, 110,
1583
    128, 130, 9, 10, 21, 22, 21, 22, 29, 30, 21, 22, 46, 47, 60, 61, 72,
1584
    73, 21, 22, 60, 61, 46, 47, 72, 73, 29, 30, 72, 73, 72, 73, 102, 103,
1585
    77, 89, 82, 90, 82, 90, 86, 91, 82, 90, 122, 126, 127, 129, 128, 130,
1586
    82, 90, 127, 129, 122, 126, 128, 130, 86, 91, 128, 130, 128, 130,
1587
    141, 142, 13, 20, 17, 27, 17, 27, 23, 29, 52, 58, 57, 66, 75, 80, 76,
1588
    81, 52, 58, 75, 80, 57, 66, 76, 81, 75, 82, 108, 109, 108, 109, 114,
1589
    115, 40, 68, 48, 70, 48, 70, 62, 72, 65, 105, 70, 106, 98, 111, 100,
1590
    112, 65, 105, 98, 111, 70, 106, 100, 112, 98, 127, 111, 131, 111,
1591
    131, 116, 133, 16, 21, 21, 28, 27, 29, 29, 31, 53, 59, 59, 67, 80,
1592
    81, 81, 85, 58, 60, 82, 83, 70, 72, 86, 87, 80, 83, 109, 110, 111,
1593
    112, 116, 117, 58, 82, 60, 83, 70, 86, 72, 87, 80, 109, 83, 110, 111,
1594
    116, 112, 117, 105, 127, 127, 131, 123, 128, 128, 132, 111, 131, 131,
1595
    143, 144, 145, 145, 146, 16, 21, 27, 29, 21, 28, 29, 31, 58, 60, 70,
1596
    72, 82, 83, 86, 87, 53, 59, 80, 81, 59, 67, 81, 85, 80, 83, 111, 112,
1597
    109, 110, 116, 117, 58, 82, 70, 86, 60, 83, 72, 87, 105, 127, 123,
1598
    128, 127, 131, 128, 132, 80, 109, 111, 116, 83, 110, 112, 117, 111,
1599
    131, 144, 145, 131, 143, 145, 146, 18, 22, 28, 30, 28, 30, 31, 32,
1600
    59, 61, 71, 73, 83, 84, 87, 88, 59, 61, 83, 84, 71, 73, 87, 88, 81,
1601
    84, 112, 113, 112, 113, 118, 119, 78, 90, 83, 91, 83, 91, 87, 92,
1602
    109, 129, 124, 130, 131, 133, 132, 134, 109, 129, 131, 133, 124, 130,
1603
    132, 134, 116, 133, 145, 146, 145, 146, 147, 148, 13, 20, 52, 58, 52,
1604
    58, 75, 82, 17, 27, 57, 66, 75, 80, 108, 109, 17, 27, 75, 80, 57, 66,
1605
    108, 109, 23, 29, 76, 81, 76, 81, 114, 115, 40, 68, 65, 105, 65, 105,
1606
    98, 127, 48, 70, 70, 106, 98, 111, 111, 131, 48, 70, 98, 111, 70,
1607
    106, 111, 131, 62, 72, 100, 112, 100, 112, 116, 133, 16, 21, 53, 59,
1608
    58, 60, 80, 83, 21, 28, 59, 67, 82, 83, 109, 110, 27, 29, 80, 81, 70,
1609
    72, 111, 112, 29, 31, 81, 85, 86, 87, 116, 117, 58, 82, 80, 109, 105,
1610
    127, 111, 131, 60, 83, 83, 110, 127, 131, 131, 143, 70, 86, 111, 116,
1611
    123, 128, 144, 145, 72, 87, 112, 117, 128, 132, 145, 146, 16, 21, 58,
1612
    60, 53, 59, 80, 83, 27, 29, 70, 72, 80, 81, 111, 112, 21, 28, 82, 83,
1613
    59, 67, 109, 110, 29, 31, 86, 87, 81, 85, 116, 117, 58, 82, 105, 127,
1614
    80, 109, 111, 131, 70, 86, 123, 128, 111, 116, 144, 145, 60, 83, 127,
1615
    131, 83, 110, 131, 143, 72, 87, 128, 132, 112, 117, 145, 146, 18, 22,
1616
    59, 61, 59, 61, 81, 84, 28, 30, 71, 73, 83, 84, 112, 113, 28, 30, 83,
1617
    84, 71, 73, 112, 113, 31, 32, 87, 88, 87, 88, 118, 119, 78, 90, 109,
1618
    129, 109, 129, 116, 133, 83, 91, 124, 130, 131, 133, 145, 146, 83,
1619
    91, 131, 133, 124, 130, 145, 146, 87, 92, 132, 134, 132, 134, 147,
1620
    148, 39, 45, 57, 70, 57, 70, 76, 86, 57, 70, 76, 100, 108, 111, 114,
1621
    116, 57, 70, 108, 111, 76, 100, 114, 116, 76, 86, 114, 116, 114, 116,
1622
    137, 138, 45, 121, 70, 123, 70, 123, 100, 128, 70, 123, 86, 128, 111,
1623
    144, 116, 145, 70, 123, 111, 144, 86, 128, 116, 145, 100, 128, 116,
1624
    145, 116, 145, 138, 149, 41, 46, 59, 71, 66, 72, 81, 87, 59, 71, 79,
1625
    101, 109, 112, 115, 117, 66, 72, 109, 112, 100, 102, 116, 118, 81,
1626
    87, 115, 117, 116, 118, 138, 139, 69, 122, 83, 124, 106, 128, 112,
1627
    132, 83, 124, 91, 130, 131, 145, 133, 146, 106, 128, 131, 145, 128,
1628
    141, 145, 147, 112, 132, 133, 146, 145, 147, 149, 150, 41, 46, 66,
1629
    72, 59, 71, 81, 87, 66, 72, 100, 102, 109, 112, 116, 118, 59, 71,
1630
    109, 112, 79, 101, 115, 117, 81, 87, 116, 118, 115, 117, 138, 139,
1631
    69, 122, 106, 128, 83, 124, 112, 132, 106, 128, 128, 141, 131, 145,
1632
    145, 147, 83, 124, 131, 145, 91, 130, 133, 146, 112, 132, 145, 147,
1633
    133, 146, 149, 150, 43, 47, 67, 73, 67, 73, 85, 88, 67, 73, 101, 103,
1634
    110, 113, 117, 119, 67, 73, 110, 113, 101, 103, 117, 119, 85, 88,
1635
    117, 119, 117, 119, 139, 140, 97, 126, 110, 130, 110, 130, 117, 134,
1636
    110, 130, 130, 142, 143, 146, 146, 148, 110, 130, 143, 146, 130, 142,
1637
    146, 148, 117, 134, 146, 148, 146, 148, 150, 151, 2, 12, 6, 15, 6,
1638
    15, 13, 20, 12, 38, 15, 40, 51, 56, 52, 58, 12, 38, 51, 56, 15, 40,
1639
    52, 58, 38, 44, 56, 68, 56, 68, 75, 82, 6, 51, 13, 52, 13, 52, 36,
1640
    55, 15, 56, 20, 58, 52, 75, 55, 78, 15, 56, 52, 75, 20, 58, 55, 78,
1641
    40, 68, 58, 82, 58, 82, 78, 90, 6, 15, 8, 17, 15, 26, 17, 27, 15, 40,
1642
    17, 42, 56, 65, 57, 66, 51, 56, 74, 75, 56, 65, 75, 80, 56, 68, 75,
1643
    96, 104, 105, 108, 109, 15, 56, 17, 57, 40, 65, 42, 66, 26, 65, 27,
1644
    66, 65, 98, 66, 99, 56, 104, 75, 108, 68, 105, 96, 109, 65, 105, 80,
1645
    109, 105, 127, 109, 129, 6, 15, 15, 26, 8, 17, 17, 27, 51, 56, 56,
1646
    65, 74, 75, 75, 80, 15, 40, 56, 65, 17, 42, 57, 66, 56, 68, 104, 105,
1647
    75, 96, 108, 109, 15, 56, 40, 65, 17, 57, 42, 66, 56, 104, 68, 105,
1648
    75, 108, 96, 109, 26, 65, 65, 98, 27, 66, 66, 99, 65, 105, 105, 127,
1649
    80, 109, 109, 129, 13, 20, 17, 27, 17, 27, 23, 29, 52, 58, 57, 66,
1650
    75, 80, 76, 81, 52, 58, 75, 80, 57, 66, 76, 81, 75, 82, 108, 109,
1651
    108, 109, 114, 115, 40, 68, 48, 70, 48, 70, 62, 72, 65, 105, 70, 106,
1652
    98, 111, 100, 112, 65, 105, 98, 111, 70, 106, 100, 112, 98, 127, 111,
1653
    131, 111, 131, 116, 133, 3, 19, 7, 20, 7, 20, 14, 25, 19, 44, 20, 45,
1654
    54, 68, 55, 69, 19, 44, 54, 68, 20, 45, 55, 69, 44, 120, 68, 121, 68,
1655
    121, 96, 122, 7, 54, 14, 55, 14, 55, 37, 64, 20, 68, 25, 69, 55, 96,
1656
    64, 97, 20, 68, 55, 96, 25, 69, 64, 97, 45, 121, 69, 122, 69, 122,
1657
    97, 126, 7, 20, 9, 21, 16, 27, 18, 28, 20, 45, 21, 46, 58, 70, 59,
1658
    71, 54, 68, 77, 82, 58, 70, 78, 83, 68, 121, 82, 122, 105, 123, 109,
1659
    124, 16, 58, 18, 59, 41, 66, 43, 67, 27, 70, 28, 71, 66, 100, 67,
1660
    101, 58, 105, 78, 109, 69, 106, 97, 110, 70, 123, 83, 124, 106, 128,
1661
    110, 130, 7, 20, 16, 27, 9, 21, 18, 28, 54, 68, 58, 70, 77, 82, 78,
1662
    83, 20, 45, 58, 70, 21, 46, 59, 71, 68, 121, 105, 123, 82, 122, 109,
1663
    124, 16, 58, 41, 66, 18, 59, 43, 67, 58, 105, 69, 106, 78, 109, 97,
1664
    110, 27, 70, 66, 100, 28, 71, 67, 101, 70, 123, 106, 128, 83, 124,
1665
    110, 130, 14, 25, 18, 28, 18, 28, 24, 30, 55, 69, 59, 71, 78, 83, 79,
1666
    84, 55, 69, 78, 83, 59, 71, 79, 84, 96, 122, 109, 124, 109, 124, 115,
1667
    125, 41, 69, 49, 71, 49, 71, 63, 73, 66, 106, 71, 107, 99, 112, 101,
1668
    113, 66, 106, 99, 112, 71, 107, 101, 113, 100, 128, 112, 132, 112,
1669
    132, 117, 134, 6, 51, 15, 56, 15, 56, 40, 68, 15, 56, 26, 65, 56,
1670
    104, 65, 105, 15, 56, 56, 104, 26, 65, 65, 105, 40, 68, 65, 105, 65,
1671
    105, 98, 127, 8, 74, 17, 75, 17, 75, 42, 96, 17, 75, 27, 80, 57, 108,
1672
    66, 109, 17, 75, 57, 108, 27, 80, 66, 109, 42, 96, 66, 109, 66, 109,
1673
    99, 129, 13, 52, 17, 57, 40, 65, 48, 70, 20, 58, 27, 66, 68, 105, 70,
1674
    106, 52, 75, 75, 108, 65, 98, 98, 111, 58, 82, 80, 109, 105, 127,
1675
    111, 131, 17, 75, 23, 76, 48, 98, 62, 100, 27, 80, 29, 81, 70, 111,
1676
    72, 112, 57, 108, 76, 114, 70, 111, 100, 116, 66, 109, 81, 115, 106,
1677
    131, 112, 133, 13, 52, 40, 65, 17, 57, 48, 70, 52, 75, 65, 98, 75,
1678
    108, 98, 111, 20, 58, 68, 105, 27, 66, 70, 106, 58, 82, 105, 127, 80,
1679
    109, 111, 131, 17, 75, 48, 98, 23, 76, 62, 100, 57, 108, 70, 111, 76,
1680
    114, 100, 116, 27, 80, 70, 111, 29, 81, 72, 112, 66, 109, 106, 131,
1681
    81, 115, 112, 133, 36, 55, 42, 66, 42, 66, 62, 72, 55, 78, 66, 99,
1682
    96, 109, 100, 112, 55, 78, 96, 109, 66, 99, 100, 112, 78, 90, 109,
1683
    129, 109, 129, 116, 133, 42, 96, 62, 100, 62, 100, 94, 102, 66, 109,
1684
    72, 112, 100, 116, 102, 118, 66, 109, 100, 116, 72, 112, 102, 118,
1685
    99, 129, 112, 133, 112, 133, 118, 135, 7, 54, 16, 58, 16, 58, 41, 69,
1686
    20, 68, 27, 70, 58, 105, 66, 106, 20, 68, 58, 105, 27, 70, 66, 106,
1687
    45, 121, 70, 123, 70, 123, 100, 128, 9, 77, 18, 78, 18, 78, 43, 97,
1688
    21, 82, 28, 83, 59, 109, 67, 110, 21, 82, 59, 109, 28, 83, 67, 110,
1689
    46, 122, 71, 124, 71, 124, 101, 130, 14, 55, 18, 59, 41, 66, 49, 71,
1690
    25, 69, 28, 71, 69, 106, 71, 107, 55, 96, 78, 109, 66, 100, 99, 112,
1691
    69, 122, 83, 124, 106, 128, 112, 132, 18, 78, 24, 79, 49, 99, 63,
1692
    101, 28, 83, 30, 84, 71, 112, 73, 113, 59, 109, 79, 115, 71, 112,
1693
    101, 117, 71, 124, 84, 125, 107, 132, 113, 134, 14, 55, 41, 66, 18,
1694
    59, 49, 71, 55, 96, 66, 100, 78, 109, 99, 112, 25, 69, 69, 106, 28,
1695
    71, 71, 107, 69, 122, 106, 128, 83, 124, 112, 132, 18, 78, 49, 99,
1696
    24, 79, 63, 101, 59, 109, 71, 112, 79, 115, 101, 117, 28, 83, 71,
1697
    112, 30, 84, 73, 113, 71, 124, 107, 132, 84, 125, 113, 134, 37, 64,
1698
    43, 67, 43, 67, 63, 73, 64, 97, 67, 101, 97, 110, 101, 113, 64, 97,
1699
    97, 110, 67, 101, 101, 113, 97, 126, 110, 130, 110, 130, 117, 134,
1700
    43, 97, 63, 101, 63, 101, 95, 103, 67, 110, 73, 113, 101, 117, 103,
1701
    119, 67, 110, 101, 117, 73, 113, 103, 119, 101, 130, 113, 134, 113,
1702
    134, 119, 136, 4, 13, 7, 16, 13, 17, 16, 21, 13, 39, 16, 41, 52, 57,
1703
    53, 59, 35, 40, 54, 58, 40, 48, 58, 60, 40, 45, 58, 69, 65, 70, 80,
1704
    83, 13, 52, 16, 53, 39, 57, 41, 59, 17, 57, 21, 59, 57, 76, 59, 79,
1705
    40, 65, 58, 80, 45, 70, 69, 83, 48, 70, 60, 83, 70, 86, 83, 91, 7,
1706
    16, 9, 18, 20, 27, 21, 28, 16, 41, 18, 43, 58, 66, 59, 67, 54, 58,
1707
    77, 78, 68, 70, 82, 83, 58, 69, 78, 97, 105, 106, 109, 110, 20, 58,
1708
    21, 59, 45, 70, 46, 71, 27, 66, 28, 67, 70, 100, 71, 101, 68, 105,
1709
    82, 109, 121, 123, 122, 124, 70, 106, 83, 110, 123, 128, 124, 130,
1710
    13, 17, 20, 27, 17, 23, 27, 29, 52, 57, 58, 66, 75, 76, 80, 81, 40,
1711
    48, 68, 70, 48, 62, 70, 72, 65, 70, 105, 106, 98, 100, 111, 112, 52,
1712
    75, 58, 80, 57, 76, 66, 81, 75, 108, 82, 109, 108, 114, 109, 115, 65,
1713
    98, 105, 111, 70, 100, 106, 112, 98, 111, 127, 131, 111, 116, 131,
1714
    133, 16, 21, 21, 28, 27, 29, 29, 31, 53, 59, 59, 67, 80, 81, 81, 85,
1715
    58, 60, 82, 83, 70, 72, 86, 87, 80, 83, 109, 110, 111, 112, 116, 117,
1716
    58, 82, 60, 83, 70, 86, 72, 87, 80, 109, 83, 110, 111, 116, 112, 117,
1717
    105, 127, 127, 131, 123, 128, 128, 132, 111, 131, 131, 143, 144, 145,
1718
    145, 146, 7, 20, 9, 21, 16, 27, 18, 28, 20, 45, 21, 46, 58, 70, 59,
1719
    71, 54, 68, 77, 82, 58, 70, 78, 83, 68, 121, 82, 122, 105, 123, 109,
1720
    124, 16, 58, 18, 59, 41, 66, 43, 67, 27, 70, 28, 71, 66, 100, 67,
1721
    101, 58, 105, 78, 109, 69, 106, 97, 110, 70, 123, 83, 124, 106, 128,
1722
    110, 130, 9, 21, 10, 22, 21, 29, 22, 30, 21, 46, 22, 47, 60, 72, 61,
1723
    73, 77, 82, 89, 90, 82, 86, 90, 91, 82, 122, 90, 126, 127, 128, 129,
1724
    130, 21, 60, 22, 61, 46, 72, 47, 73, 29, 72, 30, 73, 72, 102, 73,
1725
    103, 82, 127, 90, 129, 122, 128, 126, 130, 86, 128, 91, 130, 128,
1726
    141, 130, 142, 16, 27, 21, 29, 21, 29, 28, 31, 58, 70, 60, 72, 82,
1727
    86, 83, 87, 58, 70, 82, 86, 60, 72, 83, 87, 105, 123, 127, 128, 127,
1728
    128, 131, 132, 53, 80, 59, 81, 59, 81, 67, 85, 80, 111, 83, 112, 109,
1729
    116, 110, 117, 80, 111, 109, 116, 83, 112, 110, 117, 111, 144, 131,
1730
    145, 131, 145, 143, 146, 18, 28, 22, 30, 28, 31, 30, 32, 59, 71, 61,
1731
    73, 83, 87, 84, 88, 78, 83, 90, 91, 83, 87, 91, 92, 109, 124, 129,
1732
    130, 131, 132, 133, 134, 59, 83, 61, 84, 71, 87, 73, 88, 81, 112, 84,
1733
    113, 112, 118, 113, 119, 109, 131, 129, 133, 124, 132, 130, 134, 116,
1734
    145, 133, 146, 145, 147, 146, 148, 13, 52, 20, 58, 52, 75, 58, 82,
1735
    17, 57, 27, 66, 75, 108, 80, 109, 40, 65, 68, 105, 65, 98, 105, 127,
1736
    48, 70, 70, 106, 98, 111, 111, 131, 17, 75, 27, 80, 57, 108, 66, 109,
1737
    23, 76, 29, 81, 76, 114, 81, 115, 48, 98, 70, 111, 70, 111, 106, 131,
1738
    62, 100, 72, 112, 100, 116, 112, 133, 16, 53, 21, 59, 58, 80, 60, 83,
1739
    21, 59, 28, 67, 82, 109, 83, 110, 58, 80, 82, 109, 105, 111, 127,
1740
    131, 60, 83, 83, 110, 127, 131, 131, 143, 27, 80, 29, 81, 70, 111,
1741
    72, 112, 29, 81, 31, 85, 86, 116, 87, 117, 70, 111, 86, 116, 123,
1742
    144, 128, 145, 72, 112, 87, 117, 128, 145, 132, 146, 39, 57, 45, 70,
1743
    57, 76, 70, 86, 57, 76, 70, 100, 108, 114, 111, 116, 45, 70, 121,
1744
    123, 70, 100, 123, 128, 70, 86, 123, 128, 111, 116, 144, 145, 57,
1745
    108, 70, 111, 76, 114, 100, 116, 76, 114, 86, 116, 114, 137, 116,
1746
    138, 70, 111, 123, 144, 86, 116, 128, 145, 100, 116, 128, 145, 116,
1747
    138, 145, 149, 41, 59, 46, 71, 66, 81, 72, 87, 59, 79, 71, 101, 109,
1748
    115, 112, 117, 69, 83, 122, 124, 106, 112, 128, 132, 83, 91, 124,
1749
    130, 131, 133, 145, 146, 66, 109, 72, 112, 100, 116, 102, 118, 81,
1750
    115, 87, 117, 116, 138, 118, 139, 106, 131, 128, 145, 128, 145, 141,
1751
    147, 112, 133, 132, 146, 145, 149, 147, 150, 16, 58, 21, 60, 53, 80,
1752
    59, 83, 27, 70, 29, 72, 80, 111, 81, 112, 58, 105, 82, 127, 80, 111,
1753
    109, 131, 70, 123, 86, 128, 111, 144, 116, 145, 21, 82, 28, 83, 59,
1754
    109, 67, 110, 29, 86, 31, 87, 81, 116, 85, 117, 60, 127, 83, 131, 83,
1755
    131, 110, 143, 72, 128, 87, 132, 112, 145, 117, 146, 18, 59, 22, 61,
1756
    59, 81, 61, 84, 28, 71, 30, 73, 83, 112, 84, 113, 78, 109, 90, 129,
1757
    109, 116, 129, 133, 83, 124, 91, 130, 131, 145, 133, 146, 28, 83, 30,
1758
    84, 71, 112, 73, 113, 31, 87, 32, 88, 87, 118, 88, 119, 83, 131, 91,
1759
    133, 124, 145, 130, 146, 87, 132, 92, 134, 132, 147, 134, 148, 41,
1760
    66, 46, 72, 59, 81, 71, 87, 66, 100, 72, 102, 109, 116, 112, 118, 69,
1761
    106, 122, 128, 83, 112, 124, 132, 106, 128, 128, 141, 131, 145, 145,
1762
    147, 59, 109, 71, 112, 79, 115, 101, 117, 81, 116, 87, 118, 115, 138,
1763
    117, 139, 83, 131, 124, 145, 91, 133, 130, 146, 112, 145, 132, 147,
1764
    133, 149, 146, 150, 43, 67, 47, 73, 67, 85, 73, 88, 67, 101, 73, 103,
1765
    110, 117, 113, 119, 97, 110, 126, 130, 110, 117, 130, 134, 110, 130,
1766
    130, 142, 143, 146, 146, 148, 67, 110, 73, 113, 101, 117, 103, 119,
1767
    85, 117, 88, 119, 117, 139, 119, 140, 110, 143, 130, 146, 130, 146,
1768
    142, 148, 117, 146, 134, 148, 146, 150, 148, 151, 4, 13, 13, 17, 7,
1769
    16, 16, 21, 35, 40, 40, 48, 54, 58, 58, 60, 13, 39, 52, 57, 16, 41,
1770
    53, 59, 40, 45, 65, 70, 58, 69, 80, 83, 13, 52, 39, 57, 16, 53, 41,
1771
    59, 40, 65, 45, 70, 58, 80, 69, 83, 17, 57, 57, 76, 21, 59, 59, 79,
1772
    48, 70, 70, 86, 60, 83, 83, 91, 13, 17, 17, 23, 20, 27, 27, 29, 40,
1773
    48, 48, 62, 68, 70, 70, 72, 52, 57, 75, 76, 58, 66, 80, 81, 65, 70,
1774
    98, 100, 105, 106, 111, 112, 52, 75, 57, 76, 58, 80, 66, 81, 65, 98,
1775
    70, 100, 105, 111, 106, 112, 75, 108, 108, 114, 82, 109, 109, 115,
1776
    98, 111, 111, 116, 127, 131, 131, 133, 7, 16, 20, 27, 9, 18, 21, 28,
1777
    54, 58, 68, 70, 77, 78, 82, 83, 16, 41, 58, 66, 18, 43, 59, 67, 58,
1778
    69, 105, 106, 78, 97, 109, 110, 20, 58, 45, 70, 21, 59, 46, 71, 68,
1779
    105, 121, 123, 82, 109, 122, 124, 27, 66, 70, 100, 28, 67, 71, 101,
1780
    70, 106, 123, 128, 83, 110, 124, 130, 16, 21, 27, 29, 21, 28, 29, 31,
1781
    58, 60, 70, 72, 82, 83, 86, 87, 53, 59, 80, 81, 59, 67, 81, 85, 80,
1782
    83, 111, 112, 109, 110, 116, 117, 58, 82, 70, 86, 60, 83, 72, 87,
1783
    105, 127, 123, 128, 127, 131, 128, 132, 80, 109, 111, 116, 83, 110,
1784
    112, 117, 111, 131, 144, 145, 131, 143, 145, 146, 7, 20, 16, 27, 9,
1785
    21, 18, 28, 54, 68, 58, 70, 77, 82, 78, 83, 20, 45, 58, 70, 21, 46,
1786
    59, 71, 68, 121, 105, 123, 82, 122, 109, 124, 16, 58, 41, 66, 18, 59,
1787
    43, 67, 58, 105, 69, 106, 78, 109, 97, 110, 27, 70, 66, 100, 28, 71,
1788
    67, 101, 70, 123, 106, 128, 83, 124, 110, 130, 16, 27, 21, 29, 21,
1789
    29, 28, 31, 58, 70, 60, 72, 82, 86, 83, 87, 58, 70, 82, 86, 60, 72,
1790
    83, 87, 105, 123, 127, 128, 127, 128, 131, 132, 53, 80, 59, 81, 59,
1791
    81, 67, 85, 80, 111, 83, 112, 109, 116, 110, 117, 80, 111, 109, 116,
1792
    83, 112, 110, 117, 111, 144, 131, 145, 131, 145, 143, 146, 9, 21, 21,
1793
    29, 10, 22, 22, 30, 77, 82, 82, 86, 89, 90, 90, 91, 21, 46, 60, 72,
1794
    22, 47, 61, 73, 82, 122, 127, 128, 90, 126, 129, 130, 21, 60, 46, 72,
1795
    22, 61, 47, 73, 82, 127, 122, 128, 90, 129, 126, 130, 29, 72, 72,
1796
    102, 30, 73, 73, 103, 86, 128, 128, 141, 91, 130, 130, 142, 18, 28,
1797
    28, 31, 22, 30, 30, 32, 78, 83, 83, 87, 90, 91, 91, 92, 59, 71, 83,
1798
    87, 61, 73, 84, 88, 109, 124, 131, 132, 129, 130, 133, 134, 59, 83,
1799
    71, 87, 61, 84, 73, 88, 109, 131, 124, 132, 129, 133, 130, 134, 81,
1800
    112, 112, 118, 84, 113, 113, 119, 116, 145, 145, 147, 133, 146, 146,
1801
    148, 13, 52, 52, 75, 20, 58, 58, 82, 40, 65, 65, 98, 68, 105, 105,
1802
    127, 17, 57, 75, 108, 27, 66, 80, 109, 48, 70, 98, 111, 70, 106, 111,
1803
    131, 17, 75, 57, 108, 27, 80, 66, 109, 48, 98, 70, 111, 70, 111, 106,
1804
    131, 23, 76, 76, 114, 29, 81, 81, 115, 62, 100, 100, 116, 72, 112,
1805
    112, 133, 39, 57, 57, 76, 45, 70, 70, 86, 45, 70, 70, 100, 121, 123,
1806
    123, 128, 57, 76, 108, 114, 70, 100, 111, 116, 70, 86, 111, 116, 123,
1807
    128, 144, 145, 57, 108, 76, 114, 70, 111, 100, 116, 70, 111, 86, 116,
1808
    123, 144, 128, 145, 76, 114, 114, 137, 86, 116, 116, 138, 100, 116,
1809
    116, 138, 128, 145, 145, 149, 16, 53, 58, 80, 21, 59, 60, 83, 58, 80,
1810
    105, 111, 82, 109, 127, 131, 21, 59, 82, 109, 28, 67, 83, 110, 60,
1811
    83, 127, 131, 83, 110, 131, 143, 27, 80, 70, 111, 29, 81, 72, 112,
1812
    70, 111, 123, 144, 86, 116, 128, 145, 29, 81, 86, 116, 31, 85, 87,
1813
    117, 72, 112, 128, 145, 87, 117, 132, 146, 41, 59, 66, 81, 46, 71,
1814
    72, 87, 69, 83, 106, 112, 122, 124, 128, 132, 59, 79, 109, 115, 71,
1815
    101, 112, 117, 83, 91, 131, 133, 124, 130, 145, 146, 66, 109, 100,
1816
    116, 72, 112, 102, 118, 106, 131, 128, 145, 128, 145, 141, 147, 81,
1817
    115, 116, 138, 87, 117, 118, 139, 112, 133, 145, 149, 132, 146, 147,
1818
    150, 16, 58, 53, 80, 21, 60, 59, 83, 58, 105, 80, 111, 82, 127, 109,
1819
    131, 27, 70, 80, 111, 29, 72, 81, 112, 70, 123, 111, 144, 86, 128,
1820
    116, 145, 21, 82, 59, 109, 28, 83, 67, 110, 60, 127, 83, 131, 83,
1821
    131, 110, 143, 29, 86, 81, 116, 31, 87, 85, 117, 72, 128, 112, 145,
1822
    87, 132, 117, 146, 41, 66, 59, 81, 46, 72, 71, 87, 69, 106, 83, 112,
1823
    122, 128, 124, 132, 66, 100, 109, 116, 72, 102, 112, 118, 106, 128,
1824
    131, 145, 128, 141, 145, 147, 59, 109, 79, 115, 71, 112, 101, 117,
1825
    83, 131, 91, 133, 124, 145, 130, 146, 81, 116, 115, 138, 87, 118,
1826
    117, 139, 112, 145, 133, 149, 132, 147, 146, 150, 18, 59, 59, 81, 22,
1827
    61, 61, 84, 78, 109, 109, 116, 90, 129, 129, 133, 28, 71, 83, 112,
1828
    30, 73, 84, 113, 83, 124, 131, 145, 91, 130, 133, 146, 28, 83, 71,
1829
    112, 30, 84, 73, 113, 83, 131, 124, 145, 91, 133, 130, 146, 31, 87,
1830
    87, 118, 32, 88, 88, 119, 87, 132, 132, 147, 92, 134, 134, 148, 43,
1831
    67, 67, 85, 47, 73, 73, 88, 97, 110, 110, 117, 126, 130, 130, 134,
1832
    67, 101, 110, 117, 73, 103, 113, 119, 110, 130, 143, 146, 130, 142,
1833
    146, 148, 67, 110, 101, 117, 73, 113, 103, 119, 110, 143, 130, 146,
1834
    130, 146, 142, 148, 85, 117, 117, 139, 88, 119, 119, 140, 117, 146,
1835
    146, 150, 134, 148, 148, 151, 11, 14, 14, 18, 14, 18, 18, 22, 36, 41,
1836
    41, 49, 55, 59, 59, 61, 36, 41, 55, 59, 41, 49, 59, 61, 42, 46, 66,
1837
    71, 66, 71, 81, 84, 36, 55, 41, 59, 41, 59, 49, 61, 42, 66, 46, 71,
1838
    66, 81, 71, 84, 42, 66, 66, 81, 46, 71, 71, 84, 62, 72, 72, 87, 72,
1839
    87, 87, 92, 14, 18, 18, 24, 25, 28, 28, 30, 41, 49, 49, 63, 69, 71,
1840
    71, 73, 55, 59, 78, 79, 69, 71, 83, 84, 66, 71, 99, 101, 106, 107,
1841
    112, 113, 55, 78, 59, 79, 69, 83, 71, 84, 66, 99, 71, 101, 106, 112,
1842
    107, 113, 96, 109, 109, 115, 122, 124, 124, 125, 100, 112, 112, 117,
1843
    128, 132, 132, 134, 14, 18, 25, 28, 18, 24, 28, 30, 55, 59, 69, 71,
1844
    78, 79, 83, 84, 41, 49, 69, 71, 49, 63, 71, 73, 66, 71, 106, 107, 99,
1845
    101, 112, 113, 55, 78, 69, 83, 59, 79, 71, 84, 96, 109, 122, 124,
1846
    109, 115, 124, 125, 66, 99, 106, 112, 71, 101, 107, 113, 100, 112,
1847
    128, 132, 112, 117, 132, 134, 18, 22, 28, 30, 28, 30, 31, 32, 59, 61,
1848
    71, 73, 83, 84, 87, 88, 59, 61, 83, 84, 71, 73, 87, 88, 81, 84, 112,
1849
    113, 112, 113, 118, 119, 78, 90, 83, 91, 83, 91, 87, 92, 109, 129,
1850
    124, 130, 131, 133, 132, 134, 109, 129, 131, 133, 124, 130, 132, 134,
1851
    116, 133, 145, 146, 145, 146, 147, 148, 14, 25, 18, 28, 18, 28, 24,
1852
    30, 55, 69, 59, 71, 78, 83, 79, 84, 55, 69, 78, 83, 59, 71, 79, 84,
1853
    96, 122, 109, 124, 109, 124, 115, 125, 41, 69, 49, 71, 49, 71, 63,
1854
    73, 66, 106, 71, 107, 99, 112, 101, 113, 66, 106, 99, 112, 71, 107,
1855
    101, 113, 100, 128, 112, 132, 112, 132, 117, 134, 18, 28, 22, 30, 28,
1856
    31, 30, 32, 59, 71, 61, 73, 83, 87, 84, 88, 78, 83, 90, 91, 83, 87,
1857
    91, 92, 109, 124, 129, 130, 131, 132, 133, 134, 59, 83, 61, 84, 71,
1858
    87, 73, 88, 81, 112, 84, 113, 112, 118, 113, 119, 109, 131, 129, 133,
1859
    124, 132, 130, 134, 116, 145, 133, 146, 145, 147, 146, 148, 18, 28,
1860
    28, 31, 22, 30, 30, 32, 78, 83, 83, 87, 90, 91, 91, 92, 59, 71, 83,
1861
    87, 61, 73, 84, 88, 109, 124, 131, 132, 129, 130, 133, 134, 59, 83,
1862
    71, 87, 61, 84, 73, 88, 109, 131, 124, 132, 129, 133, 130, 134, 81,
1863
    112, 112, 118, 84, 113, 113, 119, 116, 145, 145, 147, 133, 146, 146,
1864
    148, 24, 30, 30, 32, 30, 32, 32, 33, 79, 84, 84, 88, 91, 92, 92, 93,
1865
    79, 84, 91, 92, 84, 88, 92, 93, 115, 125, 133, 134, 133, 134, 135,
1866
    136, 79, 91, 84, 92, 84, 92, 88, 93, 115, 133, 125, 134, 133, 135,
1867
    134, 136, 115, 133, 133, 135, 125, 134, 134, 136, 138, 149, 149, 150,
1868
    149, 150, 150, 151, 36, 55, 55, 78, 55, 78, 78, 90, 42, 66, 66, 99,
1869
    96, 109, 109, 129, 42, 66, 96, 109, 66, 99, 109, 129, 62, 72, 100,
1870
    112, 100, 112, 116, 133, 42, 96, 66, 109, 66, 109, 99, 129, 62, 100,
1871
    72, 112, 100, 116, 112, 133, 62, 100, 100, 116, 72, 112, 112, 133,
1872
    94, 102, 102, 118, 102, 118, 118, 135, 41, 59, 59, 79, 69, 83, 83,
1873
    91, 46, 71, 71, 101, 122, 124, 124, 130, 66, 81, 109, 115, 106, 112,
1874
    131, 133, 72, 87, 112, 117, 128, 132, 145, 146, 66, 109, 81, 115,
1875
    106, 131, 112, 133, 72, 112, 87, 117, 128, 145, 132, 146, 100, 116,
1876
    116, 138, 128, 145, 145, 149, 102, 118, 118, 139, 141, 147, 147, 150,
1877
    41, 59, 69, 83, 59, 79, 83, 91, 66, 81, 106, 112, 109, 115, 131, 133,
1878
    46, 71, 122, 124, 71, 101, 124, 130, 72, 87, 128, 132, 112, 117, 145,
1879
    146, 66, 109, 106, 131, 81, 115, 112, 133, 100, 116, 128, 145, 116,
1880
    138, 145, 149, 72, 112, 128, 145, 87, 117, 132, 146, 102, 118, 141,
1881
    147, 118, 139, 147, 150, 49, 61, 71, 84, 71, 84, 87, 92, 71, 84, 107,
1882
    113, 124, 125, 132, 134, 71, 84, 124, 125, 107, 113, 132, 134, 87,
1883
    92, 132, 134, 132, 134, 147, 148, 99, 129, 112, 133, 112, 133, 118,
1884
    135, 112, 133, 132, 146, 145, 149, 147, 150, 112, 133, 145, 149, 132,
1885
    146, 147, 150, 118, 135, 147, 150, 147, 150, 152, 153, 41, 69, 59,
1886
    83, 59, 83, 79, 91, 66, 106, 81, 112, 109, 131, 115, 133, 66, 106,
1887
    109, 131, 81, 112, 115, 133, 100, 128, 116, 145, 116, 145, 138, 149,
1888
    46, 122, 71, 124, 71, 124, 101, 130, 72, 128, 87, 132, 112, 145, 117,
1889
    146, 72, 128, 112, 145, 87, 132, 117, 146, 102, 141, 118, 147, 118,
1890
    147, 139, 150, 49, 71, 61, 84, 71, 87, 84, 92, 71, 107, 84, 113, 124,
1891
    132, 125, 134, 99, 112, 129, 133, 112, 118, 133, 135, 112, 132, 133,
1892
    146, 145, 147, 149, 150, 71, 124, 84, 125, 107, 132, 113, 134, 87,
1893
    132, 92, 134, 132, 147, 134, 148, 112, 145, 133, 149, 132, 147, 146,
1894
    150, 118, 147, 135, 150, 147, 152, 150, 153, 49, 71, 71, 87, 61, 84,
1895
    84, 92, 99, 112, 112, 118, 129, 133, 133, 135, 71, 107, 124, 132, 84,
1896
    113, 125, 134, 112, 132, 145, 147, 133, 146, 149, 150, 71, 124, 107,
1897
    132, 84, 125, 113, 134, 112, 145, 132, 147, 133, 149, 146, 150, 87,
1898
    132, 132, 147, 92, 134, 134, 148, 118, 147, 147, 152, 135, 150, 150,
1899
    153, 63, 73, 73, 88, 73, 88, 88, 93, 101, 113, 113, 119, 130, 134,
1900
    134, 136, 101, 113, 130, 134, 113, 119, 134, 136, 117, 134, 146, 148,
1901
    146, 148, 150, 151, 101, 130, 113, 134, 113, 134, 119, 136, 117, 146,
1902
    134, 148, 146, 150, 148, 151, 117, 146, 146, 150, 134, 148, 148, 151,
1903
    139, 150, 150, 153, 150, 153, 153, 154, 2, 12, 12, 38, 12, 38, 38,
1904
    44, 6, 15, 15, 40, 51, 56, 56, 68, 6, 15, 51, 56, 15, 40, 56, 68, 13,
1905
    20, 52, 58, 52, 58, 75, 82, 6, 51, 15, 56, 15, 56, 40, 68, 13, 52,
1906
    20, 58, 52, 75, 58, 82, 13, 52, 52, 75, 20, 58, 58, 82, 36, 55, 55,
1907
    78, 55, 78, 78, 90, 6, 15, 15, 40, 51, 56, 56, 68, 8, 17, 17, 42, 74,
1908
    75, 75, 96, 15, 26, 56, 65, 56, 65, 104, 105, 17, 27, 57, 66, 75, 80,
1909
    108, 109, 15, 56, 26, 65, 56, 104, 65, 105, 17, 57, 27, 66, 75, 108,
1910
    80, 109, 40, 65, 65, 98, 68, 105, 105, 127, 42, 66, 66, 99, 96, 109,
1911
    109, 129, 6, 15, 51, 56, 15, 40, 56, 68, 15, 26, 56, 65, 56, 65, 104,
1912
    105, 8, 17, 74, 75, 17, 42, 75, 96, 17, 27, 75, 80, 57, 66, 108, 109,
1913
    15, 56, 56, 104, 26, 65, 65, 105, 40, 65, 68, 105, 65, 98, 105, 127,
1914
    17, 57, 75, 108, 27, 66, 80, 109, 42, 66, 96, 109, 66, 99, 109, 129,
1915
    13, 20, 52, 58, 52, 58, 75, 82, 17, 27, 57, 66, 75, 80, 108, 109, 17,
1916
    27, 75, 80, 57, 66, 108, 109, 23, 29, 76, 81, 76, 81, 114, 115, 40,
1917
    68, 65, 105, 65, 105, 98, 127, 48, 70, 70, 106, 98, 111, 111, 131,
1918
    48, 70, 98, 111, 70, 106, 111, 131, 62, 72, 100, 112, 100, 112, 116,
1919
    133, 6, 51, 15, 56, 15, 56, 40, 68, 15, 56, 26, 65, 56, 104, 65, 105,
1920
    15, 56, 56, 104, 26, 65, 65, 105, 40, 68, 65, 105, 65, 105, 98, 127,
1921
    8, 74, 17, 75, 17, 75, 42, 96, 17, 75, 27, 80, 57, 108, 66, 109, 17,
1922
    75, 57, 108, 27, 80, 66, 109, 42, 96, 66, 109, 66, 109, 99, 129, 13,
1923
    52, 20, 58, 52, 75, 58, 82, 17, 57, 27, 66, 75, 108, 80, 109, 40, 65,
1924
    68, 105, 65, 98, 105, 127, 48, 70, 70, 106, 98, 111, 111, 131, 17,
1925
    75, 27, 80, 57, 108, 66, 109, 23, 76, 29, 81, 76, 114, 81, 115, 48,
1926
    98, 70, 111, 70, 111, 106, 131, 62, 100, 72, 112, 100, 116, 112, 133,
1927
    13, 52, 52, 75, 20, 58, 58, 82, 40, 65, 65, 98, 68, 105, 105, 127,
1928
    17, 57, 75, 108, 27, 66, 80, 109, 48, 70, 98, 111, 70, 106, 111, 131,
1929
    17, 75, 57, 108, 27, 80, 66, 109, 48, 98, 70, 111, 70, 111, 106, 131,
1930
    23, 76, 76, 114, 29, 81, 81, 115, 62, 100, 100, 116, 72, 112, 112,
1931
    133, 36, 55, 55, 78, 55, 78, 78, 90, 42, 66, 66, 99, 96, 109, 109,
1932
    129, 42, 66, 96, 109, 66, 99, 109, 129, 62, 72, 100, 112, 100, 112,
1933
    116, 133, 42, 96, 66, 109, 66, 109, 99, 129, 62, 100, 72, 112, 100,
1934
    116, 112, 133, 62, 100, 100, 116, 72, 112, 112, 133, 94, 102, 102,
1935
    118, 102, 118, 118, 135, 3, 19, 19, 44, 19, 44, 44, 120, 7, 20, 20,
1936
    45, 54, 68, 68, 121, 7, 20, 54, 68, 20, 45, 68, 121, 14, 25, 55, 69,
1937
    55, 69, 96, 122, 7, 54, 20, 68, 20, 68, 45, 121, 14, 55, 25, 69, 55,
1938
    96, 69, 122, 14, 55, 55, 96, 25, 69, 69, 122, 37, 64, 64, 97, 64, 97,
1939
    97, 126, 7, 20, 20, 45, 54, 68, 68, 121, 9, 21, 21, 46, 77, 82, 82,
1940
    122, 16, 27, 58, 70, 58, 70, 105, 123, 18, 28, 59, 71, 78, 83, 109,
1941
    124, 16, 58, 27, 70, 58, 105, 70, 123, 18, 59, 28, 71, 78, 109, 83,
1942
    124, 41, 66, 66, 100, 69, 106, 106, 128, 43, 67, 67, 101, 97, 110,
1943
    110, 130, 7, 20, 54, 68, 20, 45, 68, 121, 16, 27, 58, 70, 58, 70,
1944
    105, 123, 9, 21, 77, 82, 21, 46, 82, 122, 18, 28, 78, 83, 59, 71,
1945
    109, 124, 16, 58, 58, 105, 27, 70, 70, 123, 41, 66, 69, 106, 66, 100,
1946
    106, 128, 18, 59, 78, 109, 28, 71, 83, 124, 43, 67, 97, 110, 67, 101,
1947
    110, 130, 14, 25, 55, 69, 55, 69, 96, 122, 18, 28, 59, 71, 78, 83,
1948
    109, 124, 18, 28, 78, 83, 59, 71, 109, 124, 24, 30, 79, 84, 79, 84,
1949
    115, 125, 41, 69, 66, 106, 66, 106, 100, 128, 49, 71, 71, 107, 99,
1950
    112, 112, 132, 49, 71, 99, 112, 71, 107, 112, 132, 63, 73, 101, 113,
1951
    101, 113, 117, 134, 7, 54, 20, 68, 20, 68, 45, 121, 16, 58, 27, 70,
1952
    58, 105, 70, 123, 16, 58, 58, 105, 27, 70, 70, 123, 41, 69, 66, 106,
1953
    66, 106, 100, 128, 9, 77, 21, 82, 21, 82, 46, 122, 18, 78, 28, 83,
1954
    59, 109, 71, 124, 18, 78, 59, 109, 28, 83, 71, 124, 43, 97, 67, 110,
1955
    67, 110, 101, 130, 14, 55, 25, 69, 55, 96, 69, 122, 18, 59, 28, 71,
1956
    78, 109, 83, 124, 41, 66, 69, 106, 66, 100, 106, 128, 49, 71, 71,
1957
    107, 99, 112, 112, 132, 18, 78, 28, 83, 59, 109, 71, 124, 24, 79, 30,
1958
    84, 79, 115, 84, 125, 49, 99, 71, 112, 71, 112, 107, 132, 63, 101,
1959
    73, 113, 101, 117, 113, 134, 14, 55, 55, 96, 25, 69, 69, 122, 41, 66,
1960
    66, 100, 69, 106, 106, 128, 18, 59, 78, 109, 28, 71, 83, 124, 49, 71,
1961
    99, 112, 71, 107, 112, 132, 18, 78, 59, 109, 28, 83, 71, 124, 49, 99,
1962
    71, 112, 71, 112, 107, 132, 24, 79, 79, 115, 30, 84, 84, 125, 63,
1963
    101, 101, 117, 73, 113, 113, 134, 37, 64, 64, 97, 64, 97, 97, 126,
1964
    43, 67, 67, 101, 97, 110, 110, 130, 43, 67, 97, 110, 67, 101, 110,
1965
    130, 63, 73, 101, 113, 101, 113, 117, 134, 43, 97, 67, 110, 67, 110,
1966
    101, 130, 63, 101, 73, 113, 101, 117, 113, 134, 63, 101, 101, 117,
1967
    73, 113, 113, 134, 95, 103, 103, 119, 103, 119, 119, 136, 4, 13, 13,
1968
    39, 35, 40, 40, 45, 7, 16, 16, 41, 54, 58, 58, 69, 13, 17, 52, 57,
1969
    40, 48, 65, 70, 16, 21, 53, 59, 58, 60, 80, 83, 13, 52, 17, 57, 40,
1970
    65, 48, 70, 16, 53, 21, 59, 58, 80, 60, 83, 39, 57, 57, 76, 45, 70,
1971
    70, 86, 41, 59, 59, 79, 69, 83, 83, 91, 7, 16, 16, 41, 54, 58, 58,
1972
    69, 9, 18, 18, 43, 77, 78, 78, 97, 20, 27, 58, 66, 68, 70, 105, 106,
1973
    21, 28, 59, 67, 82, 83, 109, 110, 20, 58, 27, 66, 68, 105, 70, 106,
1974
    21, 59, 28, 67, 82, 109, 83, 110, 45, 70, 70, 100, 121, 123, 123,
1975
    128, 46, 71, 71, 101, 122, 124, 124, 130, 13, 17, 52, 57, 40, 48, 65,
1976
    70, 20, 27, 58, 66, 68, 70, 105, 106, 17, 23, 75, 76, 48, 62, 98,
1977
    100, 27, 29, 80, 81, 70, 72, 111, 112, 52, 75, 75, 108, 65, 98, 98,
1978
    111, 58, 80, 82, 109, 105, 111, 127, 131, 57, 76, 108, 114, 70, 100,
1979
    111, 116, 66, 81, 109, 115, 106, 112, 131, 133, 16, 21, 53, 59, 58,
1980
    60, 80, 83, 21, 28, 59, 67, 82, 83, 109, 110, 27, 29, 80, 81, 70, 72,
1981
    111, 112, 29, 31, 81, 85, 86, 87, 116, 117, 58, 82, 80, 109, 105,
1982
    127, 111, 131, 60, 83, 83, 110, 127, 131, 131, 143, 70, 86, 111, 116,
1983
    123, 128, 144, 145, 72, 87, 112, 117, 128, 132, 145, 146, 13, 52, 17,
1984
    57, 40, 65, 48, 70, 20, 58, 27, 66, 68, 105, 70, 106, 52, 75, 75,
1985
    108, 65, 98, 98, 111, 58, 82, 80, 109, 105, 127, 111, 131, 17, 75,
1986
    23, 76, 48, 98, 62, 100, 27, 80, 29, 81, 70, 111, 72, 112, 57, 108,
1987
    76, 114, 70, 111, 100, 116, 66, 109, 81, 115, 106, 131, 112, 133, 16,
1988
    53, 21, 59, 58, 80, 60, 83, 21, 59, 28, 67, 82, 109, 83, 110, 58, 80,
1989
    82, 109, 105, 111, 127, 131, 60, 83, 83, 110, 127, 131, 131, 143, 27,
1990
    80, 29, 81, 70, 111, 72, 112, 29, 81, 31, 85, 86, 116, 87, 117, 70,
1991
    111, 86, 116, 123, 144, 128, 145, 72, 112, 87, 117, 128, 145, 132,
1992
    146, 39, 57, 57, 76, 45, 70, 70, 86, 45, 70, 70, 100, 121, 123, 123,
1993
    128, 57, 76, 108, 114, 70, 100, 111, 116, 70, 86, 111, 116, 123, 128,
1994
    144, 145, 57, 108, 76, 114, 70, 111, 100, 116, 70, 111, 86, 116, 123,
1995
    144, 128, 145, 76, 114, 114, 137, 86, 116, 116, 138, 100, 116, 116,
1996
    138, 128, 145, 145, 149, 41, 59, 59, 79, 69, 83, 83, 91, 46, 71, 71,
1997
    101, 122, 124, 124, 130, 66, 81, 109, 115, 106, 112, 131, 133, 72,
1998
    87, 112, 117, 128, 132, 145, 146, 66, 109, 81, 115, 106, 131, 112,
1999
    133, 72, 112, 87, 117, 128, 145, 132, 146, 100, 116, 116, 138, 128,
2000
    145, 145, 149, 102, 118, 118, 139, 141, 147, 147, 150, 7, 20, 20, 45,
2001
    54, 68, 68, 121, 9, 21, 21, 46, 77, 82, 82, 122, 16, 27, 58, 70, 58,
2002
    70, 105, 123, 18, 28, 59, 71, 78, 83, 109, 124, 16, 58, 27, 70, 58,
2003
    105, 70, 123, 18, 59, 28, 71, 78, 109, 83, 124, 41, 66, 66, 100, 69,
2004
    106, 106, 128, 43, 67, 67, 101, 97, 110, 110, 130, 9, 21, 21, 46, 77,
2005
    82, 82, 122, 10, 22, 22, 47, 89, 90, 90, 126, 21, 29, 60, 72, 82, 86,
2006
    127, 128, 22, 30, 61, 73, 90, 91, 129, 130, 21, 60, 29, 72, 82, 127,
2007
    86, 128, 22, 61, 30, 73, 90, 129, 91, 130, 46, 72, 72, 102, 122, 128,
2008
    128, 141, 47, 73, 73, 103, 126, 130, 130, 142, 16, 27, 58, 70, 58,
2009
    70, 105, 123, 21, 29, 60, 72, 82, 86, 127, 128, 21, 29, 82, 86, 60,
2010
    72, 127, 128, 28, 31, 83, 87, 83, 87, 131, 132, 53, 80, 80, 111, 80,
2011
    111, 111, 144, 59, 81, 83, 112, 109, 116, 131, 145, 59, 81, 109, 116,
2012
    83, 112, 131, 145, 67, 85, 110, 117, 110, 117, 143, 146, 18, 28, 59,
2013
    71, 78, 83, 109, 124, 22, 30, 61, 73, 90, 91, 129, 130, 28, 31, 83,
2014
    87, 83, 87, 131, 132, 30, 32, 84, 88, 91, 92, 133, 134, 59, 83, 81,
2015
    112, 109, 131, 116, 145, 61, 84, 84, 113, 129, 133, 133, 146, 71, 87,
2016
    112, 118, 124, 132, 145, 147, 73, 88, 113, 119, 130, 134, 146, 148,
2017
    16, 58, 27, 70, 58, 105, 70, 123, 21, 60, 29, 72, 82, 127, 86, 128,
2018
    53, 80, 80, 111, 80, 111, 111, 144, 59, 83, 81, 112, 109, 131, 116,
2019
    145, 21, 82, 29, 86, 60, 127, 72, 128, 28, 83, 31, 87, 83, 131, 87,
2020
    132, 59, 109, 81, 116, 83, 131, 112, 145, 67, 110, 85, 117, 110, 143,
2021
    117, 146, 18, 59, 28, 71, 78, 109, 83, 124, 22, 61, 30, 73, 90, 129,
2022
    91, 130, 59, 81, 83, 112, 109, 116, 131, 145, 61, 84, 84, 113, 129,
2023
    133, 133, 146, 28, 83, 31, 87, 83, 131, 87, 132, 30, 84, 32, 88, 91,
2024
    133, 92, 134, 71, 112, 87, 118, 124, 145, 132, 147, 73, 113, 88, 119,
2025
    130, 146, 134, 148, 41, 66, 66, 100, 69, 106, 106, 128, 46, 72, 72,
2026
    102, 122, 128, 128, 141, 59, 81, 109, 116, 83, 112, 131, 145, 71, 87,
2027
    112, 118, 124, 132, 145, 147, 59, 109, 81, 116, 83, 131, 112, 145,
2028
    71, 112, 87, 118, 124, 145, 132, 147, 79, 115, 115, 138, 91, 133,
2029
    133, 149, 101, 117, 117, 139, 130, 146, 146, 150, 43, 67, 67, 101,
2030
    97, 110, 110, 130, 47, 73, 73, 103, 126, 130, 130, 142, 67, 85, 110,
2031
    117, 110, 117, 143, 146, 73, 88, 113, 119, 130, 134, 146, 148, 67,
2032
    110, 85, 117, 110, 143, 117, 146, 73, 113, 88, 119, 130, 146, 134,
2033
    148, 101, 117, 117, 139, 130, 146, 146, 150, 103, 119, 119, 140, 142,
2034
    148, 148, 151, 4, 13, 35, 40, 13, 39, 40, 45, 13, 17, 40, 48, 52, 57,
2035
    65, 70, 7, 16, 54, 58, 16, 41, 58, 69, 16, 21, 58, 60, 53, 59, 80,
2036
    83, 13, 52, 40, 65, 17, 57, 48, 70, 39, 57, 45, 70, 57, 76, 70, 86,
2037
    16, 53, 58, 80, 21, 59, 60, 83, 41, 59, 69, 83, 59, 79, 83, 91, 13,
2038
    17, 40, 48, 52, 57, 65, 70, 17, 23, 48, 62, 75, 76, 98, 100, 20, 27,
2039
    68, 70, 58, 66, 105, 106, 27, 29, 70, 72, 80, 81, 111, 112, 52, 75,
2040
    65, 98, 75, 108, 98, 111, 57, 76, 70, 100, 108, 114, 111, 116, 58,
2041
    80, 105, 111, 82, 109, 127, 131, 66, 81, 106, 112, 109, 115, 131,
2042
    133, 7, 16, 54, 58, 16, 41, 58, 69, 20, 27, 68, 70, 58, 66, 105, 106,
2043
    9, 18, 77, 78, 18, 43, 78, 97, 21, 28, 82, 83, 59, 67, 109, 110, 20,
2044
    58, 68, 105, 27, 66, 70, 106, 45, 70, 121, 123, 70, 100, 123, 128,
2045
    21, 59, 82, 109, 28, 67, 83, 110, 46, 71, 122, 124, 71, 101, 124,
2046
    130, 16, 21, 58, 60, 53, 59, 80, 83, 27, 29, 70, 72, 80, 81, 111,
2047
    112, 21, 28, 82, 83, 59, 67, 109, 110, 29, 31, 86, 87, 81, 85, 116,
2048
    117, 58, 82, 105, 127, 80, 109, 111, 131, 70, 86, 123, 128, 111, 116,
2049
    144, 145, 60, 83, 127, 131, 83, 110, 131, 143, 72, 87, 128, 132, 112,
2050
    117, 145, 146, 13, 52, 40, 65, 17, 57, 48, 70, 52, 75, 65, 98, 75,
2051
    108, 98, 111, 20, 58, 68, 105, 27, 66, 70, 106, 58, 82, 105, 127, 80,
2052
    109, 111, 131, 17, 75, 48, 98, 23, 76, 62, 100, 57, 108, 70, 111, 76,
2053
    114, 100, 116, 27, 80, 70, 111, 29, 81, 72, 112, 66, 109, 106, 131,
2054
    81, 115, 112, 133, 39, 57, 45, 70, 57, 76, 70, 86, 57, 76, 70, 100,
2055
    108, 114, 111, 116, 45, 70, 121, 123, 70, 100, 123, 128, 70, 86, 123,
2056
    128, 111, 116, 144, 145, 57, 108, 70, 111, 76, 114, 100, 116, 76,
2057
    114, 86, 116, 114, 137, 116, 138, 70, 111, 123, 144, 86, 116, 128,
2058
    145, 100, 116, 128, 145, 116, 138, 145, 149, 16, 53, 58, 80, 21, 59,
2059
    60, 83, 58, 80, 105, 111, 82, 109, 127, 131, 21, 59, 82, 109, 28, 67,
2060
    83, 110, 60, 83, 127, 131, 83, 110, 131, 143, 27, 80, 70, 111, 29,
2061
    81, 72, 112, 70, 111, 123, 144, 86, 116, 128, 145, 29, 81, 86, 116,
2062
    31, 85, 87, 117, 72, 112, 128, 145, 87, 117, 132, 146, 41, 59, 69,
2063
    83, 59, 79, 83, 91, 66, 81, 106, 112, 109, 115, 131, 133, 46, 71,
2064
    122, 124, 71, 101, 124, 130, 72, 87, 128, 132, 112, 117, 145, 146,
2065
    66, 109, 106, 131, 81, 115, 112, 133, 100, 116, 128, 145, 116, 138,
2066
    145, 149, 72, 112, 128, 145, 87, 117, 132, 146, 102, 118, 141, 147,
2067
    118, 139, 147, 150, 7, 20, 54, 68, 20, 45, 68, 121, 16, 27, 58, 70,
2068
    58, 70, 105, 123, 9, 21, 77, 82, 21, 46, 82, 122, 18, 28, 78, 83, 59,
2069
    71, 109, 124, 16, 58, 58, 105, 27, 70, 70, 123, 41, 66, 69, 106, 66,
2070
    100, 106, 128, 18, 59, 78, 109, 28, 71, 83, 124, 43, 67, 97, 110, 67,
2071
    101, 110, 130, 16, 27, 58, 70, 58, 70, 105, 123, 21, 29, 60, 72, 82,
2072
    86, 127, 128, 21, 29, 82, 86, 60, 72, 127, 128, 28, 31, 83, 87, 83,
2073
    87, 131, 132, 53, 80, 80, 111, 80, 111, 111, 144, 59, 81, 83, 112,
2074
    109, 116, 131, 145, 59, 81, 109, 116, 83, 112, 131, 145, 67, 85, 110,
2075
    117, 110, 117, 143, 146, 9, 21, 77, 82, 21, 46, 82, 122, 21, 29, 82,
2076
    86, 60, 72, 127, 128, 10, 22, 89, 90, 22, 47, 90, 126, 22, 30, 90,
2077
    91, 61, 73, 129, 130, 21, 60, 82, 127, 29, 72, 86, 128, 46, 72, 122,
2078
    128, 72, 102, 128, 141, 22, 61, 90, 129, 30, 73, 91, 130, 47, 73,
2079
    126, 130, 73, 103, 130, 142, 18, 28, 78, 83, 59, 71, 109, 124, 28,
2080
    31, 83, 87, 83, 87, 131, 132, 22, 30, 90, 91, 61, 73, 129, 130, 30,
2081
    32, 91, 92, 84, 88, 133, 134, 59, 83, 109, 131, 81, 112, 116, 145,
2082
    71, 87, 124, 132, 112, 118, 145, 147, 61, 84, 129, 133, 84, 113, 133,
2083
    146, 73, 88, 130, 134, 113, 119, 146, 148, 16, 58, 58, 105, 27, 70,
2084
    70, 123, 53, 80, 80, 111, 80, 111, 111, 144, 21, 60, 82, 127, 29, 72,
2085
    86, 128, 59, 83, 109, 131, 81, 112, 116, 145, 21, 82, 60, 127, 29,
2086
    86, 72, 128, 59, 109, 83, 131, 81, 116, 112, 145, 28, 83, 83, 131,
2087
    31, 87, 87, 132, 67, 110, 110, 143, 85, 117, 117, 146, 41, 66, 69,
2088
    106, 66, 100, 106, 128, 59, 81, 83, 112, 109, 116, 131, 145, 46, 72,
2089
    122, 128, 72, 102, 128, 141, 71, 87, 124, 132, 112, 118, 145, 147,
2090
    59, 109, 83, 131, 81, 116, 112, 145, 79, 115, 91, 133, 115, 138, 133,
2091
    149, 71, 112, 124, 145, 87, 118, 132, 147, 101, 117, 130, 146, 117,
2092
    139, 146, 150, 18, 59, 78, 109, 28, 71, 83, 124, 59, 81, 109, 116,
2093
    83, 112, 131, 145, 22, 61, 90, 129, 30, 73, 91, 130, 61, 84, 129,
2094
    133, 84, 113, 133, 146, 28, 83, 83, 131, 31, 87, 87, 132, 71, 112,
2095
    124, 145, 87, 118, 132, 147, 30, 84, 91, 133, 32, 88, 92, 134, 73,
2096
    113, 130, 146, 88, 119, 134, 148, 43, 67, 97, 110, 67, 101, 110, 130,
2097
    67, 85, 110, 117, 110, 117, 143, 146, 47, 73, 126, 130, 73, 103, 130,
2098
    142, 73, 88, 130, 134, 113, 119, 146, 148, 67, 110, 110, 143, 85,
2099
    117, 117, 146, 101, 117, 130, 146, 117, 139, 146, 150, 73, 113, 130,
2100
    146, 88, 119, 134, 148, 103, 119, 142, 148, 119, 140, 148, 151, 11,
2101
    14, 36, 41, 36, 41, 42, 46, 14, 18, 41, 49, 55, 59, 66, 71, 14, 18,
2102
    55, 59, 41, 49, 66, 71, 18, 22, 59, 61, 59, 61, 81, 84, 36, 55, 42,
2103
    66, 42, 66, 62, 72, 41, 59, 46, 71, 66, 81, 72, 87, 41, 59, 66, 81,
2104
    46, 71, 72, 87, 49, 61, 71, 84, 71, 84, 87, 92, 14, 18, 41, 49, 55,
2105
    59, 66, 71, 18, 24, 49, 63, 78, 79, 99, 101, 25, 28, 69, 71, 69, 71,
2106
    106, 107, 28, 30, 71, 73, 83, 84, 112, 113, 55, 78, 66, 99, 96, 109,
2107
    100, 112, 59, 79, 71, 101, 109, 115, 112, 117, 69, 83, 106, 112, 122,
2108
    124, 128, 132, 71, 84, 107, 113, 124, 125, 132, 134, 14, 18, 55, 59,
2109
    41, 49, 66, 71, 25, 28, 69, 71, 69, 71, 106, 107, 18, 24, 78, 79, 49,
2110
    63, 99, 101, 28, 30, 83, 84, 71, 73, 112, 113, 55, 78, 96, 109, 66,
2111
    99, 100, 112, 69, 83, 122, 124, 106, 112, 128, 132, 59, 79, 109, 115,
2112
    71, 101, 112, 117, 71, 84, 124, 125, 107, 113, 132, 134, 18, 22, 59,
2113
    61, 59, 61, 81, 84, 28, 30, 71, 73, 83, 84, 112, 113, 28, 30, 83, 84,
2114
    71, 73, 112, 113, 31, 32, 87, 88, 87, 88, 118, 119, 78, 90, 109, 129,
2115
    109, 129, 116, 133, 83, 91, 124, 130, 131, 133, 145, 146, 83, 91,
2116
    131, 133, 124, 130, 145, 146, 87, 92, 132, 134, 132, 134, 147, 148,
2117
    36, 55, 42, 66, 42, 66, 62, 72, 55, 78, 66, 99, 96, 109, 100, 112,
2118
    55, 78, 96, 109, 66, 99, 100, 112, 78, 90, 109, 129, 109, 129, 116,
2119
    133, 42, 96, 62, 100, 62, 100, 94, 102, 66, 109, 72, 112, 100, 116,
2120
    102, 118, 66, 109, 100, 116, 72, 112, 102, 118, 99, 129, 112, 133,
2121
    112, 133, 118, 135, 41, 59, 46, 71, 66, 81, 72, 87, 59, 79, 71, 101,
2122
    109, 115, 112, 117, 69, 83, 122, 124, 106, 112, 128, 132, 83, 91,
2123
    124, 130, 131, 133, 145, 146, 66, 109, 72, 112, 100, 116, 102, 118,
2124
    81, 115, 87, 117, 116, 138, 118, 139, 106, 131, 128, 145, 128, 145,
2125
    141, 147, 112, 133, 132, 146, 145, 149, 147, 150, 41, 59, 66, 81, 46,
2126
    71, 72, 87, 69, 83, 106, 112, 122, 124, 128, 132, 59, 79, 109, 115,
2127
    71, 101, 112, 117, 83, 91, 131, 133, 124, 130, 145, 146, 66, 109,
2128
    100, 116, 72, 112, 102, 118, 106, 131, 128, 145, 128, 145, 141, 147,
2129
    81, 115, 116, 138, 87, 117, 118, 139, 112, 133, 145, 149, 132, 146,
2130
    147, 150, 49, 61, 71, 84, 71, 84, 87, 92, 71, 84, 107, 113, 124, 125,
2131
    132, 134, 71, 84, 124, 125, 107, 113, 132, 134, 87, 92, 132, 134,
2132
    132, 134, 147, 148, 99, 129, 112, 133, 112, 133, 118, 135, 112, 133,
2133
    132, 146, 145, 149, 147, 150, 112, 133, 145, 149, 132, 146, 147, 150,
2134
    118, 135, 147, 150, 147, 150, 152, 153, 14, 25, 55, 69, 55, 69, 96,
2135
    122, 18, 28, 59, 71, 78, 83, 109, 124, 18, 28, 78, 83, 59, 71, 109,
2136
    124, 24, 30, 79, 84, 79, 84, 115, 125, 41, 69, 66, 106, 66, 106, 100,
2137
    128, 49, 71, 71, 107, 99, 112, 112, 132, 49, 71, 99, 112, 71, 107,
2138
    112, 132, 63, 73, 101, 113, 101, 113, 117, 134, 18, 28, 59, 71, 78,
2139
    83, 109, 124, 22, 30, 61, 73, 90, 91, 129, 130, 28, 31, 83, 87, 83,
2140
    87, 131, 132, 30, 32, 84, 88, 91, 92, 133, 134, 59, 83, 81, 112, 109,
2141
    131, 116, 145, 61, 84, 84, 113, 129, 133, 133, 146, 71, 87, 112, 118,
2142
    124, 132, 145, 147, 73, 88, 113, 119, 130, 134, 146, 148, 18, 28, 78,
2143
    83, 59, 71, 109, 124, 28, 31, 83, 87, 83, 87, 131, 132, 22, 30, 90,
2144
    91, 61, 73, 129, 130, 30, 32, 91, 92, 84, 88, 133, 134, 59, 83, 109,
2145
    131, 81, 112, 116, 145, 71, 87, 124, 132, 112, 118, 145, 147, 61, 84,
2146
    129, 133, 84, 113, 133, 146, 73, 88, 130, 134, 113, 119, 146, 148,
2147
    24, 30, 79, 84, 79, 84, 115, 125, 30, 32, 84, 88, 91, 92, 133, 134,
2148
    30, 32, 91, 92, 84, 88, 133, 134, 32, 33, 92, 93, 92, 93, 135, 136,
2149
    79, 91, 115, 133, 115, 133, 138, 149, 84, 92, 125, 134, 133, 135,
2150
    149, 150, 84, 92, 133, 135, 125, 134, 149, 150, 88, 93, 134, 136,
2151
    134, 136, 150, 151, 41, 69, 66, 106, 66, 106, 100, 128, 59, 83, 81,
2152
    112, 109, 131, 116, 145, 59, 83, 109, 131, 81, 112, 116, 145, 79, 91,
2153
    115, 133, 115, 133, 138, 149, 46, 122, 72, 128, 72, 128, 102, 141,
2154
    71, 124, 87, 132, 112, 145, 118, 147, 71, 124, 112, 145, 87, 132,
2155
    118, 147, 101, 130, 117, 146, 117, 146, 139, 150, 49, 71, 71, 107,
2156
    99, 112, 112, 132, 61, 84, 84, 113, 129, 133, 133, 146, 71, 87, 124,
2157
    132, 112, 118, 145, 147, 84, 92, 125, 134, 133, 135, 149, 150, 71,
2158
    124, 87, 132, 112, 145, 118, 147, 84, 125, 92, 134, 133, 149, 135,
2159
    150, 107, 132, 132, 147, 132, 147, 147, 152, 113, 134, 134, 148, 146,
2160
    150, 150, 153, 49, 71, 99, 112, 71, 107, 112, 132, 71, 87, 112, 118,
2161
    124, 132, 145, 147, 61, 84, 129, 133, 84, 113, 133, 146, 84, 92, 133,
2162
    135, 125, 134, 149, 150, 71, 124, 112, 145, 87, 132, 118, 147, 107,
2163
    132, 132, 147, 132, 147, 147, 152, 84, 125, 133, 149, 92, 134, 135,
2164
    150, 113, 134, 146, 150, 134, 148, 150, 153, 63, 73, 101, 113, 101,
2165
    113, 117, 134, 73, 88, 113, 119, 130, 134, 146, 148, 73, 88, 130,
2166
    134, 113, 119, 146, 148, 88, 93, 134, 136, 134, 136, 150, 151, 101,
2167
    130, 117, 146, 117, 146, 139, 150, 113, 134, 134, 148, 146, 150, 150,
2168
    153, 113, 134, 146, 150, 134, 148, 150, 153, 119, 136, 148, 151, 148,
2169
    151, 153, 154, 4, 35, 13, 40, 13, 40, 39, 45, 13, 40, 17, 48, 52, 65,
2170
    57, 70, 13, 40, 52, 65, 17, 48, 57, 70, 39, 45, 57, 70, 57, 70, 76,
2171
    86, 7, 54, 16, 58, 16, 58, 41, 69, 16, 58, 21, 60, 53, 80, 59, 83,
2172
    16, 58, 53, 80, 21, 60, 59, 83, 41, 69, 59, 83, 59, 83, 79, 91, 13,
2173
    40, 17, 48, 52, 65, 57, 70, 17, 48, 23, 62, 75, 98, 76, 100, 52, 65,
2174
    75, 98, 75, 98, 108, 111, 57, 70, 76, 100, 108, 111, 114, 116, 20,
2175
    68, 27, 70, 58, 105, 66, 106, 27, 70, 29, 72, 80, 111, 81, 112, 58,
2176
    105, 80, 111, 82, 127, 109, 131, 66, 106, 81, 112, 109, 131, 115,
2177
    133, 13, 40, 52, 65, 17, 48, 57, 70, 52, 65, 75, 98, 75, 98, 108,
2178
    111, 17, 48, 75, 98, 23, 62, 76, 100, 57, 70, 108, 111, 76, 100, 114,
2179
    116, 20, 68, 58, 105, 27, 70, 66, 106, 58, 105, 82, 127, 80, 111,
2180
    109, 131, 27, 70, 80, 111, 29, 72, 81, 112, 66, 106, 109, 131, 81,
2181
    112, 115, 133, 39, 45, 57, 70, 57, 70, 76, 86, 57, 70, 76, 100, 108,
2182
    111, 114, 116, 57, 70, 108, 111, 76, 100, 114, 116, 76, 86, 114, 116,
2183
    114, 116, 137, 138, 45, 121, 70, 123, 70, 123, 100, 128, 70, 123, 86,
2184
    128, 111, 144, 116, 145, 70, 123, 111, 144, 86, 128, 116, 145, 100,
2185
    128, 116, 145, 116, 145, 138, 149, 7, 54, 16, 58, 16, 58, 41, 69, 20,
2186
    68, 27, 70, 58, 105, 66, 106, 20, 68, 58, 105, 27, 70, 66, 106, 45,
2187
    121, 70, 123, 70, 123, 100, 128, 9, 77, 18, 78, 18, 78, 43, 97, 21,
2188
    82, 28, 83, 59, 109, 67, 110, 21, 82, 59, 109, 28, 83, 67, 110, 46,
2189
    122, 71, 124, 71, 124, 101, 130, 16, 58, 21, 60, 53, 80, 59, 83, 27,
2190
    70, 29, 72, 80, 111, 81, 112, 58, 105, 82, 127, 80, 111, 109, 131,
2191
    70, 123, 86, 128, 111, 144, 116, 145, 21, 82, 28, 83, 59, 109, 67,
2192
    110, 29, 86, 31, 87, 81, 116, 85, 117, 60, 127, 83, 131, 83, 131,
2193
    110, 143, 72, 128, 87, 132, 112, 145, 117, 146, 16, 58, 53, 80, 21,
2194
    60, 59, 83, 58, 105, 80, 111, 82, 127, 109, 131, 27, 70, 80, 111, 29,
2195
    72, 81, 112, 70, 123, 111, 144, 86, 128, 116, 145, 21, 82, 59, 109,
2196
    28, 83, 67, 110, 60, 127, 83, 131, 83, 131, 110, 143, 29, 86, 81,
2197
    116, 31, 87, 85, 117, 72, 128, 112, 145, 87, 132, 117, 146, 41, 69,
2198
    59, 83, 59, 83, 79, 91, 66, 106, 81, 112, 109, 131, 115, 133, 66,
2199
    106, 109, 131, 81, 112, 115, 133, 100, 128, 116, 145, 116, 145, 138,
2200
    149, 46, 122, 71, 124, 71, 124, 101, 130, 72, 128, 87, 132, 112, 145,
2201
    117, 146, 72, 128, 112, 145, 87, 132, 117, 146, 102, 141, 118, 147,
2202
    118, 147, 139, 150, 7, 54, 20, 68, 20, 68, 45, 121, 16, 58, 27, 70,
2203
    58, 105, 70, 123, 16, 58, 58, 105, 27, 70, 70, 123, 41, 69, 66, 106,
2204
    66, 106, 100, 128, 9, 77, 21, 82, 21, 82, 46, 122, 18, 78, 28, 83,
2205
    59, 109, 71, 124, 18, 78, 59, 109, 28, 83, 71, 124, 43, 97, 67, 110,
2206
    67, 110, 101, 130, 16, 58, 27, 70, 58, 105, 70, 123, 21, 60, 29, 72,
2207
    82, 127, 86, 128, 53, 80, 80, 111, 80, 111, 111, 144, 59, 83, 81,
2208
    112, 109, 131, 116, 145, 21, 82, 29, 86, 60, 127, 72, 128, 28, 83,
2209
    31, 87, 83, 131, 87, 132, 59, 109, 81, 116, 83, 131, 112, 145, 67,
2210
    110, 85, 117, 110, 143, 117, 146, 16, 58, 58, 105, 27, 70, 70, 123,
2211
    53, 80, 80, 111, 80, 111, 111, 144, 21, 60, 82, 127, 29, 72, 86, 128,
2212
    59, 83, 109, 131, 81, 112, 116, 145, 21, 82, 60, 127, 29, 86, 72,
2213
    128, 59, 109, 83, 131, 81, 116, 112, 145, 28, 83, 83, 131, 31, 87,
2214
    87, 132, 67, 110, 110, 143, 85, 117, 117, 146, 41, 69, 66, 106, 66,
2215
    106, 100, 128, 59, 83, 81, 112, 109, 131, 116, 145, 59, 83, 109, 131,
2216
    81, 112, 116, 145, 79, 91, 115, 133, 115, 133, 138, 149, 46, 122, 72,
2217
    128, 72, 128, 102, 141, 71, 124, 87, 132, 112, 145, 118, 147, 71,
2218
    124, 112, 145, 87, 132, 118, 147, 101, 130, 117, 146, 117, 146, 139,
2219
    150, 9, 77, 21, 82, 21, 82, 46, 122, 21, 82, 29, 86, 60, 127, 72,
2220
    128, 21, 82, 60, 127, 29, 86, 72, 128, 46, 122, 72, 128, 72, 128,
2221
    102, 141, 10, 89, 22, 90, 22, 90, 47, 126, 22, 90, 30, 91, 61, 129,
2222
    73, 130, 22, 90, 61, 129, 30, 91, 73, 130, 47, 126, 73, 130, 73, 130,
2223
    103, 142, 18, 78, 28, 83, 59, 109, 71, 124, 28, 83, 31, 87, 83, 131,
2224
    87, 132, 59, 109, 83, 131, 81, 116, 112, 145, 71, 124, 87, 132, 112,
2225
    145, 118, 147, 22, 90, 30, 91, 61, 129, 73, 130, 30, 91, 32, 92, 84,
2226
    133, 88, 134, 61, 129, 84, 133, 84, 133, 113, 146, 73, 130, 88, 134,
2227
    113, 146, 119, 148, 18, 78, 59, 109, 28, 83, 71, 124, 59, 109, 81,
2228
    116, 83, 131, 112, 145, 28, 83, 83, 131, 31, 87, 87, 132, 71, 124,
2229
    112, 145, 87, 132, 118, 147, 22, 90, 61, 129, 30, 91, 73, 130, 61,
2230
    129, 84, 133, 84, 133, 113, 146, 30, 91, 84, 133, 32, 92, 88, 134,
2231
    73, 130, 113, 146, 88, 134, 119, 148, 43, 97, 67, 110, 67, 110, 101,
2232
    130, 67, 110, 85, 117, 110, 143, 117, 146, 67, 110, 110, 143, 85,
2233
    117, 117, 146, 101, 130, 117, 146, 117, 146, 139, 150, 47, 126, 73,
2234
    130, 73, 130, 103, 142, 73, 130, 88, 134, 113, 146, 119, 148, 73,
2235
    130, 113, 146, 88, 134, 119, 148, 103, 142, 119, 148, 119, 148, 140,
2236
    151, 11, 36, 14, 41, 36, 42, 41, 46, 14, 41, 18, 49, 55, 66, 59, 71,
2237
    36, 42, 55, 66, 42, 62, 66, 72, 41, 46, 59, 71, 66, 72, 81, 87, 14,
2238
    55, 18, 59, 41, 66, 49, 71, 18, 59, 22, 61, 59, 81, 61, 84, 41, 66,
2239
    59, 81, 46, 72, 71, 87, 49, 71, 61, 84, 71, 87, 84, 92, 14, 41, 18,
2240
    49, 55, 66, 59, 71, 18, 49, 24, 63, 78, 99, 79, 101, 55, 66, 78, 99,
2241
    96, 100, 109, 112, 59, 71, 79, 101, 109, 112, 115, 117, 25, 69, 28,
2242
    71, 69, 106, 71, 107, 28, 71, 30, 73, 83, 112, 84, 113, 69, 106, 83,
2243
    112, 122, 128, 124, 132, 71, 107, 84, 113, 124, 132, 125, 134, 36,
2244
    42, 55, 66, 42, 62, 66, 72, 55, 66, 78, 99, 96, 100, 109, 112, 42,
2245
    62, 96, 100, 62, 94, 100, 102, 66, 72, 109, 112, 100, 102, 116, 118,
2246
    55, 96, 78, 109, 66, 100, 99, 112, 78, 109, 90, 129, 109, 116, 129,
2247
    133, 66, 100, 109, 116, 72, 102, 112, 118, 99, 112, 129, 133, 112,
2248
    118, 133, 135, 41, 46, 59, 71, 66, 72, 81, 87, 59, 71, 79, 101, 109,
2249
    112, 115, 117, 66, 72, 109, 112, 100, 102, 116, 118, 81, 87, 115,
2250
    117, 116, 118, 138, 139, 69, 122, 83, 124, 106, 128, 112, 132, 83,
2251
    124, 91, 130, 131, 145, 133, 146, 106, 128, 131, 145, 128, 141, 145,
2252
    147, 112, 132, 133, 146, 145, 147, 149, 150, 14, 55, 18, 59, 41, 66,
2253
    49, 71, 25, 69, 28, 71, 69, 106, 71, 107, 55, 96, 78, 109, 66, 100,
2254
    99, 112, 69, 122, 83, 124, 106, 128, 112, 132, 18, 78, 24, 79, 49,
2255
    99, 63, 101, 28, 83, 30, 84, 71, 112, 73, 113, 59, 109, 79, 115, 71,
2256
    112, 101, 117, 71, 124, 84, 125, 107, 132, 113, 134, 18, 59, 22, 61,
2257
    59, 81, 61, 84, 28, 71, 30, 73, 83, 112, 84, 113, 78, 109, 90, 129,
2258
    109, 116, 129, 133, 83, 124, 91, 130, 131, 145, 133, 146, 28, 83, 30,
2259
    84, 71, 112, 73, 113, 31, 87, 32, 88, 87, 118, 88, 119, 83, 131, 91,
2260
    133, 124, 145, 130, 146, 87, 132, 92, 134, 132, 147, 134, 148, 41,
2261
    66, 59, 81, 46, 72, 71, 87, 69, 106, 83, 112, 122, 128, 124, 132, 66,
2262
    100, 109, 116, 72, 102, 112, 118, 106, 128, 131, 145, 128, 141, 145,
2263
    147, 59, 109, 79, 115, 71, 112, 101, 117, 83, 131, 91, 133, 124, 145,
2264
    130, 146, 81, 116, 115, 138, 87, 118, 117, 139, 112, 145, 133, 149,
2265
    132, 147, 146, 150, 49, 71, 61, 84, 71, 87, 84, 92, 71, 107, 84, 113,
2266
    124, 132, 125, 134, 99, 112, 129, 133, 112, 118, 133, 135, 112, 132,
2267
    133, 146, 145, 147, 149, 150, 71, 124, 84, 125, 107, 132, 113, 134,
2268
    87, 132, 92, 134, 132, 147, 134, 148, 112, 145, 133, 149, 132, 147,
2269
    146, 150, 118, 147, 135, 150, 147, 152, 150, 153, 14, 55, 25, 69, 55,
2270
    96, 69, 122, 18, 59, 28, 71, 78, 109, 83, 124, 41, 66, 69, 106, 66,
2271
    100, 106, 128, 49, 71, 71, 107, 99, 112, 112, 132, 18, 78, 28, 83,
2272
    59, 109, 71, 124, 24, 79, 30, 84, 79, 115, 84, 125, 49, 99, 71, 112,
2273
    71, 112, 107, 132, 63, 101, 73, 113, 101, 117, 113, 134, 18, 59, 28,
2274
    71, 78, 109, 83, 124, 22, 61, 30, 73, 90, 129, 91, 130, 59, 81, 83,
2275
    112, 109, 116, 131, 145, 61, 84, 84, 113, 129, 133, 133, 146, 28, 83,
2276
    31, 87, 83, 131, 87, 132, 30, 84, 32, 88, 91, 133, 92, 134, 71, 112,
2277
    87, 118, 124, 145, 132, 147, 73, 113, 88, 119, 130, 146, 134, 148,
2278
    41, 66, 69, 106, 66, 100, 106, 128, 59, 81, 83, 112, 109, 116, 131,
2279
    145, 46, 72, 122, 128, 72, 102, 128, 141, 71, 87, 124, 132, 112, 118,
2280
    145, 147, 59, 109, 83, 131, 81, 116, 112, 145, 79, 115, 91, 133, 115,
2281
    138, 133, 149, 71, 112, 124, 145, 87, 118, 132, 147, 101, 117, 130,
2282
    146, 117, 139, 146, 150, 49, 71, 71, 107, 99, 112, 112, 132, 61, 84,
2283
    84, 113, 129, 133, 133, 146, 71, 87, 124, 132, 112, 118, 145, 147,
2284
    84, 92, 125, 134, 133, 135, 149, 150, 71, 124, 87, 132, 112, 145,
2285
    118, 147, 84, 125, 92, 134, 133, 149, 135, 150, 107, 132, 132, 147,
2286
    132, 147, 147, 152, 113, 134, 134, 148, 146, 150, 150, 153, 18, 78,
2287
    28, 83, 59, 109, 71, 124, 28, 83, 31, 87, 83, 131, 87, 132, 59, 109,
2288
    83, 131, 81, 116, 112, 145, 71, 124, 87, 132, 112, 145, 118, 147, 22,
2289
    90, 30, 91, 61, 129, 73, 130, 30, 91, 32, 92, 84, 133, 88, 134, 61,
2290
    129, 84, 133, 84, 133, 113, 146, 73, 130, 88, 134, 113, 146, 119,
2291
    148, 24, 79, 30, 84, 79, 115, 84, 125, 30, 84, 32, 88, 91, 133, 92,
2292
    134, 79, 115, 91, 133, 115, 138, 133, 149, 84, 125, 92, 134, 133,
2293
    149, 135, 150, 30, 91, 32, 92, 84, 133, 88, 134, 32, 92, 33, 93, 92,
2294
    135, 93, 136, 84, 133, 92, 135, 125, 149, 134, 150, 88, 134, 93, 136,
2295
    134, 150, 136, 151, 49, 99, 71, 112, 71, 112, 107, 132, 71, 112, 87,
2296
    118, 124, 145, 132, 147, 71, 112, 124, 145, 87, 118, 132, 147, 107,
2297
    132, 132, 147, 132, 147, 147, 152, 61, 129, 84, 133, 84, 133, 113,
2298
    146, 84, 133, 92, 135, 125, 149, 134, 150, 84, 133, 125, 149, 92,
2299
    135, 134, 150, 113, 146, 134, 150, 134, 150, 148, 153, 63, 101, 73,
2300
    113, 101, 117, 113, 134, 73, 113, 88, 119, 130, 146, 134, 148, 101,
2301
    117, 130, 146, 117, 139, 146, 150, 113, 134, 134, 148, 146, 150, 150,
2302
    153, 73, 130, 88, 134, 113, 146, 119, 148, 88, 134, 93, 136, 134,
2303
    150, 136, 151, 113, 146, 134, 150, 134, 150, 148, 153, 119, 148, 136,
2304
    151, 148, 153, 151, 154, 11, 36, 36, 42, 14, 41, 41, 46, 36, 42, 42,
2305
    62, 55, 66, 66, 72, 14, 41, 55, 66, 18, 49, 59, 71, 41, 46, 66, 72,
2306
    59, 71, 81, 87, 14, 55, 41, 66, 18, 59, 49, 71, 41, 66, 46, 72, 59,
2307
    81, 71, 87, 18, 59, 59, 81, 22, 61, 61, 84, 49, 71, 71, 87, 61, 84,
2308
    84, 92, 36, 42, 42, 62, 55, 66, 66, 72, 42, 62, 62, 94, 96, 100, 100,
2309
    102, 55, 66, 96, 100, 78, 99, 109, 112, 66, 72, 100, 102, 109, 112,
2310
    116, 118, 55, 96, 66, 100, 78, 109, 99, 112, 66, 100, 72, 102, 109,
2311
    116, 112, 118, 78, 109, 109, 116, 90, 129, 129, 133, 99, 112, 112,
2312
    118, 129, 133, 133, 135, 14, 41, 55, 66, 18, 49, 59, 71, 55, 66, 96,
2313
    100, 78, 99, 109, 112, 18, 49, 78, 99, 24, 63, 79, 101, 59, 71, 109,
2314
    112, 79, 101, 115, 117, 25, 69, 69, 106, 28, 71, 71, 107, 69, 106,
2315
    122, 128, 83, 112, 124, 132, 28, 71, 83, 112, 30, 73, 84, 113, 71,
2316
    107, 124, 132, 84, 113, 125, 134, 41, 46, 66, 72, 59, 71, 81, 87, 66,
2317
    72, 100, 102, 109, 112, 116, 118, 59, 71, 109, 112, 79, 101, 115,
2318
    117, 81, 87, 116, 118, 115, 117, 138, 139, 69, 122, 106, 128, 83,
2319
    124, 112, 132, 106, 128, 128, 141, 131, 145, 145, 147, 83, 124, 131,
2320
    145, 91, 130, 133, 146, 112, 132, 145, 147, 133, 146, 149, 150, 14,
2321
    55, 41, 66, 18, 59, 49, 71, 55, 96, 66, 100, 78, 109, 99, 112, 25,
2322
    69, 69, 106, 28, 71, 71, 107, 69, 122, 106, 128, 83, 124, 112, 132,
2323
    18, 78, 49, 99, 24, 79, 63, 101, 59, 109, 71, 112, 79, 115, 101, 117,
2324
    28, 83, 71, 112, 30, 84, 73, 113, 71, 124, 107, 132, 84, 125, 113,
2325
    134, 41, 66, 46, 72, 59, 81, 71, 87, 66, 100, 72, 102, 109, 116, 112,
2326
    118, 69, 106, 122, 128, 83, 112, 124, 132, 106, 128, 128, 141, 131,
2327
    145, 145, 147, 59, 109, 71, 112, 79, 115, 101, 117, 81, 116, 87, 118,
2328
    115, 138, 117, 139, 83, 131, 124, 145, 91, 133, 130, 146, 112, 145,
2329
    132, 147, 133, 149, 146, 150, 18, 59, 59, 81, 22, 61, 61, 84, 78,
2330
    109, 109, 116, 90, 129, 129, 133, 28, 71, 83, 112, 30, 73, 84, 113,
2331
    83, 124, 131, 145, 91, 130, 133, 146, 28, 83, 71, 112, 30, 84, 73,
2332
    113, 83, 131, 124, 145, 91, 133, 130, 146, 31, 87, 87, 118, 32, 88,
2333
    88, 119, 87, 132, 132, 147, 92, 134, 134, 148, 49, 71, 71, 87, 61,
2334
    84, 84, 92, 99, 112, 112, 118, 129, 133, 133, 135, 71, 107, 124, 132,
2335
    84, 113, 125, 134, 112, 132, 145, 147, 133, 146, 149, 150, 71, 124,
2336
    107, 132, 84, 125, 113, 134, 112, 145, 132, 147, 133, 149, 146, 150,
2337
    87, 132, 132, 147, 92, 134, 134, 148, 118, 147, 147, 152, 135, 150,
2338
    150, 153, 14, 55, 55, 96, 25, 69, 69, 122, 41, 66, 66, 100, 69, 106,
2339
    106, 128, 18, 59, 78, 109, 28, 71, 83, 124, 49, 71, 99, 112, 71, 107,
2340
    112, 132, 18, 78, 59, 109, 28, 83, 71, 124, 49, 99, 71, 112, 71, 112,
2341
    107, 132, 24, 79, 79, 115, 30, 84, 84, 125, 63, 101, 101, 117, 73,
2342
    113, 113, 134, 41, 66, 66, 100, 69, 106, 106, 128, 46, 72, 72, 102,
2343
    122, 128, 128, 141, 59, 81, 109, 116, 83, 112, 131, 145, 71, 87, 112,
2344
    118, 124, 132, 145, 147, 59, 109, 81, 116, 83, 131, 112, 145, 71,
2345
    112, 87, 118, 124, 145, 132, 147, 79, 115, 115, 138, 91, 133, 133,
2346
    149, 101, 117, 117, 139, 130, 146, 146, 150, 18, 59, 78, 109, 28, 71,
2347
    83, 124, 59, 81, 109, 116, 83, 112, 131, 145, 22, 61, 90, 129, 30,
2348
    73, 91, 130, 61, 84, 129, 133, 84, 113, 133, 146, 28, 83, 83, 131,
2349
    31, 87, 87, 132, 71, 112, 124, 145, 87, 118, 132, 147, 30, 84, 91,
2350
    133, 32, 88, 92, 134, 73, 113, 130, 146, 88, 119, 134, 148, 49, 71,
2351
    99, 112, 71, 107, 112, 132, 71, 87, 112, 118, 124, 132, 145, 147, 61,
2352
    84, 129, 133, 84, 113, 133, 146, 84, 92, 133, 135, 125, 134, 149,
2353
    150, 71, 124, 112, 145, 87, 132, 118, 147, 107, 132, 132, 147, 132,
2354
    147, 147, 152, 84, 125, 133, 149, 92, 134, 135, 150, 113, 134, 146,
2355
    150, 134, 148, 150, 153, 18, 78, 59, 109, 28, 83, 71, 124, 59, 109,
2356
    81, 116, 83, 131, 112, 145, 28, 83, 83, 131, 31, 87, 87, 132, 71,
2357
    124, 112, 145, 87, 132, 118, 147, 22, 90, 61, 129, 30, 91, 73, 130,
2358
    61, 129, 84, 133, 84, 133, 113, 146, 30, 91, 84, 133, 32, 92, 88,
2359
    134, 73, 130, 113, 146, 88, 134, 119, 148, 49, 99, 71, 112, 71, 112,
2360
    107, 132, 71, 112, 87, 118, 124, 145, 132, 147, 71, 112, 124, 145,
2361
    87, 118, 132, 147, 107, 132, 132, 147, 132, 147, 147, 152, 61, 129,
2362
    84, 133, 84, 133, 113, 146, 84, 133, 92, 135, 125, 149, 134, 150, 84,
2363
    133, 125, 149, 92, 135, 134, 150, 113, 146, 134, 150, 134, 150, 148,
2364
    153, 24, 79, 79, 115, 30, 84, 84, 125, 79, 115, 115, 138, 91, 133,
2365
    133, 149, 30, 84, 91, 133, 32, 88, 92, 134, 84, 125, 133, 149, 92,
2366
    134, 135, 150, 30, 91, 84, 133, 32, 92, 88, 134, 84, 133, 125, 149,
2367
    92, 135, 134, 150, 32, 92, 92, 135, 33, 93, 93, 136, 88, 134, 134,
2368
    150, 93, 136, 136, 151, 63, 101, 101, 117, 73, 113, 113, 134, 101,
2369
    117, 117, 139, 130, 146, 146, 150, 73, 113, 130, 146, 88, 119, 134,
2370
    148, 113, 134, 146, 150, 134, 148, 150, 153, 73, 130, 113, 146, 88,
2371
    134, 119, 148, 113, 146, 134, 150, 134, 150, 148, 153, 88, 134, 134,
2372
    150, 93, 136, 136, 151, 119, 148, 148, 153, 136, 151, 151, 154, 34,
2373
    37, 37, 43, 37, 43, 43, 47, 37, 43, 43, 63, 64, 67, 67, 73, 37, 43,
2374
    64, 67, 43, 63, 67, 73, 43, 47, 67, 73, 67, 73, 85, 88, 37, 64, 43,
2375
    67, 43, 67, 63, 73, 43, 67, 47, 73, 67, 85, 73, 88, 43, 67, 67, 85,
2376
    47, 73, 73, 88, 63, 73, 73, 88, 73, 88, 88, 93, 37, 43, 43, 63, 64,
2377
    67, 67, 73, 43, 63, 63, 95, 97, 101, 101, 103, 64, 67, 97, 101, 97,
2378
    101, 110, 113, 67, 73, 101, 103, 110, 113, 117, 119, 64, 97, 67, 101,
2379
    97, 110, 101, 113, 67, 101, 73, 103, 110, 117, 113, 119, 97, 110,
2380
    110, 117, 126, 130, 130, 134, 101, 113, 113, 119, 130, 134, 134, 136,
2381
    37, 43, 64, 67, 43, 63, 67, 73, 64, 67, 97, 101, 97, 101, 110, 113,
2382
    43, 63, 97, 101, 63, 95, 101, 103, 67, 73, 110, 113, 101, 103, 117,
2383
    119, 64, 97, 97, 110, 67, 101, 101, 113, 97, 110, 126, 130, 110, 117,
2384
    130, 134, 67, 101, 110, 117, 73, 103, 113, 119, 101, 113, 130, 134,
2385
    113, 119, 134, 136, 43, 47, 67, 73, 67, 73, 85, 88, 67, 73, 101, 103,
2386
    110, 113, 117, 119, 67, 73, 110, 113, 101, 103, 117, 119, 85, 88,
2387
    117, 119, 117, 119, 139, 140, 97, 126, 110, 130, 110, 130, 117, 134,
2388
    110, 130, 130, 142, 143, 146, 146, 148, 110, 130, 143, 146, 130, 142,
2389
    146, 148, 117, 134, 146, 148, 146, 148, 150, 151, 37, 64, 43, 67, 43,
2390
    67, 63, 73, 64, 97, 67, 101, 97, 110, 101, 113, 64, 97, 97, 110, 67,
2391
    101, 101, 113, 97, 126, 110, 130, 110, 130, 117, 134, 43, 97, 63,
2392
    101, 63, 101, 95, 103, 67, 110, 73, 113, 101, 117, 103, 119, 67, 110,
2393
    101, 117, 73, 113, 103, 119, 101, 130, 113, 134, 113, 134, 119, 136,
2394
    43, 67, 47, 73, 67, 85, 73, 88, 67, 101, 73, 103, 110, 117, 113, 119,
2395
    97, 110, 126, 130, 110, 117, 130, 134, 110, 130, 130, 142, 143, 146,
2396
    146, 148, 67, 110, 73, 113, 101, 117, 103, 119, 85, 117, 88, 119,
2397
    117, 139, 119, 140, 110, 143, 130, 146, 130, 146, 142, 148, 117, 146,
2398
    134, 148, 146, 150, 148, 151, 43, 67, 67, 85, 47, 73, 73, 88, 97,
2399
    110, 110, 117, 126, 130, 130, 134, 67, 101, 110, 117, 73, 103, 113,
2400
    119, 110, 130, 143, 146, 130, 142, 146, 148, 67, 110, 101, 117, 73,
2401
    113, 103, 119, 110, 143, 130, 146, 130, 146, 142, 148, 85, 117, 117,
2402
    139, 88, 119, 119, 140, 117, 146, 146, 150, 134, 148, 148, 151, 63,
2403
    73, 73, 88, 73, 88, 88, 93, 101, 113, 113, 119, 130, 134, 134, 136,
2404
    101, 113, 130, 134, 113, 119, 134, 136, 117, 134, 146, 148, 146, 148,
2405
    150, 151, 101, 130, 113, 134, 113, 134, 119, 136, 117, 146, 134, 148,
2406
    146, 150, 148, 151, 117, 146, 146, 150, 134, 148, 148, 151, 139, 150,
2407
    150, 153, 150, 153, 153, 154, 37, 64, 64, 97, 64, 97, 97, 126, 43,
2408
    67, 67, 101, 97, 110, 110, 130, 43, 67, 97, 110, 67, 101, 110, 130,
2409
    63, 73, 101, 113, 101, 113, 117, 134, 43, 97, 67, 110, 67, 110, 101,
2410
    130, 63, 101, 73, 113, 101, 117, 113, 134, 63, 101, 101, 117, 73,
2411
    113, 113, 134, 95, 103, 103, 119, 103, 119, 119, 136, 43, 67, 67,
2412
    101, 97, 110, 110, 130, 47, 73, 73, 103, 126, 130, 130, 142, 67, 85,
2413
    110, 117, 110, 117, 143, 146, 73, 88, 113, 119, 130, 134, 146, 148,
2414
    67, 110, 85, 117, 110, 143, 117, 146, 73, 113, 88, 119, 130, 146,
2415
    134, 148, 101, 117, 117, 139, 130, 146, 146, 150, 103, 119, 119, 140,
2416
    142, 148, 148, 151, 43, 67, 97, 110, 67, 101, 110, 130, 67, 85, 110,
2417
    117, 110, 117, 143, 146, 47, 73, 126, 130, 73, 103, 130, 142, 73, 88,
2418
    130, 134, 113, 119, 146, 148, 67, 110, 110, 143, 85, 117, 117, 146,
2419
    101, 117, 130, 146, 117, 139, 146, 150, 73, 113, 130, 146, 88, 119,
2420
    134, 148, 103, 119, 142, 148, 119, 140, 148, 151, 63, 73, 101, 113,
2421
    101, 113, 117, 134, 73, 88, 113, 119, 130, 134, 146, 148, 73, 88,
2422
    130, 134, 113, 119, 146, 148, 88, 93, 134, 136, 134, 136, 150, 151,
2423
    101, 130, 117, 146, 117, 146, 139, 150, 113, 134, 134, 148, 146, 150,
2424
    150, 153, 113, 134, 146, 150, 134, 148, 150, 153, 119, 136, 148, 151,
2425
    148, 151, 153, 154, 43, 97, 67, 110, 67, 110, 101, 130, 67, 110, 85,
2426
    117, 110, 143, 117, 146, 67, 110, 110, 143, 85, 117, 117, 146, 101,
2427
    130, 117, 146, 117, 146, 139, 150, 47, 126, 73, 130, 73, 130, 103,
2428
    142, 73, 130, 88, 134, 113, 146, 119, 148, 73, 130, 113, 146, 88,
2429
    134, 119, 148, 103, 142, 119, 148, 119, 148, 140, 151, 63, 101, 73,
2430
    113, 101, 117, 113, 134, 73, 113, 88, 119, 130, 146, 134, 148, 101,
2431
    117, 130, 146, 117, 139, 146, 150, 113, 134, 134, 148, 146, 150, 150,
2432
    153, 73, 130, 88, 134, 113, 146, 119, 148, 88, 134, 93, 136, 134,
2433
    150, 136, 151, 113, 146, 134, 150, 134, 150, 148, 153, 119, 148, 136,
2434
    151, 148, 153, 151, 154, 63, 101, 101, 117, 73, 113, 113, 134, 101,
2435
    117, 117, 139, 130, 146, 146, 150, 73, 113, 130, 146, 88, 119, 134,
2436
    148, 113, 134, 146, 150, 134, 148, 150, 153, 73, 130, 113, 146, 88,
2437
    134, 119, 148, 113, 146, 134, 150, 134, 150, 148, 153, 88, 134, 134,
2438
    150, 93, 136, 136, 151, 119, 148, 148, 153, 136, 151, 151, 154, 95,
2439
    103, 103, 119, 103, 119, 119, 136, 103, 119, 119, 140, 142, 148, 148,
2440
    151, 103, 119, 142, 148, 119, 140, 148, 151, 119, 136, 148, 151, 148,
2441
    151, 153, 154, 103, 142, 119, 148, 119, 148, 140, 151, 119, 148, 136,
2442
    151, 148, 153, 151, 154, 119, 148, 148, 153, 136, 151, 151, 154, 140,
2443
    151, 151, 154, 151, 154, 154, 155
2444
};
2445
2446
const unsigned int igraph_i_isographs_3[] =  { 0, 1, 3, 5, 6, 7, 10, 11, 15, 21,
2447
                                               23, 25, 27, 30, 31, 63
2448
                                             };
2449
const unsigned int igraph_i_isographs_3u[] = { 0, 1, 3, 7 };
2450
const unsigned int igraph_i_isographs_4[] = {
2451
    0,    1,    3,    7,    9,   10,   11,   14,   15,   18,   19,   20,   21,
2452
    22,   23,   27,   29,   30,   31,   54,   55,   63,   73,   75,   76,   77,
2453
    79,   81,   83,   84,   85,   86,   87,   90,   91,   92,   93,   94,   95,
2454
    98,   99,  100,  101,  102,  103,  106,  107,  108,  109,  110,  111,  115,
2455
    116,  117,  118,  119,  122,  123,  124,  125,  126,  127,  219,  220,  221,
2456
    223,  228,  229,  230,  231,  237,  238,  239,  246,  247,  255,  292,  293,
2457
    295,  301,  302,  303,  310,  311,  319,  365,  367,  373,  375,  382,  383,
2458
    511,  585,  587,  591,  593,  594,  595,  596,  597,  598,  599,  601,  602,
2459
    603,  604,  605,  606,  607,  625,  626,  627,  630,  631,  633,  634,  635,
2460
    638,  639,  659,  660,  661,  663,  666,  667,  669,  670,  671,  674,  675,
2461
    678,  679,  683,  686,  687,  694,  695,  703,  729,  731,  732,  733,  735,
2462
    737,  739,  741,  742,  743,  745,  746,  747,  748,  749,  750,  751,  753,
2463
    755,  756,  757,  758,  759,  761,  762,  763,  764,  765,  766,  767,  819,
2464
    822,  823,  826,  827,  830,  831,  875,  876,  877,  879,  883,  885,  886,
2465
    887,  891,  892,  893,  894,  895,  947,  949,  951,  955,  957,  958,  959,
2466
    1019, 1020, 1021, 1023, 1755, 1757, 1758, 1759, 1782, 1783, 1791, 1883, 1887,
2467
    1907, 1911, 1917, 1918, 1919, 2029, 2031, 2039, 2047, 4095
2468
};
2469
const unsigned int igraph_i_isographs_4u[] = { 0, 1, 3, 7, 11, 12, 13,
2470
                                               15, 30, 31, 63
2471
                                             };
2472
const unsigned int igraph_i_isographs_5u[] = {
2473
    0, 1, 3, 7, 11, 12, 13, 15, 30, 31, 63, 75, 76, 77, 79, 86, 87, 94,
2474
    95, 116, 117, 119, 127, 222, 223, 235, 236, 237, 239, 254, 255, 507,
2475
    511, 1023
2476
};
2477
const unsigned int igraph_i_isographs_6u[] = {
2478
    0, 1, 3, 7, 11, 12, 13, 15, 30, 31, 63, 75, 76, 77, 79, 86, 87, 94,
2479
    95, 116, 117, 119, 127, 222, 223, 235, 236, 237, 239, 254, 255, 507,
2480
    511, 1023, 1099, 1100, 1101, 1103, 1108, 1109, 1110, 1111, 1118,
2481
    1119, 1140, 1141, 1143, 1151, 1182, 1183, 1184, 1185, 1187, 1191,
2482
    1194, 1195, 1196, 1197, 1198, 1199, 1214, 1215, 1246, 1247, 1259,
2483
    1260, 1261, 1263, 1268, 1269, 1270, 1271, 1278, 1279, 1456, 1457,
2484
    1459, 1460, 1461, 1463, 1465, 1467, 1468, 1469, 1471, 1531, 1532,
2485
    1533, 1535, 1972, 1973, 1975, 1983, 2047, 3294, 3295, 3306, 3307,
2486
    3308, 3309, 3310, 3311, 3326, 3327, 3440, 3441, 3443, 3447, 3448,
2487
    3449, 3451, 3452, 3453, 3455, 3576, 3577, 3578, 3579, 3582, 3583,
2488
    3873, 3875, 3879, 3885, 3887, 3903, 3947, 3948, 3949, 3950, 3951,
2489
    3958, 3959, 3966, 3967, 4094, 4095, 7672, 7673, 7675, 7679, 7902,
2490
    7903, 7915, 7916, 7917, 7919, 7934, 7935, 8185, 8187, 8191, 16350,
2491
    16351, 16383, 32767
2492
};
2493
2494
const unsigned int igraph_i_classedges_3[] = { 1, 2, 0, 2, 2, 1, 0, 1, 2, 0, 1, 0 };
2495
const unsigned int igraph_i_classedges_3u[] = { 1, 2, 0, 2, 0, 1 };
2496
const unsigned int igraph_i_classedges_4[] = { 2, 3, 1, 3, 0, 3, 3, 2, 1, 2, 0, 2,
2497
                                               3, 1, 2, 1, 0, 1, 3, 0, 2, 0, 1, 0
2498
                                             };
2499
const unsigned int igraph_i_classedges_4u[] = { 2, 3, 1, 3, 0, 3, 1, 2, 0, 2, 0, 1 };
2500
const unsigned int igraph_i_classedges_5u[] = { 3, 4, 2, 4, 1, 4, 0, 4, 2, 3, 1, 3,
2501
                                                0, 3, 1, 2, 0, 2, 0, 1 };
2502
const unsigned int igraph_i_classedges_6u[] = { 4, 5, 3, 5, 2, 5, 1, 5, 0, 5, 3, 4,
2503
                                                2, 4, 1, 4, 0, 4, 2, 3, 1, 3, 0, 3,
2504
                                                1, 2, 0, 2, 0, 1 };
2505
2506
/**
2507
 * \function igraph_isoclass
2508
 * \brief Determine the isomorphism class of small graphs.
2509
 *
2510
 * </para><para>
2511
 * All graphs with a given number of vertices belong to a number of
2512
 * isomorphism classes, with every graph in a given class being
2513
 * isomorphic to each other.
2514
 *
2515
 * </para><para>
2516
 * This function gives the isomorphism class (a number) of a
2517
 * graph. Two graphs have the same isomorphism class if and only if
2518
 * they are isomorphic.
2519
 *
2520
 * </para><para>
2521
 * The first isomorphism class is numbered zero and it contains the edgeless
2522
 * graph. The last isomorphism class contains the full graph. The number of
2523
 * isomorphism classes for directed graphs with three vertices is 16
2524
 * (between 0 and 15), for undirected graph it is only 4. For graphs
2525
 * with four vertices it is 218 (directed) and 11 (undirected).
2526
 * For 5 and 6 vertex undirected graphs, it is 34 and 156, respectively.
2527
 * These values can also be retrieved using \ref igraph_graph_count().
2528
 * For more information, see https://oeis.org/A000273 and https://oeis.org/A000088.
2529
 *
2530
 * </para><para>
2531
 * At the moment, 3- and 4-vertex directed graphs and 3 to 6 vertex
2532
 * undirected graphs are supported.
2533
 *
2534
 * </para><para>
2535
 * Multi-edges and self-loops are ignored by this function.
2536
 *
2537
 * \param graph The graph object.
2538
 * \param isoclass Pointer to an integer, the isomorphism class will
2539
 *        be stored here.
2540
 * \return Error code.
2541
 * \sa \ref igraph_isomorphic(), \ref igraph_isoclass_subgraph(),
2542
 * \ref igraph_isoclass_create(), \ref igraph_motifs_randesu().
2543
 *
2544
 * Because of some limitations this function works only for graphs
2545
 * with three of four vertices.
2546
 *
2547
 * </para><para>
2548
 * Time complexity: O(|E|), the number of edges in the graph.
2549
 */
2550
0
igraph_error_t igraph_isoclass(const igraph_t *graph, igraph_int_t *isoclass) {
2551
0
    igraph_int_t e;
2552
0
    igraph_int_t no_of_nodes = igraph_vcount(graph);
2553
0
    igraph_int_t no_of_edges = igraph_ecount(graph);
2554
0
    unsigned int idx, mul;
2555
0
    const unsigned int *arr_idx, *arr_code;
2556
0
    unsigned int code;
2557
2558
0
    if (igraph_is_directed(graph)) {
2559
0
        switch (no_of_nodes) {
2560
0
        case 3:
2561
0
            arr_idx = igraph_i_isoclass_3_idx;
2562
0
            arr_code = igraph_i_isoclass2_3;
2563
0
            mul = 3;
2564
0
            break;
2565
0
        case 4:
2566
0
            arr_idx = igraph_i_isoclass_4_idx;
2567
0
            arr_code = igraph_i_isoclass2_4;
2568
0
            mul = 4;
2569
0
            break;
2570
0
        default:
2571
0
            IGRAPH_ERROR("Directed isoclass is only implemented for graphs with 3 or 4 vertices.",
2572
0
                         IGRAPH_UNIMPLEMENTED);
2573
0
        }
2574
0
    } else {
2575
0
        switch (no_of_nodes) {
2576
0
        case 3:
2577
0
            arr_idx = igraph_i_isoclass_3u_idx;
2578
0
            arr_code = igraph_i_isoclass2_3u;
2579
0
            mul = 3;
2580
0
            break;
2581
0
        case 4:
2582
0
            arr_idx = igraph_i_isoclass_4u_idx;
2583
0
            arr_code = igraph_i_isoclass2_4u;
2584
0
            mul = 4;
2585
0
            break;
2586
0
        case 5:
2587
0
            arr_idx = igraph_i_isoclass_5u_idx;
2588
0
            arr_code = igraph_i_isoclass2_5u;
2589
0
            mul = 5;
2590
0
            break;
2591
0
        case 6:
2592
0
            arr_idx = igraph_i_isoclass_6u_idx;
2593
0
            arr_code = igraph_i_isoclass2_6u;
2594
0
            mul = 6;
2595
0
            break;
2596
0
        default:
2597
0
            IGRAPH_ERROR("Undirected isoclass is only implemented for graphs with 3 to 6 vertices.",
2598
0
                         IGRAPH_UNIMPLEMENTED);
2599
0
        }
2600
0
    }
2601
2602
0
    code = 0;
2603
0
    for (e = 0; e < no_of_edges; e++) {
2604
0
        idx = mul * IGRAPH_FROM(graph, e) + IGRAPH_TO(graph, e);
2605
0
        code |= arr_idx[idx];
2606
0
    }
2607
2608
0
    *isoclass = (igraph_int_t) arr_code[code];
2609
2610
0
    return IGRAPH_SUCCESS;
2611
0
}
2612
2613
/**
2614
 * \function igraph_isoclass_subgraph
2615
 * \brief The isomorphism class of a subgraph of a graph.
2616
 *
2617
 * This function identifies the isomorphism class of the subgraph
2618
 * induced the vertices specified in \p vids.
2619
 *
2620
 * </para><para>
2621
 * At the moment, 3- and 4-vertex directed graphs and 3 to 6 vertex
2622
 * undirected graphs are supported.
2623
 *
2624
 * </para><para>
2625
 * Multi-edges and self-loops are ignored by this function.
2626
 *
2627
 * \param graph The graph object.
2628
 * \param vids The vertices of the subgraph. Each vertex must be included at most once.
2629
 * \param isoclass Pointer to an integer, this will be set to the
2630
 *        isomorphism class.
2631
 * \return Error code.
2632
 * \sa \ref igraph_isoclass(), \ref igraph_isomorphic(),
2633
 * \ref igraph_isoclass_create().
2634
 *
2635
 * Time complexity: O((d+n)*n), d is the average degree in the network,
2636
 * and n is the number of vertices in \c vids.
2637
 */
2638
igraph_error_t igraph_isoclass_subgraph(const igraph_t *graph, igraph_vs_t vids,
2639
0
                             igraph_int_t *isoclass) {
2640
0
    igraph_int_t subgraph_size;
2641
0
    igraph_vector_int_t vertices, neis;
2642
2643
0
    unsigned int mul, idx;
2644
0
    const unsigned int *arr_idx, *arr_code;
2645
0
    unsigned int code = 0;
2646
2647
0
    IGRAPH_VECTOR_INT_INIT_FINALLY(&vertices, 0);
2648
0
    IGRAPH_CHECK(igraph_vs_as_vector(graph, vids, &vertices));
2649
0
    subgraph_size = igraph_vector_int_size(&vertices);
2650
2651
0
    IGRAPH_VECTOR_INT_INIT_FINALLY(&neis, 0);
2652
2653
0
    if (igraph_is_directed(graph)) {
2654
0
        switch (subgraph_size) {
2655
0
        case 3:
2656
0
            arr_idx = igraph_i_isoclass_3_idx;
2657
0
            arr_code = igraph_i_isoclass2_3;
2658
0
            mul = 3;
2659
0
            break;
2660
0
        case 4:
2661
0
            arr_idx = igraph_i_isoclass_4_idx;
2662
0
            arr_code = igraph_i_isoclass2_4;
2663
0
            mul = 4;
2664
0
            break;
2665
0
        default:
2666
0
            IGRAPH_ERROR("Directed isoclass is only implemented for graphs with 3 or 4 vertices.",
2667
0
                         IGRAPH_UNIMPLEMENTED);
2668
0
        }
2669
0
    } else {
2670
0
        switch (subgraph_size) {
2671
0
        case 3:
2672
0
            arr_idx = igraph_i_isoclass_3u_idx;
2673
0
            arr_code = igraph_i_isoclass2_3u;
2674
0
            mul = 3;
2675
0
            break;
2676
0
        case 4:
2677
0
            arr_idx = igraph_i_isoclass_4u_idx;
2678
0
            arr_code = igraph_i_isoclass2_4u;
2679
0
            mul = 4;
2680
0
            break;
2681
0
        case 5:
2682
0
            arr_idx = igraph_i_isoclass_5u_idx;
2683
0
            arr_code = igraph_i_isoclass2_5u;
2684
0
            mul = 5;
2685
0
            break;
2686
0
        case 6:
2687
0
            arr_idx = igraph_i_isoclass_6u_idx;
2688
0
            arr_code = igraph_i_isoclass2_6u;
2689
0
            mul = 6;
2690
0
            break;
2691
0
        default:
2692
0
            IGRAPH_ERROR("Undirected isoclass is only implemented for graphs with 3 to 6 vertices.",
2693
0
                         IGRAPH_UNIMPLEMENTED);
2694
0
        }
2695
0
    }
2696
2697
0
    for (igraph_int_t i = 0; i < subgraph_size; i++) {
2698
0
        igraph_int_t from = VECTOR(vertices)[i];
2699
0
        IGRAPH_CHECK(igraph_neighbors(
2700
0
            graph, &neis, from, IGRAPH_OUT, IGRAPH_LOOPS, IGRAPH_MULTIPLE
2701
0
        ));
2702
0
        const igraph_int_t s = igraph_vector_int_size(&neis);
2703
0
        for (igraph_int_t j = 0; j < s; j++) {
2704
0
            igraph_int_t nei = VECTOR(neis)[j], to;
2705
0
            if (igraph_vector_int_search(&vertices, 0, nei, &to)) {
2706
0
                idx = (mul * i + to);
2707
0
                code |= arr_idx[idx];
2708
0
            }
2709
0
        }
2710
0
    }
2711
2712
0
    *isoclass = arr_code[code];
2713
0
    igraph_vector_int_destroy(&neis);
2714
0
    igraph_vector_int_destroy(&vertices);
2715
0
    IGRAPH_FINALLY_CLEAN(2);
2716
2717
0
    return IGRAPH_SUCCESS;
2718
0
}
2719
2720
/**
2721
 * \function igraph_isoclass_create
2722
 * \brief Creates a graph from the given isomorphism class.
2723
 *
2724
 * </para><para>
2725
 * This function creates the canonical representative graph of the
2726
 * given isomorphism class.
2727
 *
2728
 * </para><para>
2729
 * The isomorphism class is an integer between 0 and the number of
2730
 * unique unlabeled (i.e. non-isomorphic) graphs on the given number
2731
 * of vertices and give directedness. See https://oeis.org/A000273
2732
 * and https://oeis.org/A000088 for the number of directed and
2733
 * undirected graphs on \p size nodes.
2734
 *
2735
 * </para><para>
2736
 * At the moment, 3- and 4-vertex directed graphs and 3 to 6 vertex
2737
 * undirected graphs are supported.
2738
 *
2739
 * \param graph Pointer to an uninitialized graph object.
2740
 * \param size The number of vertices to add to the graph.
2741
 * \param number The isomorphism class.
2742
 * \param directed Boolean constant, whether to create a directed
2743
 *        graph.
2744
 * \return Error code.
2745
 * \sa \ref igraph_isoclass(),
2746
 * \ref igraph_isoclass_subgraph(),
2747
 * \ref igraph_isomorphic().
2748
 *
2749
 * Time complexity: O(|V|+|E|), the number of vertices plus the number
2750
 * of edges in the graph to create.
2751
 */
2752
igraph_error_t igraph_isoclass_create(igraph_t *graph, igraph_int_t size,
2753
0
                           igraph_int_t number, igraph_bool_t directed) {
2754
0
    igraph_vector_int_t edges;
2755
0
    const unsigned int *classedges;
2756
0
    igraph_int_t graphcount;
2757
0
    igraph_int_t pos;
2758
0
    unsigned int power;
2759
0
    unsigned int code;
2760
2761
0
    IGRAPH_VECTOR_INT_INIT_FINALLY(&edges, 0);
2762
2763
0
#define CHECK_ISOCLASS(number, directed, size, graphcount) \
2764
0
    IGRAPH_ERRORF( \
2765
0
        "Isoclass %" IGRAPH_PRId " requested, but there are only %" \
2766
0
        IGRAPH_PRId " %s graphs of size %" IGRAPH_PRId ".", IGRAPH_EINVAL, \
2767
0
        number, graphcount, directed ? "directed" : "undirected", size)
2768
2769
0
    if (directed) {
2770
0
        switch (size) {
2771
0
        case 3: {
2772
0
            classedges = igraph_i_classedges_3;
2773
0
            graphcount = sizeof(igraph_i_isographs_3) / sizeof(igraph_i_isographs_3[0]);
2774
2775
0
            if (number < 0 || number >= graphcount) {
2776
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2777
0
            }
2778
2779
0
            code = igraph_i_isographs_3[number];
2780
0
            power = 32;
2781
2782
0
            break;
2783
0
        }
2784
0
        case 4: {
2785
0
            classedges = igraph_i_classedges_4;
2786
0
            graphcount = sizeof(igraph_i_isographs_4) / sizeof(igraph_i_isographs_4[0]);
2787
2788
0
            if (number < 0 || number >= graphcount) {
2789
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2790
0
            }
2791
2792
0
            code = igraph_i_isographs_4[number];
2793
0
            power = 2048;
2794
2795
0
            break;
2796
0
        }
2797
0
        default:
2798
0
            IGRAPH_ERROR("Directed isoclasses are supported only for graphs with 3 or 4 vertices.",
2799
0
                         IGRAPH_UNIMPLEMENTED);
2800
0
        }
2801
2802
0
    } else {
2803
0
        switch (size) {
2804
0
        case 3: {
2805
0
            classedges = igraph_i_classedges_3u;
2806
0
            graphcount = sizeof(igraph_i_isographs_3u) / sizeof(igraph_i_isographs_3u[0]);
2807
2808
0
            if (number < 0 || number >= graphcount) {
2809
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2810
0
            }
2811
2812
0
            code = igraph_i_isographs_3u[number];
2813
0
            power = 4;
2814
2815
0
            break;
2816
0
        }
2817
0
        case 4: {
2818
0
            classedges = igraph_i_classedges_4u;
2819
0
            graphcount = sizeof(igraph_i_isographs_4u) / sizeof(igraph_i_isographs_4u[0]);
2820
2821
0
            if (number < 0 || number >= graphcount) {
2822
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2823
0
            }
2824
2825
0
            code = igraph_i_isographs_4u[number];
2826
0
            power = 32;
2827
2828
0
            break;
2829
0
        }
2830
0
        case 5: {
2831
0
            classedges = igraph_i_classedges_5u;
2832
0
            graphcount = sizeof(igraph_i_isographs_5u) / sizeof(igraph_i_isographs_5u[0]);
2833
2834
0
            if (number < 0 || number >= graphcount) {
2835
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2836
0
            }
2837
2838
0
            code = igraph_i_isographs_5u[number];
2839
0
            power = 512;
2840
2841
0
            break;
2842
0
        }
2843
0
        case 6: {
2844
0
            classedges = igraph_i_classedges_6u;
2845
0
            graphcount = sizeof(igraph_i_isographs_6u) / sizeof(igraph_i_isographs_6u[0]);
2846
2847
0
            if (number < 0 || number >= graphcount) {
2848
0
                CHECK_ISOCLASS(number, directed, size, graphcount);
2849
0
            }
2850
2851
0
            code = igraph_i_isographs_6u[number];
2852
0
            power = 16384;
2853
2854
0
            break;
2855
0
        }
2856
0
        default:
2857
0
            IGRAPH_ERROR("Undirected isoclasses are supported only for graphs with 3 to 6 vertices.",
2858
0
                         IGRAPH_UNIMPLEMENTED);
2859
0
        }
2860
0
    }
2861
2862
0
#undef CHECK_ISOCLASS
2863
2864
0
    pos = 0;
2865
0
    while (code > 0) {
2866
0
        if (code >= power) {
2867
0
            IGRAPH_CHECK(igraph_vector_int_push_back(&edges, classedges[2 * pos]));
2868
0
            IGRAPH_CHECK(igraph_vector_int_push_back(&edges, classedges[2 * pos + 1]));
2869
0
            code -= power;
2870
0
        }
2871
0
        power /= 2;
2872
0
        pos++;
2873
0
    }
2874
2875
0
    IGRAPH_CHECK(igraph_create(graph, &edges, size, directed));
2876
0
    igraph_vector_int_destroy(&edges);
2877
0
    IGRAPH_FINALLY_CLEAN(1);
2878
2879
0
    return IGRAPH_SUCCESS;
2880
0
}
2881
2882
/* https://oeis.org/A000088 */
2883
static igraph_int_t undirected_graph_counts[] = {
2884
    1, 1, 2, 4, 11, 34, 156, 1044, 12346, 274668, 12005168, 1018997864,
2885
#if IGRAPH_INTEGER_SIZE == 64
2886
    165091172592, 50502031367952, 29054155657235488
2887
#endif
2888
};
2889
2890
/* https://oeis.org/A000273 */
2891
static igraph_int_t directed_graph_counts[] = {
2892
    1, 1, 3, 16, 218, 9608, 1540944, 882033440,
2893
#if IGRAPH_INTEGER_SIZE == 64
2894
    1793359192848, 13027956824399552
2895
#endif
2896
};
2897
2898
/**
2899
 * \function igraph_graph_count
2900
 * \brief The number of unlabelled graphs on the given number of vertices.
2901
 *
2902
 * Gives the number of unlabelled \em simple graphs on the specified number of vertices.
2903
 * The "isoclass" of a graph of this size is at most one less than this value.
2904
 *
2905
 * </para><para>
2906
 * This function is meant to be used in conjunction with isoclass and motif finder
2907
 * functions. It will only work for small \p n values for which the result is
2908
 * represetable in an \type igraph_int_t. For larger \p n values, an overflow
2909
 * error is raised.
2910
 *
2911
 * \param n The number of vertices.
2912
 * \param directed Boolean, whether to consider directed graphs.
2913
 * \param count Pointer to an integer, the result will be stored here.
2914
 * \return Error code.
2915
 *
2916
 * \sa \ref igraph_isoclass(), \ref igraph_motifs_randesu_callback().
2917
 *
2918
 * Time complexity: O(1).
2919
 */
2920
0
igraph_error_t igraph_graph_count(igraph_int_t n, igraph_bool_t directed, igraph_int_t *count) {
2921
0
    if (n < 0) {
2922
0
        IGRAPH_ERROR("Graph size must not be negative.", IGRAPH_EINVAL);
2923
0
    }
2924
0
    if (directed) {
2925
0
        if (n >= (igraph_int_t) (sizeof directed_graph_counts / sizeof directed_graph_counts[0])) {
2926
0
            IGRAPH_ERRORF("Graph size of % " IGRAPH_PRId " too large.", IGRAPH_EOVERFLOW, n);
2927
0
        }
2928
0
        *count = directed_graph_counts[n];
2929
0
    } else {
2930
0
        if (n >= (igraph_int_t) (sizeof undirected_graph_counts / sizeof undirected_graph_counts[0])) {
2931
0
            IGRAPH_ERRORF("Graph size of % " IGRAPH_PRId " too large.", IGRAPH_EOVERFLOW, n);
2932
0
        }
2933
0
        *count = undirected_graph_counts[n];
2934
0
    }
2935
0
    return IGRAPH_SUCCESS;
2936
0
}