1 /* Copyright (c) 2007 Massachusetts Institute of Technology
3 * Permission is hereby granted, free of charge, to any person obtaining
4 * a copy of this software and associated documentation files (the
5 * "Software"), to deal in the Software without restriction, including
6 * without limitation the rights to use, copy, modify, merge, publish,
7 * distribute, sublicense, and/or sell copies of the Software, and to
8 * permit persons to whom the Software is furnished to do so, subject to
9 * the following conditions:
11 * The above copyright notice and this permission notice shall be
12 * included in all copies or substantial portions of the Software.
14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
15 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
16 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
17 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
18 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
19 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
20 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
26 /* Data on the primitive binary polynomials (a) and the corresponding
27 starting values m, for Sobol sequences in up to 1111 dimensions,
29 P. Bratley and B. L. Fox, Algorithm 659, ACM Trans.
30 Math. Soft. 14 (1), 88-100 (1988),
32 S. Joe and F. Y. Kuo, ACM Trans. Math. Soft 29 (1), 49-57 (2003). */
37 /* successive primitive binary-coefficient polynomials p(z)
38 = a_0 + a_1 z + a_2 z^2 + ... a_31 z^31, where a_i is the
39 i-th bit of sobol_a[j] for the j-th polynomial. */
40 static const uint32_t sobol_a[MAXDIM - 1] = {
41 3, 7, 11, 13, 19, 25, 37, 59, 47, 61, 55, 41, 67, 97, 91,
42 109, 103, 115, 131, 193, 137, 145, 143, 241, 157, 185, 167, 229, 171, 213,
43 191, 253, 203, 211, 239, 247, 285, 369, 299, 301, 333, 351, 355, 357, 361,
44 391, 397, 425, 451, 463, 487, 501, 529, 539, 545, 557, 563, 601, 607, 617,
45 623, 631, 637, 647, 661, 675, 677, 687, 695, 701, 719, 721, 731, 757, 761,
46 787, 789, 799, 803, 817, 827, 847, 859, 865, 875, 877, 883, 895, 901, 911,
47 949, 953, 967, 971, 973, 981, 985, 995, 1001, 1019, 1033, 1051, 1063,
48 1069, 1125, 1135, 1153, 1163, 1221, 1239, 1255, 1267, 1279, 1293, 1305,
49 1315, 1329, 1341, 1347, 1367, 1387, 1413, 1423, 1431, 1441, 1479, 1509,
50 1527, 1531, 1555, 1557, 1573, 1591, 1603, 1615, 1627, 1657, 1663, 1673,
51 1717, 1729, 1747, 1759, 1789, 1815, 1821, 1825, 1849, 1863, 1869, 1877,
52 1881, 1891, 1917, 1933, 1939, 1969, 2011, 2035, 2041, 2053, 2071, 2091,
53 2093, 2119, 2147, 2149, 2161, 2171, 2189, 2197, 2207, 2217, 2225, 2255,
54 2257, 2273, 2279, 2283, 2293, 2317, 2323, 2341, 2345, 2363, 2365, 2373,
55 2377, 2385, 2395, 2419, 2421, 2431, 2435, 2447, 2475, 2477, 2489, 2503,
56 2521, 2533, 2551, 2561, 2567, 2579, 2581, 2601, 2633, 2657, 2669,
57 2681, 2687, 2693, 2705, 2717, 2727, 2731, 2739,
58 2741, 2773, 2783, 2793, 2799, 2801, 2811, 2819, 2825, 2833, 2867, 2879,
59 2881, 2891, 2905, 2911, 2917, 2927, 2941, 2951, 2955, 2963, 2965, 2991,
60 2999, 3005, 3017, 3035, 3037, 3047, 3053, 3083, 3085, 3097, 3103, 3159,
61 3169, 3179, 3187, 3205, 3209, 3223, 3227, 3229, 3251, 3263, 3271, 3277,
62 3283, 3285, 3299, 3305, 3319, 3331, 3343, 3357, 3367, 3373, 3393, 3399,
63 3413, 3417, 3427, 3439, 3441, 3475, 3487, 3497, 3515, 3517, 3529, 3543,
64 3547, 3553, 3559, 3573, 3589, 3613, 3617, 3623, 3627, 3635, 3641, 3655,
65 3659, 3669, 3679, 3697, 3707, 3709, 3713, 3731, 3743, 3747, 3771, 3791,
66 3805, 3827, 3833, 3851, 3865, 3889, 3895, 3933, 3947, 3949, 3957, 3971,
67 3985, 3991, 3995, 4007, 4013, 4021, 4045, 4051, 4069, 4073, 4179, 4201,
68 4219, 4221, 4249, 4305, 4331, 4359, 4383, 4387, 4411, 4431, 4439, 4449,
69 4459, 4485, 4531, 4569, 4575, 4621, 4663, 4669, 4711, 4723, 4735, 4793,
70 4801, 4811, 4879, 4893, 4897, 4921, 4927, 4941, 4977, 5017, 5027, 5033,
71 5127, 5169, 5175, 5199, 5213, 5223, 5237, 5287, 5293, 5331, 5391, 5405,
72 5453, 5523, 5573, 5591, 5597, 5611, 5641, 5703, 5717, 5721, 5797, 5821,
74 5955, 5957, 6005, 6025, 6061, 6067, 6079, 6081,
75 6231, 6237, 6289, 6295, 6329, 6383, 6427, 6453, 6465, 6501, 6523, 6539,
76 6577, 6589, 6601, 6607, 6631, 6683, 6699, 6707, 6761, 6795, 6865, 6881,
77 6901, 6923, 6931, 6943, 6999, 7057, 7079, 7103, 7105, 7123, 7173, 7185,
78 7191, 7207, 7245, 7303, 7327, 7333, 7355, 7365, 7369, 7375, 7411, 7431,
79 7459, 7491, 7505, 7515, 7541, 7557, 7561, 7701, 7705, 7727, 7749, 7761,
80 7783, 7795, 7823, 7907, 7953, 7963, 7975, 8049, 8089, 8123, 8125, 8137,
81 8219, 8231, 8245, 8275, 8293, 8303, 8331, 8333, 8351, 8357, 8367, 8379,
82 8381, 8387, 8393, 8417, 8435, 8461, 8469, 8489, 8495, 8507, 8515, 8551,
83 8555, 8569, 8585, 8599, 8605, 8639, 8641, 8647, 8653, 8671, 8675, 8689,
84 8699, 8729, 8741, 8759, 8765, 8771, 8795, 8797, 8825, 8831, 8841, 8855,
85 8859, 8883, 8895, 8909, 8943, 8951, 8955, 8965, 8999, 9003, 9031, 9045,
86 9049, 9071, 9073, 9085, 9095, 9101, 9109, 9123, 9129, 9137, 9143, 9147,
87 9185, 9197, 9209, 9227, 9235, 9247, 9253, 9257, 9277, 9297, 9303, 9313,
88 9325, 9343, 9347, 9371, 9373, 9397, 9407, 9409, 9415, 9419, 9443, 9481,
89 9495, 9501, 9505, 9517, 9529, 9555, 9557, 9571, 9585, 9591, 9607, 9611,
91 9631, 9647, 9661, 9669, 9679, 9687, 9707, 9731,
92 9733, 9745, 9773, 9791, 9803, 9811, 9817, 9833, 9847, 9851, 9863, 9875,
93 9881, 9905, 9911, 9917, 9923, 9963, 9973, 10003, 10025, 10043, 10063,
94 10071, 10077, 10091, 10099, 10105, 10115, 10129, 10145, 10169, 10183,
95 10187, 10207, 10223, 10225, 10247, 10265, 10271, 10275, 10289, 10299,
96 10301, 10309, 10343, 10357, 10373, 10411, 10413, 10431, 10445, 10453,
97 10463, 10467, 10473, 10491, 10505, 10511, 10513, 10523, 10539, 10549,
98 10559, 10561, 10571, 10581, 10615, 10621, 10625, 10643, 10655, 10671,
99 10679, 10685, 10691, 10711, 10739, 10741, 10755, 10767, 10781, 10785,
100 10803, 10805, 10829, 10857, 10863, 10865, 10875, 10877, 10917, 10921,
101 10929, 10949, 10967, 10971, 10987, 10995, 11009, 11029, 11043, 11045,
102 11055, 11063, 11075, 11081, 11117, 11135, 11141, 11159, 11163, 11181,
103 11187, 11225, 11237, 11261, 11279, 11297, 11307, 11309, 11327, 11329,
104 11341, 11377, 11403, 11405, 11413, 11427, 11439, 11453, 11461, 11473,
105 11479, 11489, 11495, 11499, 11533, 11545, 11561, 11567, 11575, 11579,
106 11589, 11611, 11623, 11637, 11657, 11663, 11687, 11691, 11701, 11747,
107 11761, 11773, 11783, 11795, 11797, 11817, 11849, 11855, 11867, 11869,
109 11921, 11927, 11933, 11947, 11955, 11961,
110 11999, 12027, 12029, 12037, 12041, 12049, 12055, 12095, 12097, 12107,
111 12109, 12121, 12127, 12133, 12137, 12181, 12197, 12207, 12209, 12239,
112 12253, 12263, 12269, 12277, 12287, 12295, 12309, 12313, 12335, 12361,
113 12367, 12391, 12409, 12415, 12433, 12449, 12469, 12479, 12481, 12499,
114 12505, 12517, 12527, 12549, 12559, 12597, 12615, 12621, 12639, 12643,
115 12657, 12667, 12707, 12713, 12727, 12741, 12745, 12763, 12769, 12779,
116 12781, 12787, 12799, 12809, 12815, 12829, 12839, 12857, 12875, 12883,
117 12889, 12901, 12929, 12947, 12953, 12959, 12969, 12983, 12987, 12995,
118 13015, 13019, 13031, 13063, 13077, 13103, 13137, 13149, 13173, 13207,
119 13211, 13227, 13241, 13249, 13255, 13269, 13283, 13285, 13303, 13307,
120 13321, 13339, 13351, 13377, 13389, 13407, 13417, 13431, 13435, 13447,
121 13459, 13465, 13477, 13501, 13513, 13531, 13543, 13561, 13581, 13599,
122 13605, 13617, 13623, 13637, 13647, 13661, 13677, 13683, 13695, 13725,
123 13729, 13753, 13773, 13781, 13785, 13795, 13801, 13807, 13825, 13835,
124 13855, 13861, 13871, 13883, 13897, 13905, 13915, 13939, 13941, 13969,
125 13979, 13981, 13997, 14027, 14035, 14037, 14051, 14063, 14085, 14095,
126 14107, 14113, 14125, 14137, 14145,
127 14151, 14163, 14193, 14199, 14219, 14229,
128 14233, 14243, 14277, 14287, 14289, 14295, 14301, 14305, 14323, 14339,
129 14341, 14359, 14365, 14375, 14387, 14411, 14425, 14441, 14449, 14499,
130 14513, 14523, 14537, 14543, 14561, 14579, 14585, 14593, 14599, 14603,
131 14611, 14641, 14671, 14695, 14701, 14723, 14725, 14743, 14753, 14759,
132 14765, 14795, 14797, 14803, 14831, 14839, 14845, 14855, 14889, 14895,
133 14909, 14929, 14941, 14945, 14951, 14963, 14965, 14985, 15033, 15039,
134 15053, 15059, 15061, 15071, 15077, 15081, 15099, 15121, 15147, 15149,
135 15157, 15167, 15187, 15193, 15203, 15205, 15215, 15217, 15223, 15243,
136 15257, 15269, 15273, 15287, 15291, 15313, 15335, 15347, 15359, 15373,
137 15379, 15381, 15391, 15395, 15397, 15419, 15439, 15453, 15469, 15491,
138 15503, 15517, 15527, 15531, 15545, 15559, 15593, 15611, 15613, 15619,
139 15639, 15643, 15649, 15661, 15667, 15669, 15681, 15693, 15717, 15721,
140 15741, 15745, 15765, 15793, 15799, 15811, 15825, 15835, 15847, 15851,
141 15865, 15877, 15881, 15887, 15899, 15915, 15935, 15937, 15955, 15973,
142 15977, 16011, 16035, 16061, 16069, 16087, 16093, 16097, 16121, 16141,
143 16153, 16159, 16165, 16183, 16189, 16195, 16197, 16201, 16209, 16215,
144 16225, 16259, 16265, 16273, 16299,
145 16309, 16355, 16375, 16381,
148 /* starting direction #'s m[i] = sobol_minit[i][j] for i=0..d of the
149 * degree-d primitive polynomial sobol_a[j]. */
150 static const uint32_t sobol_minit[MAXDEG + 1][MAXDIM - 1] = {
152 {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
153 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
154 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
155 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
156 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
157 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
158 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
159 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
160 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
161 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
162 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
163 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
164 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
165 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
166 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
167 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
168 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
172 1, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3,
173 1, 3, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 3, 3, 1, 1,
174 3, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 3, 1, 3, 3,
175 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 3,
176 3, 1, 3, 3, 1, 3, 1, 1, 3, 3, 3, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 3, 1, 3, 1, 3, 3, 3, 3, 1,
177 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 3, 1, 1, 3, 3,
178 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 3, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1,
179 1, 3, 1, 1, 3, 3, 1, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1,
180 1, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 1, 3, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 3, 3, 1, 1, 3, 3,
181 1, 1, 1, 1, 3, 1, 3, 3, 1, 3, 3, 1, 1, 1, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 3, 1,
182 3, 1, 1, 3, 1, 3, 1, 1, 1, 3, 3, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 3, 3,
183 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3,
184 1, 3, 3, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 3, 3, 1, 3,
185 1, 1, 3, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 3, 1, 1,
186 3, 3, 1, 3, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 3, 1, 1, 3, 1,
187 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3,
188 1, 3, 1, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 1,
189 1, 1, 3, 3, 1, 1, 3, 3, 3, 3, 1, 1, 3, 1, 3, 3, 1, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3,
190 3, 3, 1, 1, 1, 3, 1, 3, 3, 1, 3, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 1, 3, 3, 1, 1, 3,
191 3, 1, 3, 3, 1, 3, 3, 1, 1, 3, 1, 3, 3, 1, 1, 3, 1, 3, 1, 3, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1,
192 3, 1, 1, 3, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 3, 1, 1, 3,
193 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 1, 3, 3, 3, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 3, 3, 1, 1,
194 1, 3, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 3, 1, 3, 3, 3, 1, 3, 1, 1, 3, 3, 1, 1, 3,
195 3, 1, 1, 1, 3, 1, 3, 3, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 1, 1, 1,
196 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 1, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 1, 3,
197 1, 1, 3, 3, 1, 1, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 1, 3, 3, 3, 1, 1, 1, 3, 1, 1, 1, 3, 3,
198 3, 1, 3, 3, 1, 3, 1, 1, 3, 3, 3, 1, 3, 3, 1, 1, 1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3,
199 1, 3, 1, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 1, 1,
200 3, 3, 1, 3, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3,
201 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1,
202 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 1, 3, 1, 1, 3, 3, 3, 1, 1, 3, 3, 3, 3,
203 3, 3, 3, 1, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 3, 1, 1, 3, 3, 1,
204 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 1, 3, 3, 1, 3,
205 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 3, 1, 1, 3, 1, 3, 3,
206 3, 3, 3, 1, 3, 1, 1, 3, 3, 3, 3, 1, 3, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 3, 1, 1, 3, 1,
207 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 3, 3, 1, 3, 1, 1, 3, 3, 3, 3, 3, 1, 3, 1,
208 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 3, 3, 3, 1, 3, 3, 3, 3, 1, 1,
209 3, 3, 3, 1, 3, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 3, 1, 1, 3, 3,
210 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 1, 3, 1, 3, 3, 3, 3, 3, 1},
213 7, 5, 1, 3, 3, 7, 5, 5, 7, 7, 1, 3, 3, 7, 5, 1, 1, 5, 3, 7,
214 1, 7, 5, 1, 3, 7, 7, 1, 1, 1, 5, 7, 7, 5, 1, 3, 3, 7, 5, 5, 5, 3, 3, 3, 1, 1, 5, 1, 1, 5,
215 3, 3, 3, 3, 1, 3, 7, 5, 7, 3, 7, 1, 3, 3, 5, 1, 3, 5, 5, 7, 7, 7, 1, 1, 3, 3, 1, 1, 5, 1,
216 5, 7, 5, 1, 7, 5, 3, 3, 1, 5, 7, 1, 7, 5, 1, 7, 3, 1, 7, 1, 7, 3, 3, 5, 7, 3, 3, 5, 1, 3,
217 3, 1, 3, 5, 1, 3, 3, 3, 7, 1, 1, 7, 3, 1, 3, 7, 5, 5, 7, 5, 5, 3, 1, 3, 3, 3, 1, 3, 3, 7,
218 3, 3, 1, 7, 5, 1, 7, 7, 5, 7, 5, 1, 3, 1, 7, 3, 7, 3, 5, 7, 3, 1, 3, 3, 3, 1, 5, 7, 3, 3,
219 7, 7, 7, 5, 3, 1, 7, 1, 3, 7, 5, 3, 3, 3, 7, 1, 1, 3, 1, 5, 7, 1, 3, 5, 3, 5, 3, 3, 7, 5,
220 5, 3, 3, 1, 3, 7, 7, 7, 1, 5, 7, 1, 3, 1, 1, 7, 1, 3, 1, 7, 1, 5, 3, 5, 3, 1, 1, 5, 5, 3,
221 3, 5, 7, 1, 5, 3, 7, 7, 3, 5, 3, 3, 1, 7, 3, 1, 3, 5, 7, 1, 3, 7, 1, 5, 1, 3, 1, 5, 3, 1,
222 7, 1, 5, 5, 5, 3, 7, 1, 1, 7, 3, 1, 1, 7, 5, 7, 5, 7, 7, 3, 7, 1, 3, 7, 7, 3, 5, 1, 1, 7,
223 1, 5, 5, 5, 1, 5, 1, 7, 5, 5, 7, 1, 1, 7, 1, 7, 7, 1, 1, 3, 3, 3, 7, 7, 5, 3, 7, 3, 1, 3,
224 7, 5, 3, 3, 5, 7, 1, 1, 5, 5, 7, 7, 1, 1, 1, 1, 5, 5, 5, 7, 5, 7, 1, 1, 3, 5, 1, 3, 3, 7,
225 3, 7, 5, 3, 5, 3, 1, 7, 1, 7, 7, 1, 1, 7, 7, 7, 5, 5, 1, 1, 7, 5, 5, 7, 5, 1, 1, 5, 5, 5,
226 5, 5, 5, 1, 3, 1, 5, 7, 3, 3, 5, 7, 3, 7, 1, 7, 7, 1, 3,
227 5, 1, 5, 5, 3, 7, 3, 7, 7, 5, 7, 5, 7, 1, 1, 5, 3, 5, 1,
228 5, 3, 7, 1, 5, 7, 7, 3, 5, 1, 3, 5, 1, 5, 3, 3, 3, 7, 3, 5, 1, 3, 7, 7, 3, 7, 5, 3, 3, 1,
229 7, 5, 1, 1, 3, 7, 1, 7, 1, 7, 3, 7, 3, 5, 7, 3, 5, 3, 1, 1, 1, 5, 7, 7, 3, 3, 1, 1, 1, 5,
230 5, 7, 3, 1, 1, 3, 3, 7, 3, 3, 5, 1, 3, 7, 3, 3, 7, 3, 5, 7, 5, 7, 7, 3, 3, 5, 1, 3, 5, 3,
231 1, 3, 5, 1, 1, 3, 7, 7, 1, 5, 1, 3, 7, 3, 7, 3, 5, 1, 7, 1, 1, 3, 5, 3, 7, 1, 5, 5, 1, 1,
232 3, 1, 3, 3, 7, 1, 7, 3, 1, 7, 3, 1, 7, 3, 5, 3, 5, 7, 3, 3, 3, 5, 1, 7, 7, 1, 3, 1, 3, 7,
233 7, 1, 3, 7, 3, 1, 5, 3, 1, 1, 1, 5, 3, 3, 7, 1, 5, 3, 5, 1, 3, 1, 3, 1, 5, 7, 7, 1, 1, 5,
234 3, 1, 5, 1, 1, 7, 7, 3, 5, 5, 1, 7, 1, 5, 1, 1, 3, 1, 5, 7, 5, 7, 7, 1, 5, 1, 1, 3, 5, 1,
235 5, 5, 3, 1, 3, 1, 5, 5, 3, 3, 3, 3, 1, 1, 3, 1, 3, 5, 5, 7, 5, 5, 7, 5, 7, 1, 3, 7, 7, 3,
236 5, 5, 7, 5, 5, 3, 3, 3, 1, 7, 1, 5, 5, 5, 3, 3, 5, 1, 3, 1, 3, 3, 3, 7, 1, 7, 7, 3, 7, 1,
237 1, 5, 7, 1, 7, 1, 7, 7, 1, 3, 7, 5, 1, 3, 5, 5, 5, 1, 1, 7, 1, 7, 1, 7, 7, 3, 1, 1, 5, 1,
238 5, 1, 5, 3, 5, 5, 5, 5, 5, 3, 3, 7, 3, 3, 5, 5, 3, 7, 1, 5, 7, 5, 1, 5, 5, 3, 5, 5, 7, 5,
239 3, 5, 5, 5, 1, 5, 5, 5, 5, 1, 3, 5, 3, 1, 7, 5, 5, 7, 1, 5, 3, 3, 1, 5, 3, 7, 1, 7, 5, 1,
240 1, 3, 1, 1, 7, 1, 5, 5, 3, 7, 3, 7, 5, 3, 1, 1, 3, 1, 3, 5,
241 5, 7, 5, 3, 7, 7, 7, 3, 7, 3, 7, 1, 3, 1, 7, 7, 1, 7,
242 3, 7, 3, 7, 3, 7, 3, 5, 1, 1, 7, 3, 1, 5, 5, 7, 1, 5, 5, 5, 7, 1, 5, 5, 1, 5, 5, 3, 1, 3,
243 1, 7, 3, 1, 3, 5, 7, 7, 7, 1, 1, 7, 3, 1, 5, 5, 5, 1, 1, 1, 1, 1, 5, 3, 5, 1, 3, 5, 3, 1,
244 1, 1, 1, 3, 7, 3, 7, 5, 7, 1, 5, 5, 7, 5, 3, 3, 7, 5, 3, 1, 1, 3, 1, 3, 1, 1, 3, 7, 1, 7,
245 1, 1, 5, 1, 7, 5, 3, 7, 3, 5, 3, 1, 1, 5, 5, 1, 7, 7, 3, 7, 3, 7, 1, 5, 1, 5, 3, 7, 3, 5,
246 7, 7, 7, 3, 3, 1, 1, 5, 5, 3, 7, 1, 1, 1, 3, 5, 3, 1, 1, 3, 3, 7, 5, 1, 1, 3, 7, 1, 5, 7,
247 3, 7, 5, 5, 7, 3, 5, 3, 1, 5, 3, 1, 1, 7, 5, 1, 7, 3, 7, 5, 1, 7, 1, 7, 7, 1, 1, 7, 1, 5,
248 5, 1, 1, 7, 5, 7, 1, 5, 3, 5, 3, 3, 7, 1, 5, 1, 1, 5, 5, 3, 3, 7, 5, 5, 1, 1, 1, 3, 1, 5,
249 7, 7, 1, 7, 5, 7, 3, 7, 3, 1, 3, 7, 3, 1, 5, 5, 3, 5, 1, 3, 5, 5, 5, 1, 1, 7, 7, 1, 5, 5,
250 1, 3, 5, 1, 5, 3, 5, 3, 3, 7, 5, 7, 3, 7, 3, 1, 3, 7, 7, 3, 3, 1, 1, 3, 3, 3, 3, 3, 5, 5,
251 3, 3, 3, 1, 3, 5, 7, 7, 1, 5, 7, 3, 7, 1, 1, 3, 5, 7, 5, 3, 3, 3},
254 1, 7, 9, 13, 11, 1, 3, 7, 9, 5, 13, 13, 11, 3, 15, 5, 3,
255 15, 7, 9, 13, 9, 1, 11, 7, 5, 15, 1, 15, 11, 5, 11, 1, 7, 9, 7, 7, 1, 15, 15, 15, 13,
256 3, 3, 15, 5, 9, 7, 13, 3, 7, 5, 11, 9, 1, 9, 1, 5, 7, 13, 9, 9, 1, 7, 3, 5, 1, 11, 11,
257 13, 7, 7, 9, 9, 1, 1, 3, 9, 15, 1, 5, 13, 1, 9, 9, 9, 9, 9, 13, 11, 3, 5, 11, 11, 13,
258 5, 3, 15, 1, 11, 11, 7, 13, 15, 11, 13, 9, 11, 15, 15, 13, 3, 15, 7, 9, 11, 13, 11,
259 9, 9, 5, 13, 9, 1, 13, 7, 7, 7, 7, 7, 5, 9, 7, 13, 11, 9, 11, 15, 3, 13, 11, 1, 11, 3,
260 3, 9, 11, 1, 7, 1, 15, 15, 3, 1, 9, 1, 7, 13, 11, 3, 13, 11, 7, 3, 3, 5, 13, 11, 5,
261 11, 1, 3, 9, 7, 15, 7, 5, 13, 7, 9, 13, 15, 13, 9, 7, 15, 7, 9, 5, 11, 11, 13, 13, 9,
262 3, 5, 13, 9, 11, 15, 11, 7, 1, 7, 13, 3, 13, 3, 13, 9, 15, 7, 13, 13, 3, 13, 15, 15,
263 11, 9, 13, 9, 15, 1, 1, 15, 11, 11, 7, 1, 11, 13, 9, 13, 3, 5, 11, 13, 9, 9, 13, 1,
264 11, 15, 13, 3, 13, 7, 15, 1, 15, 3, 3, 11, 7, 13, 7, 7, 9, 7, 5, 15, 9, 5, 5, 7, 15,
265 13, 15, 5, 15, 5, 3, 1, 11, 7, 1, 5, 7, 9, 3, 11, 1, 15, 1, 3, 15, 11, 13, 5, 13, 1,
266 7, 1, 15, 7, 5, 1, 1, 15, 13, 11, 11, 13, 5, 11, 7, 9, 7, 1, 5, 3, 9, 5, 5, 11, 5, 1,
267 7, 1, 11, 7, 9, 13, 15, 13, 3, 1, 11, 13, 15, 1, 1, 11, 9, 13, 3, 13, 11, 15, 13, 9,
268 9, 9, 5, 5, 5, 5, 1, 15, 5, 9,
269 11, 7, 15, 5, 3, 13, 5, 3, 11, 5, 1, 11, 13, 9, 11,
270 3, 7, 13, 15, 1, 7, 11, 1, 13, 1, 15, 1, 9, 7, 3, 9, 11, 1, 9, 13, 13, 3, 11, 7, 9, 1,
271 7, 15, 9, 1, 5, 13, 5, 11, 3, 9, 15, 11, 13, 5, 1, 7, 7, 5, 13, 7, 7, 9, 5, 11, 11, 1,
272 1, 15, 3, 13, 9, 13, 9, 9, 11, 5, 5, 13, 15, 3, 9, 15, 3, 11, 11, 15, 15, 3, 11, 15,
273 15, 3, 1, 3, 1, 3, 3, 1, 3, 13, 1, 11, 5, 15, 7, 15, 9, 1, 7, 1, 9, 11, 15, 1, 13, 9,
274 13, 11, 7, 3, 7, 3, 13, 7, 9, 7, 7, 3, 3, 9, 9, 7, 5, 11, 13, 13, 7, 7, 15, 9, 5, 5, 3,
275 3, 13, 3, 9, 3, 1, 11, 1, 3, 11, 15, 11, 11, 11, 9, 13, 7, 9, 15, 9, 11, 1, 3, 3, 9,
276 7, 15, 13, 13, 7, 15, 9, 13, 9, 15, 13, 15, 9, 13, 1, 11, 7, 11, 3, 13, 5, 1, 7, 15,
277 3, 13, 7, 13, 13, 11, 3, 5, 3, 13, 11, 9, 9, 3, 11, 11, 7, 9, 13, 11, 7, 15, 13, 7,
278 5, 3, 1, 5, 15, 15, 3, 11, 1, 7, 3, 15, 11, 5, 5, 3, 5, 5, 1, 15, 5, 1, 5, 3, 7, 5, 11,
279 3, 13, 9, 13, 15, 5, 3, 5, 9, 5, 3, 11, 1, 13, 9, 15, 3, 5, 11, 9, 1, 3, 15, 9, 9, 9,
280 11, 7, 5, 13, 1, 15, 3, 13, 9, 13, 5, 1, 5, 1, 13, 13, 7, 7, 1, 9, 5, 11, 9, 11, 13,
281 3, 15, 15, 13, 15, 7, 5, 7, 9, 7, 9, 9, 9, 11, 9, 3, 11, 15, 13, 13, 5, 9, 15, 1, 1,
282 9, 5, 13, 3, 13, 15, 3, 1, 3, 11, 13, 1, 15, 9, 9, 3, 1, 9, 1, 9, 1, 13, 11, 15, 7,
283 11, 15, 13, 15, 1, 9, 9, 7,
284 3, 5, 11, 7, 3, 9, 5, 15, 7, 5, 3, 13, 7, 1, 1, 9,
285 15, 15, 15, 11, 3, 5, 15, 13, 7, 15, 15, 11, 11, 9, 5, 15, 9, 7, 3, 13, 1, 1, 5, 1,
286 3, 1, 7, 1, 1, 5, 1, 11, 11, 9, 9, 5, 13, 7, 7, 7, 1, 1, 9, 9, 11, 11, 15, 7, 5, 5, 3,
287 11, 1, 3, 7, 13, 7, 7, 7, 3, 15, 15, 11, 9, 3, 9, 3, 15, 13, 5, 3, 3, 3, 5, 9, 15, 9,
288 9, 1, 5, 9, 9, 15, 5, 15, 7, 9, 1, 9, 9, 5, 11, 5, 15, 15, 11, 7, 7, 7, 1, 1, 11, 11,
289 13, 15, 3, 13, 5, 1, 7, 1, 11, 3, 13, 15, 3, 5, 3, 5, 7, 3, 9, 9, 5, 1, 7, 11, 9, 3, 5,
290 11, 13, 13, 13, 9, 15, 5, 7, 1, 15, 11, 9, 15, 15, 13, 13, 13, 1, 11, 9, 15, 9, 5,
291 15, 5, 7, 3, 11, 3, 15, 7, 13, 11, 7, 3, 7, 13, 5, 13, 15, 5, 13, 9, 1, 15, 11, 5, 5,
292 1, 11, 3, 3, 7, 1, 9, 7, 15, 9, 9, 3, 11, 15, 7, 1, 3, 1, 1, 1, 9, 1, 5, 15, 15, 7, 5,
293 5, 7, 9, 7, 15, 13, 13, 11, 1, 9, 11, 1, 13, 1, 7, 15, 15, 5, 5, 1, 11, 3, 9, 11, 9,
294 9, 9, 1, 9, 3, 5, 15, 1, 1, 9, 7, 3, 3, 1, 9, 9, 11, 9, 9, 13, 13, 3, 13, 11, 13, 5, 1,
295 5, 5, 9, 9, 3, 13, 13, 9, 15, 9, 11, 7, 11, 9, 13, 9, 1, 15, 9, 7, 7, 1, 7, 9, 9, 15,
296 1, 11, 1, 13, 13, 15, 9, 13, 7, 15, 3, 9, 3, 1, 13, 7, 5, 9, 3, 1, 7, 1, 1, 13, 3, 3,
297 11, 1, 7, 13, 15, 15, 5, 7, 13, 13, 15, 11, 13, 1, 13, 13, 3, 9, 15, 15, 11, 15, 9,
298 15, 1, 13, 15, 1, 1, 5,
299 11, 5, 1, 11, 11, 5, 3, 9, 1, 3, 5, 13, 9, 7, 7, 1,
300 9, 9, 15, 7, 5, 5, 15, 13, 9, 7, 13, 3, 13, 11, 13, 7, 9, 13, 13, 13, 15, 9, 5, 5, 3,
304 9, 3, 27, 15, 29, 21, 23, 19, 11, 25, 7, 13, 17, 1,
305 25, 29, 3, 31, 11, 5, 23, 27, 19, 21, 5, 1, 17, 13, 7, 15, 9, 31, 25, 3, 5, 23, 7,
306 3, 17, 23, 3, 3, 21, 25, 25, 23, 11, 19, 3, 11, 31, 7, 9, 5, 17, 23, 17, 17, 25,
307 13, 11, 31, 27, 19, 17, 23, 7, 5, 11, 19, 19, 7, 13, 21, 21, 7, 9, 11, 1, 5, 21,
308 11, 13, 25, 9, 7, 7, 27, 15, 25, 15, 21, 17, 19, 19, 21, 5, 11, 3, 5, 29, 31, 29,
309 5, 5, 1, 31, 27, 11, 13, 1, 3, 7, 11, 7, 3, 23, 13, 31, 17, 1, 27, 11, 25, 1, 23,
310 29, 17, 25, 7, 25, 27, 17, 13, 17, 23, 5, 17, 5, 13, 11, 21, 5, 11, 5, 9, 31, 19,
311 17, 9, 9, 27, 21, 15, 15, 1, 1, 29, 5, 31, 11, 17, 23, 19, 21, 25, 15, 11, 5, 5, 1,
312 19, 19, 19, 7, 13, 21, 17, 17, 25, 23, 19, 23, 15, 13, 5, 19, 25, 9, 7, 3, 21, 17,
313 25, 1, 27, 25, 27, 25, 9, 13, 3, 17, 25, 23, 9, 25, 9, 13, 17, 17, 3, 15, 7, 7, 29,
314 3, 19, 29, 29, 19, 29, 13, 15, 25, 27, 1, 3, 9, 9, 13, 31, 29, 31, 5, 15, 29, 1,
315 19, 5, 9, 19, 5, 15, 3, 5, 7, 15, 17, 17, 23, 11, 9, 23, 19, 3, 17, 1, 27, 9, 9, 17,
316 13, 25, 29, 23, 29, 11, 31, 25, 21, 29, 19, 27, 31, 3, 5, 3, 3, 13, 21, 9, 29, 3,
317 17, 11, 11, 9, 21, 19, 7, 17, 31, 25, 1, 27, 5, 15, 27, 29, 29, 29, 25, 27, 25, 3,
318 21, 17, 25, 13, 15, 17, 13, 23, 9, 3, 11, 7, 9, 9, 7, 17, 7, 1,
319 27, 1, 9, 5, 31, 21, 25, 25, 21, 11, 1, 23, 19, 27,
320 15, 3, 5, 23, 9, 25, 7, 29, 11, 9, 13, 5, 11, 1, 3, 31, 27, 3, 17, 27, 11, 13, 15,
321 29, 15, 1, 15, 23, 25, 13, 21, 15, 3, 29, 29, 5, 25, 17, 11, 7, 15, 5, 21, 7, 31,
322 13, 11, 23, 5, 7, 23, 27, 21, 29, 15, 7, 27, 27, 19, 7, 15, 27, 27, 19, 19, 9, 15,
323 1, 3, 29, 29, 5, 27, 31, 9, 1, 7, 3, 19, 19, 29, 9, 3, 21, 31, 29, 25, 1, 3, 9, 27,
324 5, 27, 25, 21, 11, 29, 31, 27, 21, 29, 17, 9, 17, 13, 11, 25, 15, 21, 11, 19, 31,
325 3, 19, 5, 3, 3, 9, 13, 13, 3, 29, 7, 5, 9, 23, 13, 21, 23, 21, 31, 11, 7, 7, 3, 23,
326 1, 23, 5, 9, 17, 21, 1, 17, 29, 7, 5, 17, 13, 25, 17, 9, 19, 9, 5, 7, 21, 19, 13, 9,
327 7, 3, 9, 3, 15, 31, 29, 29, 25, 13, 9, 21, 9, 31, 7, 15, 5, 31, 7, 15, 27, 25, 19,
328 9, 9, 25, 25, 23, 1, 9, 7, 11, 15, 19, 15, 27, 17, 11, 11, 31, 13, 25, 25, 9, 7,
329 13, 29, 19, 5, 19, 31, 25, 13, 25, 15, 5, 9, 29, 31, 9, 29, 27, 25, 27, 11, 17, 5,
330 17, 3, 23, 15, 9, 9, 17, 17, 31, 11, 19, 25, 13, 23, 15, 25, 21, 31, 19, 3, 11,
331 25, 7, 15, 19, 7, 5, 3, 13, 13, 1, 23, 5, 25, 11, 25, 15, 13, 21, 11, 23, 29, 5,
332 17, 27, 9, 19, 15, 5, 29, 23, 19, 1, 27, 3, 23, 21, 19, 27, 11, 17, 13, 27, 11,
333 31, 23, 5, 9, 21, 31, 29, 11, 21, 17, 15, 7, 15, 7, 9, 21, 27, 25,
334 29, 11, 3, 21, 13, 23, 19, 27, 17, 29, 25, 17, 9,
335 1, 19, 23, 5, 23, 1, 17, 17, 13, 27, 23, 7, 7, 11, 13, 17, 13, 11, 21, 13, 23, 1,
336 27, 13, 9, 7, 1, 27, 29, 5, 13, 25, 21, 3, 31, 15, 13, 3, 19, 13, 1, 27, 15, 17, 1,
337 3, 13, 13, 13, 31, 29, 27, 7, 7, 21, 29, 15, 17, 17, 21, 19, 17, 3, 15, 5, 27, 27,
338 3, 31, 31, 7, 21, 3, 13, 11, 17, 27, 25, 1, 9, 7, 29, 27, 21, 23, 13, 25, 29, 15,
339 17, 29, 9, 15, 3, 21, 15, 17, 17, 31, 9, 9, 23, 19, 25, 3, 1, 11, 27, 29, 1, 31,
340 29, 25, 29, 1, 23, 29, 25, 13, 3, 31, 25, 5, 5, 11, 3, 21, 9, 23, 7, 11, 23, 11, 1,
341 1, 3, 23, 25, 23, 1, 23, 3, 27, 9, 27, 3, 23, 25, 19, 29, 29, 13, 27, 5, 9, 29, 29,
342 13, 17, 3, 23, 19, 7, 13, 3, 19, 23, 5, 29, 29, 13, 13, 5, 19, 5, 17, 9, 11, 11,
343 29, 27, 23, 19, 17, 25, 13, 1, 13, 3, 11, 1, 17, 29, 1, 13, 17, 9, 17, 21, 1, 11,
344 1, 1, 25, 5, 7, 29, 29, 19, 19, 1, 29, 13, 3, 1, 31, 15, 13, 3, 1, 11, 19, 5, 29,
345 13, 29, 23, 3, 1, 31, 13, 19, 17, 5, 5, 1, 29, 23, 3, 19, 25, 19, 27, 9, 27, 13,
346 15, 29, 23, 13, 25, 25, 17, 19, 17, 15, 27, 3, 25, 17, 27, 3, 27, 31, 23, 13, 31,
347 11, 15, 7, 21, 19, 27, 19, 21, 29, 7, 31, 13, 9, 9, 7, 21, 13, 11, 9, 11, 29, 19,
348 11, 19, 21, 5, 29, 13, 7, 19, 19, 27, 23, 31, 1, 27, 21, 7, 3, 7, 11,
349 23, 13, 29, 11, 31, 19, 1, 5, 5, 11, 5, 3, 27, 5,
350 7, 11, 31, 1, 27, 31, 31, 23, 5, 21, 27, 9, 25, 3, 15, 19, 1, 19, 9, 5, 25, 21, 15,
351 25, 29, 15, 21, 11, 19, 15, 3, 7, 13, 11, 25, 17, 1, 5, 31, 13, 29, 23, 9, 5, 29,
352 7, 17, 27, 7, 17, 31, 9, 31, 9, 9, 7, 21, 3, 3, 3, 9, 11, 21, 11, 31, 9, 25, 5, 1,
353 31, 13, 29, 9, 29, 1, 11, 19, 7, 27, 13, 31, 7, 31, 7, 25, 23, 21, 29, 11, 11, 13,
354 11, 27, 1, 23, 31, 21, 23, 21, 19, 31, 5, 31, 25, 25, 19, 17, 11, 25, 7, 13, 1,
355 29, 17, 23, 15, 7, 29, 17, 13, 3, 17},
357 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
358 37, 33, 7, 5, 11, 39, 63, 59, 17, 15, 23, 29, 3, 21,
359 13, 31, 25, 9, 49, 33, 19, 29, 11, 19, 27, 15, 25, 63, 55, 17, 63, 49, 19, 41,
360 59, 3, 57, 33, 49, 53, 57, 57, 39, 21, 7, 53, 9, 55, 15, 59, 19, 49, 31, 3, 39, 5,
361 5, 41, 9, 19, 9, 57, 25, 1, 15, 51, 11, 19, 61, 53, 29, 19, 11, 9, 21, 19, 43, 13,
362 13, 41, 25, 31, 9, 11, 19, 5, 53, 37, 7, 51, 45, 7, 7, 61, 23, 45, 7, 59, 41, 1,
363 29, 61, 37, 27, 47, 15, 31, 35, 31, 17, 51, 13, 25, 45, 5, 5, 33, 39, 5, 47, 29,
364 35, 47, 63, 45, 37, 47, 59, 21, 59, 33, 51, 9, 27, 13, 25, 43, 3, 17, 21, 59, 61,
365 27, 47, 57, 11, 17, 39, 1, 63, 21, 59, 17, 13, 31, 3, 31, 7, 9, 27, 37, 23, 31, 9,
366 45, 43, 31, 63, 21, 39, 51, 27, 7, 53, 11, 1, 59, 39, 23, 49, 23, 7, 55, 59, 3,
367 19, 35, 13, 9, 13, 15, 23, 9, 7, 43, 55, 3, 19, 9, 27, 33, 27, 49, 23, 47, 19, 7,
368 11, 55, 27, 35, 5, 5, 55, 35, 37, 9, 33, 29, 47, 25, 11, 47, 53, 61, 59, 3, 53,
369 47, 5, 19, 59, 5, 47, 23, 45, 53, 3, 49, 61, 47, 39, 29, 17, 57, 5, 17, 31, 23,
370 41, 39, 5, 27, 7, 29, 29, 33, 31, 41, 31, 29, 17, 29, 29, 9, 9, 31, 27, 53, 35, 5,
371 61, 1, 49, 13, 57, 29, 5, 21, 43, 25, 57, 49, 37, 27, 11, 61, 37, 49, 5, 63, 63,
372 3, 45, 37, 63, 21, 21, 19, 27, 59, 21, 45, 23, 13, 15, 3, 43, 63, 39, 19,
373 63, 31, 41, 41, 15, 43, 63, 53, 1, 63, 31, 7, 17,
374 11, 61, 31, 51, 37, 29, 59, 25, 63, 59, 47, 15, 27, 19, 29, 45, 35, 55, 39, 19,
375 43, 21, 19, 13, 17, 51, 37, 5, 33, 35, 49, 25, 45, 1, 63, 47, 9, 63, 15, 25, 25,
376 15, 41, 13, 3, 19, 51, 49, 37, 25, 49, 13, 53, 47, 23, 35, 29, 33, 21, 35, 23, 3,
377 43, 31, 63, 9, 1, 61, 43, 3, 11, 55, 11, 35, 1, 63, 35, 49, 19, 45, 9, 57, 51, 1,
378 47, 41, 9, 11, 37, 19, 55, 23, 55, 55, 13, 7, 47, 37, 11, 43, 17, 3, 25, 19, 55,
379 59, 37, 33, 43, 1, 5, 21, 5, 63, 49, 61, 21, 51, 15, 19, 43, 47, 17, 9, 53, 45,
380 11, 51, 25, 11, 25, 47, 47, 1, 43, 29, 17, 31, 15, 59, 27, 63, 11, 41, 51, 29, 7,
381 27, 63, 31, 43, 3, 29, 39, 3, 59, 59, 1, 53, 63, 23, 63, 47, 51, 23, 61, 39, 47,
382 21, 39, 15, 3, 9, 57, 61, 39, 37, 21, 51, 1, 23, 43, 27, 25, 11, 13, 21, 43, 7,
383 11, 33, 55, 1, 37, 35, 27, 61, 39, 5, 19, 61, 61, 57, 59, 21, 59, 61, 57, 25, 55,
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385 35, 5, 31, 31, 37, 17, 45, 51, 1, 39, 49, 55, 19, 41, 13, 5, 51, 5, 49, 1, 21, 13,
386 17, 59, 51, 11, 3, 61, 1, 33, 37, 33, 61, 25, 27, 59, 7, 49, 13, 63, 3, 33, 3, 15,
387 9, 13, 35, 39, 11, 59, 59, 1, 57, 11, 5, 57, 13, 31, 13, 11, 55, 45, 9, 55, 55,
388 19, 25, 41, 23, 45, 29, 63, 59, 27, 39, 21, 37, 7,
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409 47, 25, 43, 15, 57, 45, 1, 49, 63, 57, 15, 31, 31, 7, 53, 27, 15, 47, 23, 7, 29,
410 53, 47, 9, 53, 3, 25, 55, 45, 63, 21, 17, 23, 31, 27, 27, 43, 63, 55, 63, 45, 51,
411 15, 27, 5, 37, 43, 11, 27, 5, 27, 59, 21, 7, 39, 27, 63, 35, 47, 55, 17, 17, 17,
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435 111, 105, 41, 115, 5, 69, 101, 27, 27, 101, 103, 53, 9, 21, 43, 79, 91, 65,
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447 39, 47, 53, 91, 3, 17, 51, 83, 39, 125, 85, 111,
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455 59, 41, 85, 77, 99, 55, 49, 93, 93, 119, 51, 125, 63, 13, 15, 45, 61, 19, 105,
456 115, 17, 83, 7, 7, 11, 61, 37, 63, 89, 95, 119, 113, 67, 123, 91, 33, 37, 99,
457 43, 11, 33, 65, 81, 79, 81, 107, 63, 63, 55, 89, 91, 25, 93, 101, 27, 55, 75,
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460 125, 97, 53, 41, 91, 111, 29, 31, 3, 103, 61, 71, 35, 7, 119, 29, 45, 49, 111,
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469 29, 57, 7, 65, 83, 99, 69, 19, 103, 43, 95, 25, 19, 103, 41, 125, 97, 71, 105,
470 83, 83, 61, 39, 9, 45, 117, 63, 31, 5, 117, 67, 125, 41, 117, 43, 77, 97, 15,
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475 103, 23, 125, 91, 31, 91, 51, 65, 61, 75, 69, 107, 65, 101, 59, 35, 15},
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497 41, 201, 5, 149, 35, 119, 183, 53, 11, 13, 3, 179, 229, 43, 55, 187, 233, 47,
498 133, 91, 47, 71, 93, 105, 145, 45, 255, 221, 115, 175, 19, 129, 5, 209, 197,
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505 253, 247, 129, 11, 251, 221, 153, 35, 103, 239, 7, 27, 235, 181, 5, 207, 53,
506 149, 155, 225, 165, 137, 155, 201, 97, 245, 203, 47, 39, 35, 105, 239, 49,
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510 187, 11, 91, 223, 29, 169, 231, 59, 31, 163, 41,
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512 21, 229, 93, 71, 61, 37, 183, 65, 211, 53, 11, 151, 165, 47, 5, 129, 79, 101,
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521 205, 225, 73, 45, 49, 149, 113, 253, 99, 17, 119, 105, 117, 129, 243, 75,
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526 123, 19, 109, 165, 103, 123, 219, 129, 155,
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582 161, 231, 43, 499, 73, 327, 263, 331, 249, 493, 37, 25, 115, 3, 167, 197,
583 127, 357, 497, 103, 125, 191, 165, 55, 101, 95, 79, 351, 341, 43, 125, 135,
584 173, 289, 373, 133, 421, 241, 281, 213, 177, 363, 151, 227, 145, 363, 239,
585 431, 81, 397, 241, 67, 291, 255, 405, 421, 399, 75, 399, 105, 329, 41, 425,
586 7, 283, 375, 475, 427, 277, 209, 411, 3, 137, 195, 289, 509, 121, 55, 147,
587 275, 251, 19, 129, 285, 415, 487, 491, 193, 219, 403, 23, 97, 65, 285, 75,
588 21, 373, 261, 339, 239, 495, 415, 333, 107, 435, 297, 213, 149, 463, 199,
589 323, 45, 19, 301, 121, 499, 187, 229, 63, 425, 99, 281, 35, 125, 349, 87,
590 101, 59, 195, 511, 355, 73, 263, 243, 101, 165, 141, 11, 389, 219, 187, 449,
591 447, 393, 477, 305, 221, 51, 355, 209, 499, 479, 265, 377, 145, 411, 173,
592 11, 433, 483, 135, 385, 341, 89, 209, 391, 33, 395, 319, 451, 119, 341, 227,
593 375, 61, 331, 493, 411, 293, 47, 203, 375, 167, 395, 155, 5, 237, 361, 489,
594 127, 21, 345, 101, 371, 233, 431, 109, 119, 277, 125, 263, 73, 135, 123, 83,
595 123, 405, 69, 75, 287, 401, 23, 283, 393, 41, 379, 431, 11, 475, 505, 19,
597 499, 489, 443, 165, 91, 83, 291, 319, 199,
598 107, 245, 389, 143, 137, 89, 125, 281, 381, 215, 131, 299, 249, 375, 455,
599 43, 73, 281, 217, 297, 229, 431, 357, 81, 357, 171, 451, 481, 13, 387, 491,
600 489, 439, 385, 487, 177, 393, 33, 71, 375, 443, 129, 407, 395, 127, 65, 333,
601 309, 119, 197, 435, 497, 373, 71, 379, 509, 387, 159, 265, 477, 463, 449,
602 47, 353, 249, 335, 505, 89, 141, 55, 235, 187, 87, 363, 93, 363, 101, 67,
603 215, 321, 331, 305, 261, 411, 491, 479, 65, 307, 469, 415, 131, 315, 487,
604 83, 455, 19, 113, 163, 503, 99, 499, 251, 239, 81, 167, 391, 255, 317, 363,
605 359, 395, 419, 307, 251, 267, 171, 461, 183, 465, 165, 163, 293, 477, 223,
606 403, 389, 97, 335, 357, 297, 19, 469, 501, 249, 85, 213, 311, 265, 379, 297,
607 283, 393, 449, 463, 289, 159, 289, 499, 407, 129, 137, 221, 43, 89, 403,
608 271, 75, 83, 445, 453, 389, 149, 143, 423, 499, 317, 445, 157, 137, 453,
609 163, 87, 23, 391, 119, 427, 323, 173, 89, 259, 377, 511, 249, 31, 363, 229,
610 353, 329, 493, 427, 57, 205, 389, 91, 83, 13, 219, 439, 45, 35, 371, 441, 17,
611 267, 501, 53, 25, 333, 17, 201, 475, 257, 417, 345, 381, 377, 55, 403, 77,
612 389, 347, 363, 211, 413, 419, 5, 167, 219, 201, 285, 425, 11, 77, 269, 489,
614 425, 125, 81, 331, 437, 271, 397, 299, 475,
615 271, 249, 413, 233, 261, 495, 171, 69, 27, 409, 21, 421, 367, 81, 483, 255,
616 15, 219, 365, 497, 181, 75, 431, 99, 325, 407, 229, 281, 63, 83, 493, 5, 113,
617 15, 271, 37, 87, 451, 299, 83, 451, 311, 441, 47, 455, 47, 253, 13, 109, 369,
618 347, 11, 409, 275, 63, 441, 15},
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622 519, 307, 931, 1023, 517, 771, 151, 1023,
623 539, 725, 45, 927, 707, 29, 125, 371, 275, 279, 817, 389, 453, 989, 1015,
624 29, 169, 743, 99, 923, 981, 181, 693, 309, 227, 111, 219, 897, 377, 425,
625 609, 227, 19, 221, 143, 581, 147, 919, 127, 725, 793, 289, 411, 835, 921,
626 957, 443, 349, 813, 5, 105, 457, 393, 539, 101, 197, 697, 27, 343, 515, 69,
627 485, 383, 855, 693, 133, 87, 743, 747, 475, 87, 469, 763, 721, 345, 479,
628 965, 527, 121, 271, 353, 467, 177, 245, 627, 113, 357, 7, 691, 725, 355,
629 889, 635, 737, 429, 545, 925, 357, 873, 187, 351, 677, 999, 921, 477, 233,
630 765, 495, 81, 953, 479, 89, 173, 473, 131, 961, 411, 291, 967, 65, 511, 13,
631 805, 945, 369, 827, 295, 163, 835, 259, 207, 331, 29, 315, 999, 133, 967,
632 41, 117, 677, 471, 717, 881, 755, 351, 723, 259, 879, 455, 721, 289, 149,
633 199, 805, 987, 851, 423, 597, 129, 11, 733, 549, 153, 285, 451, 559, 377,
634 109, 357, 143, 693, 615, 677, 701, 475, 767, 85, 229, 509, 547, 151, 389,
635 711, 785, 657, 319, 509, 99, 1007, 775, 359, 697, 677, 85, 497, 105, 615,
636 891, 71, 449, 835, 609, 377, 693, 665, 627, 215, 911, 503, 729, 131, 19,
637 895, 199, 161, 239, 633, 1013, 537, 255, 23, 149, 679, 1021, 595, 199, 557,
638 659, 251, 829, 727, 439, 495, 647, 223,
639 949, 625, 87, 481, 85, 799, 917, 769, 949,
640 739, 115, 499, 945, 547, 225, 1015, 469, 737, 495, 353, 103, 17, 665, 639,
641 525, 75, 447, 185, 43, 729, 577, 863, 735, 317, 99, 17, 477, 893, 537, 519,
642 1017, 375, 297, 325, 999, 353, 343, 729, 135, 489, 859, 267, 141, 831, 141,
643 893, 249, 807, 53, 613, 131, 547, 977, 131, 999, 175, 31, 341, 739, 467,
644 675, 241, 645, 247, 391, 583, 183, 973, 433, 367, 131, 467, 571, 309, 385,
645 977, 111, 917, 935, 473, 345, 411, 313, 97, 149, 959, 841, 839, 669, 431,
646 51, 41, 301, 247, 1015, 377, 329, 945, 269, 67, 979, 581, 643, 823, 557, 91,
647 405, 117, 801, 509, 347, 893, 303, 227, 783, 555, 867, 99, 703, 111, 797,
648 873, 541, 919, 513, 343, 319, 517, 135, 871, 917, 285, 663, 301, 15, 763,
649 89, 323, 757, 317, 807, 309, 1013, 345, 499, 279, 711, 915, 411, 281, 193,
650 739, 365, 315, 375, 809, 469, 487, 621, 857, 975, 537, 939, 585, 129, 625,
651 447, 129, 1017, 133, 83, 3, 415, 661, 53, 115, 903, 49, 79, 55, 385, 261,
652 345, 297, 199, 385, 617, 25, 515, 275, 849, 401, 471, 377, 661, 535, 505,
653 939, 465, 225, 929, 219, 955, 659, 441, 117, 527, 427, 515, 287, 191, 33,
654 389, 197, 825, 63, 417, 949, 35, 571, 9, 131, 609, 439, 95, 19, 569, 893,
656 125, 471, 187, 257, 67, 949, 621, 453, 411,
657 621, 955, 309, 783, 893, 597, 377, 753, 145, 637, 941, 593, 317, 555, 375,
658 575, 175, 403, 571, 555, 109, 377, 931, 499, 649, 653, 329, 279, 271, 647,
659 721, 665, 429, 957, 803, 767, 425, 477, 995, 105, 495, 575, 687, 385, 227,
660 923, 563, 723, 481, 717, 111, 633, 113, 369, 955, 253, 321, 409, 909, 367,
661 33, 967, 453, 863, 449, 539, 781, 911, 113, 7, 219, 725, 1015, 971, 1021,
662 525, 785, 873, 191, 893, 297, 507, 215, 21, 153, 645, 913, 755, 371, 881,
663 113, 903, 225, 49, 587, 201, 927, 429, 599, 513, 97, 319, 331, 833, 325,
664 887, 139, 927, 399, 163, 307, 803, 169, 1019, 869, 537, 907, 479, 335, 697,
665 479, 353, 769, 787, 1023, 855, 493, 883, 521, 735, 297, 1011, 991, 879,
666 855, 591, 415, 917, 375, 453, 553, 189, 841, 339, 211, 601, 57, 765, 745,
667 621, 209, 875, 639, 7, 595, 971, 263, 1009, 201, 23, 77, 621, 33, 535, 963,
668 661, 523, 263, 917, 103, 623, 231, 47, 301, 549, 337, 675, 189, 357, 1005,
669 789, 189, 319, 721, 1005, 525, 675, 539, 191, 813, 917, 51, 167, 415, 579,
670 755, 605, 721, 837, 529, 31, 327, 799, 961, 279, 409, 847, 649, 241, 285,
671 545, 407, 161, 591, 73, 313, 811, 17, 663, 269, 261, 37, 783, 127, 917, 231,
673 921, 343, 751, 139, 221, 79, 817, 393, 545,
674 11, 781, 71, 1, 699, 767, 917, 9, 107, 341, 587, 903, 965, 599, 507, 843,
675 739, 579, 397, 397, 325, 775, 565, 925, 75, 55, 979, 931, 93, 957, 857, 753,
676 965, 795, 67, 5, 87, 909, 97, 995, 271, 875, 671, 613, 33, 351, 69, 811, 669,
677 729, 401, 647, 241, 435, 447, 721, 271, 745, 53, 775, 99, 343, 451, 427,
678 593, 339, 845, 243, 345, 17, 573, 421, 517, 971, 499, 435, 769, 75, 203,
679 793, 985, 343, 955, 735, 523, 659, 703, 303, 421, 951, 405, 631, 825, 735,
680 433, 841, 485, 49, 749, 107, 669, 211, 497, 143, 99, 57, 277, 969, 107, 397,
681 563, 551, 447, 381, 187, 57, 405, 731, 769, 923, 955, 915, 737, 595, 341,
682 253, 823, 197, 321, 315, 181, 885, 497, 159, 571, 981, 899, 785, 947, 217,
683 217, 135, 753, 623, 565, 717, 903, 581, 955, 621, 361, 869, 87, 943, 907,
684 853, 353, 335, 197, 771, 433, 743, 195, 91, 1023, 63, 301, 647, 205, 485,
685 927, 1003, 987, 359, 577, 147, 141, 1017, 701, 273, 89, 589, 487, 859, 343,
686 91, 847, 341, 173, 287, 1003, 289, 639, 983, 685, 697, 35, 701, 645, 911,
687 501, 705, 873, 763, 745, 657, 559, 699, 315, 347, 429, 197, 165, 955, 859,
688 167, 303, 833, 531, 473, 635, 641, 195, 589, 821, 205, 3, 635, 371, 891,
690 77, 623, 993, 401, 525, 427, 71, 655, 951,
691 357, 851, 899, 535, 493, 323, 1003, 343, 515, 859, 1017, 5, 423, 315, 1011,
692 703, 41, 777, 163, 95, 831, 79, 975, 235, 633, 723, 297, 589, 317, 679, 981,
693 195, 399, 1003, 121, 501, 155},
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698 7, 2011, 1001, 49, 825, 415, 1441, 383, 1581,
699 623, 1621, 1319, 1387, 619, 839, 217, 75, 1955, 505, 281, 1629, 1379, 53,
700 1111, 1399, 301, 209, 49, 155, 1647, 631, 129, 1569, 335, 67, 1955, 1611,
701 2021, 1305, 121, 37, 877, 835, 1457, 669, 1405, 935, 1735, 665, 551, 789,
702 1543, 1267, 1027, 1, 1911, 163, 1929, 67, 1975, 1681, 1413, 191, 1711,
703 1307, 401, 725, 1229, 1403, 1609, 2035, 917, 921, 1789, 41, 2003, 187, 67,
704 1635, 717, 1449, 277, 1903, 1179, 363, 1211, 1231, 647, 1261, 1029, 1485,
705 1309, 1149, 317, 1335, 171, 243, 271, 1055, 1601, 1129, 1653, 205, 1463,
706 1681, 1621, 197, 951, 573, 1697, 1265, 1321, 1805, 1235, 1853, 1307, 945,
707 1197, 1411, 833, 273, 1517, 1747, 1095, 1345, 869, 57, 1383, 221, 1713,
708 335, 1751, 1141, 839, 523, 1861, 1105, 389, 1177, 1877, 805, 93, 1591,
709 423, 1835, 99, 1781, 1515, 1909, 1011, 303, 385, 1635, 357, 973, 1781,
710 1707, 1363, 1053, 649, 1469, 623, 1429, 1241, 1151, 1055, 503, 921, 3,
711 349, 1149, 293, 45, 303, 877, 1565, 1583, 1001, 663, 1535, 395, 1141,
712 1481, 1797, 643, 1507, 465, 2027, 1695, 367, 937, 719, 545, 1991, 83, 819,
713 239, 1791, 1461, 1647, 1501, 1161, 1629, 139, 1595, 1921, 1267, 1415,
714 509, 347, 777, 1083, 363, 269, 1015,
715 1809, 1105, 1429, 1471, 2019, 381, 2025,
716 1223, 827, 1733, 887, 1321, 803, 1951, 1297, 1995, 833, 1107, 1135, 1181,
717 1251, 983, 1389, 1565, 273, 137, 71, 735, 1005, 933, 67, 1471, 551, 457,
718 1667, 1729, 919, 285, 1629, 1815, 653, 1919, 1039, 531, 393, 1411, 359,
719 221, 699, 1485, 471, 1357, 1715, 595, 1677, 153, 1903, 1281, 215, 781,
720 543, 293, 1807, 965, 1695, 443, 1985, 321, 879, 1227, 1915, 839, 1945,
721 1993, 1165, 51, 557, 723, 1491, 817, 1237, 947, 1215, 1911, 1225, 1965,
722 1889, 1503, 1177, 73, 1767, 303, 177, 1897, 1401, 321, 921, 217, 1779,
723 327, 1889, 333, 615, 1665, 1825, 1639, 237, 1205, 361, 129, 1655, 983,
724 1089, 1171, 401, 677, 643, 749, 303, 1407, 1873, 1579, 1491, 1393, 1247,
725 789, 763, 49, 5, 1607, 1891, 735, 1557, 1909, 1765, 1777, 1127, 813, 695,
726 97, 731, 1503, 1751, 333, 769, 865, 693, 377, 1919, 957, 1359, 1627, 1039,
727 1783, 1065, 1665, 1917, 1947, 991, 1997, 841, 459, 221, 327, 1595, 1881,
728 1269, 1007, 129, 1413, 475, 1105, 791, 1983, 1359, 503, 691, 659, 691,
729 343, 1375, 1919, 263, 1373, 603, 1383, 297, 781, 145, 285, 767, 1739,
730 1715, 715, 317, 1333, 85, 831, 1615, 81, 1667, 1467, 1457, 1453, 1825,
731 109, 387, 1207, 2039, 213, 1351, 1329, 1173,
732 57, 1769, 951, 183, 23, 451, 1155, 1551,
733 2037, 811, 635, 1671, 1451, 863, 1499, 1673, 363, 1029, 1077, 1525, 277,
734 1023, 655, 665, 1869, 1255, 965, 277, 1601, 329, 1603, 1901, 395, 65,
735 1307, 2029, 21, 1321, 543, 1569, 1185, 1905, 1701, 413, 2041, 1697, 725,
736 1417, 1847, 411, 211, 915, 1891, 17, 1877, 1699, 687, 1089, 1973, 1809,
737 851, 1495, 1257, 63, 1323, 1307, 609, 881, 1543, 177, 617, 1505, 1747,
738 1537, 925, 183, 77, 1723, 1877, 1703, 397, 459, 521, 257, 1177, 389, 1947,
739 1553, 1583, 1831, 261, 485, 289, 1281, 1543, 1591, 1123, 573, 821, 1065,
740 1933, 1373, 2005, 905, 207, 173, 1573, 1597, 573, 1883, 1795, 1499, 1743,
741 553, 335, 333, 1645, 791, 871, 1157, 969, 557, 141, 223, 1129, 1685, 423,
742 1069, 391, 99, 95, 1847, 531, 1859, 1833, 1833, 341, 237, 1997, 1799, 409,
743 431, 1917, 363, 335, 1039, 1085, 1657, 1975, 1527, 1111, 659, 389, 899,
744 595, 1439, 1861, 1979, 1569, 1087, 1009, 165, 1895, 1481, 1583, 29, 1193,
745 1673, 1075, 301, 1081, 1377, 1747, 1497, 1103, 1789, 887, 739, 1577, 313,
746 1367, 1299, 1801, 1131, 1837, 73, 1865, 1065, 843, 635, 55, 1655, 913,
747 1037, 223, 1871, 1161, 461, 479, 511, 1721, 1107, 389, 151, 35, 375, 1099,
748 937, 1185, 1701, 769, 639, 1633,
749 1609, 379, 1613, 2031, 685, 289, 975, 671,
750 1599, 1447, 871, 647, 99, 139, 1427, 959, 89, 117, 841, 891, 1959, 223,
751 1697, 1145, 499, 1435, 1809, 1413, 1445, 1675, 171, 1073, 1349, 1545,
752 2039, 1027, 1563, 859, 215, 1673, 1919, 1633, 779, 411, 1845, 1477, 1489,
753 447, 1545, 351, 1989, 495, 183, 1639, 1385, 1805, 1097, 1249, 1431, 1571,
754 591, 697, 1509, 709, 31, 1563, 165, 513, 1425, 1299, 1081, 145, 1841,
755 1211, 941, 609, 845, 1169, 1865, 1593, 347, 293, 1277, 157, 211, 93, 1679,
756 1799, 527, 41, 473, 563, 187, 1525, 575, 1579, 857, 703, 1211, 647, 709,
757 981, 285, 697, 163, 981, 153, 1515, 47, 1553, 599, 225, 1147, 381, 135,
758 821, 1965, 609, 1033, 983, 503, 1117, 327, 453, 2005, 1257, 343, 1649,
759 1199, 599, 1877, 569, 695, 1587, 1475, 187, 973, 233, 511, 51, 1083, 665,
760 1321, 531, 1875, 1939, 859, 1507, 1979, 1203, 1965, 737, 921, 1565, 1943,
761 819, 223, 365, 167, 1705, 413, 1577, 745, 1573, 655, 1633, 1003, 91, 1123,
762 477, 1741, 1663, 35, 715, 37, 1513, 815, 941, 1379, 263, 1831, 1735, 1111,
763 1449, 353, 1941, 1655, 1349, 877, 285, 1723, 125, 1753, 985, 723, 175,
764 439, 791, 1051, 1261, 717, 1555, 1757, 1777, 577, 1583, 1957, 873, 331,
765 1163, 313, 1, 1963, 963, 1905, 821,
766 1677, 185, 709, 545, 1723, 215, 1885,
767 1249, 583, 1803, 839, 885, 485, 413, 1767, 425, 129, 1035, 329, 1263,
768 1881, 1779, 1565, 359, 367, 453, 707, 1419, 831, 1889, 887, 1871, 1869,
769 747, 223, 1547, 1799, 433, 1441, 553, 2021, 1303, 1505, 1735, 1619, 1065,
770 1161, 2047, 347, 867, 881, 1447, 329, 781, 1065, 219, 589, 645, 1257,
771 1833, 749, 1841, 1733, 1179, 1191, 1025, 1639, 1955, 1423, 1685, 1711,
772 493, 549, 783, 1653, 397, 895, 233, 759, 1505, 677, 1449, 1573, 1297,
773 1821, 1691, 791, 289, 1187, 867, 1535, 575, 183},
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780 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
781 3915, 97, 3047, 937, 2897, 953, 127, 1201,
782 3819, 193, 2053, 3061, 3759, 1553, 2007, 2493, 603, 3343, 3751, 1059,
783 783, 1789, 1589, 283, 1093, 3919, 2747, 277, 2605, 2169, 2905, 721, 4069,
784 233, 261, 1137, 3993, 3619, 2881, 1275, 3865, 1299, 3757, 1193, 733, 993,
785 1153, 2945, 3163, 3179, 437, 271, 3493, 3971, 1005, 2615, 2253, 1131,
786 585, 2775, 2171, 2383, 2937, 2447, 1745, 663, 1515, 3767, 2709, 1767,
787 3185, 3017, 2815, 1829, 87, 3341, 793, 2627, 2169, 1875, 3745, 367, 3783,
788 783, 827, 3253, 2639, 2955, 3539, 1579, 2109, 379, 2939, 3019, 1999,
789 2253, 2911, 3733, 481, 1767, 1055, 4019, 4085, 105, 1829, 2097, 2379,
790 1567, 2713, 737, 3423, 3941, 2659, 3961, 1755, 3613, 1937, 1559, 2287,
791 2743, 67, 2859, 325, 2601, 1149, 3259, 2403, 3947, 2011, 175, 3389, 3915,
792 1315, 2447, 141, 359, 3609, 3933, 729, 2051, 1755, 2149, 2107, 1741,
793 1051, 3681, 471, 1055, 845, 257, 1559, 1061, 2803, 2219, 1315, 1369,
794 3211, 4027, 105, 11, 1077, 2857, 337, 3553, 3503, 3917, 2665, 3823, 3403,
795 3711, 2085, 1103, 1641, 701, 4095, 2883, 1435, 653, 2363, 1597, 767, 869,
796 1825, 1117, 1297, 501, 505, 149, 873, 2673, 551, 1499, 2793, 3277, 2143,
797 3663, 533, 3991, 575, 1877, 1009, 3929, 473, 3009, 2595, 3249, 675, 3593,
798 2453, 1567, 973, 595, 1335, 1715, 589, 85,
799 2265, 3069, 461, 1659, 2627, 1307, 1731, 1501, 1699, 3545, 3803, 2157,
800 453, 2813, 2047, 2999, 3841, 2361, 1079, 573, 69, 1363, 1597, 3427, 2899,
801 2771, 1327, 1117, 1523, 3521, 2393, 2537, 1979, 3179, 683, 2453, 453,
802 1227, 779, 671, 3483, 2135, 3139, 3381, 3945, 57, 1541, 3405, 3381, 2371,
803 2879, 1985, 987, 3017, 3031, 3839, 1401, 3749, 2977, 681, 1175, 1519,
804 3355, 907, 117, 771, 3741, 3337, 1743, 1227, 3335, 2755, 1909, 3603,
805 2397, 653, 87, 2025, 2617, 3257, 287, 3051, 3809, 897, 2215, 63, 2043,
806 1757, 3671, 297, 3131, 1305, 293, 3865, 3173, 3397, 2269, 3673, 717,
807 3041, 3341, 3595, 3819, 2871, 3973, 1129, 513, 871, 1485, 3977, 2473,
808 1171, 1143, 3063, 3547, 2183, 3993, 133, 2529, 2699, 233, 2355, 231,
809 3241, 611, 1309, 3829, 1839, 1495, 301, 1169, 1613, 2673, 243, 3601,
810 3669, 2813, 2671, 2679, 3463, 2477, 1795, 617, 2317, 1855, 1057, 1703,
811 1761, 2515, 801, 1205, 1311, 473, 3963, 697, 1221, 251, 381, 3887, 1761,
812 3093, 3721, 2079, 4085, 379, 3601, 3845, 433, 1781, 29, 1897, 1599, 2163,
813 75, 3475, 3957, 1641, 3911, 2959, 2833, 1279, 1099, 403, 799, 2183, 2699,
814 1711, 2037, 727, 289, 1785, 1575, 3633, 2367, 1261, 3953, 1735, 171,
816 2867, 859, 2951, 3211, 15, 1279, 1323, 599,
817 1651, 3951, 1011, 315, 3513, 3351, 1725, 3793, 2399, 287, 4017, 3571,
818 1007, 541, 3115, 429, 1585, 1285, 755, 1211, 3047, 915, 3611, 2697, 2129,
819 3669, 81, 3939, 2437, 915, 779, 3567, 3701, 2479, 3807, 1893, 3927, 2619,
820 2543, 3633, 2007, 3857, 3837, 487, 1769, 3759, 3105, 2727, 3155, 2479,
821 1341, 1657, 2767, 2541, 577, 2105, 799, 17, 2871, 3637, 953, 65, 69, 2897,
822 3841, 3559, 4067, 2335, 3409, 1087, 425, 2813, 1705, 1701, 1237, 821,
823 1375, 3673, 2693, 3925, 1541, 1871, 2285, 847, 4035, 1101, 2029, 855,
824 2733, 2503, 121, 2855, 1069, 3463, 3505, 1539, 607, 1349, 575, 2301,
825 2321, 1101, 333, 291, 2171, 4085, 2173, 2541, 1195, 925, 4039, 1379, 699,
826 1979, 275, 953, 1755, 1643, 325, 101, 2263, 3329, 3673, 3413, 1977, 2727,
827 2313, 1419, 887, 609, 2475, 591, 2613, 2081, 3805, 3435, 2409, 111, 3557,
828 3607, 903, 231, 3059, 473, 2959, 2925, 3861, 2043, 3887, 351, 2865, 369,
829 1377, 2639, 1261, 3625, 3279, 2201, 2949, 3049, 449, 1297, 897, 1891,
830 411, 2773, 749, 2753, 1825, 853, 2775, 3547, 3923, 3923, 987, 3723, 2189,
831 3877, 3577, 297, 2763, 1845, 3083, 2951, 483, 2169, 3985, 245, 3655,
832 3441, 1023, 235, 835, 3693, 3585, 327, 1003, 543, 3059, 2637,
833 2923, 87, 3617, 1031, 1043, 903, 2913,
834 2177, 2641, 3279, 389, 2009, 525, 4085, 3299, 987, 2409, 813, 2683, 373,
835 2695, 3775, 2375, 1119, 2791, 223, 325, 587, 1379, 2877, 2867, 3793, 655,
836 831, 3425, 1663, 1681, 2657, 1865, 3943, 2977, 1979, 2271, 3247, 1267,
837 1747, 811, 159, 429, 2001, 1195, 3065, 553, 1499, 3529, 1081, 2877, 3077,
838 845, 1793, 2409, 3995, 2559, 4081, 1195, 2955, 1117, 1409, 785, 287,
839 1521, 1607, 85, 3055, 3123, 2533, 2329, 3477, 799, 3683, 3715, 337, 3139,
840 3311, 431, 3511, 2299, 365, 2941, 3067, 1331, 1081, 1097, 2853, 2299,
841 495, 1745, 749, 3819, 619, 1059, 3559, 183, 3743, 723, 949, 3501, 733,
842 2599, 3983, 3961, 911, 1899, 985, 2493, 1795, 653, 157, 433, 2361, 3093,
843 3119, 3679, 2367, 1701, 1445, 1321, 2397, 1241, 3305, 3985, 2349, 4067,
844 3805, 3073, 2837, 1567, 3783, 451, 2441, 1181, 487, 543, 1201, 3735,
845 2517, 733, 1535, 2175, 3613, 3019},
847 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
848 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
849 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
850 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
851 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
852 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
853 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
854 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
855 2319, 653, 1379, 1675, 1951, 7075, 2087,
856 7147, 1427, 893, 171, 2019, 7235, 5697, 3615, 1961, 7517, 6849, 2893,
857 1883, 2863, 2173, 4543, 73, 381, 3893, 6045, 1643, 7669, 1027, 1549,
858 3983, 1985, 6589, 7497, 2745, 2375, 7047, 1117, 1171, 1975, 5199, 3915,
859 3695, 8113, 4303, 3773, 7705, 6855, 1675, 2245, 2817, 1719, 569, 1021,
860 2077, 5945, 1833, 2631, 4851, 6371, 833, 7987, 331, 1899, 8093, 6719,
861 6903, 5903, 5657, 5007, 2689, 6637, 2675, 1645, 1819, 689, 6709, 7717,
862 6295, 7013, 7695, 3705, 7069, 2621, 3631, 6571, 6259, 7261, 3397, 7645,
863 1115, 4753, 2047, 7579, 2271, 5403, 4911, 7629, 4225, 1209, 6955, 6951,
864 1829, 5579, 5231, 1783, 4285, 7425, 599, 5785, 3275, 5643, 2263, 657,
865 6769, 6261, 1251, 3249, 4447, 4111, 3991, 1215, 131, 4397, 3487, 7585,
866 5565, 7199, 3573, 7105, 7409, 1671, 949, 3889, 5971, 3333, 225, 3647,
867 5403, 3409, 7459, 6879, 5789, 6567, 5581, 4919, 1927, 4407, 8085, 4691,
868 611, 3005, 591, 753, 589, 171, 5729, 5891, 1033, 3049, 6567, 5257, 8003,
869 1757, 4489, 4923, 6379, 5171, 1757, 689, 3081, 1389, 4113, 455, 2761,
870 847, 7575, 5829, 633, 6629, 1103, 7635, 803, 6175, 6587, 2711, 3879, 67,
871 1179, 4761, 7281, 1557, 3379, 2459, 4273, 4127, 7147, 35,
872 3549, 395, 3735, 5787, 4179, 5889, 5057,
873 7473, 4713, 2133, 2897, 1841, 2125, 1029, 1695, 6523, 1143, 5105, 7133,
874 3351, 2775, 3971, 4503, 7589, 5155, 4305, 1641, 4717, 2427, 5617, 1267,
875 399, 5831, 4305, 4241, 3395, 3045, 4899, 1713, 171, 411, 7099, 5473,
876 5209, 1195, 1077, 1309, 2953, 7343, 4887, 3229, 6759, 6721, 6775, 675,
877 4039, 2493, 7511, 3269, 4199, 6625, 7943, 2013, 4145, 667, 513, 2303,
878 4591, 7941, 2741, 987, 8061, 3161, 5951, 1431, 831, 5559, 7405, 1357,
879 4319, 4235, 5421, 2559, 4415, 2439, 823, 1725, 6219, 4903, 6699, 5451,
880 349, 7703, 2927, 7809, 6179, 1417, 5987, 3017, 4983, 3479, 4525, 4643,
881 4911, 227, 5475, 2287, 5581, 6817, 1937, 1421, 4415, 7977, 1789, 3907,
882 6815, 6789, 6003, 5609, 4507, 337, 7427, 7943, 3075, 6427, 1019, 7121,
883 4763, 81, 3587, 2929, 1795, 8067, 2415, 1265, 4025, 5599, 4771, 3025,
884 2313, 6129, 7611, 6881, 5253, 4413, 7869, 105, 3173, 1629, 2537, 1023,
885 4409, 7209, 4413, 7107, 7469, 33, 1955, 2881, 5167, 6451, 4211, 179,
886 5573, 7879, 3387, 7759, 5455, 7157, 1891, 5683, 5689, 6535, 3109, 6555,
887 6873, 1249, 4251, 6437, 49, 2745, 1201, 7327, 4179, 6783, 623, 2779,
888 5963, 2585, 6927, 5333, 4033, 285, 7467, 4443, 4917, 3,
889 4319, 5517, 3449, 813, 5499, 2515, 5771,
890 3357, 2073, 4395, 4925, 2643, 7215, 5817, 1199, 1597, 1619, 7535, 4833,
891 609, 4797, 8171, 6847, 793, 6757, 8165, 3371, 2431, 5235, 4739, 7703,
892 7223, 6525, 5891, 5605, 4433, 3533, 5267, 5125, 5037, 225, 6717, 1121,
893 5741, 2013, 4327, 4839, 569, 5227, 7677, 4315, 2391, 5551, 859, 3627,
894 6377, 3903, 4311, 6527, 7573, 4905, 7731, 1909, 1555, 3279, 1949, 1887,
895 6675, 5509, 2033, 5473, 3539, 5033, 5935, 6095, 4761, 1771, 1271, 1717,
896 4415, 5083, 6277, 3147, 7695, 2461, 4783, 4539, 5833, 5583, 651, 1419,
897 2605, 5511, 3913, 5795, 2333, 2329, 4431, 3725, 6069, 2699, 7055, 6879,
898 1017, 3121, 2547, 4603, 2385, 6915, 6103, 5669, 7833, 2001, 4287, 6619,
899 955, 2761, 5711, 6291, 3415, 3909, 2841, 5627, 4939, 7671, 6059, 6275,
900 6517, 1931, 4583, 7301, 1267, 7509, 1435, 2169, 6939, 3515, 2985, 2787,
901 2123, 1969, 3307, 353, 4359, 7059, 5273, 5873, 6657, 6765, 6229, 3179,
902 1583, 6237, 2155, 371, 273, 7491, 3309, 6805, 3015, 6831, 7819, 713,
903 4747, 3935, 4109, 1311, 709, 3089, 7059, 4247, 2989, 1509, 4919, 1841,
904 3045, 3821, 6929, 4655, 1333, 6429, 6649, 2131, 5265, 1051, 261, 8057,
905 3379, 2179, 1993, 5655, 3063, 6381,
906 3587, 7417, 1579, 1541, 2107, 5085, 2873,
907 6141, 955, 3537, 2157, 841, 1999, 1465, 5171, 5651, 1535, 7235, 4349,
908 1263, 1453, 1005, 6893, 2919, 1947, 1635, 3963, 397, 969, 4569, 655,
909 6737, 2995, 7235, 7713, 973, 4821, 2377, 1673, 1, 6541}
~ianmdlvl / nlopt.git / blob