untabify source files, make indenting more uniform with GNU indent -kr --no-tabs...

[nlopt.git] / src / util / soboldata.h

diff --git a/src/util/soboldata.h b/src/util/soboldata.h
index 19efa5b0a25e2497411d79f5ef0d9f17261675ee..cddf551f53fb5dc702a55d3f2186d0f128d8068d 100644 (file)
--- a/src/util/soboldata.h
+++ b/src/util/soboldata.h
@@ -37,844 +37,876 @@
 /* successive primitive binary-coefficient polynomials p(z)
    = a_0 + a_1 z + a_2 z^2 + ... a_31 z^31, where a_i is the 
      i-th bit of sobol_a[j] for the j-th polynomial. */
-static const uint32_t sobol_a[MAXDIM-1] = {
-     3,7,11,13,19,25,37,59,47,61,55,41,67,97,91,
-     109,103,115,131,193,137,145,143,241,157,185,167,229,171,213,
-     191,253,203,211,239,247,285,369,299,301,333,351,355,357,361,
-     391,397,425,451,463,487,501,529,539,545,557,563,601,607,617,
-     623,631,637,647,661,675,677,687,695,701,719,721,731,757,761,
-     787,789,799,803,817,827,847,859,865,875,877,883,895,901,911,
-     949,953,967,971,973,981,985,995,1001,1019,1033,1051,1063,
-     1069,1125,1135,1153,1163,1221,1239,1255,1267,1279,1293,1305,
-     1315,1329,1341,1347,1367,1387,1413,1423,1431,1441,1479,1509,
-     1527,1531,1555,1557,1573,1591,1603,1615,1627,1657,1663,1673,
-     1717,1729,1747,1759,1789,1815,1821,1825,1849,1863,1869,1877,
-     1881,1891,1917,1933,1939,1969,2011,2035,2041,2053,2071,2091,
-     2093,2119,2147,2149,2161,2171,2189,2197,2207,2217,2225,2255,
-     2257,2273,2279,2283,2293,2317,2323,2341,2345,2363,2365,2373,
-     2377,2385,2395,2419,2421,2431,2435,2447,2475,2477,2489,2503,
-     2521,2533,2551,2561,2567,2579,2581,2601,2633,2657,2669,
-     2681,2687,2693,2705,2717,2727,2731,2739,
-     2741,2773,2783,2793,2799,2801,2811,2819,2825,2833,2867,2879,
-     2881,2891,2905,2911,2917,2927,2941,2951,2955,2963,2965,2991,
-     2999,3005,3017,3035,3037,3047,3053,3083,3085,3097,3103,3159,
-     3169,3179,3187,3205,3209,3223,3227,3229,3251,3263,3271,3277,
-     3283,3285,3299,3305,3319,3331,3343,3357,3367,3373,3393,3399,
-     3413,3417,3427,3439,3441,3475,3487,3497,3515,3517,3529,3543,
-     3547,3553,3559,3573,3589,3613,3617,3623,3627,3635,3641,3655,
-     3659,3669,3679,3697,3707,3709,3713,3731,3743,3747,3771,3791,
-     3805,3827,3833,3851,3865,3889,3895,3933,3947,3949,3957,3971,
-     3985,3991,3995,4007,4013,4021,4045,4051,4069,4073,4179,4201,
-     4219,4221,4249,4305,4331,4359,4383,4387,4411,4431,4439,4449,
-     4459,4485,4531,4569,4575,4621,4663,4669,4711,4723,4735,4793,
-     4801,4811,4879,4893,4897,4921,4927,4941,4977,5017,5027,5033,
-     5127,5169,5175,5199,5213,5223,5237,5287,5293,5331,5391,5405,
-     5453,5523,5573,5591,5597,5611,5641,5703,5717,5721,5797,5821,
-     5909,5913,
-     5955,5957,6005,6025,6061,6067,6079,6081,
-     6231,6237,6289,6295,6329,6383,6427,6453,6465,6501,6523,6539,
-     6577,6589,6601,6607,6631,6683,6699,6707,6761,6795,6865,6881,
-     6901,6923,6931,6943,6999,7057,7079,7103,7105,7123,7173,7185,
-     7191,7207,7245,7303,7327,7333,7355,7365,7369,7375,7411,7431,
-     7459,7491,7505,7515,7541,7557,7561,7701,7705,7727,7749,7761,
-     7783,7795,7823,7907,7953,7963,7975,8049,8089,8123,8125,8137,
-     8219,8231,8245,8275,8293,8303,8331,8333,8351,8357,8367,8379,
-     8381,8387,8393,8417,8435,8461,8469,8489,8495,8507,8515,8551,
-     8555,8569,8585,8599,8605,8639,8641,8647,8653,8671,8675,8689,
-     8699,8729,8741,8759,8765,8771,8795,8797,8825,8831,8841,8855,
-     8859,8883,8895,8909,8943,8951,8955,8965,8999,9003,9031,9045,
-     9049,9071,9073,9085,9095,9101,9109,9123,9129,9137,9143,9147,
-     9185,9197,9209,9227,9235,9247,9253,9257,9277,9297,9303,9313,
-     9325,9343,9347,9371,9373,9397,9407,9409,9415,9419,9443,9481,
-     9495,9501,9505,9517,9529,9555,9557,9571,9585,9591,9607,9611,
-     9621,9625,
-     9631,9647,9661,9669,9679,9687,9707,9731,
-     9733,9745,9773,9791,9803,9811,9817,9833,9847,9851,9863,9875,
-     9881,9905,9911,9917,9923,9963,9973,10003,10025,10043,10063,
-     10071,10077,10091,10099,10105,10115,10129,10145,10169,10183,
-     10187,10207,10223,10225,10247,10265,10271,10275,10289,10299,
-     10301,10309,10343,10357,10373,10411,10413,10431,10445,10453,
-     10463,10467,10473,10491,10505,10511,10513,10523,10539,10549,
-     10559,10561,10571,10581,10615,10621,10625,10643,10655,10671,
-     10679,10685,10691,10711,10739,10741,10755,10767,10781,10785,
-     10803,10805,10829,10857,10863,10865,10875,10877,10917,10921,
-     10929,10949,10967,10971,10987,10995,11009,11029,11043,11045,
-     11055,11063,11075,11081,11117,11135,11141,11159,11163,11181,
-     11187,11225,11237,11261,11279,11297,11307,11309,11327,11329,
-     11341,11377,11403,11405,11413,11427,11439,11453,11461,11473,
-     11479,11489,11495,11499,11533,11545,11561,11567,11575,11579,
-     11589,11611,11623,11637,11657,11663,11687,11691,11701,11747,
-     11761,11773,11783,11795,11797,11817,11849,11855,11867,11869,
-     11873,11883,11919,
-     11921,11927,11933,11947,11955,11961,
-     11999,12027,12029,12037,12041,12049,12055,12095,12097,12107,
-     12109,12121,12127,12133,12137,12181,12197,12207,12209,12239,
-     12253,12263,12269,12277,12287,12295,12309,12313,12335,12361,
-     12367,12391,12409,12415,12433,12449,12469,12479,12481,12499,
-     12505,12517,12527,12549,12559,12597,12615,12621,12639,12643,
-     12657,12667,12707,12713,12727,12741,12745,12763,12769,12779,
-     12781,12787,12799,12809,12815,12829,12839,12857,12875,12883,
-     12889,12901,12929,12947,12953,12959,12969,12983,12987,12995,
-     13015,13019,13031,13063,13077,13103,13137,13149,13173,13207,
-     13211,13227,13241,13249,13255,13269,13283,13285,13303,13307,
-     13321,13339,13351,13377,13389,13407,13417,13431,13435,13447,
-     13459,13465,13477,13501,13513,13531,13543,13561,13581,13599,
-     13605,13617,13623,13637,13647,13661,13677,13683,13695,13725,
-     13729,13753,13773,13781,13785,13795,13801,13807,13825,13835,
-     13855,13861,13871,13883,13897,13905,13915,13939,13941,13969,
-     13979,13981,13997,14027,14035,14037,14051,14063,14085,14095,
-     14107,14113,14125,14137,14145,
-     14151,14163,14193,14199,14219,14229,
-     14233,14243,14277,14287,14289,14295,14301,14305,14323,14339,
-     14341,14359,14365,14375,14387,14411,14425,14441,14449,14499,
-     14513,14523,14537,14543,14561,14579,14585,14593,14599,14603,
-     14611,14641,14671,14695,14701,14723,14725,14743,14753,14759,
-     14765,14795,14797,14803,14831,14839,14845,14855,14889,14895,
-     14909,14929,14941,14945,14951,14963,14965,14985,15033,15039,
-     15053,15059,15061,15071,15077,15081,15099,15121,15147,15149,
-     15157,15167,15187,15193,15203,15205,15215,15217,15223,15243,
-     15257,15269,15273,15287,15291,15313,15335,15347,15359,15373,
-     15379,15381,15391,15395,15397,15419,15439,15453,15469,15491,
-     15503,15517,15527,15531,15545,15559,15593,15611,15613,15619,
-     15639,15643,15649,15661,15667,15669,15681,15693,15717,15721,
-     15741,15745,15765,15793,15799,15811,15825,15835,15847,15851,
-     15865,15877,15881,15887,15899,15915,15935,15937,15955,15973,
-     15977,16011,16035,16061,16069,16087,16093,16097,16121,16141,
-     16153,16159,16165,16183,16189,16195,16197,16201,16209,16215,
-     16225,16259,16265,16273,16299,
-     16309,16355,16375,16381,
+static const uint32_t sobol_a[MAXDIM - 1] = {
+    3, 7, 11, 13, 19, 25, 37, 59, 47, 61, 55, 41, 67, 97, 91,
+    109, 103, 115, 131, 193, 137, 145, 143, 241, 157, 185, 167, 229, 171, 213,
+    191, 253, 203, 211, 239, 247, 285, 369, 299, 301, 333, 351, 355, 357, 361,
+    391, 397, 425, 451, 463, 487, 501, 529, 539, 545, 557, 563, 601, 607, 617,
+    623, 631, 637, 647, 661, 675, 677, 687, 695, 701, 719, 721, 731, 757, 761,
+    787, 789, 799, 803, 817, 827, 847, 859, 865, 875, 877, 883, 895, 901, 911,
+    949, 953, 967, 971, 973, 981, 985, 995, 1001, 1019, 1033, 1051, 1063,
+    1069, 1125, 1135, 1153, 1163, 1221, 1239, 1255, 1267, 1279, 1293, 1305,
+    1315, 1329, 1341, 1347, 1367, 1387, 1413, 1423, 1431, 1441, 1479, 1509,
+    1527, 1531, 1555, 1557, 1573, 1591, 1603, 1615, 1627, 1657, 1663, 1673,
+    1717, 1729, 1747, 1759, 1789, 1815, 1821, 1825, 1849, 1863, 1869, 1877,
+    1881, 1891, 1917, 1933, 1939, 1969, 2011, 2035, 2041, 2053, 2071, 2091,
+    2093, 2119, 2147, 2149, 2161, 2171, 2189, 2197, 2207, 2217, 2225, 2255,
+    2257, 2273, 2279, 2283, 2293, 2317, 2323, 2341, 2345, 2363, 2365, 2373,
+    2377, 2385, 2395, 2419, 2421, 2431, 2435, 2447, 2475, 2477, 2489, 2503,
+    2521, 2533, 2551, 2561, 2567, 2579, 2581, 2601, 2633, 2657, 2669,
+    2681, 2687, 2693, 2705, 2717, 2727, 2731, 2739,
+    2741, 2773, 2783, 2793, 2799, 2801, 2811, 2819, 2825, 2833, 2867, 2879,
+    2881, 2891, 2905, 2911, 2917, 2927, 2941, 2951, 2955, 2963, 2965, 2991,
+    2999, 3005, 3017, 3035, 3037, 3047, 3053, 3083, 3085, 3097, 3103, 3159,
+    3169, 3179, 3187, 3205, 3209, 3223, 3227, 3229, 3251, 3263, 3271, 3277,
+    3283, 3285, 3299, 3305, 3319, 3331, 3343, 3357, 3367, 3373, 3393, 3399,
+    3413, 3417, 3427, 3439, 3441, 3475, 3487, 3497, 3515, 3517, 3529, 3543,
+    3547, 3553, 3559, 3573, 3589, 3613, 3617, 3623, 3627, 3635, 3641, 3655,
+    3659, 3669, 3679, 3697, 3707, 3709, 3713, 3731, 3743, 3747, 3771, 3791,
+    3805, 3827, 3833, 3851, 3865, 3889, 3895, 3933, 3947, 3949, 3957, 3971,
+    3985, 3991, 3995, 4007, 4013, 4021, 4045, 4051, 4069, 4073, 4179, 4201,
+    4219, 4221, 4249, 4305, 4331, 4359, 4383, 4387, 4411, 4431, 4439, 4449,
+    4459, 4485, 4531, 4569, 4575, 4621, 4663, 4669, 4711, 4723, 4735, 4793,
+    4801, 4811, 4879, 4893, 4897, 4921, 4927, 4941, 4977, 5017, 5027, 5033,
+    5127, 5169, 5175, 5199, 5213, 5223, 5237, 5287, 5293, 5331, 5391, 5405,
+    5453, 5523, 5573, 5591, 5597, 5611, 5641, 5703, 5717, 5721, 5797, 5821,
+    5909, 5913,
+    5955, 5957, 6005, 6025, 6061, 6067, 6079, 6081,
+    6231, 6237, 6289, 6295, 6329, 6383, 6427, 6453, 6465, 6501, 6523, 6539,
+    6577, 6589, 6601, 6607, 6631, 6683, 6699, 6707, 6761, 6795, 6865, 6881,
+    6901, 6923, 6931, 6943, 6999, 7057, 7079, 7103, 7105, 7123, 7173, 7185,
+    7191, 7207, 7245, 7303, 7327, 7333, 7355, 7365, 7369, 7375, 7411, 7431,
+    7459, 7491, 7505, 7515, 7541, 7557, 7561, 7701, 7705, 7727, 7749, 7761,
+    7783, 7795, 7823, 7907, 7953, 7963, 7975, 8049, 8089, 8123, 8125, 8137,
+    8219, 8231, 8245, 8275, 8293, 8303, 8331, 8333, 8351, 8357, 8367, 8379,
+    8381, 8387, 8393, 8417, 8435, 8461, 8469, 8489, 8495, 8507, 8515, 8551,
+    8555, 8569, 8585, 8599, 8605, 8639, 8641, 8647, 8653, 8671, 8675, 8689,
+    8699, 8729, 8741, 8759, 8765, 8771, 8795, 8797, 8825, 8831, 8841, 8855,
+    8859, 8883, 8895, 8909, 8943, 8951, 8955, 8965, 8999, 9003, 9031, 9045,
+    9049, 9071, 9073, 9085, 9095, 9101, 9109, 9123, 9129, 9137, 9143, 9147,
+    9185, 9197, 9209, 9227, 9235, 9247, 9253, 9257, 9277, 9297, 9303, 9313,
+    9325, 9343, 9347, 9371, 9373, 9397, 9407, 9409, 9415, 9419, 9443, 9481,
+    9495, 9501, 9505, 9517, 9529, 9555, 9557, 9571, 9585, 9591, 9607, 9611,
+    9621, 9625,
+    9631, 9647, 9661, 9669, 9679, 9687, 9707, 9731,
+    9733, 9745, 9773, 9791, 9803, 9811, 9817, 9833, 9847, 9851, 9863, 9875,
+    9881, 9905, 9911, 9917, 9923, 9963, 9973, 10003, 10025, 10043, 10063,
+    10071, 10077, 10091, 10099, 10105, 10115, 10129, 10145, 10169, 10183,
+    10187, 10207, 10223, 10225, 10247, 10265, 10271, 10275, 10289, 10299,
+    10301, 10309, 10343, 10357, 10373, 10411, 10413, 10431, 10445, 10453,
+    10463, 10467, 10473, 10491, 10505, 10511, 10513, 10523, 10539, 10549,
+    10559, 10561, 10571, 10581, 10615, 10621, 10625, 10643, 10655, 10671,
+    10679, 10685, 10691, 10711, 10739, 10741, 10755, 10767, 10781, 10785,
+    10803, 10805, 10829, 10857, 10863, 10865, 10875, 10877, 10917, 10921,
+    10929, 10949, 10967, 10971, 10987, 10995, 11009, 11029, 11043, 11045,
+    11055, 11063, 11075, 11081, 11117, 11135, 11141, 11159, 11163, 11181,
+    11187, 11225, 11237, 11261, 11279, 11297, 11307, 11309, 11327, 11329,
+    11341, 11377, 11403, 11405, 11413, 11427, 11439, 11453, 11461, 11473,
+    11479, 11489, 11495, 11499, 11533, 11545, 11561, 11567, 11575, 11579,
+    11589, 11611, 11623, 11637, 11657, 11663, 11687, 11691, 11701, 11747,
+    11761, 11773, 11783, 11795, 11797, 11817, 11849, 11855, 11867, 11869,
+    11873, 11883, 11919,
+    11921, 11927, 11933, 11947, 11955, 11961,
+    11999, 12027, 12029, 12037, 12041, 12049, 12055, 12095, 12097, 12107,
+    12109, 12121, 12127, 12133, 12137, 12181, 12197, 12207, 12209, 12239,
+    12253, 12263, 12269, 12277, 12287, 12295, 12309, 12313, 12335, 12361,
+    12367, 12391, 12409, 12415, 12433, 12449, 12469, 12479, 12481, 12499,
+    12505, 12517, 12527, 12549, 12559, 12597, 12615, 12621, 12639, 12643,
+    12657, 12667, 12707, 12713, 12727, 12741, 12745, 12763, 12769, 12779,
+    12781, 12787, 12799, 12809, 12815, 12829, 12839, 12857, 12875, 12883,
+    12889, 12901, 12929, 12947, 12953, 12959, 12969, 12983, 12987, 12995,
+    13015, 13019, 13031, 13063, 13077, 13103, 13137, 13149, 13173, 13207,
+    13211, 13227, 13241, 13249, 13255, 13269, 13283, 13285, 13303, 13307,
+    13321, 13339, 13351, 13377, 13389, 13407, 13417, 13431, 13435, 13447,
+    13459, 13465, 13477, 13501, 13513, 13531, 13543, 13561, 13581, 13599,
+    13605, 13617, 13623, 13637, 13647, 13661, 13677, 13683, 13695, 13725,
+    13729, 13753, 13773, 13781, 13785, 13795, 13801, 13807, 13825, 13835,
+    13855, 13861, 13871, 13883, 13897, 13905, 13915, 13939, 13941, 13969,
+    13979, 13981, 13997, 14027, 14035, 14037, 14051, 14063, 14085, 14095,
+    14107, 14113, 14125, 14137, 14145,
+    14151, 14163, 14193, 14199, 14219, 14229,
+    14233, 14243, 14277, 14287, 14289, 14295, 14301, 14305, 14323, 14339,
+    14341, 14359, 14365, 14375, 14387, 14411, 14425, 14441, 14449, 14499,
+    14513, 14523, 14537, 14543, 14561, 14579, 14585, 14593, 14599, 14603,
+    14611, 14641, 14671, 14695, 14701, 14723, 14725, 14743, 14753, 14759,
+    14765, 14795, 14797, 14803, 14831, 14839, 14845, 14855, 14889, 14895,
+    14909, 14929, 14941, 14945, 14951, 14963, 14965, 14985, 15033, 15039,
+    15053, 15059, 15061, 15071, 15077, 15081, 15099, 15121, 15147, 15149,
+    15157, 15167, 15187, 15193, 15203, 15205, 15215, 15217, 15223, 15243,
+    15257, 15269, 15273, 15287, 15291, 15313, 15335, 15347, 15359, 15373,
+    15379, 15381, 15391, 15395, 15397, 15419, 15439, 15453, 15469, 15491,
+    15503, 15517, 15527, 15531, 15545, 15559, 15593, 15611, 15613, 15619,
+    15639, 15643, 15649, 15661, 15667, 15669, 15681, 15693, 15717, 15721,
+    15741, 15745, 15765, 15793, 15799, 15811, 15825, 15835, 15847, 15851,
+    15865, 15877, 15881, 15887, 15899, 15915, 15935, 15937, 15955, 15973,
+    15977, 16011, 16035, 16061, 16069, 16087, 16093, 16097, 16121, 16141,
+    16153, 16159, 16165, 16183, 16189, 16195, 16197, 16201, 16209, 16215,
+    16225, 16259, 16265, 16273, 16299,
+    16309, 16355, 16375, 16381,
 };
 
 /* starting direction #'s m[i] = sobol_minit[i][j] for i=0..d of the
  * degree-d primitive polynomial sobol_a[j]. */
-static const uint32_t sobol_minit[MAXDEG+1][MAXDIM-1] = {
-     /* [0][*] */
-     { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 },
-     /* [1][*] */
-     { 0,
-       1,3,1,3,1,3,3,1,3,1,3,1,3,1,1,3,1,3,1,3,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     1,1,3,3,3,1,3,3,1,3,1,3,3,1,3,3,3,1,1,
-     3,3,1,3,1,3,1,1,1,3,3,3,3,1,3,1,1,3,1,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     1,3,1,1,3,3,3,1,3,3,3,3,3,1,3,3,3,1,1,1,
-     3,3,1,3,3,1,3,1,3,1,3,1,3,3,3,3,3,3,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     1,3,3,3,3,3,3,3,3,1,1,3,3,1,1,3,1,3,3,3,3,3,1},
-     /* [2][*] */
-     { 0,0,
-       7,5,1,3,3,7,5,5,7,7,1,3,3,7,5,1,1,5,3,7,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     5,5,5,1,3,1,5,7,3,3,5,7,3,7,1,7,7,1,3,
-     5,1,5,5,3,7,3,7,7,5,7,5,7,1,1,5,3,5,1,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     1,3,1,1,7,1,5,5,3,7,3,7,5,3,1,1,3,1,3,5,
-     5,7,5,3,7,7,7,3,7,3,7,1,3,1,7,7,1,7,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     3,3,3,1,3,5,7,7,1,5,7,3,7,1,1,3,5,7,5,3,3,3},
-     /* [3][*] */
-     { 0,0,0,0,
-       1,7,9,13,11,1,3,7,9,5,13,13,11,3,15,5,3,
-     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,
-     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,
-     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,
-     5,3,15,1,11,11,7,13,15,11,13,9,11,15,15,13,3,15,7,9,11,13,11,
-     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,
-     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,
-     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,
-     3,5,13,9,11,15,11,7,1,7,13,3,13,3,13,9,15,7,13,13,3,13,15,15,
-     11,9,13,9,15,1,1,15,11,11,7,1,11,13,9,13,3,5,11,13,9,9,13,1,
-     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,
-     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,
-     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,
-     7,1,11,7,9,13,15,13,3,1,11,13,15,1,1,11,9,13,3,13,11,15,13,9,
-     9,9,5,5,5,5,1,15,5,9,
-     11,7,15,5,3,13,5,3,11,5,1,11,13,9,11,
-     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,
-     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,
-     1,15,3,13,9,13,9,9,11,5,5,13,15,3,9,15,3,11,11,15,15,3,11,15,
-     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,
-     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,
-     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,
-     7,15,13,13,7,15,9,13,9,15,13,15,9,13,1,11,7,11,3,13,5,1,7,15,
-     3,13,7,13,13,11,3,5,3,13,11,9,9,3,11,11,7,9,13,11,7,15,13,7,
-     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,
-     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,
-     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,
-     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,
-     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,
-     11,15,13,15,1,9,9,7,
-     3,5,11,7,3,9,5,15,7,5,3,13,7,1,1,9,
-     15,15,15,11,3,5,15,13,7,15,15,11,11,9,5,15,9,7,3,13,1,1,5,1,
-     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,
-     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,
-     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,
-     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,
-     11,13,13,13,9,15,5,7,1,15,11,9,15,15,13,13,13,1,11,9,15,9,5,
-     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,
-     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,
-     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,
-     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,
-     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,
-     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,
-     11,1,7,13,15,15,5,7,13,13,15,11,13,1,13,13,3,9,15,15,11,15,9,
-     15,1,13,15,1,1,5,
-     11,5,1,11,11,5,3,9,1,3,5,13,9,7,7,1,
-     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,
-     3,3,1,3,15},
-     /* [4][*] */
-     { 0,0,0,0,0,0,
-       9,3,27,15,29,21,23,19,11,25,7,13,17,1,
-     25,29,3,31,11,5,23,27,19,21,5,1,17,13,7,15,9,31,25,3,5,23,7,
-     3,17,23,3,3,21,25,25,23,11,19,3,11,31,7,9,5,17,23,17,17,25,
-     13,11,31,27,19,17,23,7,5,11,19,19,7,13,21,21,7,9,11,1,5,21,
-     11,13,25,9,7,7,27,15,25,15,21,17,19,19,21,5,11,3,5,29,31,29,
-     5,5,1,31,27,11,13,1,3,7,11,7,3,23,13,31,17,1,27,11,25,1,23,
-     29,17,25,7,25,27,17,13,17,23,5,17,5,13,11,21,5,11,5,9,31,19,
-     17,9,9,27,21,15,15,1,1,29,5,31,11,17,23,19,21,25,15,11,5,5,1,
-     19,19,19,7,13,21,17,17,25,23,19,23,15,13,5,19,25,9,7,3,21,17,
-     25,1,27,25,27,25,9,13,3,17,25,23,9,25,9,13,17,17,3,15,7,7,29,
-     3,19,29,29,19,29,13,15,25,27,1,3,9,9,13,31,29,31,5,15,29,1,
-     19,5,9,19,5,15,3,5,7,15,17,17,23,11,9,23,19,3,17,1,27,9,9,17,
-     13,25,29,23,29,11,31,25,21,29,19,27,31,3,5,3,3,13,21,9,29,3,
-     17,11,11,9,21,19,7,17,31,25,1,27,5,15,27,29,29,29,25,27,25,3,
-     21,17,25,13,15,17,13,23,9,3,11,7,9,9,7,17,7,1,
-     27,1,9,5,31,21,25,25,21,11,1,23,19,27,
-     15,3,5,23,9,25,7,29,11,9,13,5,11,1,3,31,27,3,17,27,11,13,15,
-     29,15,1,15,23,25,13,21,15,3,29,29,5,25,17,11,7,15,5,21,7,31,
-     13,11,23,5,7,23,27,21,29,15,7,27,27,19,7,15,27,27,19,19,9,15,
-     1,3,29,29,5,27,31,9,1,7,3,19,19,29,9,3,21,31,29,25,1,3,9,27,
-     5,27,25,21,11,29,31,27,21,29,17,9,17,13,11,25,15,21,11,19,31,
-     3,19,5,3,3,9,13,13,3,29,7,5,9,23,13,21,23,21,31,11,7,7,3,23,
-     1,23,5,9,17,21,1,17,29,7,5,17,13,25,17,9,19,9,5,7,21,19,13,9,
-     7,3,9,3,15,31,29,29,25,13,9,21,9,31,7,15,5,31,7,15,27,25,19,
-     9,9,25,25,23,1,9,7,11,15,19,15,27,17,11,11,31,13,25,25,9,7,
-     13,29,19,5,19,31,25,13,25,15,5,9,29,31,9,29,27,25,27,11,17,5,
-     17,3,23,15,9,9,17,17,31,11,19,25,13,23,15,25,21,31,19,3,11,
-     25,7,15,19,7,5,3,13,13,1,23,5,25,11,25,15,13,21,11,23,29,5,
-     17,27,9,19,15,5,29,23,19,1,27,3,23,21,19,27,11,17,13,27,11,
-     31,23,5,9,21,31,29,11,21,17,15,7,15,7,9,21,27,25,
-     29,11,3,21,13,23,19,27,17,29,25,17,9,
-     1,19,23,5,23,1,17,17,13,27,23,7,7,11,13,17,13,11,21,13,23,1,
-     27,13,9,7,1,27,29,5,13,25,21,3,31,15,13,3,19,13,1,27,15,17,1,
-     3,13,13,13,31,29,27,7,7,21,29,15,17,17,21,19,17,3,15,5,27,27,
-     3,31,31,7,21,3,13,11,17,27,25,1,9,7,29,27,21,23,13,25,29,15,
-     17,29,9,15,3,21,15,17,17,31,9,9,23,19,25,3,1,11,27,29,1,31,
-     29,25,29,1,23,29,25,13,3,31,25,5,5,11,3,21,9,23,7,11,23,11,1,
-     1,3,23,25,23,1,23,3,27,9,27,3,23,25,19,29,29,13,27,5,9,29,29,
-     13,17,3,23,19,7,13,3,19,23,5,29,29,13,13,5,19,5,17,9,11,11,
-     29,27,23,19,17,25,13,1,13,3,11,1,17,29,1,13,17,9,17,21,1,11,
-     1,1,25,5,7,29,29,19,19,1,29,13,3,1,31,15,13,3,1,11,19,5,29,
-     13,29,23,3,1,31,13,19,17,5,5,1,29,23,3,19,25,19,27,9,27,13,
-     15,29,23,13,25,25,17,19,17,15,27,3,25,17,27,3,27,31,23,13,31,
-     11,15,7,21,19,27,19,21,29,7,31,13,9,9,7,21,13,11,9,11,29,19,
-     11,19,21,5,29,13,7,19,19,27,23,31,1,27,21,7,3,7,11,
-     23,13,29,11,31,19,1,5,5,11,5,3,27,5,
-     7,11,31,1,27,31,31,23,5,21,27,9,25,3,15,19,1,19,9,5,25,21,15,
-     25,29,15,21,11,19,15,3,7,13,11,25,17,1,5,31,13,29,23,9,5,29,
-     7,17,27,7,17,31,9,31,9,9,7,21,3,3,3,9,11,21,11,31,9,25,5,1,
-     31,13,29,9,29,1,11,19,7,27,13,31,7,31,7,25,23,21,29,11,11,13,
-     11,27,1,23,31,21,23,21,19,31,5,31,25,25,19,17,11,25,7,13,1,
-     29,17,23,15,7,29,17,13,3,17},
-     /* [5][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,
-       37,33,7,5,11,39,63,59,17,15,23,29,3,21,
-     13,31,25,9,49,33,19,29,11,19,27,15,25,63,55,17,63,49,19,41,
-     59,3,57,33,49,53,57,57,39,21,7,53,9,55,15,59,19,49,31,3,39,5,
-     5,41,9,19,9,57,25,1,15,51,11,19,61,53,29,19,11,9,21,19,43,13,
-     13,41,25,31,9,11,19,5,53,37,7,51,45,7,7,61,23,45,7,59,41,1,
-     29,61,37,27,47,15,31,35,31,17,51,13,25,45,5,5,33,39,5,47,29,
-     35,47,63,45,37,47,59,21,59,33,51,9,27,13,25,43,3,17,21,59,61,
-     27,47,57,11,17,39,1,63,21,59,17,13,31,3,31,7,9,27,37,23,31,9,
-     45,43,31,63,21,39,51,27,7,53,11,1,59,39,23,49,23,7,55,59,3,
-     19,35,13,9,13,15,23,9,7,43,55,3,19,9,27,33,27,49,23,47,19,7,
-     11,55,27,35,5,5,55,35,37,9,33,29,47,25,11,47,53,61,59,3,53,
-     47,5,19,59,5,47,23,45,53,3,49,61,47,39,29,17,57,5,17,31,23,
-     41,39,5,27,7,29,29,33,31,41,31,29,17,29,29,9,9,31,27,53,35,5,
-     61,1,49,13,57,29,5,21,43,25,57,49,37,27,11,61,37,49,5,63,63,
-     3,45,37,63,21,21,19,27,59,21,45,23,13,15,3,43,63,39,19,
-     63,31,41,41,15,43,63,53,1,63,31,7,17,
-     11,61,31,51,37,29,59,25,63,59,47,15,27,19,29,45,35,55,39,19,
-     43,21,19,13,17,51,37,5,33,35,49,25,45,1,63,47,9,63,15,25,25,
-     15,41,13,3,19,51,49,37,25,49,13,53,47,23,35,29,33,21,35,23,3,
-     43,31,63,9,1,61,43,3,11,55,11,35,1,63,35,49,19,45,9,57,51,1,
-     47,41,9,11,37,19,55,23,55,55,13,7,47,37,11,43,17,3,25,19,55,
-     59,37,33,43,1,5,21,5,63,49,61,21,51,15,19,43,47,17,9,53,45,
-     11,51,25,11,25,47,47,1,43,29,17,31,15,59,27,63,11,41,51,29,7,
-     27,63,31,43,3,29,39,3,59,59,1,53,63,23,63,47,51,23,61,39,47,
-     21,39,15,3,9,57,61,39,37,21,51,1,23,43,27,25,11,13,21,43,7,
-     11,33,55,1,37,35,27,61,39,5,19,61,61,57,59,21,59,61,57,25,55,
-     27,31,41,33,63,19,57,35,13,63,35,17,11,11,49,41,55,5,45,17,
-     35,5,31,31,37,17,45,51,1,39,49,55,19,41,13,5,51,5,49,1,21,13,
-     17,59,51,11,3,61,1,33,37,33,61,25,27,59,7,49,13,63,3,33,3,15,
-     9,13,35,39,11,59,59,1,57,11,5,57,13,31,13,11,55,45,9,55,55,
-     19,25,41,23,45,29,63,59,27,39,21,37,7,
-     61,49,35,39,9,29,7,25,23,57,5,19,15,33,49,37,25,17,45,29,15,
-     25,3,3,49,11,39,15,19,57,39,15,11,3,57,31,55,61,19,5,41,35,
-     59,61,39,41,53,53,63,31,9,59,13,35,55,41,49,5,41,25,27,43,5,
-     5,43,5,5,17,5,15,27,29,17,9,3,55,31,1,45,45,13,57,17,3,61,15,
-     49,15,47,9,37,45,9,51,61,21,33,11,21,63,63,47,57,61,49,9,59,
-     19,29,21,23,55,23,43,41,57,9,39,27,41,35,61,29,57,63,21,31,
-     59,35,49,3,49,47,49,33,21,19,21,35,11,17,37,23,59,13,37,35,
-     55,57,1,29,45,11,1,15,9,33,19,53,43,39,23,7,13,13,1,19,41,55,
-     1,13,15,59,55,15,3,57,37,31,17,1,3,21,29,25,55,9,37,33,53,41,
-     51,19,57,13,63,43,19,7,13,37,33,19,15,63,51,11,49,23,57,47,
-     51,15,53,41,1,15,37,61,11,35,29,33,23,55,11,59,19,61,61,45,
-     13,49,13,63,5,61,5,31,17,61,63,13,27,57,1,21,5,11,39,57,51,
-     53,39,25,41,39,37,23,31,25,33,17,57,29,27,23,47,41,29,19,47,
-     41,25,5,51,43,39,29,7,31,45,51,49,55,17,43,49,45,9,29,3,5,47,
-     9,15,19,
-     51,45,57,63,9,21,59,3,9,13,45,23,15,
-     31,21,15,51,35,9,11,61,23,53,29,51,45,31,29,5,35,29,53,35,17,
-     59,55,27,51,59,27,47,15,29,37,7,49,55,5,19,45,29,19,57,33,53,
-     45,21,9,3,35,29,43,31,39,3,45,1,41,29,5,59,41,33,35,27,19,13,
-     25,27,43,33,35,17,17,23,7,35,15,61,61,53,5,15,23,11,13,43,55,
-     47,25,43,15,57,45,1,49,63,57,15,31,31,7,53,27,15,47,23,7,29,
-     53,47,9,53,3,25,55,45,63,21,17,23,31,27,27,43,63,55,63,45,51,
-     15,27,5,37,43,11,27,5,27,59,21,7,39,27,63,35,47,55,17,17,17,
-     3,19,21,13,49,61,39,15},
-     /* [6][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       13,33,115,41,79,17,29,119,75,73,105,7,
-     59,65,21,3,113,61,89,45,107,21,71,79,19,71,61,41,57,121,87,
-     119,55,85,121,119,11,23,61,11,35,33,43,107,113,101,29,87,119,
-     97,29,17,89,5,127,89,119,117,103,105,41,83,25,41,55,69,117,
-     49,127,29,1,99,53,83,15,31,73,115,35,21,89,5,1,91,53,35,95,
-     83,19,85,55,51,101,33,41,55,45,95,61,27,37,89,75,57,61,15,
-     117,15,21,27,25,27,123,39,109,93,51,21,91,109,107,45,15,93,
-     127,3,53,81,79,107,79,87,35,109,73,35,83,107,1,51,7,59,33,
-     115,43,111,45,121,105,125,87,101,41,95,75,1,57,117,21,27,67,
-     29,53,117,63,1,77,89,115,49,127,15,79,81,29,65,103,33,73,79,
-     29,21,113,31,33,107,95,111,59,99,117,63,63,99,39,9,35,63,125,
-     99,45,93,33,93,9,105,75,51,115,11,37,17,41,21,43,73,19,93,7,
-     95,81,93,79,81,55,9,51,63,45,89,73,19,115,39,47,81,39,5,5,45,
-     53,65,49,17,105,13,107,5,5,19,73,59,43,83,97,115,27,1,69,103,
-     3,99,103,63,67,25,121,97,77,13,83,103,41,11,27,81,37,33,125,
-     71,41,41,59,41,87,123,
-     43,101,63,45,39,21,97,15,97,111,21,49,
-     13,17,79,91,65,105,75,1,45,67,83,107,125,87,15,81,95,105,65,
-     45,59,103,23,103,99,67,99,47,117,71,89,35,53,73,9,115,49,37,
-     1,35,9,45,81,19,127,17,17,105,89,49,101,7,37,33,11,95,95,17,
-     111,105,41,115,5,69,101,27,27,101,103,53,9,21,43,79,91,65,
-     117,87,125,55,45,63,85,83,97,45,83,87,113,93,95,5,17,77,77,
-     127,123,45,81,85,121,119,27,85,41,49,15,107,21,51,119,11,87,
-     101,115,63,63,37,121,109,7,43,69,19,77,49,71,59,35,7,13,55,
-     101,127,103,85,109,29,61,67,21,111,67,23,57,75,71,101,123,41,
-     107,101,107,125,27,47,119,41,19,127,33,31,109,7,91,91,39,125,
-     105,47,125,123,91,9,103,45,23,117,9,125,73,11,37,61,79,21,5,
-     47,117,67,53,85,33,81,121,47,61,51,127,29,65,45,41,95,57,73,
-     33,117,61,111,59,123,65,47,105,23,29,107,37,81,67,29,115,119,
-     75,73,99,103,7,57,45,61,95,49,101,101,35,47,119,39,67,31,103,
-     7,61,127,87,3,35,29,73,95,103,71,75,51,87,57,97,11,105,87,41,
-     73,109,69,35,121,39,111,1,77,
-     39,47,53,91,3,17,51,83,39,125,85,111,
-     21,69,85,29,55,11,117,1,47,17,65,63,47,117,17,115,51,25,33,
-     123,123,83,51,113,95,121,51,91,109,43,55,35,55,87,33,37,5,3,
-     45,21,105,127,35,17,35,37,97,97,21,77,123,17,89,53,105,75,25,
-     125,13,47,21,125,23,55,63,61,5,17,93,57,121,69,73,93,121,105,
-     75,91,67,95,75,9,69,97,99,93,11,53,19,73,5,33,79,107,65,69,
-     79,125,25,93,55,61,17,117,69,97,87,111,37,93,59,79,95,53,115,
-     53,85,85,65,59,23,75,21,67,27,99,79,27,3,95,27,69,19,75,47,
-     59,41,85,77,99,55,49,93,93,119,51,125,63,13,15,45,61,19,105,
-     115,17,83,7,7,11,61,37,63,89,95,119,113,67,123,91,33,37,99,
-     43,11,33,65,81,79,81,107,63,63,55,89,91,25,93,101,27,55,75,
-     121,79,43,125,73,27,109,35,21,71,113,89,59,95,41,45,113,119,
-     113,39,59,73,15,13,59,67,121,27,7,105,15,59,59,35,91,89,23,
-     125,97,53,41,91,111,29,31,3,103,61,71,35,7,119,29,45,49,111,
-     41,109,59,125,13,27,19,79,9,75,83,81,33,91,109,33,29,107,111,
-     101,107,109,65,59,43,37,
-     1,9,15,109,37,111,113,119,79,73,65,
-     71,93,17,101,87,97,43,23,75,109,41,49,53,31,97,105,109,119,
-     51,9,53,113,97,73,89,79,49,61,105,13,99,53,71,7,87,21,101,5,
-     71,31,123,121,121,73,79,115,13,39,101,19,37,51,83,97,55,81,
-     91,127,105,89,63,47,49,75,37,77,15,49,107,23,23,35,19,69,17,
-     59,63,73,29,125,61,65,95,101,81,57,69,83,37,11,37,95,1,73,27,
-     29,57,7,65,83,99,69,19,103,43,95,25,19,103,41,125,97,71,105,
-     83,83,61,39,9,45,117,63,31,5,117,67,125,41,117,43,77,97,15,
-     29,5,59,25,63,87,39,39,77,85,37,81,73,89,29,125,109,21,23,
-     119,105,43,93,97,15,125,29,51,69,37,45,31,75,109,119,53,5,
-     101,125,121,35,29,7,63,17,63,13,69,15,105,51,127,105,9,57,95,
-     59,109,35,49,23,33,107,55,33,57,79,73,69,59,107,55,11,63,95,
-     103,23,125,91,31,91,51,65,61,75,69,107,65,101,59,35,15},
-     /* [7][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       7,23,39,217,141,27,53,181,169,35,15,
-     207,45,247,185,117,41,81,223,151,81,189,61,95,185,23,73,113,
-     239,85,9,201,83,53,183,203,91,149,101,13,111,239,3,205,253,
-     247,121,189,169,179,197,175,217,249,195,95,63,19,7,5,75,217,
-     245,111,189,165,169,141,221,249,159,253,207,249,219,23,49,
-     127,237,5,25,177,37,103,65,167,81,87,119,45,79,143,57,79,187,
-     143,183,75,97,211,149,175,37,135,189,225,241,63,33,43,13,73,
-     213,57,239,183,117,21,29,115,43,205,223,15,3,159,51,101,127,
-     99,239,171,113,171,119,189,245,201,27,185,229,105,153,189,33,
-     35,137,77,97,17,181,55,197,201,155,37,197,137,223,25,179,91,
-     23,235,53,253,49,181,249,53,173,97,247,67,115,103,159,239,69,
-     173,217,95,221,247,97,91,123,223,213,129,181,87,239,85,89,
-     249,141,39,57,249,71,101,159,33,137,189,71,253,205,171,13,
-     249,109,131,199,189,179,31,99,113,41,173,23,189,197,3,135,9,
-     95,195,27,183,1,123,73,53,99,197,59,27,101,55,193,31,61,119,
-     11,7,255,233,53,157,193,97,83,65,81,239,167,69,71,109,
-     97,137,71,193,189,115,79,205,37,227,
-     53,33,91,229,245,105,77,229,161,103,93,13,161,229,223,69,15,
-     25,23,233,93,25,217,247,61,75,27,9,223,213,55,197,145,89,199,
-     41,201,5,149,35,119,183,53,11,13,3,179,229,43,55,187,233,47,
-     133,91,47,71,93,105,145,45,255,221,115,175,19,129,5,209,197,
-     57,177,115,187,119,77,211,111,33,113,23,87,137,41,7,83,43,
-     121,145,5,219,27,11,111,207,55,97,63,229,53,33,149,23,187,
-     153,91,193,183,59,211,93,139,59,179,163,209,77,39,111,79,229,
-     85,237,199,137,147,25,73,121,129,83,87,93,205,167,53,107,229,
-     213,95,219,109,175,13,209,97,61,147,19,13,123,73,35,141,81,
-     19,171,255,111,107,233,113,133,89,9,231,95,69,33,1,253,219,
-     253,247,129,11,251,221,153,35,103,239,7,27,235,181,5,207,53,
-     149,155,225,165,137,155,201,97,245,203,47,39,35,105,239,49,
-     15,253,7,237,213,55,87,199,27,175,49,41,229,85,3,149,179,129,
-     185,249,197,15,97,197,139,203,63,33,251,217,199,199,99,249,
-     33,229,177,13,209,147,97,31,125,177,137,
-     187,11,91,223,29,169,231,59,31,163,41,
-     57,87,247,25,127,101,207,187,73,61,105,27,91,171,243,33,3,1,
-     21,229,93,71,61,37,183,65,211,53,11,151,165,47,5,129,79,101,
-     147,169,181,19,95,77,139,197,219,97,239,183,143,9,13,209,23,
-     215,53,137,203,19,151,171,133,219,231,3,15,253,225,33,111,
-     183,213,169,119,111,15,201,123,121,225,113,113,225,161,165,1,
-     139,55,3,93,217,193,97,29,69,231,161,93,69,143,137,9,87,183,
-     113,183,73,215,137,89,251,163,41,227,145,57,81,57,11,135,145,
-     161,175,159,25,55,167,157,211,97,247,249,23,129,159,71,197,
-     127,141,219,5,233,131,217,101,131,33,157,173,69,207,239,81,
-     205,11,41,169,65,193,77,201,173,1,221,157,1,15,113,147,137,
-     205,225,73,45,49,149,113,253,99,17,119,105,117,129,243,75,
-     203,53,29,247,35,247,171,31,199,213,29,251,7,251,187,91,11,
-     149,13,205,37,249,137,139,9,7,113,183,205,187,39,3,79,155,
-     227,89,185,51,127,63,83,41,133,183,181,127,19,255,219,59,251,
-     3,187,57,217,115,217,229,181,185,149,83,115,11,
-     123,19,109,165,103,123,219,129,155,
-     207,177,9,49,181,231,33,233,67,155,41,9,95,123,65,117,249,85,
-     169,129,241,173,251,225,147,165,69,81,239,95,23,83,227,249,
-     143,171,193,9,21,57,73,97,57,29,239,151,159,191,47,51,1,223,
-     251,251,151,41,119,127,131,33,209,123,53,241,25,31,183,107,
-     25,115,39,11,213,239,219,109,185,35,133,123,185,27,55,245,61,
-     75,205,213,169,163,63,55,49,83,195,51,31,41,15,203,41,63,127,
-     161,5,143,7,199,251,95,75,101,15,43,237,197,117,167,155,21,
-     83,205,255,49,101,213,237,135,135,21,73,93,115,7,85,223,237,
-     79,89,5,57,239,67,65,201,155,71,85,195,89,181,119,135,147,
-     237,173,41,155,67,113,111,21,183,23,103,207,253,69,219,205,
-     195,43,197,229,139,177,129,69,97,201,163,189,11,99,91,253,
-     239,91,145,19,179,231,121,7,225,237,125,191,119,59,175,237,
-     131,79,43,45,205,199,251,153,207,37,179,113,255,107,217,61,7,
-     181,247,31,13,113,145,107,233,233,43,79,23,169,137,129,183,
-     53,91,55,103,223,87,177,157,79,213,139,
-     183,231,205,143,129,243,205,93,59,
-     15,89,9,11,47,133,227,75,9,91,19,171,163,79,7,103,5,119,155,
-     75,11,71,95,17,13,243,207,187},
-     /* [8][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       235,307,495,417,57,151,19,119,375,451,
-     55,449,501,53,185,317,17,21,487,13,347,393,15,391,307,189,
-     381,71,163,99,467,167,433,337,257,179,47,385,23,117,369,425,
-     207,433,301,147,333,85,221,423,49,3,43,229,227,201,383,281,
-     229,207,21,343,251,397,173,507,421,443,399,53,345,77,385,317,
-     155,187,269,501,19,169,235,415,61,247,183,5,257,401,451,95,
-     455,49,489,75,459,377,87,463,155,233,115,429,211,419,143,487,
-     195,209,461,193,157,193,363,181,271,445,381,231,135,327,403,
-     171,197,181,343,113,313,393,311,415,267,247,425,233,289,55,
-     39,247,327,141,5,189,183,27,337,341,327,87,429,357,265,251,
-     437,201,29,339,257,377,17,53,327,47,375,393,369,403,125,429,
-     257,157,217,85,267,117,337,447,219,501,41,41,193,509,131,207,
-     505,421,149,111,177,167,223,291,91,29,305,151,177,337,183,
-     361,435,307,507,77,181,507,315,145,423,71,103,493,271,469,
-     339,237,437,483,31,219,61,131,391,233,219,69,57,459,225,421,
-     7,461,111,451,277,185,193,125,251,199,73,71,7,409,417,149,
-     193,53,437,29,467,229,31,35,75,105,
-     503,75,317,401,367,131,365,441,433,93,377,405,465,259,283,
-     443,143,445,3,461,329,309,77,323,155,347,45,381,315,463,207,
-     321,157,109,479,313,345,167,439,307,235,473,79,101,245,19,
-     381,251,35,25,107,187,115,113,321,115,445,61,77,293,405,13,
-     53,17,171,299,41,79,3,485,331,13,257,59,201,497,81,451,199,
-     171,81,253,365,75,451,149,483,81,453,469,485,305,163,401,15,
-     91,3,129,35,239,355,211,387,101,299,67,375,405,357,267,363,
-     79,83,437,457,39,97,473,289,179,57,23,49,79,71,341,287,95,
-     229,271,475,49,241,261,495,353,381,13,291,37,251,105,399,81,
-     89,265,507,205,145,331,129,119,503,249,1,289,463,163,443,63,
-     123,361,261,49,429,137,355,175,507,59,277,391,25,185,381,197,
-     39,5,429,119,247,177,329,465,421,271,467,151,45,429,137,471,
-     11,17,409,347,199,463,177,11,51,361,95,497,163,351,127,395,
-     511,327,353,49,105,151,321,331,329,509,107,109,303,467,287,
-     161,45,385,289,363,331,265,407,37,433,315,343,63,51,185,71,
-     27,267,
-     503,239,293,245,281,297,75,461,371,
-     129,189,189,339,287,111,111,379,93,27,185,347,337,247,507,
-     161,231,43,499,73,327,263,331,249,493,37,25,115,3,167,197,
-     127,357,497,103,125,191,165,55,101,95,79,351,341,43,125,135,
-     173,289,373,133,421,241,281,213,177,363,151,227,145,363,239,
-     431,81,397,241,67,291,255,405,421,399,75,399,105,329,41,425,
-     7,283,375,475,427,277,209,411,3,137,195,289,509,121,55,147,
-     275,251,19,129,285,415,487,491,193,219,403,23,97,65,285,75,
-     21,373,261,339,239,495,415,333,107,435,297,213,149,463,199,
-     323,45,19,301,121,499,187,229,63,425,99,281,35,125,349,87,
-     101,59,195,511,355,73,263,243,101,165,141,11,389,219,187,449,
-     447,393,477,305,221,51,355,209,499,479,265,377,145,411,173,
-     11,433,483,135,385,341,89,209,391,33,395,319,451,119,341,227,
-     375,61,331,493,411,293,47,203,375,167,395,155,5,237,361,489,
-     127,21,345,101,371,233,431,109,119,277,125,263,73,135,123,83,
-     123,405,69,75,287,401,23,283,393,41,379,431,11,475,505,19,
-     365,265,271,
-     499,489,443,165,91,83,291,319,199,
-     107,245,389,143,137,89,125,281,381,215,131,299,249,375,455,
-     43,73,281,217,297,229,431,357,81,357,171,451,481,13,387,491,
-     489,439,385,487,177,393,33,71,375,443,129,407,395,127,65,333,
-     309,119,197,435,497,373,71,379,509,387,159,265,477,463,449,
-     47,353,249,335,505,89,141,55,235,187,87,363,93,363,101,67,
-     215,321,331,305,261,411,491,479,65,307,469,415,131,315,487,
-     83,455,19,113,163,503,99,499,251,239,81,167,391,255,317,363,
-     359,395,419,307,251,267,171,461,183,465,165,163,293,477,223,
-     403,389,97,335,357,297,19,469,501,249,85,213,311,265,379,297,
-     283,393,449,463,289,159,289,499,407,129,137,221,43,89,403,
-     271,75,83,445,453,389,149,143,423,499,317,445,157,137,453,
-     163,87,23,391,119,427,323,173,89,259,377,511,249,31,363,229,
-     353,329,493,427,57,205,389,91,83,13,219,439,45,35,371,441,17,
-     267,501,53,25,333,17,201,475,257,417,345,381,377,55,403,77,
-     389,347,363,211,413,419,5,167,219,201,285,425,11,77,269,489,
-     281,403,79,
-     425,125,81,331,437,271,397,299,475,
-     271,249,413,233,261,495,171,69,27,409,21,421,367,81,483,255,
-     15,219,365,497,181,75,431,99,325,407,229,281,63,83,493,5,113,
-     15,271,37,87,451,299,83,451,311,441,47,455,47,253,13,109,369,
-     347,11,409,275,63,441,15},
-     /* [9][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       519,307,931,1023,517,771,151,1023,
-     539,725,45,927,707,29,125,371,275,279,817,389,453,989,1015,
-     29,169,743,99,923,981,181,693,309,227,111,219,897,377,425,
-     609,227,19,221,143,581,147,919,127,725,793,289,411,835,921,
-     957,443,349,813,5,105,457,393,539,101,197,697,27,343,515,69,
-     485,383,855,693,133,87,743,747,475,87,469,763,721,345,479,
-     965,527,121,271,353,467,177,245,627,113,357,7,691,725,355,
-     889,635,737,429,545,925,357,873,187,351,677,999,921,477,233,
-     765,495,81,953,479,89,173,473,131,961,411,291,967,65,511,13,
-     805,945,369,827,295,163,835,259,207,331,29,315,999,133,967,
-     41,117,677,471,717,881,755,351,723,259,879,455,721,289,149,
-     199,805,987,851,423,597,129,11,733,549,153,285,451,559,377,
-     109,357,143,693,615,677,701,475,767,85,229,509,547,151,389,
-     711,785,657,319,509,99,1007,775,359,697,677,85,497,105,615,
-     891,71,449,835,609,377,693,665,627,215,911,503,729,131,19,
-     895,199,161,239,633,1013,537,255,23,149,679,1021,595,199,557,
-     659,251,829,727,439,495,647,223,
-     949,625,87,481,85,799,917,769,949,
-     739,115,499,945,547,225,1015,469,737,495,353,103,17,665,639,
-     525,75,447,185,43,729,577,863,735,317,99,17,477,893,537,519,
-     1017,375,297,325,999,353,343,729,135,489,859,267,141,831,141,
-     893,249,807,53,613,131,547,977,131,999,175,31,341,739,467,
-     675,241,645,247,391,583,183,973,433,367,131,467,571,309,385,
-     977,111,917,935,473,345,411,313,97,149,959,841,839,669,431,
-     51,41,301,247,1015,377,329,945,269,67,979,581,643,823,557,91,
-     405,117,801,509,347,893,303,227,783,555,867,99,703,111,797,
-     873,541,919,513,343,319,517,135,871,917,285,663,301,15,763,
-     89,323,757,317,807,309,1013,345,499,279,711,915,411,281,193,
-     739,365,315,375,809,469,487,621,857,975,537,939,585,129,625,
-     447,129,1017,133,83,3,415,661,53,115,903,49,79,55,385,261,
-     345,297,199,385,617,25,515,275,849,401,471,377,661,535,505,
-     939,465,225,929,219,955,659,441,117,527,427,515,287,191,33,
-     389,197,825,63,417,949,35,571,9,131,609,439,95,19,569,893,
-     451,397,971,801,
-     125,471,187,257,67,949,621,453,411,
-     621,955,309,783,893,597,377,753,145,637,941,593,317,555,375,
-     575,175,403,571,555,109,377,931,499,649,653,329,279,271,647,
-     721,665,429,957,803,767,425,477,995,105,495,575,687,385,227,
-     923,563,723,481,717,111,633,113,369,955,253,321,409,909,367,
-     33,967,453,863,449,539,781,911,113,7,219,725,1015,971,1021,
-     525,785,873,191,893,297,507,215,21,153,645,913,755,371,881,
-     113,903,225,49,587,201,927,429,599,513,97,319,331,833,325,
-     887,139,927,399,163,307,803,169,1019,869,537,907,479,335,697,
-     479,353,769,787,1023,855,493,883,521,735,297,1011,991,879,
-     855,591,415,917,375,453,553,189,841,339,211,601,57,765,745,
-     621,209,875,639,7,595,971,263,1009,201,23,77,621,33,535,963,
-     661,523,263,917,103,623,231,47,301,549,337,675,189,357,1005,
-     789,189,319,721,1005,525,675,539,191,813,917,51,167,415,579,
-     755,605,721,837,529,31,327,799,961,279,409,847,649,241,285,
-     545,407,161,591,73,313,811,17,663,269,261,37,783,127,917,231,
-     577,975,793,
-     921,343,751,139,221,79,817,393,545,
-     11,781,71,1,699,767,917,9,107,341,587,903,965,599,507,843,
-     739,579,397,397,325,775,565,925,75,55,979,931,93,957,857,753,
-     965,795,67,5,87,909,97,995,271,875,671,613,33,351,69,811,669,
-     729,401,647,241,435,447,721,271,745,53,775,99,343,451,427,
-     593,339,845,243,345,17,573,421,517,971,499,435,769,75,203,
-     793,985,343,955,735,523,659,703,303,421,951,405,631,825,735,
-     433,841,485,49,749,107,669,211,497,143,99,57,277,969,107,397,
-     563,551,447,381,187,57,405,731,769,923,955,915,737,595,341,
-     253,823,197,321,315,181,885,497,159,571,981,899,785,947,217,
-     217,135,753,623,565,717,903,581,955,621,361,869,87,943,907,
-     853,353,335,197,771,433,743,195,91,1023,63,301,647,205,485,
-     927,1003,987,359,577,147,141,1017,701,273,89,589,487,859,343,
-     91,847,341,173,287,1003,289,639,983,685,697,35,701,645,911,
-     501,705,873,763,745,657,559,699,315,347,429,197,165,955,859,
-     167,303,833,531,473,635,641,195,589,821,205,3,635,371,891,
-     249,123,
-     77,623,993,401,525,427,71,655,951,
-     357,851,899,535,493,323,1003,343,515,859,1017,5,423,315,1011,
-     703,41,777,163,95,831,79,975,235,633,723,297,589,317,679,981,
-     195,399,1003,121,501,155},
-     /* [10][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       7,2011,1001,49,825,415,1441,383,1581,
-     623,1621,1319,1387,619,839,217,75,1955,505,281,1629,1379,53,
-     1111,1399,301,209,49,155,1647,631,129,1569,335,67,1955,1611,
-     2021,1305,121,37,877,835,1457,669,1405,935,1735,665,551,789,
-     1543,1267,1027,1,1911,163,1929,67,1975,1681,1413,191,1711,
-     1307,401,725,1229,1403,1609,2035,917,921,1789,41,2003,187,67,
-     1635,717,1449,277,1903,1179,363,1211,1231,647,1261,1029,1485,
-     1309,1149,317,1335,171,243,271,1055,1601,1129,1653,205,1463,
-     1681,1621,197,951,573,1697,1265,1321,1805,1235,1853,1307,945,
-     1197,1411,833,273,1517,1747,1095,1345,869,57,1383,221,1713,
-     335,1751,1141,839,523,1861,1105,389,1177,1877,805,93,1591,
-     423,1835,99,1781,1515,1909,1011,303,385,1635,357,973,1781,
-     1707,1363,1053,649,1469,623,1429,1241,1151,1055,503,921,3,
-     349,1149,293,45,303,877,1565,1583,1001,663,1535,395,1141,
-     1481,1797,643,1507,465,2027,1695,367,937,719,545,1991,83,819,
-     239,1791,1461,1647,1501,1161,1629,139,1595,1921,1267,1415,
-     509,347,777,1083,363,269,1015,
-     1809,1105,1429,1471,2019,381,2025,
-     1223,827,1733,887,1321,803,1951,1297,1995,833,1107,1135,1181,
-     1251,983,1389,1565,273,137,71,735,1005,933,67,1471,551,457,
-     1667,1729,919,285,1629,1815,653,1919,1039,531,393,1411,359,
-     221,699,1485,471,1357,1715,595,1677,153,1903,1281,215,781,
-     543,293,1807,965,1695,443,1985,321,879,1227,1915,839,1945,
-     1993,1165,51,557,723,1491,817,1237,947,1215,1911,1225,1965,
-     1889,1503,1177,73,1767,303,177,1897,1401,321,921,217,1779,
-     327,1889,333,615,1665,1825,1639,237,1205,361,129,1655,983,
-     1089,1171,401,677,643,749,303,1407,1873,1579,1491,1393,1247,
-     789,763,49,5,1607,1891,735,1557,1909,1765,1777,1127,813,695,
-     97,731,1503,1751,333,769,865,693,377,1919,957,1359,1627,1039,
-     1783,1065,1665,1917,1947,991,1997,841,459,221,327,1595,1881,
-     1269,1007,129,1413,475,1105,791,1983,1359,503,691,659,691,
-     343,1375,1919,263,1373,603,1383,297,781,145,285,767,1739,
-     1715,715,317,1333,85,831,1615,81,1667,1467,1457,1453,1825,
-     109,387,1207,2039,213,1351,1329,1173,
-     57,1769,951,183,23,451,1155,1551,
-     2037,811,635,1671,1451,863,1499,1673,363,1029,1077,1525,277,
-     1023,655,665,1869,1255,965,277,1601,329,1603,1901,395,65,
-     1307,2029,21,1321,543,1569,1185,1905,1701,413,2041,1697,725,
-     1417,1847,411,211,915,1891,17,1877,1699,687,1089,1973,1809,
-     851,1495,1257,63,1323,1307,609,881,1543,177,617,1505,1747,
-     1537,925,183,77,1723,1877,1703,397,459,521,257,1177,389,1947,
-     1553,1583,1831,261,485,289,1281,1543,1591,1123,573,821,1065,
-     1933,1373,2005,905,207,173,1573,1597,573,1883,1795,1499,1743,
-     553,335,333,1645,791,871,1157,969,557,141,223,1129,1685,423,
-     1069,391,99,95,1847,531,1859,1833,1833,341,237,1997,1799,409,
-     431,1917,363,335,1039,1085,1657,1975,1527,1111,659,389,899,
-     595,1439,1861,1979,1569,1087,1009,165,1895,1481,1583,29,1193,
-     1673,1075,301,1081,1377,1747,1497,1103,1789,887,739,1577,313,
-     1367,1299,1801,1131,1837,73,1865,1065,843,635,55,1655,913,
-     1037,223,1871,1161,461,479,511,1721,1107,389,151,35,375,1099,
-     937,1185,1701,769,639,1633,
-     1609,379,1613,2031,685,289,975,671,
-     1599,1447,871,647,99,139,1427,959,89,117,841,891,1959,223,
-     1697,1145,499,1435,1809,1413,1445,1675,171,1073,1349,1545,
-     2039,1027,1563,859,215,1673,1919,1633,779,411,1845,1477,1489,
-     447,1545,351,1989,495,183,1639,1385,1805,1097,1249,1431,1571,
-     591,697,1509,709,31,1563,165,513,1425,1299,1081,145,1841,
-     1211,941,609,845,1169,1865,1593,347,293,1277,157,211,93,1679,
-     1799,527,41,473,563,187,1525,575,1579,857,703,1211,647,709,
-     981,285,697,163,981,153,1515,47,1553,599,225,1147,381,135,
-     821,1965,609,1033,983,503,1117,327,453,2005,1257,343,1649,
-     1199,599,1877,569,695,1587,1475,187,973,233,511,51,1083,665,
-     1321,531,1875,1939,859,1507,1979,1203,1965,737,921,1565,1943,
-     819,223,365,167,1705,413,1577,745,1573,655,1633,1003,91,1123,
-     477,1741,1663,35,715,37,1513,815,941,1379,263,1831,1735,1111,
-     1449,353,1941,1655,1349,877,285,1723,125,1753,985,723,175,
-     439,791,1051,1261,717,1555,1757,1777,577,1583,1957,873,331,
-     1163,313,1,1963,963,1905,821,
-     1677,185,709,545,1723,215,1885,
-     1249,583,1803,839,885,485,413,1767,425,129,1035,329,1263,
-     1881,1779,1565,359,367,453,707,1419,831,1889,887,1871,1869,
-     747,223,1547,1799,433,1441,553,2021,1303,1505,1735,1619,1065,
-     1161,2047,347,867,881,1447,329,781,1065,219,589,645,1257,
-     1833,749,1841,1733,1179,1191,1025,1639,1955,1423,1685,1711,
-     493,549,783,1653,397,895,233,759,1505,677,1449,1573,1297,
-     1821,1691,791,289,1187,867,1535,575,183},
-     /* [11][*] */
-     { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-       3915,97,3047,937,2897,953,127,1201,
-     3819,193,2053,3061,3759,1553,2007,2493,603,3343,3751,1059,
-     783,1789,1589,283,1093,3919,2747,277,2605,2169,2905,721,4069,
-     233,261,1137,3993,3619,2881,1275,3865,1299,3757,1193,733,993,
-     1153,2945,3163,3179,437,271,3493,3971,1005,2615,2253,1131,
-     585,2775,2171,2383,2937,2447,1745,663,1515,3767,2709,1767,
-     3185,3017,2815,1829,87,3341,793,2627,2169,1875,3745,367,3783,
-     783,827,3253,2639,2955,3539,1579,2109,379,2939,3019,1999,
-     2253,2911,3733,481,1767,1055,4019,4085,105,1829,2097,2379,
-     1567,2713,737,3423,3941,2659,3961,1755,3613,1937,1559,2287,
-     2743,67,2859,325,2601,1149,3259,2403,3947,2011,175,3389,3915,
-     1315,2447,141,359,3609,3933,729,2051,1755,2149,2107,1741,
-     1051,3681,471,1055,845,257,1559,1061,2803,2219,1315,1369,
-     3211,4027,105,11,1077,2857,337,3553,3503,3917,2665,3823,3403,
-     3711,2085,1103,1641,701,4095,2883,1435,653,2363,1597,767,869,
-     1825,1117,1297,501,505,149,873,2673,551,1499,2793,3277,2143,
-     3663,533,3991,575,1877,1009,3929,473,3009,2595,3249,675,3593,
-     2453,1567,973,595,1335,1715,589,85,
-     2265,3069,461,1659,2627,1307,1731,1501,1699,3545,3803,2157,
-     453,2813,2047,2999,3841,2361,1079,573,69,1363,1597,3427,2899,
-     2771,1327,1117,1523,3521,2393,2537,1979,3179,683,2453,453,
-     1227,779,671,3483,2135,3139,3381,3945,57,1541,3405,3381,2371,
-     2879,1985,987,3017,3031,3839,1401,3749,2977,681,1175,1519,
-     3355,907,117,771,3741,3337,1743,1227,3335,2755,1909,3603,
-     2397,653,87,2025,2617,3257,287,3051,3809,897,2215,63,2043,
-     1757,3671,297,3131,1305,293,3865,3173,3397,2269,3673,717,
-     3041,3341,3595,3819,2871,3973,1129,513,871,1485,3977,2473,
-     1171,1143,3063,3547,2183,3993,133,2529,2699,233,2355,231,
-     3241,611,1309,3829,1839,1495,301,1169,1613,2673,243,3601,
-     3669,2813,2671,2679,3463,2477,1795,617,2317,1855,1057,1703,
-     1761,2515,801,1205,1311,473,3963,697,1221,251,381,3887,1761,
-     3093,3721,2079,4085,379,3601,3845,433,1781,29,1897,1599,2163,
-     75,3475,3957,1641,3911,2959,2833,1279,1099,403,799,2183,2699,
-     1711,2037,727,289,1785,1575,3633,2367,1261,3953,1735,171,
+static const uint32_t sobol_minit[MAXDEG + 1][MAXDIM - 1] = {
+    /* [0][*] */
+    {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+     1, 1, 1, 1, 1},
+    /* [1][*] */
+    {0,
+     1, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     1, 1, 3, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 3, 1, 1,
+     3, 3, 1, 3, 1, 3, 1, 1, 1, 3, 3, 3, 3, 1, 3, 1, 1, 3, 1,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     1, 3, 1, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 1, 1,
+     3, 3, 1, 3, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 1, 3, 1, 3, 3, 3, 3, 3, 1},
+    /* [2][*] */
+    {0, 0,
+     7, 5, 1, 3, 3, 7, 5, 5, 7, 7, 1, 3, 3, 7, 5, 1, 1, 5, 3, 7,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     5, 5, 5, 1, 3, 1, 5, 7, 3, 3, 5, 7, 3, 7, 1, 7, 7, 1, 3,
+     5, 1, 5, 5, 3, 7, 3, 7, 7, 5, 7, 5, 7, 1, 1, 5, 3, 5, 1,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     1, 3, 1, 1, 7, 1, 5, 5, 3, 7, 3, 7, 5, 3, 1, 1, 3, 1, 3, 5,
+     5, 7, 5, 3, 7, 7, 7, 3, 7, 3, 7, 1, 3, 1, 7, 7, 1, 7,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     3, 3, 3, 1, 3, 5, 7, 7, 1, 5, 7, 3, 7, 1, 1, 3, 5, 7, 5, 3, 3, 3},
+    /* [3][*] */
+    {0, 0, 0, 0,
+     1, 7, 9, 13, 11, 1, 3, 7, 9, 5, 13, 13, 11, 3, 15, 5, 3,
+     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,
+     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,
+     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,
+     5, 3, 15, 1, 11, 11, 7, 13, 15, 11, 13, 9, 11, 15, 15, 13, 3, 15, 7, 9, 11, 13, 11,
+     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,
+     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,
+     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,
+     3, 5, 13, 9, 11, 15, 11, 7, 1, 7, 13, 3, 13, 3, 13, 9, 15, 7, 13, 13, 3, 13, 15, 15,
+     11, 9, 13, 9, 15, 1, 1, 15, 11, 11, 7, 1, 11, 13, 9, 13, 3, 5, 11, 13, 9, 9, 13, 1,
+     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,
+     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,
+     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,
+     7, 1, 11, 7, 9, 13, 15, 13, 3, 1, 11, 13, 15, 1, 1, 11, 9, 13, 3, 13, 11, 15, 13, 9,
+     9, 9, 5, 5, 5, 5, 1, 15, 5, 9,
+     11, 7, 15, 5, 3, 13, 5, 3, 11, 5, 1, 11, 13, 9, 11,
+     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,
+     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,
+     1, 15, 3, 13, 9, 13, 9, 9, 11, 5, 5, 13, 15, 3, 9, 15, 3, 11, 11, 15, 15, 3, 11, 15,
+     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,
+     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,
+     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,
+     7, 15, 13, 13, 7, 15, 9, 13, 9, 15, 13, 15, 9, 13, 1, 11, 7, 11, 3, 13, 5, 1, 7, 15,
+     3, 13, 7, 13, 13, 11, 3, 5, 3, 13, 11, 9, 9, 3, 11, 11, 7, 9, 13, 11, 7, 15, 13, 7,
+     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,
+     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,
+     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,
+     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,
+     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,
+     11, 15, 13, 15, 1, 9, 9, 7,
+     3, 5, 11, 7, 3, 9, 5, 15, 7, 5, 3, 13, 7, 1, 1, 9,
+     15, 15, 15, 11, 3, 5, 15, 13, 7, 15, 15, 11, 11, 9, 5, 15, 9, 7, 3, 13, 1, 1, 5, 1,
+     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,
+     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,
+     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,
+     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,
+     11, 13, 13, 13, 9, 15, 5, 7, 1, 15, 11, 9, 15, 15, 13, 13, 13, 1, 11, 9, 15, 9, 5,
+     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,
+     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,
+     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,
+     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,
+     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,
+     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,
+     11, 1, 7, 13, 15, 15, 5, 7, 13, 13, 15, 11, 13, 1, 13, 13, 3, 9, 15, 15, 11, 15, 9,
+     15, 1, 13, 15, 1, 1, 5,
+     11, 5, 1, 11, 11, 5, 3, 9, 1, 3, 5, 13, 9, 7, 7, 1,
+     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,
+     3, 3, 1, 3, 15},
+    /* [4][*] */
+    {0, 0, 0, 0, 0, 0,
+     9, 3, 27, 15, 29, 21, 23, 19, 11, 25, 7, 13, 17, 1,
+     25, 29, 3, 31, 11, 5, 23, 27, 19, 21, 5, 1, 17, 13, 7, 15, 9, 31, 25, 3, 5, 23, 7,
+     3, 17, 23, 3, 3, 21, 25, 25, 23, 11, 19, 3, 11, 31, 7, 9, 5, 17, 23, 17, 17, 25,
+     13, 11, 31, 27, 19, 17, 23, 7, 5, 11, 19, 19, 7, 13, 21, 21, 7, 9, 11, 1, 5, 21,
+     11, 13, 25, 9, 7, 7, 27, 15, 25, 15, 21, 17, 19, 19, 21, 5, 11, 3, 5, 29, 31, 29,
+     5, 5, 1, 31, 27, 11, 13, 1, 3, 7, 11, 7, 3, 23, 13, 31, 17, 1, 27, 11, 25, 1, 23,
+     29, 17, 25, 7, 25, 27, 17, 13, 17, 23, 5, 17, 5, 13, 11, 21, 5, 11, 5, 9, 31, 19,
+     17, 9, 9, 27, 21, 15, 15, 1, 1, 29, 5, 31, 11, 17, 23, 19, 21, 25, 15, 11, 5, 5, 1,
+     19, 19, 19, 7, 13, 21, 17, 17, 25, 23, 19, 23, 15, 13, 5, 19, 25, 9, 7, 3, 21, 17,
+     25, 1, 27, 25, 27, 25, 9, 13, 3, 17, 25, 23, 9, 25, 9, 13, 17, 17, 3, 15, 7, 7, 29,
+     3, 19, 29, 29, 19, 29, 13, 15, 25, 27, 1, 3, 9, 9, 13, 31, 29, 31, 5, 15, 29, 1,
+     19, 5, 9, 19, 5, 15, 3, 5, 7, 15, 17, 17, 23, 11, 9, 23, 19, 3, 17, 1, 27, 9, 9, 17,
+     13, 25, 29, 23, 29, 11, 31, 25, 21, 29, 19, 27, 31, 3, 5, 3, 3, 13, 21, 9, 29, 3,
+     17, 11, 11, 9, 21, 19, 7, 17, 31, 25, 1, 27, 5, 15, 27, 29, 29, 29, 25, 27, 25, 3,
+     21, 17, 25, 13, 15, 17, 13, 23, 9, 3, 11, 7, 9, 9, 7, 17, 7, 1,
+     27, 1, 9, 5, 31, 21, 25, 25, 21, 11, 1, 23, 19, 27,
+     15, 3, 5, 23, 9, 25, 7, 29, 11, 9, 13, 5, 11, 1, 3, 31, 27, 3, 17, 27, 11, 13, 15,
+     29, 15, 1, 15, 23, 25, 13, 21, 15, 3, 29, 29, 5, 25, 17, 11, 7, 15, 5, 21, 7, 31,
+     13, 11, 23, 5, 7, 23, 27, 21, 29, 15, 7, 27, 27, 19, 7, 15, 27, 27, 19, 19, 9, 15,
+     1, 3, 29, 29, 5, 27, 31, 9, 1, 7, 3, 19, 19, 29, 9, 3, 21, 31, 29, 25, 1, 3, 9, 27,
+     5, 27, 25, 21, 11, 29, 31, 27, 21, 29, 17, 9, 17, 13, 11, 25, 15, 21, 11, 19, 31,
+     3, 19, 5, 3, 3, 9, 13, 13, 3, 29, 7, 5, 9, 23, 13, 21, 23, 21, 31, 11, 7, 7, 3, 23,
+     1, 23, 5, 9, 17, 21, 1, 17, 29, 7, 5, 17, 13, 25, 17, 9, 19, 9, 5, 7, 21, 19, 13, 9,
+     7, 3, 9, 3, 15, 31, 29, 29, 25, 13, 9, 21, 9, 31, 7, 15, 5, 31, 7, 15, 27, 25, 19,
+     9, 9, 25, 25, 23, 1, 9, 7, 11, 15, 19, 15, 27, 17, 11, 11, 31, 13, 25, 25, 9, 7,
+     13, 29, 19, 5, 19, 31, 25, 13, 25, 15, 5, 9, 29, 31, 9, 29, 27, 25, 27, 11, 17, 5,
+     17, 3, 23, 15, 9, 9, 17, 17, 31, 11, 19, 25, 13, 23, 15, 25, 21, 31, 19, 3, 11,
+     25, 7, 15, 19, 7, 5, 3, 13, 13, 1, 23, 5, 25, 11, 25, 15, 13, 21, 11, 23, 29, 5,
+     17, 27, 9, 19, 15, 5, 29, 23, 19, 1, 27, 3, 23, 21, 19, 27, 11, 17, 13, 27, 11,
+     31, 23, 5, 9, 21, 31, 29, 11, 21, 17, 15, 7, 15, 7, 9, 21, 27, 25,
+     29, 11, 3, 21, 13, 23, 19, 27, 17, 29, 25, 17, 9,
+     1, 19, 23, 5, 23, 1, 17, 17, 13, 27, 23, 7, 7, 11, 13, 17, 13, 11, 21, 13, 23, 1,
+     27, 13, 9, 7, 1, 27, 29, 5, 13, 25, 21, 3, 31, 15, 13, 3, 19, 13, 1, 27, 15, 17, 1,
+     3, 13, 13, 13, 31, 29, 27, 7, 7, 21, 29, 15, 17, 17, 21, 19, 17, 3, 15, 5, 27, 27,
+     3, 31, 31, 7, 21, 3, 13, 11, 17, 27, 25, 1, 9, 7, 29, 27, 21, 23, 13, 25, 29, 15,
+     17, 29, 9, 15, 3, 21, 15, 17, 17, 31, 9, 9, 23, 19, 25, 3, 1, 11, 27, 29, 1, 31,
+     29, 25, 29, 1, 23, 29, 25, 13, 3, 31, 25, 5, 5, 11, 3, 21, 9, 23, 7, 11, 23, 11, 1,
+     1, 3, 23, 25, 23, 1, 23, 3, 27, 9, 27, 3, 23, 25, 19, 29, 29, 13, 27, 5, 9, 29, 29,
+     13, 17, 3, 23, 19, 7, 13, 3, 19, 23, 5, 29, 29, 13, 13, 5, 19, 5, 17, 9, 11, 11,
+     29, 27, 23, 19, 17, 25, 13, 1, 13, 3, 11, 1, 17, 29, 1, 13, 17, 9, 17, 21, 1, 11,
+     1, 1, 25, 5, 7, 29, 29, 19, 19, 1, 29, 13, 3, 1, 31, 15, 13, 3, 1, 11, 19, 5, 29,
+     13, 29, 23, 3, 1, 31, 13, 19, 17, 5, 5, 1, 29, 23, 3, 19, 25, 19, 27, 9, 27, 13,
+     15, 29, 23, 13, 25, 25, 17, 19, 17, 15, 27, 3, 25, 17, 27, 3, 27, 31, 23, 13, 31,
+     11, 15, 7, 21, 19, 27, 19, 21, 29, 7, 31, 13, 9, 9, 7, 21, 13, 11, 9, 11, 29, 19,
+     11, 19, 21, 5, 29, 13, 7, 19, 19, 27, 23, 31, 1, 27, 21, 7, 3, 7, 11,
+     23, 13, 29, 11, 31, 19, 1, 5, 5, 11, 5, 3, 27, 5,
+     7, 11, 31, 1, 27, 31, 31, 23, 5, 21, 27, 9, 25, 3, 15, 19, 1, 19, 9, 5, 25, 21, 15,
+     25, 29, 15, 21, 11, 19, 15, 3, 7, 13, 11, 25, 17, 1, 5, 31, 13, 29, 23, 9, 5, 29,
+     7, 17, 27, 7, 17, 31, 9, 31, 9, 9, 7, 21, 3, 3, 3, 9, 11, 21, 11, 31, 9, 25, 5, 1,
+     31, 13, 29, 9, 29, 1, 11, 19, 7, 27, 13, 31, 7, 31, 7, 25, 23, 21, 29, 11, 11, 13,
+     11, 27, 1, 23, 31, 21, 23, 21, 19, 31, 5, 31, 25, 25, 19, 17, 11, 25, 7, 13, 1,
+     29, 17, 23, 15, 7, 29, 17, 13, 3, 17},
+    /* [5][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     37, 33, 7, 5, 11, 39, 63, 59, 17, 15, 23, 29, 3, 21,
+     13, 31, 25, 9, 49, 33, 19, 29, 11, 19, 27, 15, 25, 63, 55, 17, 63, 49, 19, 41,
+     59, 3, 57, 33, 49, 53, 57, 57, 39, 21, 7, 53, 9, 55, 15, 59, 19, 49, 31, 3, 39, 5,
+     5, 41, 9, 19, 9, 57, 25, 1, 15, 51, 11, 19, 61, 53, 29, 19, 11, 9, 21, 19, 43, 13,
+     13, 41, 25, 31, 9, 11, 19, 5, 53, 37, 7, 51, 45, 7, 7, 61, 23, 45, 7, 59, 41, 1,
+     29, 61, 37, 27, 47, 15, 31, 35, 31, 17, 51, 13, 25, 45, 5, 5, 33, 39, 5, 47, 29,
+     35, 47, 63, 45, 37, 47, 59, 21, 59, 33, 51, 9, 27, 13, 25, 43, 3, 17, 21, 59, 61,
+     27, 47, 57, 11, 17, 39, 1, 63, 21, 59, 17, 13, 31, 3, 31, 7, 9, 27, 37, 23, 31, 9,
+     45, 43, 31, 63, 21, 39, 51, 27, 7, 53, 11, 1, 59, 39, 23, 49, 23, 7, 55, 59, 3,
+     19, 35, 13, 9, 13, 15, 23, 9, 7, 43, 55, 3, 19, 9, 27, 33, 27, 49, 23, 47, 19, 7,
+     11, 55, 27, 35, 5, 5, 55, 35, 37, 9, 33, 29, 47, 25, 11, 47, 53, 61, 59, 3, 53,
+     47, 5, 19, 59, 5, 47, 23, 45, 53, 3, 49, 61, 47, 39, 29, 17, 57, 5, 17, 31, 23,
+     41, 39, 5, 27, 7, 29, 29, 33, 31, 41, 31, 29, 17, 29, 29, 9, 9, 31, 27, 53, 35, 5,
+     61, 1, 49, 13, 57, 29, 5, 21, 43, 25, 57, 49, 37, 27, 11, 61, 37, 49, 5, 63, 63,
+     3, 45, 37, 63, 21, 21, 19, 27, 59, 21, 45, 23, 13, 15, 3, 43, 63, 39, 19,
+     63, 31, 41, 41, 15, 43, 63, 53, 1, 63, 31, 7, 17,
+     11, 61, 31, 51, 37, 29, 59, 25, 63, 59, 47, 15, 27, 19, 29, 45, 35, 55, 39, 19,
+     43, 21, 19, 13, 17, 51, 37, 5, 33, 35, 49, 25, 45, 1, 63, 47, 9, 63, 15, 25, 25,
+     15, 41, 13, 3, 19, 51, 49, 37, 25, 49, 13, 53, 47, 23, 35, 29, 33, 21, 35, 23, 3,
+     43, 31, 63, 9, 1, 61, 43, 3, 11, 55, 11, 35, 1, 63, 35, 49, 19, 45, 9, 57, 51, 1,
+     47, 41, 9, 11, 37, 19, 55, 23, 55, 55, 13, 7, 47, 37, 11, 43, 17, 3, 25, 19, 55,
+     59, 37, 33, 43, 1, 5, 21, 5, 63, 49, 61, 21, 51, 15, 19, 43, 47, 17, 9, 53, 45,
+     11, 51, 25, 11, 25, 47, 47, 1, 43, 29, 17, 31, 15, 59, 27, 63, 11, 41, 51, 29, 7,
+     27, 63, 31, 43, 3, 29, 39, 3, 59, 59, 1, 53, 63, 23, 63, 47, 51, 23, 61, 39, 47,
+     21, 39, 15, 3, 9, 57, 61, 39, 37, 21, 51, 1, 23, 43, 27, 25, 11, 13, 21, 43, 7,
+     11, 33, 55, 1, 37, 35, 27, 61, 39, 5, 19, 61, 61, 57, 59, 21, 59, 61, 57, 25, 55,
+     27, 31, 41, 33, 63, 19, 57, 35, 13, 63, 35, 17, 11, 11, 49, 41, 55, 5, 45, 17,
+     35, 5, 31, 31, 37, 17, 45, 51, 1, 39, 49, 55, 19, 41, 13, 5, 51, 5, 49, 1, 21, 13,
+     17, 59, 51, 11, 3, 61, 1, 33, 37, 33, 61, 25, 27, 59, 7, 49, 13, 63, 3, 33, 3, 15,
+     9, 13, 35, 39, 11, 59, 59, 1, 57, 11, 5, 57, 13, 31, 13, 11, 55, 45, 9, 55, 55,
+     19, 25, 41, 23, 45, 29, 63, 59, 27, 39, 21, 37, 7,
+     61, 49, 35, 39, 9, 29, 7, 25, 23, 57, 5, 19, 15, 33, 49, 37, 25, 17, 45, 29, 15,
+     25, 3, 3, 49, 11, 39, 15, 19, 57, 39, 15, 11, 3, 57, 31, 55, 61, 19, 5, 41, 35,
+     59, 61, 39, 41, 53, 53, 63, 31, 9, 59, 13, 35, 55, 41, 49, 5, 41, 25, 27, 43, 5,
+     5, 43, 5, 5, 17, 5, 15, 27, 29, 17, 9, 3, 55, 31, 1, 45, 45, 13, 57, 17, 3, 61, 15,
+     49, 15, 47, 9, 37, 45, 9, 51, 61, 21, 33, 11, 21, 63, 63, 47, 57, 61, 49, 9, 59,
+     19, 29, 21, 23, 55, 23, 43, 41, 57, 9, 39, 27, 41, 35, 61, 29, 57, 63, 21, 31,
+     59, 35, 49, 3, 49, 47, 49, 33, 21, 19, 21, 35, 11, 17, 37, 23, 59, 13, 37, 35,
+     55, 57, 1, 29, 45, 11, 1, 15, 9, 33, 19, 53, 43, 39, 23, 7, 13, 13, 1, 19, 41, 55,
+     1, 13, 15, 59, 55, 15, 3, 57, 37, 31, 17, 1, 3, 21, 29, 25, 55, 9, 37, 33, 53, 41,
+     51, 19, 57, 13, 63, 43, 19, 7, 13, 37, 33, 19, 15, 63, 51, 11, 49, 23, 57, 47,
+     51, 15, 53, 41, 1, 15, 37, 61, 11, 35, 29, 33, 23, 55, 11, 59, 19, 61, 61, 45,
+     13, 49, 13, 63, 5, 61, 5, 31, 17, 61, 63, 13, 27, 57, 1, 21, 5, 11, 39, 57, 51,
+     53, 39, 25, 41, 39, 37, 23, 31, 25, 33, 17, 57, 29, 27, 23, 47, 41, 29, 19, 47,
+     41, 25, 5, 51, 43, 39, 29, 7, 31, 45, 51, 49, 55, 17, 43, 49, 45, 9, 29, 3, 5, 47,
+     9, 15, 19,
+     51, 45, 57, 63, 9, 21, 59, 3, 9, 13, 45, 23, 15,
+     31, 21, 15, 51, 35, 9, 11, 61, 23, 53, 29, 51, 45, 31, 29, 5, 35, 29, 53, 35, 17,
+     59, 55, 27, 51, 59, 27, 47, 15, 29, 37, 7, 49, 55, 5, 19, 45, 29, 19, 57, 33, 53,
+     45, 21, 9, 3, 35, 29, 43, 31, 39, 3, 45, 1, 41, 29, 5, 59, 41, 33, 35, 27, 19, 13,
+     25, 27, 43, 33, 35, 17, 17, 23, 7, 35, 15, 61, 61, 53, 5, 15, 23, 11, 13, 43, 55,
+     47, 25, 43, 15, 57, 45, 1, 49, 63, 57, 15, 31, 31, 7, 53, 27, 15, 47, 23, 7, 29,
+     53, 47, 9, 53, 3, 25, 55, 45, 63, 21, 17, 23, 31, 27, 27, 43, 63, 55, 63, 45, 51,
+     15, 27, 5, 37, 43, 11, 27, 5, 27, 59, 21, 7, 39, 27, 63, 35, 47, 55, 17, 17, 17,
+     3, 19, 21, 13, 49, 61, 39, 15},
+    /* [6][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     13, 33, 115, 41, 79, 17, 29, 119, 75, 73, 105, 7,
+     59, 65, 21, 3, 113, 61, 89, 45, 107, 21, 71, 79, 19, 71, 61, 41, 57, 121, 87,
+     119, 55, 85, 121, 119, 11, 23, 61, 11, 35, 33, 43, 107, 113, 101, 29, 87, 119,
+     97, 29, 17, 89, 5, 127, 89, 119, 117, 103, 105, 41, 83, 25, 41, 55, 69, 117,
+     49, 127, 29, 1, 99, 53, 83, 15, 31, 73, 115, 35, 21, 89, 5, 1, 91, 53, 35, 95,
+     83, 19, 85, 55, 51, 101, 33, 41, 55, 45, 95, 61, 27, 37, 89, 75, 57, 61, 15,
+     117, 15, 21, 27, 25, 27, 123, 39, 109, 93, 51, 21, 91, 109, 107, 45, 15, 93,
+     127, 3, 53, 81, 79, 107, 79, 87, 35, 109, 73, 35, 83, 107, 1, 51, 7, 59, 33,
+     115, 43, 111, 45, 121, 105, 125, 87, 101, 41, 95, 75, 1, 57, 117, 21, 27, 67,
+     29, 53, 117, 63, 1, 77, 89, 115, 49, 127, 15, 79, 81, 29, 65, 103, 33, 73, 79,
+     29, 21, 113, 31, 33, 107, 95, 111, 59, 99, 117, 63, 63, 99, 39, 9, 35, 63, 125,
+     99, 45, 93, 33, 93, 9, 105, 75, 51, 115, 11, 37, 17, 41, 21, 43, 73, 19, 93, 7,
+     95, 81, 93, 79, 81, 55, 9, 51, 63, 45, 89, 73, 19, 115, 39, 47, 81, 39, 5, 5, 45,
+     53, 65, 49, 17, 105, 13, 107, 5, 5, 19, 73, 59, 43, 83, 97, 115, 27, 1, 69, 103,
+     3, 99, 103, 63, 67, 25, 121, 97, 77, 13, 83, 103, 41, 11, 27, 81, 37, 33, 125,
+     71, 41, 41, 59, 41, 87, 123,
+     43, 101, 63, 45, 39, 21, 97, 15, 97, 111, 21, 49,
+     13, 17, 79, 91, 65, 105, 75, 1, 45, 67, 83, 107, 125, 87, 15, 81, 95, 105, 65,
+     45, 59, 103, 23, 103, 99, 67, 99, 47, 117, 71, 89, 35, 53, 73, 9, 115, 49, 37,
+     1, 35, 9, 45, 81, 19, 127, 17, 17, 105, 89, 49, 101, 7, 37, 33, 11, 95, 95, 17,
+     111, 105, 41, 115, 5, 69, 101, 27, 27, 101, 103, 53, 9, 21, 43, 79, 91, 65,
+     117, 87, 125, 55, 45, 63, 85, 83, 97, 45, 83, 87, 113, 93, 95, 5, 17, 77, 77,
+     127, 123, 45, 81, 85, 121, 119, 27, 85, 41, 49, 15, 107, 21, 51, 119, 11, 87,
+     101, 115, 63, 63, 37, 121, 109, 7, 43, 69, 19, 77, 49, 71, 59, 35, 7, 13, 55,
+     101, 127, 103, 85, 109, 29, 61, 67, 21, 111, 67, 23, 57, 75, 71, 101, 123, 41,
+     107, 101, 107, 125, 27, 47, 119, 41, 19, 127, 33, 31, 109, 7, 91, 91, 39, 125,
+     105, 47, 125, 123, 91, 9, 103, 45, 23, 117, 9, 125, 73, 11, 37, 61, 79, 21, 5,
+     47, 117, 67, 53, 85, 33, 81, 121, 47, 61, 51, 127, 29, 65, 45, 41, 95, 57, 73,
+     33, 117, 61, 111, 59, 123, 65, 47, 105, 23, 29, 107, 37, 81, 67, 29, 115, 119,
+     75, 73, 99, 103, 7, 57, 45, 61, 95, 49, 101, 101, 35, 47, 119, 39, 67, 31, 103,
+     7, 61, 127, 87, 3, 35, 29, 73, 95, 103, 71, 75, 51, 87, 57, 97, 11, 105, 87, 41,
+     73, 109, 69, 35, 121, 39, 111, 1, 77,
+     39, 47, 53, 91, 3, 17, 51, 83, 39, 125, 85, 111,
+     21, 69, 85, 29, 55, 11, 117, 1, 47, 17, 65, 63, 47, 117, 17, 115, 51, 25, 33,
+     123, 123, 83, 51, 113, 95, 121, 51, 91, 109, 43, 55, 35, 55, 87, 33, 37, 5, 3,
+     45, 21, 105, 127, 35, 17, 35, 37, 97, 97, 21, 77, 123, 17, 89, 53, 105, 75, 25,
+     125, 13, 47, 21, 125, 23, 55, 63, 61, 5, 17, 93, 57, 121, 69, 73, 93, 121, 105,
+     75, 91, 67, 95, 75, 9, 69, 97, 99, 93, 11, 53, 19, 73, 5, 33, 79, 107, 65, 69,
+     79, 125, 25, 93, 55, 61, 17, 117, 69, 97, 87, 111, 37, 93, 59, 79, 95, 53, 115,
+     53, 85, 85, 65, 59, 23, 75, 21, 67, 27, 99, 79, 27, 3, 95, 27, 69, 19, 75, 47,
+     59, 41, 85, 77, 99, 55, 49, 93, 93, 119, 51, 125, 63, 13, 15, 45, 61, 19, 105,
+     115, 17, 83, 7, 7, 11, 61, 37, 63, 89, 95, 119, 113, 67, 123, 91, 33, 37, 99,
+     43, 11, 33, 65, 81, 79, 81, 107, 63, 63, 55, 89, 91, 25, 93, 101, 27, 55, 75,
+     121, 79, 43, 125, 73, 27, 109, 35, 21, 71, 113, 89, 59, 95, 41, 45, 113, 119,
+     113, 39, 59, 73, 15, 13, 59, 67, 121, 27, 7, 105, 15, 59, 59, 35, 91, 89, 23,
+     125, 97, 53, 41, 91, 111, 29, 31, 3, 103, 61, 71, 35, 7, 119, 29, 45, 49, 111,
+     41, 109, 59, 125, 13, 27, 19, 79, 9, 75, 83, 81, 33, 91, 109, 33, 29, 107, 111,
+     101, 107, 109, 65, 59, 43, 37,
+     1, 9, 15, 109, 37, 111, 113, 119, 79, 73, 65,
+     71, 93, 17, 101, 87, 97, 43, 23, 75, 109, 41, 49, 53, 31, 97, 105, 109, 119,
+     51, 9, 53, 113, 97, 73, 89, 79, 49, 61, 105, 13, 99, 53, 71, 7, 87, 21, 101, 5,
+     71, 31, 123, 121, 121, 73, 79, 115, 13, 39, 101, 19, 37, 51, 83, 97, 55, 81,
+     91, 127, 105, 89, 63, 47, 49, 75, 37, 77, 15, 49, 107, 23, 23, 35, 19, 69, 17,
+     59, 63, 73, 29, 125, 61, 65, 95, 101, 81, 57, 69, 83, 37, 11, 37, 95, 1, 73, 27,
+     29, 57, 7, 65, 83, 99, 69, 19, 103, 43, 95, 25, 19, 103, 41, 125, 97, 71, 105,
+     83, 83, 61, 39, 9, 45, 117, 63, 31, 5, 117, 67, 125, 41, 117, 43, 77, 97, 15,
+     29, 5, 59, 25, 63, 87, 39, 39, 77, 85, 37, 81, 73, 89, 29, 125, 109, 21, 23,
+     119, 105, 43, 93, 97, 15, 125, 29, 51, 69, 37, 45, 31, 75, 109, 119, 53, 5,
+     101, 125, 121, 35, 29, 7, 63, 17, 63, 13, 69, 15, 105, 51, 127, 105, 9, 57, 95,
+     59, 109, 35, 49, 23, 33, 107, 55, 33, 57, 79, 73, 69, 59, 107, 55, 11, 63, 95,
+     103, 23, 125, 91, 31, 91, 51, 65, 61, 75, 69, 107, 65, 101, 59, 35, 15},
+    /* [7][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     7, 23, 39, 217, 141, 27, 53, 181, 169, 35, 15,
+     207, 45, 247, 185, 117, 41, 81, 223, 151, 81, 189, 61, 95, 185, 23, 73, 113,
+     239, 85, 9, 201, 83, 53, 183, 203, 91, 149, 101, 13, 111, 239, 3, 205, 253,
+     247, 121, 189, 169, 179, 197, 175, 217, 249, 195, 95, 63, 19, 7, 5, 75, 217,
+     245, 111, 189, 165, 169, 141, 221, 249, 159, 253, 207, 249, 219, 23, 49,
+     127, 237, 5, 25, 177, 37, 103, 65, 167, 81, 87, 119, 45, 79, 143, 57, 79, 187,
+     143, 183, 75, 97, 211, 149, 175, 37, 135, 189, 225, 241, 63, 33, 43, 13, 73,
+     213, 57, 239, 183, 117, 21, 29, 115, 43, 205, 223, 15, 3, 159, 51, 101, 127,
+     99, 239, 171, 113, 171, 119, 189, 245, 201, 27, 185, 229, 105, 153, 189, 33,
+     35, 137, 77, 97, 17, 181, 55, 197, 201, 155, 37, 197, 137, 223, 25, 179, 91,
+     23, 235, 53, 253, 49, 181, 249, 53, 173, 97, 247, 67, 115, 103, 159, 239, 69,
+     173, 217, 95, 221, 247, 97, 91, 123, 223, 213, 129, 181, 87, 239, 85, 89,
+     249, 141, 39, 57, 249, 71, 101, 159, 33, 137, 189, 71, 253, 205, 171, 13,
+     249, 109, 131, 199, 189, 179, 31, 99, 113, 41, 173, 23, 189, 197, 3, 135, 9,
+     95, 195, 27, 183, 1, 123, 73, 53, 99, 197, 59, 27, 101, 55, 193, 31, 61, 119,
+     11, 7, 255, 233, 53, 157, 193, 97, 83, 65, 81, 239, 167, 69, 71, 109,
+     97, 137, 71, 193, 189, 115, 79, 205, 37, 227,
+     53, 33, 91, 229, 245, 105, 77, 229, 161, 103, 93, 13, 161, 229, 223, 69, 15,
+     25, 23, 233, 93, 25, 217, 247, 61, 75, 27, 9, 223, 213, 55, 197, 145, 89, 199,
+     41, 201, 5, 149, 35, 119, 183, 53, 11, 13, 3, 179, 229, 43, 55, 187, 233, 47,
+     133, 91, 47, 71, 93, 105, 145, 45, 255, 221, 115, 175, 19, 129, 5, 209, 197,
+     57, 177, 115, 187, 119, 77, 211, 111, 33, 113, 23, 87, 137, 41, 7, 83, 43,
+     121, 145, 5, 219, 27, 11, 111, 207, 55, 97, 63, 229, 53, 33, 149, 23, 187,
+     153, 91, 193, 183, 59, 211, 93, 139, 59, 179, 163, 209, 77, 39, 111, 79, 229,
+     85, 237, 199, 137, 147, 25, 73, 121, 129, 83, 87, 93, 205, 167, 53, 107, 229,
+     213, 95, 219, 109, 175, 13, 209, 97, 61, 147, 19, 13, 123, 73, 35, 141, 81,
+     19, 171, 255, 111, 107, 233, 113, 133, 89, 9, 231, 95, 69, 33, 1, 253, 219,
+     253, 247, 129, 11, 251, 221, 153, 35, 103, 239, 7, 27, 235, 181, 5, 207, 53,
+     149, 155, 225, 165, 137, 155, 201, 97, 245, 203, 47, 39, 35, 105, 239, 49,
+     15, 253, 7, 237, 213, 55, 87, 199, 27, 175, 49, 41, 229, 85, 3, 149, 179, 129,
+     185, 249, 197, 15, 97, 197, 139, 203, 63, 33, 251, 217, 199, 199, 99, 249,
+     33, 229, 177, 13, 209, 147, 97, 31, 125, 177, 137,
+     187, 11, 91, 223, 29, 169, 231, 59, 31, 163, 41,
+     57, 87, 247, 25, 127, 101, 207, 187, 73, 61, 105, 27, 91, 171, 243, 33, 3, 1,
+     21, 229, 93, 71, 61, 37, 183, 65, 211, 53, 11, 151, 165, 47, 5, 129, 79, 101,
+     147, 169, 181, 19, 95, 77, 139, 197, 219, 97, 239, 183, 143, 9, 13, 209, 23,
+     215, 53, 137, 203, 19, 151, 171, 133, 219, 231, 3, 15, 253, 225, 33, 111,
+     183, 213, 169, 119, 111, 15, 201, 123, 121, 225, 113, 113, 225, 161, 165, 1,
+     139, 55, 3, 93, 217, 193, 97, 29, 69, 231, 161, 93, 69, 143, 137, 9, 87, 183,
+     113, 183, 73, 215, 137, 89, 251, 163, 41, 227, 145, 57, 81, 57, 11, 135, 145,
+     161, 175, 159, 25, 55, 167, 157, 211, 97, 247, 249, 23, 129, 159, 71, 197,
+     127, 141, 219, 5, 233, 131, 217, 101, 131, 33, 157, 173, 69, 207, 239, 81,
+     205, 11, 41, 169, 65, 193, 77, 201, 173, 1, 221, 157, 1, 15, 113, 147, 137,
+     205, 225, 73, 45, 49, 149, 113, 253, 99, 17, 119, 105, 117, 129, 243, 75,
+     203, 53, 29, 247, 35, 247, 171, 31, 199, 213, 29, 251, 7, 251, 187, 91, 11,
+     149, 13, 205, 37, 249, 137, 139, 9, 7, 113, 183, 205, 187, 39, 3, 79, 155,
+     227, 89, 185, 51, 127, 63, 83, 41, 133, 183, 181, 127, 19, 255, 219, 59, 251,
+     3, 187, 57, 217, 115, 217, 229, 181, 185, 149, 83, 115, 11,
+     123, 19, 109, 165, 103, 123, 219, 129, 155,
+     207, 177, 9, 49, 181, 231, 33, 233, 67, 155, 41, 9, 95, 123, 65, 117, 249, 85,
+     169, 129, 241, 173, 251, 225, 147, 165, 69, 81, 239, 95, 23, 83, 227, 249,
+     143, 171, 193, 9, 21, 57, 73, 97, 57, 29, 239, 151, 159, 191, 47, 51, 1, 223,
+     251, 251, 151, 41, 119, 127, 131, 33, 209, 123, 53, 241, 25, 31, 183, 107,
+     25, 115, 39, 11, 213, 239, 219, 109, 185, 35, 133, 123, 185, 27, 55, 245, 61,
+     75, 205, 213, 169, 163, 63, 55, 49, 83, 195, 51, 31, 41, 15, 203, 41, 63, 127,
+     161, 5, 143, 7, 199, 251, 95, 75, 101, 15, 43, 237, 197, 117, 167, 155, 21,
+     83, 205, 255, 49, 101, 213, 237, 135, 135, 21, 73, 93, 115, 7, 85, 223, 237,
+     79, 89, 5, 57, 239, 67, 65, 201, 155, 71, 85, 195, 89, 181, 119, 135, 147,
+     237, 173, 41, 155, 67, 113, 111, 21, 183, 23, 103, 207, 253, 69, 219, 205,
+     195, 43, 197, 229, 139, 177, 129, 69, 97, 201, 163, 189, 11, 99, 91, 253,
+     239, 91, 145, 19, 179, 231, 121, 7, 225, 237, 125, 191, 119, 59, 175, 237,
+     131, 79, 43, 45, 205, 199, 251, 153, 207, 37, 179, 113, 255, 107, 217, 61, 7,
+     181, 247, 31, 13, 113, 145, 107, 233, 233, 43, 79, 23, 169, 137, 129, 183,
+     53, 91, 55, 103, 223, 87, 177, 157, 79, 213, 139,
+     183, 231, 205, 143, 129, 243, 205, 93, 59,
+     15, 89, 9, 11, 47, 133, 227, 75, 9, 91, 19, 171, 163, 79, 7, 103, 5, 119, 155,
+     75, 11, 71, 95, 17, 13, 243, 207, 187},
+    /* [8][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     235, 307, 495, 417, 57, 151, 19, 119, 375, 451,
+     55, 449, 501, 53, 185, 317, 17, 21, 487, 13, 347, 393, 15, 391, 307, 189,
+     381, 71, 163, 99, 467, 167, 433, 337, 257, 179, 47, 385, 23, 117, 369, 425,
+     207, 433, 301, 147, 333, 85, 221, 423, 49, 3, 43, 229, 227, 201, 383, 281,
+     229, 207, 21, 343, 251, 397, 173, 507, 421, 443, 399, 53, 345, 77, 385, 317,
+     155, 187, 269, 501, 19, 169, 235, 415, 61, 247, 183, 5, 257, 401, 451, 95,
+     455, 49, 489, 75, 459, 377, 87, 463, 155, 233, 115, 429, 211, 419, 143, 487,
+     195, 209, 461, 193, 157, 193, 363, 181, 271, 445, 381, 231, 135, 327, 403,
+     171, 197, 181, 343, 113, 313, 393, 311, 415, 267, 247, 425, 233, 289, 55,
+     39, 247, 327, 141, 5, 189, 183, 27, 337, 341, 327, 87, 429, 357, 265, 251,
+     437, 201, 29, 339, 257, 377, 17, 53, 327, 47, 375, 393, 369, 403, 125, 429,
+     257, 157, 217, 85, 267, 117, 337, 447, 219, 501, 41, 41, 193, 509, 131, 207,
+     505, 421, 149, 111, 177, 167, 223, 291, 91, 29, 305, 151, 177, 337, 183,
+     361, 435, 307, 507, 77, 181, 507, 315, 145, 423, 71, 103, 493, 271, 469,
+     339, 237, 437, 483, 31, 219, 61, 131, 391, 233, 219, 69, 57, 459, 225, 421,
+     7, 461, 111, 451, 277, 185, 193, 125, 251, 199, 73, 71, 7, 409, 417, 149,
+     193, 53, 437, 29, 467, 229, 31, 35, 75, 105,
+     503, 75, 317, 401, 367, 131, 365, 441, 433, 93, 377, 405, 465, 259, 283,
+     443, 143, 445, 3, 461, 329, 309, 77, 323, 155, 347, 45, 381, 315, 463, 207,
+     321, 157, 109, 479, 313, 345, 167, 439, 307, 235, 473, 79, 101, 245, 19,
+     381, 251, 35, 25, 107, 187, 115, 113, 321, 115, 445, 61, 77, 293, 405, 13,
+     53, 17, 171, 299, 41, 79, 3, 485, 331, 13, 257, 59, 201, 497, 81, 451, 199,
+     171, 81, 253, 365, 75, 451, 149, 483, 81, 453, 469, 485, 305, 163, 401, 15,
+     91, 3, 129, 35, 239, 355, 211, 387, 101, 299, 67, 375, 405, 357, 267, 363,
+     79, 83, 437, 457, 39, 97, 473, 289, 179, 57, 23, 49, 79, 71, 341, 287, 95,
+     229, 271, 475, 49, 241, 261, 495, 353, 381, 13, 291, 37, 251, 105, 399, 81,
+     89, 265, 507, 205, 145, 331, 129, 119, 503, 249, 1, 289, 463, 163, 443, 63,
+     123, 361, 261, 49, 429, 137, 355, 175, 507, 59, 277, 391, 25, 185, 381, 197,
+     39, 5, 429, 119, 247, 177, 329, 465, 421, 271, 467, 151, 45, 429, 137, 471,
+     11, 17, 409, 347, 199, 463, 177, 11, 51, 361, 95, 497, 163, 351, 127, 395,
+     511, 327, 353, 49, 105, 151, 321, 331, 329, 509, 107, 109, 303, 467, 287,
+     161, 45, 385, 289, 363, 331, 265, 407, 37, 433, 315, 343, 63, 51, 185, 71,
+     27, 267,
+     503, 239, 293, 245, 281, 297, 75, 461, 371,
+     129, 189, 189, 339, 287, 111, 111, 379, 93, 27, 185, 347, 337, 247, 507,
+     161, 231, 43, 499, 73, 327, 263, 331, 249, 493, 37, 25, 115, 3, 167, 197,
+     127, 357, 497, 103, 125, 191, 165, 55, 101, 95, 79, 351, 341, 43, 125, 135,
+     173, 289, 373, 133, 421, 241, 281, 213, 177, 363, 151, 227, 145, 363, 239,
+     431, 81, 397, 241, 67, 291, 255, 405, 421, 399, 75, 399, 105, 329, 41, 425,
+     7, 283, 375, 475, 427, 277, 209, 411, 3, 137, 195, 289, 509, 121, 55, 147,
+     275, 251, 19, 129, 285, 415, 487, 491, 193, 219, 403, 23, 97, 65, 285, 75,
+     21, 373, 261, 339, 239, 495, 415, 333, 107, 435, 297, 213, 149, 463, 199,
+     323, 45, 19, 301, 121, 499, 187, 229, 63, 425, 99, 281, 35, 125, 349, 87,
+     101, 59, 195, 511, 355, 73, 263, 243, 101, 165, 141, 11, 389, 219, 187, 449,
+     447, 393, 477, 305, 221, 51, 355, 209, 499, 479, 265, 377, 145, 411, 173,
+     11, 433, 483, 135, 385, 341, 89, 209, 391, 33, 395, 319, 451, 119, 341, 227,
+     375, 61, 331, 493, 411, 293, 47, 203, 375, 167, 395, 155, 5, 237, 361, 489,
+     127, 21, 345, 101, 371, 233, 431, 109, 119, 277, 125, 263, 73, 135, 123, 83,
+     123, 405, 69, 75, 287, 401, 23, 283, 393, 41, 379, 431, 11, 475, 505, 19,
+     365, 265, 271,
+     499, 489, 443, 165, 91, 83, 291, 319, 199,
+     107, 245, 389, 143, 137, 89, 125, 281, 381, 215, 131, 299, 249, 375, 455,
+     43, 73, 281, 217, 297, 229, 431, 357, 81, 357, 171, 451, 481, 13, 387, 491,
+     489, 439, 385, 487, 177, 393, 33, 71, 375, 443, 129, 407, 395, 127, 65, 333,
+     309, 119, 197, 435, 497, 373, 71, 379, 509, 387, 159, 265, 477, 463, 449,
+     47, 353, 249, 335, 505, 89, 141, 55, 235, 187, 87, 363, 93, 363, 101, 67,
+     215, 321, 331, 305, 261, 411, 491, 479, 65, 307, 469, 415, 131, 315, 487,
+     83, 455, 19, 113, 163, 503, 99, 499, 251, 239, 81, 167, 391, 255, 317, 363,
+     359, 395, 419, 307, 251, 267, 171, 461, 183, 465, 165, 163, 293, 477, 223,
+     403, 389, 97, 335, 357, 297, 19, 469, 501, 249, 85, 213, 311, 265, 379, 297,
+     283, 393, 449, 463, 289, 159, 289, 499, 407, 129, 137, 221, 43, 89, 403,
+     271, 75, 83, 445, 453, 389, 149, 143, 423, 499, 317, 445, 157, 137, 453,
+     163, 87, 23, 391, 119, 427, 323, 173, 89, 259, 377, 511, 249, 31, 363, 229,
+     353, 329, 493, 427, 57, 205, 389, 91, 83, 13, 219, 439, 45, 35, 371, 441, 17,
+     267, 501, 53, 25, 333, 17, 201, 475, 257, 417, 345, 381, 377, 55, 403, 77,
+     389, 347, 363, 211, 413, 419, 5, 167, 219, 201, 285, 425, 11, 77, 269, 489,
+     281, 403, 79,
+     425, 125, 81, 331, 437, 271, 397, 299, 475,
+     271, 249, 413, 233, 261, 495, 171, 69, 27, 409, 21, 421, 367, 81, 483, 255,
+     15, 219, 365, 497, 181, 75, 431, 99, 325, 407, 229, 281, 63, 83, 493, 5, 113,
+     15, 271, 37, 87, 451, 299, 83, 451, 311, 441, 47, 455, 47, 253, 13, 109, 369,
+     347, 11, 409, 275, 63, 441, 15},
+    /* [9][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     519, 307, 931, 1023, 517, 771, 151, 1023,
+     539, 725, 45, 927, 707, 29, 125, 371, 275, 279, 817, 389, 453, 989, 1015,
+     29, 169, 743, 99, 923, 981, 181, 693, 309, 227, 111, 219, 897, 377, 425,
+     609, 227, 19, 221, 143, 581, 147, 919, 127, 725, 793, 289, 411, 835, 921,
+     957, 443, 349, 813, 5, 105, 457, 393, 539, 101, 197, 697, 27, 343, 515, 69,
+     485, 383, 855, 693, 133, 87, 743, 747, 475, 87, 469, 763, 721, 345, 479,
+     965, 527, 121, 271, 353, 467, 177, 245, 627, 113, 357, 7, 691, 725, 355,
+     889, 635, 737, 429, 545, 925, 357, 873, 187, 351, 677, 999, 921, 477, 233,
+     765, 495, 81, 953, 479, 89, 173, 473, 131, 961, 411, 291, 967, 65, 511, 13,
+     805, 945, 369, 827, 295, 163, 835, 259, 207, 331, 29, 315, 999, 133, 967,
+     41, 117, 677, 471, 717, 881, 755, 351, 723, 259, 879, 455, 721, 289, 149,
+     199, 805, 987, 851, 423, 597, 129, 11, 733, 549, 153, 285, 451, 559, 377,
+     109, 357, 143, 693, 615, 677, 701, 475, 767, 85, 229, 509, 547, 151, 389,
+     711, 785, 657, 319, 509, 99, 1007, 775, 359, 697, 677, 85, 497, 105, 615,
+     891, 71, 449, 835, 609, 377, 693, 665, 627, 215, 911, 503, 729, 131, 19,
+     895, 199, 161, 239, 633, 1013, 537, 255, 23, 149, 679, 1021, 595, 199, 557,
+     659, 251, 829, 727, 439, 495, 647, 223,
+     949, 625, 87, 481, 85, 799, 917, 769, 949,
+     739, 115, 499, 945, 547, 225, 1015, 469, 737, 495, 353, 103, 17, 665, 639,
+     525, 75, 447, 185, 43, 729, 577, 863, 735, 317, 99, 17, 477, 893, 537, 519,
+     1017, 375, 297, 325, 999, 353, 343, 729, 135, 489, 859, 267, 141, 831, 141,
+     893, 249, 807, 53, 613, 131, 547, 977, 131, 999, 175, 31, 341, 739, 467,
+     675, 241, 645, 247, 391, 583, 183, 973, 433, 367, 131, 467, 571, 309, 385,
+     977, 111, 917, 935, 473, 345, 411, 313, 97, 149, 959, 841, 839, 669, 431,
+     51, 41, 301, 247, 1015, 377, 329, 945, 269, 67, 979, 581, 643, 823, 557, 91,
+     405, 117, 801, 509, 347, 893, 303, 227, 783, 555, 867, 99, 703, 111, 797,
+     873, 541, 919, 513, 343, 319, 517, 135, 871, 917, 285, 663, 301, 15, 763,
+     89, 323, 757, 317, 807, 309, 1013, 345, 499, 279, 711, 915, 411, 281, 193,
+     739, 365, 315, 375, 809, 469, 487, 621, 857, 975, 537, 939, 585, 129, 625,
+     447, 129, 1017, 133, 83, 3, 415, 661, 53, 115, 903, 49, 79, 55, 385, 261,
+     345, 297, 199, 385, 617, 25, 515, 275, 849, 401, 471, 377, 661, 535, 505,
+     939, 465, 225, 929, 219, 955, 659, 441, 117, 527, 427, 515, 287, 191, 33,
+     389, 197, 825, 63, 417, 949, 35, 571, 9, 131, 609, 439, 95, 19, 569, 893,
+     451, 397, 971, 801,
+     125, 471, 187, 257, 67, 949, 621, 453, 411,
+     621, 955, 309, 783, 893, 597, 377, 753, 145, 637, 941, 593, 317, 555, 375,
+     575, 175, 403, 571, 555, 109, 377, 931, 499, 649, 653, 329, 279, 271, 647,
+     721, 665, 429, 957, 803, 767, 425, 477, 995, 105, 495, 575, 687, 385, 227,
+     923, 563, 723, 481, 717, 111, 633, 113, 369, 955, 253, 321, 409, 909, 367,
+     33, 967, 453, 863, 449, 539, 781, 911, 113, 7, 219, 725, 1015, 971, 1021,
+     525, 785, 873, 191, 893, 297, 507, 215, 21, 153, 645, 913, 755, 371, 881,
+     113, 903, 225, 49, 587, 201, 927, 429, 599, 513, 97, 319, 331, 833, 325,
+     887, 139, 927, 399, 163, 307, 803, 169, 1019, 869, 537, 907, 479, 335, 697,
+     479, 353, 769, 787, 1023, 855, 493, 883, 521, 735, 297, 1011, 991, 879,
+     855, 591, 415, 917, 375, 453, 553, 189, 841, 339, 211, 601, 57, 765, 745,
+     621, 209, 875, 639, 7, 595, 971, 263, 1009, 201, 23, 77, 621, 33, 535, 963,
+     661, 523, 263, 917, 103, 623, 231, 47, 301, 549, 337, 675, 189, 357, 1005,
+     789, 189, 319, 721, 1005, 525, 675, 539, 191, 813, 917, 51, 167, 415, 579,
+     755, 605, 721, 837, 529, 31, 327, 799, 961, 279, 409, 847, 649, 241, 285,
+     545, 407, 161, 591, 73, 313, 811, 17, 663, 269, 261, 37, 783, 127, 917, 231,
+     577, 975, 793,
+     921, 343, 751, 139, 221, 79, 817, 393, 545,
+     11, 781, 71, 1, 699, 767, 917, 9, 107, 341, 587, 903, 965, 599, 507, 843,
+     739, 579, 397, 397, 325, 775, 565, 925, 75, 55, 979, 931, 93, 957, 857, 753,
+     965, 795, 67, 5, 87, 909, 97, 995, 271, 875, 671, 613, 33, 351, 69, 811, 669,
+     729, 401, 647, 241, 435, 447, 721, 271, 745, 53, 775, 99, 343, 451, 427,
+     593, 339, 845, 243, 345, 17, 573, 421, 517, 971, 499, 435, 769, 75, 203,
+     793, 985, 343, 955, 735, 523, 659, 703, 303, 421, 951, 405, 631, 825, 735,
+     433, 841, 485, 49, 749, 107, 669, 211, 497, 143, 99, 57, 277, 969, 107, 397,
+     563, 551, 447, 381, 187, 57, 405, 731, 769, 923, 955, 915, 737, 595, 341,
+     253, 823, 197, 321, 315, 181, 885, 497, 159, 571, 981, 899, 785, 947, 217,
+     217, 135, 753, 623, 565, 717, 903, 581, 955, 621, 361, 869, 87, 943, 907,
+     853, 353, 335, 197, 771, 433, 743, 195, 91, 1023, 63, 301, 647, 205, 485,
+     927, 1003, 987, 359, 577, 147, 141, 1017, 701, 273, 89, 589, 487, 859, 343,
+     91, 847, 341, 173, 287, 1003, 289, 639, 983, 685, 697, 35, 701, 645, 911,
+     501, 705, 873, 763, 745, 657, 559, 699, 315, 347, 429, 197, 165, 955, 859,
+     167, 303, 833, 531, 473, 635, 641, 195, 589, 821, 205, 3, 635, 371, 891,
+     249, 123,
+     77, 623, 993, 401, 525, 427, 71, 655, 951,
+     357, 851, 899, 535, 493, 323, 1003, 343, 515, 859, 1017, 5, 423, 315, 1011,
+     703, 41, 777, 163, 95, 831, 79, 975, 235, 633, 723, 297, 589, 317, 679, 981,
+     195, 399, 1003, 121, 501, 155},
+    /* [10][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     7, 2011, 1001, 49, 825, 415, 1441, 383, 1581,
+     623, 1621, 1319, 1387, 619, 839, 217, 75, 1955, 505, 281, 1629, 1379, 53,
+     1111, 1399, 301, 209, 49, 155, 1647, 631, 129, 1569, 335, 67, 1955, 1611,
+     2021, 1305, 121, 37, 877, 835, 1457, 669, 1405, 935, 1735, 665, 551, 789,
+     1543, 1267, 1027, 1, 1911, 163, 1929, 67, 1975, 1681, 1413, 191, 1711,
+     1307, 401, 725, 1229, 1403, 1609, 2035, 917, 921, 1789, 41, 2003, 187, 67,
+     1635, 717, 1449, 277, 1903, 1179, 363, 1211, 1231, 647, 1261, 1029, 1485,
+     1309, 1149, 317, 1335, 171, 243, 271, 1055, 1601, 1129, 1653, 205, 1463,
+     1681, 1621, 197, 951, 573, 1697, 1265, 1321, 1805, 1235, 1853, 1307, 945,
+     1197, 1411, 833, 273, 1517, 1747, 1095, 1345, 869, 57, 1383, 221, 1713,
+     335, 1751, 1141, 839, 523, 1861, 1105, 389, 1177, 1877, 805, 93, 1591,
+     423, 1835, 99, 1781, 1515, 1909, 1011, 303, 385, 1635, 357, 973, 1781,
+     1707, 1363, 1053, 649, 1469, 623, 1429, 1241, 1151, 1055, 503, 921, 3,
+     349, 1149, 293, 45, 303, 877, 1565, 1583, 1001, 663, 1535, 395, 1141,
+     1481, 1797, 643, 1507, 465, 2027, 1695, 367, 937, 719, 545, 1991, 83, 819,
+     239, 1791, 1461, 1647, 1501, 1161, 1629, 139, 1595, 1921, 1267, 1415,
+     509, 347, 777, 1083, 363, 269, 1015,
+     1809, 1105, 1429, 1471, 2019, 381, 2025,
+     1223, 827, 1733, 887, 1321, 803, 1951, 1297, 1995, 833, 1107, 1135, 1181,
+     1251, 983, 1389, 1565, 273, 137, 71, 735, 1005, 933, 67, 1471, 551, 457,
+     1667, 1729, 919, 285, 1629, 1815, 653, 1919, 1039, 531, 393, 1411, 359,
+     221, 699, 1485, 471, 1357, 1715, 595, 1677, 153, 1903, 1281, 215, 781,
+     543, 293, 1807, 965, 1695, 443, 1985, 321, 879, 1227, 1915, 839, 1945,
+     1993, 1165, 51, 557, 723, 1491, 817, 1237, 947, 1215, 1911, 1225, 1965,
+     1889, 1503, 1177, 73, 1767, 303, 177, 1897, 1401, 321, 921, 217, 1779,
+     327, 1889, 333, 615, 1665, 1825, 1639, 237, 1205, 361, 129, 1655, 983,
+     1089, 1171, 401, 677, 643, 749, 303, 1407, 1873, 1579, 1491, 1393, 1247,
+     789, 763, 49, 5, 1607, 1891, 735, 1557, 1909, 1765, 1777, 1127, 813, 695,
+     97, 731, 1503, 1751, 333, 769, 865, 693, 377, 1919, 957, 1359, 1627, 1039,
+     1783, 1065, 1665, 1917, 1947, 991, 1997, 841, 459, 221, 327, 1595, 1881,
+     1269, 1007, 129, 1413, 475, 1105, 791, 1983, 1359, 503, 691, 659, 691,
+     343, 1375, 1919, 263, 1373, 603, 1383, 297, 781, 145, 285, 767, 1739,
+     1715, 715, 317, 1333, 85, 831, 1615, 81, 1667, 1467, 1457, 1453, 1825,
+     109, 387, 1207, 2039, 213, 1351, 1329, 1173,
+     57, 1769, 951, 183, 23, 451, 1155, 1551,
+     2037, 811, 635, 1671, 1451, 863, 1499, 1673, 363, 1029, 1077, 1525, 277,
+     1023, 655, 665, 1869, 1255, 965, 277, 1601, 329, 1603, 1901, 395, 65,
+     1307, 2029, 21, 1321, 543, 1569, 1185, 1905, 1701, 413, 2041, 1697, 725,
+     1417, 1847, 411, 211, 915, 1891, 17, 1877, 1699, 687, 1089, 1973, 1809,
+     851, 1495, 1257, 63, 1323, 1307, 609, 881, 1543, 177, 617, 1505, 1747,
+     1537, 925, 183, 77, 1723, 1877, 1703, 397, 459, 521, 257, 1177, 389, 1947,
+     1553, 1583, 1831, 261, 485, 289, 1281, 1543, 1591, 1123, 573, 821, 1065,
+     1933, 1373, 2005, 905, 207, 173, 1573, 1597, 573, 1883, 1795, 1499, 1743,
+     553, 335, 333, 1645, 791, 871, 1157, 969, 557, 141, 223, 1129, 1685, 423,
+     1069, 391, 99, 95, 1847, 531, 1859, 1833, 1833, 341, 237, 1997, 1799, 409,
+     431, 1917, 363, 335, 1039, 1085, 1657, 1975, 1527, 1111, 659, 389, 899,
+     595, 1439, 1861, 1979, 1569, 1087, 1009, 165, 1895, 1481, 1583, 29, 1193,
+     1673, 1075, 301, 1081, 1377, 1747, 1497, 1103, 1789, 887, 739, 1577, 313,
+     1367, 1299, 1801, 1131, 1837, 73, 1865, 1065, 843, 635, 55, 1655, 913,
+     1037, 223, 1871, 1161, 461, 479, 511, 1721, 1107, 389, 151, 35, 375, 1099,
+     937, 1185, 1701, 769, 639, 1633,
+     1609, 379, 1613, 2031, 685, 289, 975, 671,
+     1599, 1447, 871, 647, 99, 139, 1427, 959, 89, 117, 841, 891, 1959, 223,
+     1697, 1145, 499, 1435, 1809, 1413, 1445, 1675, 171, 1073, 1349, 1545,
+     2039, 1027, 1563, 859, 215, 1673, 1919, 1633, 779, 411, 1845, 1477, 1489,
+     447, 1545, 351, 1989, 495, 183, 1639, 1385, 1805, 1097, 1249, 1431, 1571,
+     591, 697, 1509, 709, 31, 1563, 165, 513, 1425, 1299, 1081, 145, 1841,
+     1211, 941, 609, 845, 1169, 1865, 1593, 347, 293, 1277, 157, 211, 93, 1679,
+     1799, 527, 41, 473, 563, 187, 1525, 575, 1579, 857, 703, 1211, 647, 709,
+     981, 285, 697, 163, 981, 153, 1515, 47, 1553, 599, 225, 1147, 381, 135,
+     821, 1965, 609, 1033, 983, 503, 1117, 327, 453, 2005, 1257, 343, 1649,
+     1199, 599, 1877, 569, 695, 1587, 1475, 187, 973, 233, 511, 51, 1083, 665,
+     1321, 531, 1875, 1939, 859, 1507, 1979, 1203, 1965, 737, 921, 1565, 1943,
+     819, 223, 365, 167, 1705, 413, 1577, 745, 1573, 655, 1633, 1003, 91, 1123,
+     477, 1741, 1663, 35, 715, 37, 1513, 815, 941, 1379, 263, 1831, 1735, 1111,
+     1449, 353, 1941, 1655, 1349, 877, 285, 1723, 125, 1753, 985, 723, 175,
+     439, 791, 1051, 1261, 717, 1555, 1757, 1777, 577, 1583, 1957, 873, 331,
+     1163, 313, 1, 1963, 963, 1905, 821,
+     1677, 185, 709, 545, 1723, 215, 1885,
+     1249, 583, 1803, 839, 885, 485, 413, 1767, 425, 129, 1035, 329, 1263,
+     1881, 1779, 1565, 359, 367, 453, 707, 1419, 831, 1889, 887, 1871, 1869,
+     747, 223, 1547, 1799, 433, 1441, 553, 2021, 1303, 1505, 1735, 1619, 1065,
+     1161, 2047, 347, 867, 881, 1447, 329, 781, 1065, 219, 589, 645, 1257,
+     1833, 749, 1841, 1733, 1179, 1191, 1025, 1639, 1955, 1423, 1685, 1711,
+     493, 549, 783, 1653, 397, 895, 233, 759, 1505, 677, 1449, 1573, 1297,
+     1821, 1691, 791, 289, 1187, 867, 1535, 575, 183},
+    /* [11][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     3915, 97, 3047, 937, 2897, 953, 127, 1201,
+     3819, 193, 2053, 3061, 3759, 1553, 2007, 2493, 603, 3343, 3751, 1059,
+     783, 1789, 1589, 283, 1093, 3919, 2747, 277, 2605, 2169, 2905, 721, 4069,
+     233, 261, 1137, 3993, 3619, 2881, 1275, 3865, 1299, 3757, 1193, 733, 993,
+     1153, 2945, 3163, 3179, 437, 271, 3493, 3971, 1005, 2615, 2253, 1131,
+     585, 2775, 2171, 2383, 2937, 2447, 1745, 663, 1515, 3767, 2709, 1767,
+     3185, 3017, 2815, 1829, 87, 3341, 793, 2627, 2169, 1875, 3745, 367, 3783,
+     783, 827, 3253, 2639, 2955, 3539, 1579, 2109, 379, 2939, 3019, 1999,
+     2253, 2911, 3733, 481, 1767, 1055, 4019, 4085, 105, 1829, 2097, 2379,
+     1567, 2713, 737, 3423, 3941, 2659, 3961, 1755, 3613, 1937, 1559, 2287,
+     2743, 67, 2859, 325, 2601, 1149, 3259, 2403, 3947, 2011, 175, 3389, 3915,
+     1315, 2447, 141, 359, 3609, 3933, 729, 2051, 1755, 2149, 2107, 1741,
+     1051, 3681, 471, 1055, 845, 257, 1559, 1061, 2803, 2219, 1315, 1369,
+     3211, 4027, 105, 11, 1077, 2857, 337, 3553, 3503, 3917, 2665, 3823, 3403,
+     3711, 2085, 1103, 1641, 701, 4095, 2883, 1435, 653, 2363, 1597, 767, 869,
+     1825, 1117, 1297, 501, 505, 149, 873, 2673, 551, 1499, 2793, 3277, 2143,
+     3663, 533, 3991, 575, 1877, 1009, 3929, 473, 3009, 2595, 3249, 675, 3593,
+     2453, 1567, 973, 595, 1335, 1715, 589, 85,
+     2265, 3069, 461, 1659, 2627, 1307, 1731, 1501, 1699, 3545, 3803, 2157,
+     453, 2813, 2047, 2999, 3841, 2361, 1079, 573, 69, 1363, 1597, 3427, 2899,
+     2771, 1327, 1117, 1523, 3521, 2393, 2537, 1979, 3179, 683, 2453, 453,
+     1227, 779, 671, 3483, 2135, 3139, 3381, 3945, 57, 1541, 3405, 3381, 2371,
+     2879, 1985, 987, 3017, 3031, 3839, 1401, 3749, 2977, 681, 1175, 1519,
+     3355, 907, 117, 771, 3741, 3337, 1743, 1227, 3335, 2755, 1909, 3603,
+     2397, 653, 87, 2025, 2617, 3257, 287, 3051, 3809, 897, 2215, 63, 2043,
+     1757, 3671, 297, 3131, 1305, 293, 3865, 3173, 3397, 2269, 3673, 717,
+     3041, 3341, 3595, 3819, 2871, 3973, 1129, 513, 871, 1485, 3977, 2473,
+     1171, 1143, 3063, 3547, 2183, 3993, 133, 2529, 2699, 233, 2355, 231,
+     3241, 611, 1309, 3829, 1839, 1495, 301, 1169, 1613, 2673, 243, 3601,
+     3669, 2813, 2671, 2679, 3463, 2477, 1795, 617, 2317, 1855, 1057, 1703,
+     1761, 2515, 801, 1205, 1311, 473, 3963, 697, 1221, 251, 381, 3887, 1761,
+     3093, 3721, 2079, 4085, 379, 3601, 3845, 433, 1781, 29, 1897, 1599, 2163,
+     75, 3475, 3957, 1641, 3911, 2959, 2833, 1279, 1099, 403, 799, 2183, 2699,
+     1711, 2037, 727, 289, 1785, 1575, 3633, 2367, 1261, 3953, 1735, 171,
      1959,
-     2867,859,2951,3211,15,1279,1323,599,
-     1651,3951,1011,315,3513,3351,1725,3793,2399,287,4017,3571,
-     1007,541,3115,429,1585,1285,755,1211,3047,915,3611,2697,2129,
-     3669,81,3939,2437,915,779,3567,3701,2479,3807,1893,3927,2619,
-     2543,3633,2007,3857,3837,487,1769,3759,3105,2727,3155,2479,
-     1341,1657,2767,2541,577,2105,799,17,2871,3637,953,65,69,2897,
-     3841,3559,4067,2335,3409,1087,425,2813,1705,1701,1237,821,
-     1375,3673,2693,3925,1541,1871,2285,847,4035,1101,2029,855,
-     2733,2503,121,2855,1069,3463,3505,1539,607,1349,575,2301,
-     2321,1101,333,291,2171,4085,2173,2541,1195,925,4039,1379,699,
-     1979,275,953,1755,1643,325,101,2263,3329,3673,3413,1977,2727,
-     2313,1419,887,609,2475,591,2613,2081,3805,3435,2409,111,3557,
-     3607,903,231,3059,473,2959,2925,3861,2043,3887,351,2865,369,
-     1377,2639,1261,3625,3279,2201,2949,3049,449,1297,897,1891,
-     411,2773,749,2753,1825,853,2775,3547,3923,3923,987,3723,2189,
-     3877,3577,297,2763,1845,3083,2951,483,2169,3985,245,3655,
-     3441,1023,235,835,3693,3585,327,1003,543,3059,2637,
-     2923,87,3617,1031,1043,903,2913,
-     2177,2641,3279,389,2009,525,4085,3299,987,2409,813,2683,373,
-     2695,3775,2375,1119,2791,223,325,587,1379,2877,2867,3793,655,
-     831,3425,1663,1681,2657,1865,3943,2977,1979,2271,3247,1267,
-     1747,811,159,429,2001,1195,3065,553,1499,3529,1081,2877,3077,
-     845,1793,2409,3995,2559,4081,1195,2955,1117,1409,785,287,
-     1521,1607,85,3055,3123,2533,2329,3477,799,3683,3715,337,3139,
-     3311,431,3511,2299,365,2941,3067,1331,1081,1097,2853,2299,
-     495,1745,749,3819,619,1059,3559,183,3743,723,949,3501,733,
-     2599,3983,3961,911,1899,985,2493,1795,653,157,433,2361,3093,
-     3119,3679,2367,1701,1445,1321,2397,1241,3305,3985,2349,4067,
-     3805,3073,2837,1567,3783,451,2441,1181,487,543,1201,3735,
-     2517,733,1535,2175,3613,3019},
-     /* [12][*] */
-     {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-     2319,653,1379,1675,1951,7075,2087,
-     7147,1427,893,171,2019,7235,5697,3615,1961,7517,6849,2893,
-     1883,2863,2173,4543,73,381,3893,6045,1643,7669,1027,1549,
-     3983,1985,6589,7497,2745,2375,7047,1117,1171,1975,5199,3915,
-     3695,8113,4303,3773,7705,6855,1675,2245,2817,1719,569,1021,
-     2077,5945,1833,2631,4851,6371,833,7987,331,1899,8093,6719,
-     6903,5903,5657,5007,2689,6637,2675,1645,1819,689,6709,7717,
-     6295,7013,7695,3705,7069,2621,3631,6571,6259,7261,3397,7645,
-     1115,4753,2047,7579,2271,5403,4911,7629,4225,1209,6955,6951,
-     1829,5579,5231,1783,4285,7425,599,5785,3275,5643,2263,657,
-     6769,6261,1251,3249,4447,4111,3991,1215,131,4397,3487,7585,
-     5565,7199,3573,7105,7409,1671,949,3889,5971,3333,225,3647,
-     5403,3409,7459,6879,5789,6567,5581,4919,1927,4407,8085,4691,
-     611,3005,591,753,589,171,5729,5891,1033,3049,6567,5257,8003,
-     1757,4489,4923,6379,5171,1757,689,3081,1389,4113,455,2761,
-     847,7575,5829,633,6629,1103,7635,803,6175,6587,2711,3879,67,
-     1179,4761,7281,1557,3379,2459,4273,4127,7147,35,
-     3549,395,3735,5787,4179,5889,5057,
-     7473,4713,2133,2897,1841,2125,1029,1695,6523,1143,5105,7133,
-     3351,2775,3971,4503,7589,5155,4305,1641,4717,2427,5617,1267,
-     399,5831,4305,4241,3395,3045,4899,1713,171,411,7099,5473,
-     5209,1195,1077,1309,2953,7343,4887,3229,6759,6721,6775,675,
-     4039,2493,7511,3269,4199,6625,7943,2013,4145,667,513,2303,
-     4591,7941,2741,987,8061,3161,5951,1431,831,5559,7405,1357,
-     4319,4235,5421,2559,4415,2439,823,1725,6219,4903,6699,5451,
-     349,7703,2927,7809,6179,1417,5987,3017,4983,3479,4525,4643,
-     4911,227,5475,2287,5581,6817,1937,1421,4415,7977,1789,3907,
-     6815,6789,6003,5609,4507,337,7427,7943,3075,6427,1019,7121,
-     4763,81,3587,2929,1795,8067,2415,1265,4025,5599,4771,3025,
-     2313,6129,7611,6881,5253,4413,7869,105,3173,1629,2537,1023,
-     4409,7209,4413,7107,7469,33,1955,2881,5167,6451,4211,179,
-     5573,7879,3387,7759,5455,7157,1891,5683,5689,6535,3109,6555,
-     6873,1249,4251,6437,49,2745,1201,7327,4179,6783,623,2779,
-     5963,2585,6927,5333,4033,285,7467,4443,4917,3,
-     4319,5517,3449,813,5499,2515,5771,
-     3357,2073,4395,4925,2643,7215,5817,1199,1597,1619,7535,4833,
-     609,4797,8171,6847,793,6757,8165,3371,2431,5235,4739,7703,
-     7223,6525,5891,5605,4433,3533,5267,5125,5037,225,6717,1121,
-     5741,2013,4327,4839,569,5227,7677,4315,2391,5551,859,3627,
-     6377,3903,4311,6527,7573,4905,7731,1909,1555,3279,1949,1887,
-     6675,5509,2033,5473,3539,5033,5935,6095,4761,1771,1271,1717,
-     4415,5083,6277,3147,7695,2461,4783,4539,5833,5583,651,1419,
-     2605,5511,3913,5795,2333,2329,4431,3725,6069,2699,7055,6879,
-     1017,3121,2547,4603,2385,6915,6103,5669,7833,2001,4287,6619,
-     955,2761,5711,6291,3415,3909,2841,5627,4939,7671,6059,6275,
-     6517,1931,4583,7301,1267,7509,1435,2169,6939,3515,2985,2787,
-     2123,1969,3307,353,4359,7059,5273,5873,6657,6765,6229,3179,
-     1583,6237,2155,371,273,7491,3309,6805,3015,6831,7819,713,
-     4747,3935,4109,1311,709,3089,7059,4247,2989,1509,4919,1841,
-     3045,3821,6929,4655,1333,6429,6649,2131,5265,1051,261,8057,
-     3379,2179,1993,5655,3063,6381,
-     3587,7417,1579,1541,2107,5085,2873,
-     6141,955,3537,2157,841,1999,1465,5171,5651,1535,7235,4349,
-     1263,1453,1005,6893,2919,1947,1635,3963,397,969,4569,655,
-     6737,2995,7235,7713,973,4821,2377,1673,1,6541}
+     2867, 859, 2951, 3211, 15, 1279, 1323, 599,
+     1651, 3951, 1011, 315, 3513, 3351, 1725, 3793, 2399, 287, 4017, 3571,
+     1007, 541, 3115, 429, 1585, 1285, 755, 1211, 3047, 915, 3611, 2697, 2129,
+     3669, 81, 3939, 2437, 915, 779, 3567, 3701, 2479, 3807, 1893, 3927, 2619,
+     2543, 3633, 2007, 3857, 3837, 487, 1769, 3759, 3105, 2727, 3155, 2479,
+     1341, 1657, 2767, 2541, 577, 2105, 799, 17, 2871, 3637, 953, 65, 69, 2897,
+     3841, 3559, 4067, 2335, 3409, 1087, 425, 2813, 1705, 1701, 1237, 821,
+     1375, 3673, 2693, 3925, 1541, 1871, 2285, 847, 4035, 1101, 2029, 855,
+     2733, 2503, 121, 2855, 1069, 3463, 3505, 1539, 607, 1349, 575, 2301,
+     2321, 1101, 333, 291, 2171, 4085, 2173, 2541, 1195, 925, 4039, 1379, 699,
+     1979, 275, 953, 1755, 1643, 325, 101, 2263, 3329, 3673, 3413, 1977, 2727,
+     2313, 1419, 887, 609, 2475, 591, 2613, 2081, 3805, 3435, 2409, 111, 3557,
+     3607, 903, 231, 3059, 473, 2959, 2925, 3861, 2043, 3887, 351, 2865, 369,
+     1377, 2639, 1261, 3625, 3279, 2201, 2949, 3049, 449, 1297, 897, 1891,
+     411, 2773, 749, 2753, 1825, 853, 2775, 3547, 3923, 3923, 987, 3723, 2189,
+     3877, 3577, 297, 2763, 1845, 3083, 2951, 483, 2169, 3985, 245, 3655,
+     3441, 1023, 235, 835, 3693, 3585, 327, 1003, 543, 3059, 2637,
+     2923, 87, 3617, 1031, 1043, 903, 2913,
+     2177, 2641, 3279, 389, 2009, 525, 4085, 3299, 987, 2409, 813, 2683, 373,
+     2695, 3775, 2375, 1119, 2791, 223, 325, 587, 1379, 2877, 2867, 3793, 655,
+     831, 3425, 1663, 1681, 2657, 1865, 3943, 2977, 1979, 2271, 3247, 1267,
+     1747, 811, 159, 429, 2001, 1195, 3065, 553, 1499, 3529, 1081, 2877, 3077,
+     845, 1793, 2409, 3995, 2559, 4081, 1195, 2955, 1117, 1409, 785, 287,
+     1521, 1607, 85, 3055, 3123, 2533, 2329, 3477, 799, 3683, 3715, 337, 3139,
+     3311, 431, 3511, 2299, 365, 2941, 3067, 1331, 1081, 1097, 2853, 2299,
+     495, 1745, 749, 3819, 619, 1059, 3559, 183, 3743, 723, 949, 3501, 733,
+     2599, 3983, 3961, 911, 1899, 985, 2493, 1795, 653, 157, 433, 2361, 3093,
+     3119, 3679, 2367, 1701, 1445, 1321, 2397, 1241, 3305, 3985, 2349, 4067,
+     3805, 3073, 2837, 1567, 3783, 451, 2441, 1181, 487, 543, 1201, 3735,
+     2517, 733, 1535, 2175, 3613, 3019},
+    /* [12][*] */
+    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+     2319, 653, 1379, 1675, 1951, 7075, 2087,
+     7147, 1427, 893, 171, 2019, 7235, 5697, 3615, 1961, 7517, 6849, 2893,
+     1883, 2863, 2173, 4543, 73, 381, 3893, 6045, 1643, 7669, 1027, 1549,
+     3983, 1985, 6589, 7497, 2745, 2375, 7047, 1117, 1171, 1975, 5199, 3915,
+     3695, 8113, 4303, 3773, 7705, 6855, 1675, 2245, 2817, 1719, 569, 1021,
+     2077, 5945, 1833, 2631, 4851, 6371, 833, 7987, 331, 1899, 8093, 6719,
+     6903, 5903, 5657, 5007, 2689, 6637, 2675, 1645, 1819, 689, 6709, 7717,
+     6295, 7013, 7695, 3705, 7069, 2621, 3631, 6571, 6259, 7261, 3397, 7645,
+     1115, 4753, 2047, 7579, 2271, 5403, 4911, 7629, 4225, 1209, 6955, 6951,
+     1829, 5579, 5231, 1783, 4285, 7425, 599, 5785, 3275, 5643, 2263, 657,
+     6769, 6261, 1251, 3249, 4447, 4111, 3991, 1215, 131, 4397, 3487, 7585,
+     5565, 7199, 3573, 7105, 7409, 1671, 949, 3889, 5971, 3333, 225, 3647,
+     5403, 3409, 7459, 6879, 5789, 6567, 5581, 4919, 1927, 4407, 8085, 4691,
+     611, 3005, 591, 753, 589, 171, 5729, 5891, 1033, 3049, 6567, 5257, 8003,
+     1757, 4489, 4923, 6379, 5171, 1757, 689, 3081, 1389, 4113, 455, 2761,
+     847, 7575, 5829, 633, 6629, 1103, 7635, 803, 6175, 6587, 2711, 3879, 67,
+     1179, 4761, 7281, 1557, 3379, 2459, 4273, 4127, 7147, 35,
+     3549, 395, 3735, 5787, 4179, 5889, 5057,
+     7473, 4713, 2133, 2897, 1841, 2125, 1029, 1695, 6523, 1143, 5105, 7133,
+     3351, 2775, 3971, 4503, 7589, 5155, 4305, 1641, 4717, 2427, 5617, 1267,
+     399, 5831, 4305, 4241, 3395, 3045, 4899, 1713, 171, 411, 7099, 5473,
+     5209, 1195, 1077, 1309, 2953, 7343, 4887, 3229, 6759, 6721, 6775, 675,
+     4039, 2493, 7511, 3269, 4199, 6625, 7943, 2013, 4145, 667, 513, 2303,
+     4591, 7941, 2741, 987, 8061, 3161, 5951, 1431, 831, 5559, 7405, 1357,
+     4319, 4235, 5421, 2559, 4415, 2439, 823, 1725, 6219, 4903, 6699, 5451,
+     349, 7703, 2927, 7809, 6179, 1417, 5987, 3017, 4983, 3479, 4525, 4643,
+     4911, 227, 5475, 2287, 5581, 6817, 1937, 1421, 4415, 7977, 1789, 3907,
+     6815, 6789, 6003, 5609, 4507, 337, 7427, 7943, 3075, 6427, 1019, 7121,
+     4763, 81, 3587, 2929, 1795, 8067, 2415, 1265, 4025, 5599, 4771, 3025,
+     2313, 6129, 7611, 6881, 5253, 4413, 7869, 105, 3173, 1629, 2537, 1023,
+     4409, 7209, 4413, 7107, 7469, 33, 1955, 2881, 5167, 6451, 4211, 179,
+     5573, 7879, 3387, 7759, 5455, 7157, 1891, 5683, 5689, 6535, 3109, 6555,
+     6873, 1249, 4251, 6437, 49, 2745, 1201, 7327, 4179, 6783, 623, 2779,
+     5963, 2585, 6927, 5333, 4033, 285, 7467, 4443, 4917, 3,
+     4319, 5517, 3449, 813, 5499, 2515, 5771,
+     3357, 2073, 4395, 4925, 2643, 7215, 5817, 1199, 1597, 1619, 7535, 4833,
+     609, 4797, 8171, 6847, 793, 6757, 8165, 3371, 2431, 5235, 4739, 7703,
+     7223, 6525, 5891, 5605, 4433, 3533, 5267, 5125, 5037, 225, 6717, 1121,
+     5741, 2013, 4327, 4839, 569, 5227, 7677, 4315, 2391, 5551, 859, 3627,
+     6377, 3903, 4311, 6527, 7573, 4905, 7731, 1909, 1555, 3279, 1949, 1887,
+     6675, 5509, 2033, 5473, 3539, 5033, 5935, 6095, 4761, 1771, 1271, 1717,
+     4415, 5083, 6277, 3147, 7695, 2461, 4783, 4539, 5833, 5583, 651, 1419,
+     2605, 5511, 3913, 5795, 2333, 2329, 4431, 3725, 6069, 2699, 7055, 6879,
+     1017, 3121, 2547, 4603, 2385, 6915, 6103, 5669, 7833, 2001, 4287, 6619,
+     955, 2761, 5711, 6291, 3415, 3909, 2841, 5627, 4939, 7671, 6059, 6275,
+     6517, 1931, 4583, 7301, 1267, 7509, 1435, 2169, 6939, 3515, 2985, 2787,
+     2123, 1969, 3307, 353, 4359, 7059, 5273, 5873, 6657, 6765, 6229, 3179,
+     1583, 6237, 2155, 371, 273, 7491, 3309, 6805, 3015, 6831, 7819, 713,
+     4747, 3935, 4109, 1311, 709, 3089, 7059, 4247, 2989, 1509, 4919, 1841,
+     3045, 3821, 6929, 4655, 1333, 6429, 6649, 2131, 5265, 1051, 261, 8057,
+     3379, 2179, 1993, 5655, 3063, 6381,
+     3587, 7417, 1579, 1541, 2107, 5085, 2873,
+     6141, 955, 3537, 2157, 841, 1999, 1465, 5171, 5651, 1535, 7235, 4349,
+     1263, 1453, 1005, 6893, 2919, 1947, 1635, 3963, 397, 969, 4569, 655,
+     6737, 2995, 7235, 7713, 973, 4821, 2377, 1673, 1, 6541}
 };
 
 #endif