b := (1, 748,1472,1014)( 2, 978, 271,1043)(   3,  47,1077, 602)
(   4,  68, 931, 437)(   5,1034, 137,1004)(   6,1254, 838, 970)
(   7,1532, 817,1047)(   8, 302)(   9,1076, 264, 518)
(  10, 572, 926,  75)(  11,1087,  71, 950)(  12,1530, 420, 985)
(  13, 249,1111,1053)(  14, 821,1309, 270)(  15, 144,1452,1041)
(  16,1224, 325,1409)(  17,1090, 764, 675)(  18, 315, 982, 644)
(  19, 733,1095,1099)(  20, 112, 187, 286)(  21, 625)
(  22,1498, 923, 849)(  23,1420, 876, 495)(  24, 662,1445,  30)
(  25, 377, 902,1195)(  26, 811, 494,1313)(  27, 350,1135,1173)
(  28,1298, 298,1317)(  29, 802,1442,1557)(  31,1504,1208,1383)
(  32,1290, 937, 565)(  33, 806,1185,1384)(  34,1394,1567, 110)
(  35,1222,1073, 697)(  36, 409,1358,1497)(  37, 590,1343, 478)
(  38, 676, 419, 965)(  39,1291, 132, 507)(  40, 809, 611, 159)
(  41, 747, 829,1344)(  42, 541, 668,1466)(  43, 343,1140,1234)
(  44, 266, 571,1248)(  45,1194,1120,1203)(  46, 195,1361,1283)
(  48,  79, 945,1438)(  49,1207,1364, 365)(  50, 202, 329, 880)
(  51, 827, 672,1515)(  52,  62, 166, 189)(  53,1463, 522, 781)
(  54, 501, 300,1130)(  55,1006, 607, 250)(  56, 633,1199,1288)
(  57, 654, 290, 782)(  58, 122,  72, 221)(  59, 735,1372,1143)
(  60, 791, 589,  99)(  61,1240,1575, 816)(  63,1416,1571, 115)
(  64,1413, 374, 248)(  65,1055, 552,1189)(  66, 562, 414, 934)
(  67, 545, 474,  73)(  69, 200, 390, 688)(  70, 924, 366,1062)
(  74, 837, 536,1019)(  76,1514, 584, 702)(  77,1029, 470, 324)
(  78,1308, 418,1539)(  80,1187,1553,1058)(  81, 256,1192,1276)
(  82, 124,1174,1356)(  83, 411,1031, 652)(  84, 928, 241,1387)
(  85, 787,1220, 119)(  86, 759, 640,1419)(  87,1048, 738, 188)
(  88,1226, 936, 176)(  89, 233, 881,1334)(  90,1441,1078, 779)
(  91, 491, 255,1037)(  92,1521,1116,1239)(  93, 558,1547,1378)
(  94, 434, 967, 267)(  95,1165, 798, 466)(  96,1052, 670, 517)
(  97,1324,1476, 285)(  98,1015, 653,1266)( 100, 422,1256, 990)
( 101, 941,1186,1296)( 102, 775,1397,1439)( 103,1457, 175,1548)
( 104,1381,1488, 326)( 105, 588,1430,1410)( 106, 772,1151,1213)
( 107, 743,1518,1525)( 108, 475, 231,1513)( 109,1385,1091, 543)
( 111,1154, 835, 199)( 113, 874, 727, 674)( 114,1494, 280,1342)
( 116, 247, 841, 852)( 117,1462, 870,1316)( 118, 999, 603, 957)
( 120, 788,1407,1362)( 121,1400,1101,1084)( 123, 632,1176,1357)
( 125, 129,1080, 349)( 126,1478,1072, 641)( 127, 472, 700,1206)
( 128, 683,1417,1326)( 130, 442, 215, 887)( 131, 949, 977, 258)
( 133, 453,1251, 417)( 134, 292, 885, 751)( 135, 311,1089, 771)
( 136,1310,1261, 801)( 138, 379, 883, 823)( 139, 586,1200, 142)
( 140, 436,1218, 968)( 141, 783,1148,1538)( 143, 899, 561, 307)
( 145, 156,1440,1183)( 146, 995, 208, 956)( 147,1481,1008, 211)
( 148, 388,1527,1280)( 149, 869, 863, 486)( 150,1503,1426, 842)
( 151, 917,1431,1447)( 152,1126, 314, 441)( 153, 557,1558, 960)
( 154,1474, 410,1531)( 155,1560, 918, 629)( 157, 573,1007, 396)
( 158, 742,1526,1460)( 160, 479,1196,1237)( 161,1064, 716, 591)
( 162, 761, 609,1392)( 163,1100,1097,1184)( 164,1127, 293,1511)
( 165, 237, 642,1153)( 167, 895,1323, 537)( 168, 352, 600,1259)
( 169, 360)( 170,1079, 656,1177)( 171, 661, 875,1272)
( 172,1352,1051, 655)( 173, 525,1271, 391)( 174, 580,1569, 416)
( 177,1255,1499, 445)( 178, 938, 867,1305)( 179,1175, 948,1096)
( 180, 469, 446, 309)( 181,1150,1536, 531)( 182, 833, 269,1509)
( 183, 454, 276, 750)( 184,1390,1507,1496)( 185,1119)
( 186, 191,1327, 554)( 190, 608, 574, 229)( 192, 622, 839,1036)
( 193, 929, 503, 278)( 194, 539, 889, 814)( 196, 401)
( 197,1085, 636, 730)( 198, 395,1049, 793)( 201,1375, 996, 626)
( 203,1374, 526,1393)( 204,1285,1333, 421)( 205,1044, 765,1229)
( 206,1414,1157,1054)( 207, 262,1448,1301)( 209, 993, 665, 594)
( 210, 372, 677,1406)( 212,1246,1299, 544)( 213, 375, 404, 713)
( 214,1190, 915,1422)( 216,1464,1125,1147)( 217,1171, 834, 722)
( 218, 513,1479, 234)( 219,1436,1483, 305)( 220,1331)
( 222, 639, 740,1542)( 223, 527, 939, 741)( 224, 784, 301, 657)
( 225,1210,1572,1162)( 226, 347, 354,1322)( 227, 843, 861, 872)
( 228,1026, 610, 865)( 230, 601, 471, 893)( 232, 595)
( 235, 774, 371, 890)( 236, 853, 451,1468)( 238,1519, 444,1432)
( 239, 762, 498, 370)( 242, 868,1012, 752)( 243, 460, 456,1404)
( 244,1329,1139, 807)( 245, 933, 846,1412)( 246, 651, 438, 896)
( 251, 663, 858,1418)( 252,1169,1337, 336)( 253,1528, 828,1244)
( 254, 323, 514, 989)( 257, 287, 685,1179)( 259, 954,1013, 447)
( 260, 907, 383, 450)( 261,1570,1415, 483)( 263,1069, 477,1216)
( 265, 900, 972, 678)( 268,1109,1152,1423)( 272,1018, 489, 649)
( 273, 402,1303, 296)( 274,1110,1443,1493)( 275,1286,1005, 428)
( 277,1379)( 279, 667,1554, 581)( 281, 794, 464, 947)
( 282,1262, 547,1163)( 283,1023, 690,1471)( 284, 596, 734,1113)
( 288,1353, 399, 505)( 289,1405, 998, 648)( 291,1311, 898,1335)
( 294, 393,1345,1278)( 295,1427,1451, 851)( 297,1330)
( 299,1001, 756, 512)( 303,1512,1260,1172)( 304,1249,1551,1167)
( 306, 773, 951,1160)( 308, 341,1534,1307)( 310,1016, 659, 455)
( 312, 736,1523,1535)( 313, 684,1501,1071)( 316, 988, 725, 638)
( 317,1347,1568, 944)( 318, 878,1081, 715)( 319, 974, 340, 535)
( 320, 630, 342, 431)( 321, 368,1517, 836)( 322, 760, 440, 942)
( 327, 692, 796, 623)( 328,1348)( 330,1219,1321,1188)
( 331,1565, 826, 680)( 332,1269, 521, 921)( 333, 520, 542, 551)
( 334,1549, 804, 362)( 335, 406, 768,1070)( 337, 769,1319,1377)
( 338,1082)( 339, 905,1265,1552)( 344,1166,1380,1122)
( 345,1180, 540, 871)( 346,1461)( 348, 397, 746, 701)
( 351,1304, 549,1562)( 353,1350, 530, 615)( 355,1399,1223,1098)
( 356,1181, 493,1328)( 357, 903, 724,1230)( 358, 490, 904, 658)
( 359, 583,1145,1040)( 361,1274,1411,1247)( 363,1042, 767, 497)
( 364, 786, 618, 744)( 367, 392, 673, 879)( 369, 534)
( 373,1258,1325,1456)( 376, 693,1027, 624)( 378,1277,1010, 394)
( 380,1066, 593, 770)( 381,1408, 894, 484)( 382,1475,1341,1233)
( 384, 425, 920,1339)( 385,1134,1250, 575)( 386, 415,1075, 635)
( 387, 901,1282,1060)( 389,1201,1270, 840)( 398, 482,1129, 966)
( 400,1141,1446, 578)( 403,1025, 612,1401)( 405, 932,1158,1359)
( 407, 579,1137, 805)( 408,1032, 785, 705)( 412, 506, 598,1133)
( 413,1214,1221,1435)( 423, 516,1011, 592)( 424, 430, 780,1459)
( 426, 620,1297, 969)( 427, 463,1520,1074)( 429, 488, 987, 614)
( 432, 689, 686,1403)( 433,1458, 569, 729)( 435,1149,1093, 443)
( 439,1473, 538,1205)( 448, 953,1490,1289)( 449, 886)
( 452,1524,1039, 650)( 457, 555, 465, 510)( 458,1391)
( 459, 671,1017, 606)( 461, 709, 943, 994)( 462,1433, 824,1489)
( 467, 981, 755,1144)( 468, 891, 830,1268)( 473, 753)
( 476, 718, 912, 529)( 480,1336,1065, 582)( 481,1450, 528,1559)
( 485, 698, 682, 548)( 487, 524,1302,1191)( 492,1388)
( 496, 935,1106, 532)( 499,1284,1480,1035)( 500,1495, 976, 758)
( 502,1033, 695,1057)( 504, 958)( 508,1215, 559, 946)
( 509,1434,1300, 984)( 511, 643,1306,1444)( 515, 866, 964,1138)
( 519,1128, 986, 631)( 523,1068, 792, 570)( 533,1132, 797,1086)
( 546,1541,1563, 822)( 550,1529,1168,1398)( 553,1421,1396, 825)
( 556, 916,1312,1318)( 560, 597, 645, 712)( 563,1275, 997, 720)
( 564, 763,1267, 906)( 566, 739, 855,1164)( 567,1155,1295,1485)
( 568,1510, 854,1556)( 576,1178)( 577,1228, 844,1545)
( 585, 862, 708,1114)( 587,1257,1346, 819)( 599,1294,1273,1063)
( 604, 721, 909, 820)( 605, 681,1465,1000)( 613, 617, 795, 732)
( 616,1094, 803, 952)( 619,1355, 927, 911)( 621,1502, 818, 975)
( 627,1293,1003, 687)( 628,1252,1131, 856)( 634,1170,1059, 757)
( 637, 860, 800,1028)( 646,1050, 699,1024)( 647,1508,1088, 664)
( 660,1491, 908, 992)( 666,1030, 679, 799)( 669,1376,1115,1083)
( 691,1193,1046, 714)( 694,1231, 882, 711)( 696, 973, 706, 930)
( 703, 831, 955, 983)( 704,1564,1455,1061)( 707,1092)
( 710,1124,1561, 971)( 717, 980)( 719,1373,1263, 848)
( 723, 979, 776, 991)( 726, 897,1287,1009)( 728,1382,1121,1021)
( 731,1314,1366,1045)( 737,1470,1242,1067)( 745,1253,1360,1020)
( 749,1238,1363,1056)( 754,1533,1484,1022)( 766, 815, 857,1002)
( 777,1107,1123, 962)( 778,1340, 813,1038)( 789, 845,1365, 859)
( 790, 914)( 808,1281)( 810,1142,1469, 963)( 812,1102)
( 832,1198, 877,1424)( 847,1544,1108,1537)( 850,1395)
( 864,1368,1371,1428)( 873,1338,1315,1104)( 884,1146,1332,1202)
( 888,1225,1555,1367)( 892,1492)( 910,1467,1105,1477)
( 913,1209,1454,1550)( 919,1449,1112,1156)( 922,1354,1118,1161)
( 925,1320,1486, 961)( 940,1487)( 959,1482,1292,1506)(1103,1402)
(1117,1437,1370,1217)(1136,1429,1182,1279)(1159,1566,1369,1543)
(1197,1505,1546,1516)(1204,1264,1389,1453)(1211,1241)(1212,1425)
(1232,1236,1500,1386)(1235,1351,1574,1540)(1243,1245,1573,1349);