b := (1, 967, 650, 291)( 2, 968, 649, 292)(   3,  31, 656, 520)
(   4,  32, 655, 519)(   5, 795, 654,1056)(   6, 796, 653,1055)
(   7,1263, 660,1353)(   8,1264, 659,1354)(   9,1583)(  10,1584)
(  11,1225, 645, 777)(  12,1226, 646, 778)(  13, 363, 644,  84)
(  14, 364, 643,  83)(  15, 382, 657, 806)(  16, 381, 658, 805)
(  17,1051, 652,1295)(  18,1052, 651,1296)(  19, 472, 648, 226)
(  20, 471, 647, 225)(  21,1198,1498, 308)(  22,1197,1497, 307)
(  23,1390,1165, 304)(  24,1389,1166, 303)(  25, 186, 272, 301)
(  26, 185, 271, 302)(  27, 298)(  28, 297)(  29, 452, 349, 300)
(  30, 451, 350, 299)(  33, 849,1524, 294)(  34, 850,1523, 293)
(  35,1129,1494, 305)(  36,1130,1493, 306)(  37,1624,1209, 295)
(  38,1623,1210, 296)(  39, 571, 495, 676)(  40, 572, 496, 675)
(  41, 991, 410, 285)(  42, 992, 409, 286)(  43,1194, 437, 641)
(  44,1193, 438, 642)(  45, 201,1628,1097)(  46, 202,1627,1098)
(  47,1484,1142,1163)(  48,1483,1141,1164)(  51, 957, 819, 468)
(  52, 958, 820, 467)(  53, 310,1008,1535)(  54, 309,1007,1536)
(  55,1065, 384,1424)(  56,1066, 383,1423)(  57, 174, 931, 241)
(  58, 173, 932, 242)(  59, 548, 453,1083)(  60, 547, 454,1084)
(  61, 718, 950,1250)(  62, 717, 949,1249)(  63, 822, 478, 485)
(  64, 821, 477, 486)(  65,1312,1246, 988)(  66,1311,1245, 987)(  67,1457)
(  68,1458)(  69, 105, 229, 799)(  70, 106, 230, 800)(  71, 871,1024, 417)
(  72, 872,1023, 418)(  73,1543,1158, 708)(  74,1544,1157, 707)
(  75, 973,1538,1550)(  76, 974,1537,1549)(  77, 963, 311,1124)
(  78, 964, 312,1123)(  79, 965, 504, 196)(  80, 966, 503, 195)
(  81, 972,1277,1603)(  82, 971,1278,1604)(  85, 962, 710,1315)
(  86, 961, 709,1316)(  87, 975,1558, 856)(  88, 976,1557, 855)
(  89, 977, 881,1203)(  90, 978, 882,1204)(  91, 969)(  92, 970)
(  93, 630, 339,1378)(  94, 629, 340,1377)(  95, 763)(  96, 764)
(  97, 902, 603, 441)(  98, 901, 604, 442)(  99, 138,1460, 834)
( 100, 137,1459, 833)( 101,1105,1445, 683)( 102,1106,1446, 684)
( 103,1502, 733,1487)( 104,1501, 734,1488)( 107, 344,1425,1054)
( 108, 343,1426,1053)( 109, 491,1058, 386)( 110, 492,1057, 385)
( 111, 673,1342, 567)( 112, 674,1341, 568)( 113,1357,1393,1469)
( 114,1358,1394,1470)( 115,1572,1287,1227)( 116,1571,1288,1228)
( 119,1447,1104, 743)( 120,1448,1103, 744)( 121, 701, 899, 889)
( 122, 702, 900, 890)( 123, 415, 867, 585)( 124, 416, 868, 586)
( 125,1414, 217, 716)( 126,1413, 218, 715)( 127, 354, 422,1509)
( 128, 353, 421,1510)( 129,1031, 911,1415)( 130,1032, 912,1416)
( 131, 250, 781,1266)( 132, 249, 782,1265)( 133, 694, 278,1117)
( 134, 693, 277,1118)( 135,1216)( 136,1215)( 139,1632,1307,1140)
( 140,1631,1308,1139)( 141, 283,1561, 919)( 142, 284,1562, 920)
( 143,1294,1037,1340)( 144,1293,1038,1339)( 145, 874, 983, 318)
( 146, 873, 984, 317)( 147, 768,1373, 959)( 148, 767,1374, 960)
( 149, 212,1360,1395)( 150, 211,1359,1396)( 151,1515)( 152,1516)
( 153, 680,1480,1107)( 154, 679,1479,1108)( 155, 773,1035, 836)
( 156, 774,1036, 835)( 157,1322, 634,1618)( 158,1321, 633,1617)
( 159, 483, 175, 403)( 160, 484, 176, 404)( 161,1474, 757, 248)
( 162,1473, 758, 247)( 163, 602, 252, 739)( 164, 601, 251, 740)
( 165,1462, 628, 883)( 166,1461, 627, 884)( 167,1090,1356,1034)
( 168,1089,1355,1033)( 169, 780,1260, 916)( 170, 779,1259, 915)
( 171,1214,1187, 256)( 172,1213,1188, 255)( 177, 188,1467,1546)
( 178, 187,1468,1545)( 179, 564,1381, 664)( 180, 563,1382, 663)
( 183, 431,1329, 898)( 184, 432,1330, 897)( 189, 934,1317, 955)
( 190, 933,1318, 956)( 191,1138, 848,1013)( 192,1137, 847,1014)
( 193,1438,1050,1591)( 194,1437,1049,1592)( 197, 622)( 198, 621)
( 199, 830,1121, 464)( 200, 829,1122, 463)( 203, 314, 864,1607)
( 204, 313, 863,1608)( 205,1555)( 206,1556)( 207, 332,1350,1593)
( 208, 331,1349,1594)( 209, 828,1289,1236)( 210, 827,1290,1235)
( 213,1085, 429, 553)( 214,1086, 430, 554)( 215,1095, 896, 426)
( 216,1096, 895, 425)( 219, 792, 724, 600)( 220, 791, 723, 599)
( 221, 793, 939, 329)( 222, 794, 940, 330)( 223, 790, 946,1429)
( 224, 789, 945,1430)( 227, 801)( 228, 802)( 231, 804,1241,1596)
( 232, 803,1242,1595)( 233, 798,1419, 737)( 234, 797,1420, 738)
( 235, 461,1022,1444)( 236, 462,1021,1443)( 237,1284)( 238,1283)
( 239,1074,1161, 538)( 240,1073,1162, 537)( 243,1338,1367,1397)
( 244,1337,1368,1398)( 245, 998,1372,1633)( 246, 997,1371,1634)
( 253,1174, 638, 358)( 254,1173, 637, 357)( 257, 502, 527, 371)
( 258, 501, 528, 372)( 259,1599,1527,1331)( 260,1600,1528,1332)( 261, 619)
( 262, 620)( 263, 944,1511, 722)( 264, 943,1512, 721)( 265,1569,1172, 281)
( 266,1570,1171, 282)( 267, 999, 348, 493)( 268,1000, 347, 494)
( 269, 894,1485,1346)( 270, 893,1486,1345)( 273, 727)( 274, 728)
( 275,1155,1301, 846)( 276,1156,1302, 845)( 279,1380, 775,1267)
( 280,1379, 776,1268)( 287,1276, 838, 513)( 288,1275, 837, 514)
( 289,1298, 770, 424)( 290,1297, 769, 423)( 315, 662, 712, 562)
( 316, 661, 711, 561)( 319,1026,1286, 954)( 320,1025,1285, 953)
( 321,1465, 506,1182)( 322,1466, 505,1181)( 323, 536, 367,1491)
( 324, 535, 368,1492)( 327, 545,1432,1041)( 328, 546,1431,1042)( 333, 886)
( 334, 885)( 335,1131, 736, 752)( 336,1132, 735, 751)( 337, 408,1064, 398)
( 338, 407,1063, 397)( 341, 980, 595,1559)( 342, 979, 596,1560)
( 345, 448, 529, 379)( 346, 447, 530, 380)( 351, 989,1529, 839)
( 352, 990,1530, 840)( 355,1081,1224, 550)( 356,1082,1223, 549)
( 359,1532,1496,1217)( 360,1531,1495,1218)( 361,1252)( 362,1251)
( 365,1503, 888, 534)( 366,1504, 887, 533)( 369,1212,1279, 522)
( 370,1211,1280, 521)( 373,1518,1610, 524)( 374,1517,1609, 523)
( 375,1179,1153, 526)( 376,1180,1154, 525)( 377, 531)( 378, 532)( 387,1067)
( 388,1068)( 389,1589, 582,1070)( 390,1590, 581,1069)( 391,1439,1009,1062)
( 392,1440,1010,1061)( 393, 745,1629, 446)( 394, 746,1630, 445)
( 395, 605,1146,1059)( 396, 606,1145,1060)( 399,1196)( 400,1195)
( 401, 456,1147, 686)( 402, 455,1148, 685)( 405, 937, 817, 469)
( 406, 938, 818, 470)( 411, 578,1004,1150)( 412, 577,1003,1149)
( 413, 705,1622,1281)( 414, 706,1621,1282)( 419, 517,1352,1513)
( 420, 518,1351,1514)( 427,1362,1400,1383)( 428,1361,1399,1384)( 433,1143)
( 434,1144)( 435,1072,1119, 540)( 436,1071,1120, 539)( 443, 876, 682,1274)
( 444, 875, 681,1273)( 457,1230, 858, 996)( 458,1229, 857, 995)
( 459,1540,1614, 879)( 460,1539,1613, 880)( 465,1151, 725, 812)
( 466,1152, 726, 811)( 473, 808)( 474, 807)( 475, 587, 750, 816)
( 476, 588, 749, 815)( 479,1011,1018, 814)( 480,1012,1017, 813)
( 481,1615,1412, 810)( 482,1616,1411, 809)( 489, 877, 755, 512)
( 490, 878, 756, 511)( 497, 921, 573, 824)( 498, 922, 574, 823)
( 499, 762,1626,1126)( 500, 761,1625,1125)( 507,1452, 700,1436)
( 508,1451, 699,1435)( 509, 608)( 510, 607)( 515, 714, 748, 935)
( 516, 713, 747, 936)( 541, 926,1077,1563)( 542, 925,1078,1564)
( 543,1001,1075, 576)( 544,1002,1076, 575)( 551,1611,1080,1541)
( 552,1612,1079,1542)( 555, 753, 669, 825)( 556, 754, 670, 826)
( 557, 930, 677,1015)( 558, 929, 678,1016)( 559,1170, 667,1508)
( 560,1169, 668,1507)( 565,1619, 671, 841)( 566,1620, 672, 842)
( 569, 766, 666, 589)( 570, 765, 665, 590)( 579,1320)( 580,1319)
( 583,1219,1636,1506)( 584,1220,1635,1505)( 591,1175,1428,1046)
( 592,1176,1427,1045)( 593,1553,1441,1533)( 594,1554,1442,1534)( 609, 732)
( 610, 731)( 611, 981)( 612, 982)( 613, 862)( 614, 861)( 615,1387)( 616,1388)
( 617, 625)( 618, 626)( 623,1408)( 624,1407)( 631, 859,1370,1402)
( 632, 860,1369,1401)( 635, 786,1270, 985)( 636, 785,1269, 986)
( 639,1239,1475,1030)( 640,1240,1476,1029)( 687,1455,1110,1525)
( 688,1456,1109,1526)( 689,1253,1115, 948)( 690,1254,1116, 947)
( 691,1547,1112,1327)( 692,1548,1111,1328)( 695, 905,1113,1091)
( 696, 906,1114,1092)( 697,1310,1606,1568)( 698,1309,1605,1567)
( 719,1134,1028,1334)( 720,1133,1027,1333)( 729,1481,1601,1272)
( 730,1482,1602,1271)( 741, 910,1433,1047)( 742, 909,1434,1048)( 759,1234)
( 760,1233)( 771,1258,1566,1477)( 772,1257,1565,1478)( 783,1261)( 784,1262)
( 787,1256,1303,1191)( 788,1255,1304,1192)( 843,1375,1200,1184)
( 844,1376,1199,1183)( 853,1409,1464,1247)( 854,1410,1463,1248)
( 865,1325,1347,1208)( 866,1326,1348,1207)( 869,1168,1099,1520)
( 870,1167,1100,1519)( 891,1314,1300,1238)( 892,1313,1299,1237)
( 903,1366,1406,1186)( 904,1365,1405,1185)( 907,1006)( 908,1005)( 913,1159)
( 914,1160)( 917,1637, 993,1201)( 918,1638, 994,1202)( 923,1292,1232,1102)
( 924,1291,1231,1101)( 927,1343,1244,1093)( 928,1344,1243,1094)
( 941,1490,1418,1222)( 942,1489,1417,1221)( 951,1392)( 952,1391)(1039,1575)
(1040,1576)(1043,1422)(1044,1421)(1087,1136)(1088,1135)(1127,1205,1323,1552)
(1128,1206,1324,1551)(1189,1450)(1190,1449)(1363,1404)(1364,1403)
(1385,1453,1471,1521)(1386,1454,1472,1522)(1573,1579)(1574,1580)(1577,1585)
(1578,1586);