bin1 := (1,2,5,11,23,25,13,6,12,24,14,7,3)(4,8,16,29,48,73,110,122,82,53,34,19, 9)(10,20,35,54,83,123,160,176,128,87,56,36,21)(15,26,42,64,99,145,203, 208,148,102,67,44,27)(17,30,49,74,111,161,222,227,166,116,77,50,31)(18, 32,51,79,119,173,238,241,175,121,81,52,33)(22,37,57,88,129,184,247,253, 189,132,90,58,38)(28,45,68,103,149,209,277,287,215,152,104,69,46)(39,40, 60,92,134,193,259,340,256,191,133,91,59)(41,61,94,137,194,260,347,329, 248,185,130,89,62)(43,65,100,146,204,269,365,376,275,207,147,101,66)(47, 70,105,153,216,289,396,404,293,217,155,106,71)(55,84,78,117,168,231,313, 278,326,243,178,124,85)(63,96,140,198,264,352,482,490,356,265,199,141,97) (72,107,156,218,295,408,563,441,322,240,219,157,108)(75,112,162,223,302, 418,507,366,420,304,224,163,113)(76,114,80,120,174,239,321,336,254,190, 154,135,93)(86,125,179,192,257,342,465,608,448,327,244,180,126)(95,138, 196,262,349,474,639,647,478,350,263,197,139)(98,142,200,266,358,494,673, 585,422,306,226,165,143)(109,158,220,298,413,445,325,242,177,183,246,221, 159)(115,136,195,261,348,471,633,769,582,421,305,225,164)(118,170,234, 315,433,594,446,387,283,213,151,212,171)(127,181,202,144,201,267,361,500, 612,451,328,245,182)(131,186,229,167,228,308,398,290,397,452,330,249,187) (150,210,279,301,416,574,484,353,483,527,381,280,211)(169,232,314,432, 593,766,580,516,372,273,206,272,233)(172,235,316,434,595,780,742,552,402, 292,401,317,236)(188,250,331,453,341,463,622,813,781,613,455,332,251) (205,270,368,509,692,834,641,475,640,693,510,369,271)(214,284,388,535, 470,631,821,1016,926,722,536,389,285)(230,310,428,590,777,924,862,661, 488,355,487,429,311)(237,318,436,596,783,987,788,600,440,572,597,437,319) (252,333,456,614,498,360,497,677,881,806,615,457,334)(255,337,435,424, 307,423,410,296,409,564,617,459,338)(258,344,468,629,796,609,449,531,385, 282,384,454,345)(268,335,458,616,602,442,323,297,411,565,684,503,363) (274,373,517,703,908,1104,1308,1311,1107,909,704,518,374)(276,377,523, 711,799,610,450,567,412,566,714,525,378)(281,382,528,637,473,636,828, 1025,1121,921,716,529,383)(286,390,537,669,492,357,491,666,869,929,723, 538,391)(288,393,541,728,792,606,447,534,721,568,605,544,394)(291,399, 548,735,573,675,496,359,495,674,737,549,400)(294,405,557,749,715,526,379, 392,539,724,604,444,406)(299,414,569,598,438,320,300,415,571,759,603,443, 324)(303,419,579,765,837,643,476,642,836,691,508,367,380)(309,426,588, 776,978,1105,1039,840,645,477,644,589,427)(312,430,591,778,981,1177,976, 772,584,771,758,592,431)(339,460,618,807,811,621,787,989,784,988,809,619, 461)(343,466,627,819,973,770,583,698,514,371,513,628,467)(346,462,620, 810,1004,804,879,676,551,740,808,630,469)(351,479,649,847,1050,923,720, 533,386,532,719,652,480)(354,485,657,855,898,702,635,472,634,826,856,658, 486)(362,501,682,886,785,599,439,570,697,904,887,683,502)(364,504,686, 891,1094,1122,922,718,530,717,895,689,505)(370,511,694,830,1028,1218, 1400,1463,1302,1101,901,695,512)(375,519,705,873,668,872,1077,1278,1315, 1110,910,706,520)(395,545,732,940,801,611,800,747,556,746,942,733,546) (403,553,743,948,1014,820,1013,1184,982,1151,949,744,554)(407,560,753, 959,794,607,793,998,1152,951,798,754,561)(417,576,763,966,1165,1119,1320, 1261,1058,854,656,736,577)(425,543,731,939,1141,1170,969,767,581,701,907, 775,587)(464,624,816,1010,1126,927,1061,860,660,859,1011,817,625)(481, 653,851,1054,1000,797,960,1163,1160,1256,1056,852,654)(489,662,863,1066, 1267,1307,1138,1342,1142,1268,1067,864,663)(493,670,874,1078,994,790,993, 1195,1383,1281,1080,875,671)(499,679,884,1087,914,709,522,708,912,1111, 1005,805,680)(506,521,707,911,774,586,559,752,958,1161,1099,896,690)(515, 699,905,760,651,850,1053,1251,1430,1306,1103,906,700)(524,712,918,963, 757,601,789,782,985,1189,1117,919,713)(540,725,931,1131,1003,803,947,885, 681,802,1002,933,726)(542,729,937,1083,878,773,977,1178,1188,1344,1139, 938,730)(547,555,745,950,1006,1071,867,665,866,1069,1147,943,734)(550, 738,944,1148,1023,827,1022,1211,1295,1349,1149,945,739)(558,750,956,1156, 971,768,970,1171,1364,1355,1159,957,751)(562,755,961,984,779,983,1186, 1196,996,791,995,962,756)(575,761,964,1164,1358,1300,1459,1408,1223,1032, 835,965,762)(578,688,894,1097,1294,1457,1466,1303,1102,903,696,902,764) (623,814,1008,1203,1312,1108,1227,1037,839,1036,1204,1009,815)(626,795, 999,1198,1146,1129,930,975,1175,1191,986,1012,818)(632,823,1019,1209, 1245,1123,1325,1382,1260,1266,1065,1020,824)(638,831,1029,1219,1291,1324, 1157,1352,1515,1403,1221,1030,832)(646,841,1040,1232,1415,1354,1158,1353, 1162,1357,1233,1041,842)(648,844,1044,1237,1350,1150,946,741,880,1084, 1240,1046,845)(650,848,1051,1246,1174,974,1173,1366,1524,1427,1249,1052, 849)(655,664,865,1068,1201,1079,1280,1277,1450,1435,1258,1057,853)(659, 857,1059,1220,1402,1399,1248,1425,1252,1431,1263,1060,858)(667,870,1075, 1273,1167,967,1166,1359,1518,1449,1276,1076,871)(672,876,1081,1282,1199, 1185,1378,1538,1385,1200,1187,1082,877)(678,882,1085,1283,1090,889,685, 888,1088,1285,1284,1086,883)(687,892,1095,1194,991,786,990,1193,1381, 1404,1292,1096,893)(710,915,1114,955,920,1118,980,1182,1375,1333,1127, 928,916)(727,934,1134,1074,1128,1334,1502,1374,1493,1507,1338,1135,935) (748,953,1154,1181,979,1180,1372,1494,1327,1124,1326,1155,954)(812,1007, 1202,1386,1257,1235,1043,968,1168,1360,1380,1192,992)(822,1017,1207,1388, 1468,1304,1467,1517,1407,1414,1231,1208,1018)(825,972,1172,1365,1513, 1584,1537,1465,1527,1368,1190,1210,1021)(829,1026,1216,1395,1547,1464, 1603,1523,1647,1551,1398,1217,1027)(833,843,1042,1234,1416,1274,1446, 1586,1648,1525,1405,1222,1031)(838,1034,1225,1396,1548,1448,1275,1447, 1279,1452,1411,1226,1035)(846,1047,1241,1420,1331,1498,1637,1699,1668, 1565,1421,1242,1048)(861,1062,1264,1254,1055,1253,1250,1428,1569,1581, 1440,1265,1063)(868,1072,1271,1444,1328,1371,1531,1651,1645,1514,1445, 1272,1073)(890,1091,1288,1319,1116,1318,1485,1623,1617,1480,1313,1109, 1092)(897,899,900,1100,1299,1458,1594,1676,1595,1557,1409,1224,1033)(913, 1112,1316,1297,1098,1296,1293,1455,1590,1622,1484,1317,1113)(917,1001, 1144,941,1143,1140,1345,1497,1330,1125,925,1064,1115)(932,1132,1336,1482, 1314,1481,1618,1589,1488,1627,1504,1337,1133)(936,997,1197,1348,1512, 1638,1500,1332,1499,1377,1183,1339,1136)(952,1145,1347,1370,1179,1369, 1529,1489,1322,1120,1321,1351,1153)(1015,1205,1387,1542,1579,1607,1470, 1305,1469,1363,1521,1379,1206)(1024,1213,1392,1545,1620,1698,1703,1691, 1605,1519,1546,1393,1214)(1038,1228,1412,1424,1247,1423,1567,1670,1704, 1662,1559,1413,1229)(1045,1238,1418,1561,1478,1614,1680,1709,1682,1591, 1562,1419,1239)(1049,1243,1422,1505,1640,1706,1642,1506,1641,1511,1346, 1362,1244)(1070,1269,1442,1582,1474,1528,1479,1615,1592,1456,1583,1443, 1270)(1089,1286,1453,1391,1212,1390,1544,1657,1679,1681,1588,1454,1287) (1093,1289,1341,1137,1340,1508,1643,1612,1476,1310,1106,1230,1290)(1130, 1335,1503,1434,1575,1633,1495,1329,1373,1533,1526,1367,1176)(1169,1236, 1417,1560,1563,1665,1621,1653,1536,1376,1535,1520,1361)(1215,1323,1490, 1629,1701,1702,1630,1491,1384,1516,1356,1298,1394)(1255,1432,1574,1462, 1601,1689,1711,1700,1624,1486,1438,1540,1433)(1259,1436,1262,1439,1578, 1550,1397,1549,1401,1553,1659,1577,1437)(1301,1460,1597,1522,1509,1343, 1472,1477,1613,1697,1688,1600,1461)(1309,1473,1609,1660,1555,1406,1554, 1410,1558,1656,1543,1389,1441)(1426,1552,1602,1690,1715,1716,1707,1696, 1684,1596,1556,1646,1568)(1429,1571,1673,1631,1492,1566,1669,1611,1695, 1667,1564,1666,1572)(1451,1483,1619,1626,1487,1625,1599,1686,1714,1678, 1585,1539,1587)(1471,1608,1694,1663,1710,1687,1639,1705,1644,1510,1636, 1674,1573)(1475,1530,1650,1683,1593,1604,1654,1541,1576,1675,1685,1598, 1610)(1496,1634,1655,1708,1713,1677,1580,1652,1532,1632,1534,1501,1635) (1570,1671,1712,1693,1606,1692,1661,1616,1649,1628,1664,1658,1672);