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