bin1 := (1,422)(2,176)(3,1627)(4,1475)(5,1592)(6,446)(7,1356)(8,2151)(9,965)(10,
     960)(11,1187)(12,1397)(13,405)(14,48)(15,298)(16,1438)(17,1942)(18,1602)
     (19,1225)(21,984)(23,165)(24,250)(25,1531)(26,1887)(27,790)(28,1632)(30,
     1076)(32,2241)(33,677)(35,1141)(36,1578)(37,1951)(38,892)(39,1640)(40,
     1931)(41,262)(42,1156)(43,2081)(44,408)(45,628)(46,49)(47,771)(51,1374)
     (52,201)(53,2196)(54,1815)(55,374)(56,1091)(57,1015)(59,1258)(61,1946)
     (62,765)(63,990)(64,254)(65,457)(66,1969)(67,407)(68,1439)(69,1647)(70,
     1486)(71,1199)(72,606)(73,863)(74,637)(75,2095)(76,1746)(77,1777)(78,
     1369)(79,798)(80,1822)(81,1346)(82,1105)(84,1957)(85,594)(86,1235)(87,
     1792)(88,1373)(89,2097)(90,1000)(92,2153)(93,1184)(94,1918)(95,1175)(96,
     775)(98,667)(99,1309)(101,2230)(102,2189)(103,983)(104,140)(105,1526)
     (107,1670)(108,1204)(109,1856)(110,1188)(112,143)(115,1852)(117,1911)
     (118,580)(120,186)(121,352)(122,1628)(123,1591)(124,799)(125,1598)(126,
     1029)(128,998)(129,1035)(130,1337)(132,1929)(133,1410)(135,1340)(136,
     2098)(137,232)(138,1796)(139,1840)(141,2062)(144,591)(145,1806)(146,1594)
     (147,1849)(148,882)(149,2107)(150,857)(151,1800)(152,985)(153,1294)(154,
     712)(155,971)(156,862)(157,635)(158,167)(159,1646)(160,828)(161,1474)
     (162,1888)(163,1303)(164,1116)(166,2042)(169,2144)(170,448)(171,746)(172,
     2108)(173,585)(174,360)(175,1811)(177,1250)(178,503)(179,957)(181,1657)
     (182,2116)(183,1724)(184,1295)(185,925)(187,2059)(188,342)(189,913)(190,
     1599)(191,776)(192,979)(193,2052)(194,743)(195,2027)(196,1709)(197,1732)
     (198,1955)(199,1823)(200,2285)(202,2195)(203,651)(204,218)(205,1798)(206,
     1982)(207,476)(209,1605)(210,1914)(211,1718)(212,618)(213,494)(214,959)
     (215,597)(216,1051)(217,1832)(219,1799)(220,1028)(221,948)(222,2012)(223,
     751)(224,1345)(225,1998)(226,1079)(228,1795)(229,2121)(231,1738)(233,445)
     (234,2057)(236,1275)(238,906)(239,1143)(243,1130)(244,713)(248,439)(249,
     898)(251,623)(252,2202)(253,1265)(255,848)(256,659)(257,966)(258,2192)
     (259,1639)(261,1252)(263,2051)(267,1382)(268,611)(269,739)(270,1492)(272,
     1851)(273,1885)(276,1132)(277,1062)(278,339)(279,1866)(280,1634)(281,630)
     (282,850)(283,1490)(284,1179)(285,1227)(286,499)(287,778)(288,2133)(289,
     1975)(290,1807)(292,1615)(293,2111)(294,1686)(295,2130)(297,1341)(299,
     1491)(300,919)(301,1644)(302,741)(303,1703)(304,1260)(305,962)(306,1965)
     (307,1060)(308,1612)(309,689)(310,416)(311,903)(312,1663)(314,2125)(315,
     705)(317,767)(318,1520)(319,1129)(320,549)(321,818)(322,1924)(323,943)
     (324,1633)(325,1077)(326,487)(327,1655)(328,1145)(329,359)(331,1532)(332,
     2018)(333,518)(335,1488)(336,536)(341,1017)(343,1717)(344,866)(345,2127)
     (346,1926)(347,996)(348,2115)(349,504)(350,1769)(351,779)(353,1209)(354,
     1702)(355,1898)(356,1784)(358,613)(361,1166)(362,1551)(363,2221)(364,508)
     (366,368)(367,986)(369,1580)(370,379)(371,958)(372,1706)(373,2017)(375,
     2056)(376,1977)(377,904)(378,519)(380,1280)(381,2235)(382,1939)(383,1406)
     (384,1751)(385,954)(386,625)(387,1993)(388,1766)(389,1452)(390,1296)(391,
     1274)(393,955)(394,1330)(395,1461)(396,1772)(397,2147)(398,2273)(399,
     1238)(400,2222)(401,1339)(402,1361)(403,514)(406,897)(409,887)(410,1945)
     (411,640)(412,1585)(413,811)(414,2229)(415,1431)(417,1972)(419,1527)(420,
     2142)(421,1528)(423,728)(424,572)(425,1791)(426,1620)(427,1220)(428,780)
     (430,559)(431,2267)(432,1952)(433,951)(434,755)(436,950)(437,1414)(438,
     1282)(440,1976)(441,820)(442,737)(443,1150)(444,2078)(447,2208)(450,1386)
     (451,610)(452,1026)(453,2167)(454,2120)(455,715)(456,1970)(458,836)(460,
     2031)(461,1861)(462,546)(463,1834)(464,2299)(465,726)(466,2092)(467,815)
     (468,1897)(469,1565)(470,1674)(471,1388)(472,1548)(473,1016)(474,1433)
     (477,1685)(478,2106)(479,1923)(482,1190)(484,717)(485,1055)(486,496)(488,
     2174)(489,2191)(490,515)(491,1314)(492,875)(493,1917)(495,2085)(500,1641)
     (502,648)(505,2025)(506,1537)(507,1658)(509,1596)(510,2058)(511,1964)
     (512,1762)(513,714)(516,600)(521,1561)(522,1837)(523,1419)(524,700)(526,
     864)(527,1148)(528,558)(529,1080)(530,1854)(532,1695)(533,1937)(534,1571)
     (535,757)(540,2259)(541,1331)(542,1215)(543,1992)(544,1719)(545,823)(547,
     1995)(551,2207)(552,662)(554,2282)(555,1162)(556,1353)(557,1659)(560,687)
     (561,1189)(562,1170)(563,1902)(565,1272)(567,1889)(568,2050)(569,1562)
     (570,1740)(571,1465)(575,1693)(576,1621)(577,1018)(578,1948)(579,747)
     (581,647)(583,1103)(584,1416)(587,1626)(588,980)(589,2119)(590,1037)(592,
     1371)(593,1829)(595,1455)(596,718)(598,1178)(599,605)(601,1376)(602,1944)
     (604,1530)(607,1083)(608,889)(609,641)(612,1396)(614,2246)(615,1423)(616,
     2091)(617,1404)(619,1359)(620,1137)(621,1874)(622,2024)(624,1539)(626,
     2234)(627,1437)(629,735)(631,1857)(632,1865)(633,1364)(634,1949)(638,
     1257)(639,914)(642,1198)(643,2280)(644,912)(645,1570)(649,2213)(650,1614)
     (653,1544)(654,1523)(655,664)(656,1661)(657,1413)(658,1248)(660,2284)
     (661,867)(665,706)(666,2105)(669,1630)(670,1058)(671,1322)(673,1008)(674,
     1841)(676,1451)(678,1509)(679,1533)(680,1978)(681,1489)(682,2281)(683,
     1293)(684,1786)(685,691)(686,1243)(688,2143)(690,722)(692,1027)(693,1095)
     (694,1030)(695,1780)(696,936)(697,2177)(699,1879)(702,1301)(703,974)(704,
     1115)(707,1169)(708,2216)(709,1928)(710,1417)(711,2276)(716,2183)(719,
     1078)(721,878)(723,2231)(725,1962)(727,1872)(730,2003)(732,2014)(733,840)
     (734,935)(736,1072)(738,1711)(742,1816)(745,2040)(749,2101)(750,1843)
     (752,2049)(753,972)(754,1764)(756,833)(758,856)(759,1550)(760,834)(761,
     1399)(762,791)(763,2100)(764,2190)(766,872)(768,814)(769,964)(770,1300)
     (772,1753)(774,894)(777,1334)(781,967)(782,1880)(783,1380)(784,1312)(785,
     1297)(786,2047)(787,1636)(788,2238)(789,1042)(793,1824)(794,2237)(795,
     1133)(796,1443)(797,2080)(800,1471)(801,1316)(802,1067)(803,2083)(805,
     1910)(806,1442)(807,1521)(808,1212)(809,1197)(810,2249)(812,2065)(816,
     949)(817,2166)(819,1411)(821,1124)(822,1422)(825,939)(826,1546)(827,1185)
     (829,1183)(830,1081)(831,1289)(835,1052)(838,2090)(839,1277)(841,2188)
     (842,1177)(843,2272)(844,1600)(845,1617)(846,2039)(847,1261)(849,2008)
     (851,953)(853,2094)(854,1244)(855,2262)(858,1859)(859,1597)(860,1625)
     (861,1047)(865,2291)(869,1838)(870,1056)(871,1001)(873,1234)(874,2069)
     (877,977)(879,1651)(880,2289)(883,1589)(884,2114)(885,1020)(886,2157)
     (888,2002)(891,1556)(895,1102)(896,2131)(899,937)(900,1307)(901,1348)
     (902,1684)(905,1071)(907,1763)(908,1529)(909,1379)(910,1121)(911,1040)
     (915,1473)(916,1508)(917,1516)(918,1642)(920,1453)(921,2184)(922,1352)
     (924,1660)(926,1722)(927,2245)(928,1354)(929,2232)(931,1099)(932,1173)
     (933,1679)(934,1648)(938,1211)(940,1310)(941,1025)(942,1616)(944,1256)
     (946,1934)(947,1378)(952,1123)(956,1680)(961,1707)(968,1604)(969,1581)
     (970,1705)(973,1708)(975,1906)(976,991)(978,1559)(981,1408)(982,1291)
     (989,1996)(994,2034)(995,1959)(997,1794)(999,1869)(1002,1760)(1003,1730)
     (1004,2071)(1005,2203)(1006,1921)(1007,2023)(1009,1884)(1010,2134)(1011,
     1736)(1014,1415)(1019,2075)(1021,1061)(1022,1891)(1023,2161)(1024,1259)
     (1031,1805)(1033,1761)(1034,1045)(1036,1603)(1038,2209)(1039,1721)(1043,
     2242)(1044,1652)(1046,1278)(1048,2070)(1049,2149)(1050,1114)(1053,1827)
     (1054,1457)(1057,1462)(1063,1159)(1065,1895)(1066,2013)(1068,2254)(1069,
     1900)(1070,1176)(1075,1542)(1082,1697)(1084,2063)(1085,1313)(1086,1681)
     (1087,1662)(1088,2263)(1090,1255)(1092,1389)(1093,2156)(1094,2252)(1096,
     1172)(1100,1704)(1104,2215)(1106,1844)(1107,1497)(1108,2074)(1109,1545)
     (1110,1119)(1112,1676)(1117,1788)(1120,2020)(1122,1298)(1125,1370)(1126,
     1608)(1128,1990)(1135,2175)(1136,2181)(1138,1778)(1139,1393)(1142,1893)
     (1144,1214)(1146,1899)(1147,1167)(1152,1714)(1153,1449)(1154,2200)(1155,
     1818)(1158,1595)(1163,1430)(1164,1870)(1168,1501)(1180,1756)(1181,1285)
     (1182,1428)(1186,1909)(1191,2253)(1192,2218)(1194,1288)(1196,1601)(1200,
     1943)(1203,1210)(1205,1368)(1206,1432)(1207,2185)(1208,1672)(1213,1927)
     (1216,2076)(1217,1326)(1218,2220)(1219,1324)(1221,1276)(1222,2139)(1226,
     2297)(1230,1826)(1233,1269)(1236,2026)(1237,1329)(1239,2274)(1245,2036)
     (1246,1771)(1247,1863)(1249,2277)(1253,1710)(1254,2292)(1263,1905)(1264,
     1850)(1267,1335)(1268,1894)(1270,2137)(1271,1781)(1273,1611)(1279,1883)
     (1281,1882)(1283,1776)(1286,1540)(1287,1424)(1290,1405)(1292,1701)(1299,
     1493)(1302,1470)(1304,1782)(1305,1575)(1306,2197)(1308,1347)(1311,1908)
     (1315,1505)(1317,1384)(1319,1479)(1320,2271)(1325,2148)(1328,1752)(1336,
     1828)(1338,1733)(1343,2265)(1344,1590)(1350,1385)(1351,2118)(1355,1494)
     (1358,1750)(1360,1429)(1362,2019)(1363,1793)(1366,2266)(1367,1783)(1372,
     1675)(1375,1754)(1377,2201)(1383,1436)(1387,1989)(1394,2286)(1395,1916)
     (1398,2104)(1400,1877)(1401,1999)(1402,1860)(1403,2193)(1407,2086)(1409,
     1858)(1412,1961)(1418,2224)(1420,1691)(1425,2005)(1426,1538)(1427,2152)
     (1434,1448)(1435,2146)(1440,1845)(1441,2072)(1444,1820)(1445,1496)(1446,
     1915)(1447,1668)(1454,1773)(1456,2294)(1458,1510)(1460,2225)(1464,2199)
     (1467,2172)(1472,2029)(1477,1478)(1480,1484)(1481,1803)(1482,2164)(1483,
     1500)(1487,2112)(1495,1919)(1498,1637)(1499,1514)(1502,2170)(1503,2158)
     (1504,1624)(1506,1669)(1507,1563)(1511,2240)(1512,2250)(1513,1713)(1515,
     1689)(1517,1749)(1518,1831)(1519,1716)(1522,2088)(1534,1618)(1535,1682)
     (1543,2228)(1547,1819)(1549,1907)(1552,1586)(1554,1912)(1555,1734)(1558,
     1787)(1560,2288)(1564,1802)(1566,1985)(1568,1833)(1572,1741)(1573,2016)
     (1574,2041)(1582,2054)(1583,1842)(1584,2290)(1593,1920)(1606,2093)(1609,
     1765)(1610,2077)(1613,2260)(1619,1742)(1622,2045)(1623,2239)(1631,1726)
     (1635,2099)(1645,2295)(1649,1677)(1656,1980)(1666,2300)(1667,2033)(1678,
     1904)(1688,1892)(1690,2160)(1692,1963)(1694,1986)(1696,2163)(1698,2123)
     (1699,1779)(1712,2030)(1720,1757)(1723,2264)(1725,1973)(1727,2082)(1728,
     2128)(1729,1983)(1731,1774)(1735,2247)(1737,2141)(1739,2136)(1744,2001)
     (1745,2278)(1748,1876)(1755,2223)(1759,2204)(1767,2211)(1768,1991)(1770,
     2173)(1785,2180)(1789,1875)(1790,1886)(1797,2061)(1801,2007)(1804,2236)
     (1808,2038)(1809,2032)(1812,2279)(1813,2275)(1830,2162)(1835,2168)(1839,
     2138)(1848,2226)(1864,1933)(1867,2113)(1868,2048)(1878,2000)(1881,2298)
     (1930,1966)(1936,2010)(1940,2287)(1947,1987)(1950,1968)(1953,1967)(1954,
     2261)(1958,2198)(1960,2255)(1971,2283)(1974,2060)(1979,2243)(1988,2053)
     (1994,2110)(2006,2044)(2009,2046)(2011,2122)(2021,2256)(2043,2182)(2064,
     2176)(2066,2109)(2068,2206)(2084,2124)(2087,2140)(2102,2194)(2117,2210)
     (2145,2251)(2154,2268)(2155,2248)(2178,2214)(2270,2293);