bin1 := (1,1416,1867,557,1387)(2,355,290,317,702)(3,244,1208,2062,1286)(4,1833, 1201,1998,294)(5,852,1439,2290,2075)(6,857,1029,859,1829)(7,1504,1460, 959,1811)(8,1624,1850,1398,824)(9,514,1612,543,2157)(10,553,888,1303, 1978)(11,978,2086,2206,591)(12,1709,456,2138,122)(13,2017,825,1412,404) (14,1940,1473,107,1309)(15,57,1411,808,2197)(16,318,2058,1337,1950)(17, 1671,132,890,1649)(18,1701,1966,1677,1440)(19,539,581,2212,2275)(20,1588, 979,1145,2117)(21,718,314,2055,2172)(22,901,236,1383,1848)(23,1325,1531, 610,447)(24,1220,1924,1585,1282)(25,837,275,1090,1027)(26,597,123,1689, 61)(27,2208,1933,1979,376)(28,1721,1765,366,1741)(29,1379,819,1164,2082) (30,1375,155,1256,2237)(31,483,298,1610,163)(32,608,2076,1187,117)(33, 521,701,903,509)(34,2285,1157,2194,1381)(35,1696,69,1909,2106)(36,2034, 1003,974,368)(37,1970,585,2038,1055)(38,1739,1712,1362,1073)(39,209,2095, 1729,70)(40,1808,1139,1988,1631)(41,454,1373,946,642)(42,840,167,833,871) (43,1419,999,744,1424)(44,620,1485,2053,2268)(45,577,1389,898,1045)(46, 698,1338,774,965)(47,100,1755,489,190)(48,1943,1265,523,522)(49,2140, 1035,1058,858)(50,798,1088,1787,1820)(51,1046,1327,1536,512)(52,94,411, 624,1926)(53,2286,1082,2031,1713)(54,1670,1791,1715,1277)(55,1587,1606, 147,1517)(56,611,1372,1642,1468)(58,2240,2150,1528,1461)(59,2175,1754, 1039,338)(60,692,1803,2173,1291)(62,1999,301,469,371)(63,1040,739,2056, 1267)(64,375,1511,2161,2145)(65,568,1562,531,1321)(66,2190,690,2022,1518) (67,1968,1925,1896,1057)(68,232,2083,1285,76)(71,419,1537,1084,186)(72, 2188,1875,952,757)(73,2227,754,383,992)(74,1488,547,285,1264)(75,1061, 1744,1669,2142)(77,2019,1131,2050,1817)(78,291,2263,559,1519)(79,231, 1783,1577,1650)(80,1005,254,1002,2217)(81,1371,1842,983,341)(82,947,1453, 584,1205)(83,1335,1491,981,1471)(84,1197,609,131,929)(85,1431,971,1756, 598)(86,365,1066,2032,1692)(87,328,810,1644,630)(88,2163,900,295,2288) (89,386,678,251,507)(90,2177,2064,2033,1401)(91,111,596,697,2238)(92, 1021,2242,427,438)(93,1640,1780,390,1527)(95,268,1075,283,1657)(96,941, 614,780,953)(97,2121,1972,822,712)(98,148,1087,1920,2282)(99,1266,1133, 1688,671)(101,300,873,595,1449)(102,498,791,2279,350)(103,230,1564,1024, 1400)(104,962,1162,1665,940)(105,1602,1065,880,1204)(106,2297,1478,153, 919)(108,1596,731,906,1782)(109,818,594,110,2146)(112,1898,356,1818,1258) (113,1897,1346,1837,1251)(114,1740,1222,1651,1778)(115,1178,437,452,1645) (116,1070,1120,1248,1589)(118,751,462,1758,589)(119,151,431,987,883)(120, 1700,734,899,1742)(121,612,1217,1768,1563)(124,1509,1661,653,938)(125, 175,1443,1566,745)(126,1184,637,2276,2100)(127,320,817,949,2213)(128,399, 897,1104,1221)(129,2215,1839,220,2205)(130,2178,1733,445,540)(133,828, 2180,579,831)(134,1098,1903,1674,1599)(135,1751,479,660,2187)(136,1477, 490,1215,872)(137,1716,1800,1822,2159)(138,663,2070,639,730)(139,1894, 2254,1290,1501)(140,1912,1885,1816,1799)(141,2136,716,1849,606)(142,1607, 225,2246,1341)(143,1414,1743,459,182)(144,2230,228,1116,1914)(145,1959, 467,1579,1489)(146,576,1308,654,776)(149,2291,2071,302,1219)(150,580, 1253,1001,1064)(152,1142,520,277,2015)(154,1691,2243,1344,2199)(156,538, 2300,753,1832)(157,950,2289,1014,1156)(158,1444,771,1708,1074)(159,1326, 1376,1185,1318)(160,1022,928,2265,1257)(161,1971,2211,1615,1150)(162,926, 1505,2049,1834)(164,1621,428,1532,920)(165,308,652,1573,1272)(166,1913, 1176,1097,1479)(168,1584,1883,651,281)(169,767,1515,1872,786)(170,324, 2261,1706,1295)(171,762,1935,815,1609)(172,2007,1339,813,391)(173,333, 396,1974,1982)(174,1900,1450,1838,1851)(176,1037,1899,561,331)(177,1332, 212,619,1077)(178,1745,788,278,2224)(179,1223,1353,1377,493)(180,2036, 262,1628,1043)(181,794,1893,1543,1105)(183,1685,1526,2273,1165)(184,2030, 621,2171,1180)(185,1869,1154,2222,1583)(187,603,2192,1687,2155)(188,1786, 2144,1202,2107)(189,1459,1191,939,2060)(191,666,884,1226,1643)(192,2260, 1009,556,1457)(193,787,1405,1092,1568)(194,1085,436,2193,1163)(195,1241, 261,434,1425)(196,1393,783,1130,1902)(197,1827,2241,964,1892)(198,855, 1958,524,1008)(199,1948,1859,417,491)(200,503,696,2186,1618)(201,218,717, 2089,574)(202,1629,1109,500,1633)(203,2113,1918,2195,1386)(204,1031,287, 555,1516)(205,1183,255,945,1158)(206,508,455,1015,2167)(207,246,722,1231, 2181)(208,2248,567,527,2125)(210,1856,554,1409,1275)(211,2258,1738,704, 1941)(213,1672,2068,1207,1232)(214,1033,395,1560,2244)(215,961,1432,1481, 293)(216,1289,800,996,2001)(217,2231,1147,309,1359)(219,448,1186,1347, 1455)(221,2012,1815,1392,2141)(222,1996,1301,2245,602)(223,1679,1385, 1179,1360)(224,1710,627,881,1244)(226,917,1625,1627,2214)(227,269,243, 673,1032)(229,1772,1774,2253,247)(233,2047,911,258,1955)(234,991,839, 2023,930)(235,2066,470,2174,1766)(237,650,882,765,905)(238,749,709,1426, 1340)(239,1654,362,1274,299)(240,307,1964,1825,2010)(241,1254,1006,1693, 1368)(242,1804,1748,1019,2088)(245,1129,1641,1237,1533)(248,1441,336, 1623,1806)(249,2116,360,957,1399)(250,1284,397,1095,566)(252,1921,795, 686,2274)(253,723,1545,1474,936)(256,994,1937,864,1044)(257,647,2123,801, 1446)(259,625,1805,2233,1072)(260,856,1731,2057,1662)(263,1102,1987,316, 1635)(264,1882,1216,1170,1348)(265,2085,1136,836,1397)(266,1530,892,679, 1211)(267,2256,548,1826,2210)(270,1934,1866,430,516)(271,847,1601,1458, 1278)(272,385,2232,517,1750)(273,812,1429,444,1946)(274,2101,1788,1865, 1351)(276,1192,1175,482,313)(279,1730,643,1582,2078)(280,912,1315,670, 693)(282,1456,537,796,1863)(284,1553,1413,1655,325)(286,1514,760,2156, 306)(288,1025,1153,1570,1451)(289,2073,2182,2061,1976)(292,2132,737,1287, 2264)(296,435,1356,2196,1358)(297,923,1980,2097,1682)(303,1209,348,402, 578)(304,1364,711,1962,421)(305,1173,2257,821,802)(310,1855,1394,1551, 1595)(311,1422,1513,471,1638)(312,569,536,1388,1555)(315,844,1250,1047, 976)(319,1495,1775,410,1174)(321,590,958,1711,1659)(322,1407,904,369,412) (323,2098,720,1472,773)(326,2063,1128,743,570)(327,1622,334,1342,835) (329,1243,1030,466,1320)(330,1236,2143,505,1646)(332,1767,518,403,2148) (335,1542,1408,1723,1454)(337,401,1957,1876,2202)(339,1054,2002,475,2094) (340,370,1870,1512,1402)(342,1378,1746,909,453)(343,1111,458,1574,1760) (344,488,2122,682,1119)(345,733,1762,2045,593)(346,1753,2028,1608,1734) (347,2041,1720,1249,982)(349,1038,1960,913,1981)(351,1410,756,1928,2131) (352,876,977,1028,680)(353,1361,2130,2079,1967)(354,422,530,1382,1905) (357,1592,799,2025,468)(358,526,2162,1549,2018)(359,542,433,2139,777) (361,914,1255,853,1853)(363,1199,1891,1493,377)(364,1036,830,1300,1480) (367,382,587,1213,405)(372,908,758,632,735)(373,1059,1177,496,1617)(374, 1434,1556,1292,2298)(378,2292,392,772,1026)(379,1994,2152,943,446)(380, 640,1367,443,1352)(381,1329,1944,535,1749)(384,2000,2035,1167,1821)(387, 1990,1007,1023,997)(388,740,2267,2046,684)(389,2235,1152,2228,550)(393, 644,703,1790,1732)(394,727,1182,1437,2087)(398,615,1843,1571,1995)(400, 721,472,993,1522)(406,779,2081,846,534)(407,558,1106,1017,1193)(408,2004, 1273,1333,665)(409,2252,1166,790,2108)(413,1500,1271,2226,1448)(414,1813, 878,885,960)(415,891,809,1683,1667)(416,677,1171,1576,1591)(418,2135, 1051,1605,1814)(420,1901,588,549,1951)(423,2165,1965,1854,1323)(424,1151, 572,1593,1927)(425,2247,1390,1507,1598)(426,1977,915,1836,1132)(429,1486, 998,2124,2198)(432,2074,622,519,1487)(439,1939,1123,2221,1476)(440,2280, 784,1510,600)(441,1135,1475,634,761)(442,708,785,1370,1469)(449,944,1307, 797,541)(450,1639,1795,499,649)(451,990,2011,1620,546)(457,2151,2239,460, 1801)(461,968,1860,545,2219)(463,814,528,1956,631)(464,1626,1989,1835, 562)(465,1637,1091,683,502)(473,1881,1148,1049,1770)(474,1991,1936,1438, 487)(476,1717,1262,1118,1846)(477,1314,1218,2278,874)(478,1350,1603,1294, 1535)(480,755,638,1668,1143)(481,573,726,1789,714)(484,1698,623,1586,688) (485,1331,599,868,1506)(486,582,1910,1985,494)(492,1831,1365,1707,988) (495,1929,1847,1042,1719)(497,1369,511,2203,501)(504,1225,1694,921,725) (506,1916,963,1283,1888)(510,2054,1879,935,1141)(513,1203,2281,918,1144) (515,1288,2207,1794,1613)(525,1169,706,1195,646)(529,1604,2110,1239,691) (532,2262,1306,854,1159)(533,1930,2147,1004,2270)(544,1319,893,2223,894) (551,2251,1984,750,1080)(552,933,1963,748,1697)(560,1227,1680,1496,1520) (563,1012,1660,877,1311)(564,975,1349,1550,967)(565,1415,636,1304,1864) (571,1261,1676,747,658)(575,1565,986,2072,1890)(583,586,2112,592,2209) (601,1993,955,1600,715)(604,2204,661,820,954)(605,1423,980,1857,848)(607, 2184,2250,1212,1020)(613,1056,845,1146,1666)(616,1200,2096,2090,1764) (617,2039,1196,1887,1445)(618,956,2092,1041,995)(626,1252,1048,732,1206) (628,1523,1737,1828,1069)(629,2259,1138,1324,2119)(633,2293,1558,1447, 829)(635,1862,2027,2296,1779)(641,1992,942,657,1269)(645,1076,1594,1366, 2168)(648,1467,1704,781,778)(655,1430,989,1798,1490)(656,793,1858,1113, 1658)(659,1886,1648,1242,1189)(662,1590,1124,1632,811)(664,2103,1718, 1137,2009)(667,1793,2126,1299,841)(668,1736,972,1374,803)(669,1727,1575, 826,2189)(672,707,2099,2170,2154)(674,1126,2129,1099,1071)(675,2024,1260, 1503,1663)(676,886,834,931,1188)(681,1483,1529,2016,1538)(685,1112,1115, 1634,1868)(687,2044,1567,1052,1492)(689,2225,1728,1081,1874)(694,849, 1525,1330,1198)(695,1845,2006,1561,2020)(699,1011,1690,1259,1345)(700, 2051,1724,1681,863)(705,1268,1016,870,1747)(710,1597,1228,764,2109)(713, 1752,789,807,768)(719,1436,2137,1121,1452)(724,1317,1942,970,1089)(728, 1735,1792,827,2229)(729,766,2134,1878,1973)(736,1096,866,1578,746)(738, 860,2133,934,861)(741,1224,2003,1931,1773)(742,1686,2105,2283,2160)(752, 2158,1406,1420,896)(759,2201,2021,1210,1155)(763,2118,823,1725,1630)(769, 1194,2255,865,1703)(770,1384,1852,1781,1494)(775,1322,1761,2295,1296) (782,805,2287,2014,792)(804,1871,1108,1945,2200)(806,1355,1470,1919,1214) (816,1554,1547,838,1953)(832,1552,1917,1100,1418)(842,1678,1830,2069, 1086)(843,2176,1880,1062,1094)(850,1823,910,2013,1652)(851,1785,1539, 2091,1247)(862,1812,2169,951,1404)(867,1949,2269,2299,1442)(869,1873, 2272,1907,2234)(875,2043,1161,1524,895)(879,1312,1819,969,1107)(887,1140, 1034,1463,1464)(889,1544,1653,2216,2166)(902,1298,1908,1502,1983)(907, 1328,1245,1427,1771)(916,1172,1190,1986,1877)(922,1824,1498,1777,1302) (924,1802,1619,1053,1149)(925,1952,1614,1363,1769)(927,1540,1616,1906, 1181)(932,1664,2040,1083,1063)(937,2065,1922,1354,1809)(948,1580,1889, 1078,2266)(966,2026,1263,2185,1234)(973,1969,1060,1932,1611)(984,985, 1435,1702,1336)(1000,1915,1018,2249,2115)(1010,1923,1050,2127,1114)(1013, 1997,1313,1421,1246)(1067,1499,1521,1238,1675)(1068,1433,2077,1240,1684) (1079,1391,1807,1357,1160)(1093,1310,2183,1911,1673)(1101,2153,1726,1497, 1403)(1103,2179,1465,1462,1861)(1110,1293,1695,2191,1572)(1117,1961,1305, 1954,1428)(1122,2120,1938,1581,2277)(1125,1810,1484,1276,2104)(1127,1784, 2218,1647,1714)(1134,1947,2042,1797,1233)(1168,1559,2059,1466,1230)(1229, 1776,2084,1548,1844)(1235,1569,1380,1757,1796)(1270,2080,1297,1541,1759) (1279,1482,2093,1840,2048)(1280,1546,1508,2164,1281)(1316,2149,2005,1534, 1656)(1334,2294,1841,2236,1895)(1343,2111,2008,1763,1904)(1395,1396,2067, 2029,1636)(1417,1722,1975,1705,2037)(1557,2128,1884,2102,2052)(1699,2284, 2271,2220,2114);