bin1 := (1,3,6)(2,4,8)(7,10,14)(9,12,17)(11,15,21)(13,18,25)(16,22,30)(19,26,35)
     (20,27,37)(23,31,41)(24,32,43)(28,38,29)(33,44,55)(34,45,57)(36,47,60)
     (39,50,64)(40,51,66)(42,52,67)(46,58,74)(48,61,78)(49,62,80)(53,68,87)
     (54,69,89)(56,71,92)(59,75,95)(63,81,102)(65,83,105)(70,90,113)(72,93,
     117)(73,94,119)(76,96,122)(77,97,124)(79,99,127)(82,103,132)(84,106,136)
     (85,107,138)(86,108,140)(88,110,143)(91,114,146)(98,125,158)(100,128,162)
     (101,129,164)(104,133,167)(109,141,176)(111,144,180)(112,145,182)(115,
     147,185)(116,148,187)(118,150,190)(120,152,193)(121,153,195)(123,155,198)
     (126,159,201)(130,165,207)(131,166,209)(134,168,212)(135,169,214)(137,
     171,217)(139,173,220)(142,177,223)(149,188,235)(151,191,239)(154,196,245)
     (156,199,249)(157,200,251)(160,202,254)(161,203,256)(163,204,257)(170,
     215,268)(172,218,272)(174,221,276)(175,222,278)(178,224,281)(179,225,283)
     (181,227,286)(183,229,289)(184,230,291)(186,232,294)(189,236,297)(192,
     240,302)(194,242,305)(197,246,308)(205,258,320)(206,259,322)(208,261,325)
     (210,263,328)(211,264,330)(213,266,333)(216,269,335)(219,273,338)(226,
     284,350)(228,287,354)(231,292,360)(233,295,364)(234,296,366)(237,298,369)
     (238,299,371)(241,303,376)(243,306,380)(244,307,382)(247,309,385)(250,
     311,388)(252,313,391)(253,314,393)(255,316,396)(260,323,404)(262,326,408)
     (265,331,414)(267,334,418)(270,336,421)(271,337,423)(274,339,426)(275,
     340,428)(277,342,431)(279,344,434)(280,345,436)(282,347,439)(285,351,442)
     (288,355,447)(290,357,450)(293,361,453)(300,372,465)(301,373,466)(304,
     377,469)(310,386,479)(312,389,483)(315,394,489)(317,397,493)(318,398,495)
     (319,399,497)(321,401,500)(324,405,503)(327,409,508)(329,411,511)(332,
     415,514)(341,429,529)(343,432,533)(346,437,539)(348,440,543)(349,441,545)
     (352,443,548)(353,444,550)(356,448,555)(358,451,559)(359,452,561)(362,
     454,564)(363,455,566)(365,457,569)(367,459,572)(368,460,574)(370,462,577)
     (374,467,582)(375,468,584)(378,470,587)(379,471,589)(381,473,592)(383,
     475,595)(384,476,597)(387,480,599)(390,484,604)(392,486,607)(395,490,610)
     (400,498,619)(402,501,623)(403,502,625)(406,504,628)(407,505,630)(410,
     509,635)(412,512,639)(413,513,641)(416,515,644)(417,516,645)(419,518,648)
     (420,519,650)(422,521,653)(424,523,656)(425,524,658)(427,526,661)(430,
     530,664)(433,534,669)(435,536,672)(438,540,675)(445,551,687)(446,552,688)
     (449,556,691)(456,567,703)(458,570,707)(461,575,713)(463,578,717)(464,
     579,719)(472,590,731)(474,593,735)(477,598,478)(481,600,743)(482,601,745)
     (485,605,750)(487,608,754)(488,609,756)(491,611,759)(492,612,761)(494,
     614,764)(496,616,767)(499,620,770)(506,631,782)(507,632,783)(510,636,786)
     (517,646,796)(520,651,802)(522,654,806)(525,659,812)(527,662,816)(528,
     663,818)(531,665,821)(532,666,823)(535,670,828)(537,673,832)(538,674,834)
     (541,676,837)(542,677,839)(544,679,842)(546,681,845)(547,682,847)(549,
     684,850)(553,689,855)(554,690,857)(557,692,860)(558,693,862)(560,695,865)
     (562,697,868)(563,698,870)(565,700,873)(568,704,876)(571,708,881)(573,
     710,884)(576,714,887)(580,720,894)(581,721,896)(583,723,899)(585,725,902)
     (586,726,904)(588,728,907)(591,732,910)(594,736,915)(596,738,918)(602,
     746,927)(603,747,928)(606,751,931)(613,762,943)(615,765,947)(617,768,951)
     (618,769,953)(621,771,956)(622,772,958)(624,774,961)(626,776,964)(627,
     777,966)(629,779,969)(633,784,974)(634,785,976)(637,787,979)(638,788,981)
     (640,790,984)(642,792,987)(643,793,989)(647,797,994)(649,799,997)(652,
     803,1000)(655,807,1005)(657,809,1008)(660,813,1011)(667,824,1023)(668,
     825,1024)(671,829,1027)(678,840,1039)(680,843,1043)(683,848,1049)(685,
     851,1053)(686,852,1055)(694,863,1067)(696,866,1071)(699,871,1077)(701,
     874,1081)(702,875,1083)(705,877,1086)(706,878,1088)(709,882,1093)(711,
     885,1097)(712,886,1099)(715,888,1102)(716,889,1104)(718,891,1107)(722,
     897,1114)(724,900,1118)(727,905,1124)(729,908,1128)(730,909,1130)(733,
     911,1133)(734,912,1135)(737,916,1139)(739,919,1143)(740,920,1145)(741,
     921,1147)(742,922,1149)(744,924,1152)(748,929,1157)(749,930,1159)(752,
     932,1162)(753,933,1164)(755,935,1167)(757,937,1170)(758,938,1172)(760,
     940,1175)(763,944,1178)(766,948,1181)(773,959,1193)(775,962,1197)(778,
     967,1203)(780,970,1207)(781,971,1209)(789,982,1221)(791,985,1225)(794,
     990,1231)(795,991,1233)(798,995,1238)(800,998,1242)(801,999,1244)(804,
     1001,1247)(805,1002,1249)(808,1006,1254)(810,1009,1258)(811,1010,1260)
     (814,1012,1263)(815,1013,1265)(817,1015,1268)(819,1017,1271)(820,1018,
     1273)(822,1020,1276)(826,1025,1281)(827,1026,1283)(830,1028,1286)(831,
     1029,1288)(833,1031,1291)(835,1033,1294)(836,1034,1296)(838,1036,1299)
     (841,1040,1302)(844,1044,1307)(846,1046,1310)(849,1050,1313)(853,1056,
     1320)(854,1057,1322)(856,1059,1325)(858,1061,1328)(859,1062,1330)(861,
     1064,1333)(864,1068,1336)(867,1072,1341)(869,1074,1344)(872,1078,1347)
     (879,1089,1359)(880,1090,1360)(883,1094,1363)(890,1105,1375)(892,1108,
     1379)(893,1109,1381)(895,1111,1384)(898,1115,1387)(901,1119,1392)(903,
     1121,1395)(906,1125,1398)(913,1136,1410)(914,1137,1411)(917,1140,1413)
     (923,1150,1424)(925,1153,1428)(926,1154,1430)(934,1165,1442)(936,1168,
     1446)(939,1173,1452)(941,1176,1456)(942,1177,1458)(945,1179,1461)(946,
     1180,1463)(949,1182,1466)(950,1183,1468)(952,1185,1471)(954,1187,1474)
     (955,1188,1476)(957,1190,1479)(960,1194,1482)(963,1198,1487)(965,1200,
     1490)(968,1204,1493)(972,1210,1500)(973,1211,1502)(975,1213,1505)(977,
     1215,1508)(978,1216,1510)(980,1218,1513)(983,1222,1516)(986,1226,1520)
     (988,1228,1523)(992,1234,1530)(993,1235,1531)(996,1239,1534)(1003,1250,
     1546)(1004,1251,1547)(1007,1255,1550)(1014,1266,1562)(1016,1269,1566)
     (1019,1274,1572)(1021,1277,1576)(1022,1278,1578)(1030,1289,1590)(1032,
     1292,1594)(1035,1297,1600)(1037,1300,1604)(1038,1301,1606)(1041,1303,
     1609)(1042,1304,1611)(1045,1308,1616)(1047,1311,1620)(1048,1312,1622)
     (1051,1314,1625)(1052,1315,1627)(1054,1317,1630)(1058,1323,1637)(1060,
     1326,1640)(1063,1331,1646)(1065,1334,1650)(1066,1335,1652)(1069,1337,
     1655)(1070,1338,1657)(1073,1342,1662)(1075,1345,1666)(1076,1346,1668)
     (1079,1348,1671)(1080,1349,1673)(1082,1351,1676)(1084,1353,1679)(1085,
     1354,1681)(1087,1356,1684)(1091,1361,1689)(1092,1362,1691)(1095,1364,
     1694)(1096,1365,1696)(1098,1367,1699)(1100,1369,1702)(1101,1370,1704)
     (1103,1372,1707)(1106,1376,1710)(1110,1382,1717)(1112,1385,1721)(1113,
     1386,1723)(1116,1388,1726)(1117,1389,1728)(1120,1393,1733)(1122,1396,
     1737)(1123,1397,1739)(1126,1399,1742)(1127,1400,1744)(1129,1402,1747)
     (1131,1404,1750)(1132,1405,1752)(1134,1407,1755)(1138,1412,1760)(1141,
     1414,1763)(1142,1415,1765)(1144,1417,1768)(1146,1419,1771)(1148,1421,
     1774)(1151,1425,1777)(1155,1431,1784)(1156,1432,1786)(1158,1434,1788)
     (1160,1436,1791)(1161,1437,1793)(1163,1439,1796)(1166,1443,1799)(1169,
     1447,1804)(1171,1449,1807)(1174,1453,1810)(1184,1469,1827)(1186,1472,
     1831)(1189,1477,1837)(1191,1480,1841)(1192,1481,1843)(1195,1483,1846)
     (1196,1484,1848)(1199,1488,1853)(1201,1491,1857)(1202,1492,1859)(1205,
     1494,1862)(1206,1495,1864)(1208,1497,1867)(1212,1503,1874)(1214,1506,
     1878)(1217,1511,1884)(1219,1514,1888)(1220,1515,1890)(1223,1517,1893)
     (1224,1518,1519)(1227,1521,1897)(1229,1524,1901)(1230,1525,1903)(1232,
     1527,1906)(1236,1532,1911)(1237,1533,1913)(1240,1535,1916)(1241,1536,
     1918)(1243,1538,1921)(1245,1540,1924)(1246,1541,1926)(1248,1543,1929)
     (1252,1548,1934)(1253,1549,1936)(1256,1551,1939)(1257,1552,1941)(1259,
     1554,1944)(1261,1556,1947)(1262,1557,1949)(1264,1559,1952)(1267,1563,
     1955)(1270,1567,1960)(1272,1569,1963)(1275,1573,1966)(1279,1579,1973)
     (1280,1580,1975)(1282,1582,1978)(1284,1584,1981)(1285,1585,1983)(1287,
     1587,1986)(1290,1591,1989)(1293,1595,1994)(1295,1597,1997)(1298,1601,
     2000)(1305,1612,2012)(1306,1613,2013)(1309,1617,2016)(1316,1628,2028)
     (1318,1631,2032)(1319,1632,2034)(1321,1634,2037)(1324,1638,2040)(1327,
     1641,2044)(1329,1643,2047)(1332,1647,2050)(1339,1658,2062)(1340,1659,
     2063)(1343,1663,2066)(1350,1674,2078)(1352,1677,2082)(1355,1682,2088)
     (1357,1685,2092)(1358,1686,2094)(1366,1697,2106)(1368,1700,2110)(1371,
     1705,2116)(1373,1708,2120)(1374,1709,2122)(1377,1711,2125)(1378,1712,
     2127)(1380,1714,2129)(1383,1718,2132)(1390,1729,2144)(1391,1730,2145)
     (1394,1734,2148)(1401,1745,2160)(1403,1748,2164)(1406,1753,2170)(1408,
     1756,2174)(1409,1757,2176)(1416,1766,2186)(1418,1769,2190)(1420,1772,
     2194)(1422,1775,2198)(1423,1776,2200)(1426,1778,2203)(1427,1779,2205)
     (1429,1781,2208)(1433,1787,2215)(1435,1789,2217)(1438,1794,2223)(1440,
     1797,2227)(1441,1798,2229)(1444,1800,2232)(1445,1801,2234)(1448,1805,
     2239)(1450,1808,2243)(1451,1809,2245)(1454,1811,2248)(1455,1812,2250)
     (1457,1814,2253)(1459,1816,2256)(1460,1817,2258)(1462,1819,2261)(1464,
     1821,2264)(1465,1822,2266)(1467,1824,2269)(1470,1828,2272)(1473,1832,
     2277)(1475,1834,2280)(1478,1838,2283)(1485,1849,2295)(1486,1850,2296)
     (1489,1854,2299)(1496,1865,2311)(1498,1868,2315)(1499,1869,2317)(1501,
     1871,2320)(1504,1875,2323)(1507,1879,2328)(1509,1881,2331)(1512,1885,
     2334)(1522,1898,2346)(1526,1904,2353)(1528,1907,2357)(1529,1908,2359)
     (1537,1919,2371)(1539,1922,2375)(1542,1927,2381)(1544,1930,2385)(1545,
     1931,2387)(1553,1942,2399)(1555,1945,2403)(1558,1950,2409)(1560,1953,
     2413)(1561,1954,2415)(1564,1956,2418)(1565,1957,2420)(1568,1961,2425)
     (1570,1964,2429)(1571,1965,2431)(1574,1967,2434)(1575,1968,2436)(1577,
     1970,2439)(1581,1976,2446)(1583,1979,2450)(1586,1984,2455)(1588,1987,
     2459)(1589,1988,2461)(1592,1990,2464)(1593,1991,2466)(1596,1995,2471)
     (1598,1998,2475)(1599,1999,2477)(1602,2001,2480)(1603,2002,2482)(1605,
     2004,2485)(1607,2006,2488)(1608,2007,2490)(1610,2009,2493)(1614,2014,
     2498)(1615,2015,2500)(1618,2017,2503)(1619,2018,2505)(1621,2020,2508)
     (1623,2022,2511)(1624,2023,2513)(1626,2025,2516)(1629,2029,2519)(1633,
     2035,2526)(1635,2038,2530)(1636,2039,2532)(1639,2041,2535)(1642,2045,
     2540)(1644,2048,2544)(1645,2049,2546)(1648,2051,2549)(1649,2052,2551)
     (1651,2054,2554)(1653,2056,2557)(1654,2057,2559)(1656,2059,2562)(1660,
     2064,2567)(1661,2065,2569)(1664,2067,2572)(1665,2068,2574)(1667,2070,
     2577)(1669,2072,2580)(1670,2073,2582)(1672,2075,2585)(1675,2079,2588)
     (1678,2083,2593)(1680,2085,2596)(1683,2089,2599)(1687,2095,2606)(1688,
     2096,2608)(1690,2098,2611)(1692,2100,2614)(1693,2101,2616)(1695,2103,
     2619)(1698,2107,2622)(1701,2111,2627)(1703,2113,2630)(1706,2117,2633)
     (1713,1982,2128)(1715,2130,2646)(1716,2131,2648)(1719,2133,2651)(1720,
     2134,2653)(1722,2136,2656)(1724,2138,2659)(1725,2139,2661)(1727,2141,
     2664)(1731,2146,2669)(1732,2147,2671)(1735,2149,2674)(1736,2150,2676)
     (1738,2152,2679)(1740,2154,2682)(1741,2155,2684)(1743,2157,2687)(1746,
     2161,2690)(1749,2165,2695)(1751,2167,2698)(1754,2171,2701)(1758,2177,
     2708)(1759,2178,2709)(1761,2180,2712)(1762,2181,2714)(1764,2183,2717)
     (1767,2187,2720)(1770,2191,2723)(1773,2195,2726)(1780,2206,2738)(1782,
     2209,2742)(1783,2210,2744)(1785,2212,2747)(1790,2218,2753)(1792,2220,
     2756)(1795,2224,2759)(1802,2235,2771)(1803,2236,2772)(1806,2240,2775)
     (1813,2251,2787)(1815,2254,2791)(1818,2259,2797)(1820,2262,2801)(1823,
     2267,2807)(1825,2270,2811)(1826,2271,2813)(1829,2273,2816)(1830,2274,
     2818)(1833,2278,2823)(1835,2281,2827)(1836,2282,2829)(1839,2284,2832)
     (1840,2285,2834)(1842,2287,2837)(1844,2289,2840)(1845,2290,2842)(1847,
     2292,2845)(1851,2297,2850)(1852,2298,2852)(1855,2300,2855)(1856,2301,
     2857)(1858,2303,2860)(1860,2305,2863)(1861,2306,2865)(1863,2308,2868)
     (1866,2312,2871)(1870,2318,2878)(1872,2321,2882)(1873,2322,2884)(1876,
     2324,2887)(1877,2325,2889)(1880,2329,2894)(1882,2332,2898)(1883,2333,
     2900)(1886,2335,2903)(1887,2336,2905)(1889,2338,2908)(1891,2340,2911)
     (1892,2341,2913)(1894,2343,2916)(1895,2344,2917)(1896,2345,2919)(1899,
     2347,2922)(1900,2348,2924)(1902,2350,2927)(1905,2354,2930)(1909,2360,
     2937)(1910,2361,2939)(1912,2363,2942)(1914,2365,2945)(1915,2366,2947)
     (1917,2368,2950)(1920,2372,2953)(1923,2376,2958)(1925,2378,2961)(1928,
     2382,2964)(1932,2388,2971)(1933,2389,2973)(1935,2391,2976)(1937,2393,
     2979)(1938,2394,2981)(1940,2396,2984)(1943,2400,2987)(1946,2404,2992)
     (1948,2406,2995)(1951,2410,2998)(1958,2421,3010)(1959,2422,3011)(1962,
     2426,3014)(1969,2437,3026)(1971,2440,3030)(1972,2441,3032)(1974,2443,
     3035)(1977,2447,3038)(1980,2451,3043)(1985,2456,3047)(1992,2467,3059)
     (1993,2468,3060)(1996,2472,3063)(2003,2483,3075)(2005,2486,3079)(2008,
     2491,3085)(2010,2494,3089)(2011,2495,3091)(2019,2506,3102)(2021,2509,
     3106)(2024,2514,3112)(2026,2517,3116)(2027,2518,3118)(2030,2520,3121)
     (2031,2521,3123)(2033,2523,3126)(2036,2527,3129)(2042,2536,3139)(2043,
     2537,3140)(2046,2541,3143)(2053,2552,3155)(2055,2555,3159)(2058,2560,
     3165)(2060,2563,3169)(2061,2564,3171)(2069,2575,3183)(2071,2578,3187)
     (2074,2583,3193)(2076,2586,3197)(2077,2587,3199)(2080,2589,3202)(2081,
     2590,3204)(2084,2594,3209)(2086,2597,3213)(2087,2598,3215)(2090,2600,
     3218)(2091,2601,3220)(2093,2603,3223)(2097,2609,3230)(2099,2612,3234)
     (2102,2617,3240)(2104,2620,3244)(2105,2621,3246)(2108,2623,3249)(2109,
     2624,3251)(2112,2628,3256)(2114,2631,3260)(2115,2632,3262)(2118,2634,
     3265)(2119,2635,3267)(2121,2637,3270)(2123,2639,3273)(2124,2640,3275)
     (2126,2642,3278)(2135,2654,3290)(2137,2657,3294)(2140,2662,3300)(2142,
     2665,3304)(2143,2666,3306)(2151,2677,3318)(2153,2680,3322)(2156,2685,
     3328)(2158,2688,3332)(2159,2689,3334)(2162,2691,3337)(2163,2692,3339)
     (2166,2696,3344)(2168,2699,3348)(2169,2700,3350)(2172,2702,3353)(2173,
     2703,3355)(2175,2705,3316)(2179,2710,3362)(2182,2715,3368)(2184,2718,
     3372)(2185,2719,3374)(2188,2721,3377)(2189,2722,3379)(2192,2724,3381)
     (2193,2725,3383)(2196,2727,3386)(2197,2728,3388)(2199,2730,3391)(2201,
     2732,3394)(2202,2733,3396)(2204,2735,3399)(2207,2739,3402)(2211,2745,
     3409)(2213,2748,3413)(2214,2749,3415)(2216,2750,3417)(2219,2754,3422)
     (2221,2757,3426)(2222,2758,3428)(2225,2760,3431)(2226,2761,3433)(2228,
     2763,3436)(2230,2765,3439)(2231,2766,3441)(2233,2768,3444)(2237,2773,
     3449)(2238,2774,3451)(2241,2776,3454)(2242,2777,3456)(2244,2779,3459)
     (2246,2781,3462)(2247,2782,3464)(2249,2784,3467)(2252,2788,3336)(2255,
     2792,3474)(2257,2794,3477)(2260,2798,3480)(2263,2802,3485)(2265,2804,
     3405)(2268,2808,3489)(2275,2819,3501)(2276,2820,3502)(2279,2824,3505)
     (2286,2835,3517)(2288,2838,3521)(2291,2843,3527)(2293,2846,3531)(2294,
     2847,3533)(2302,2858,3545)(2304,2861,3549)(2307,2866,3555)(2309,2869,
     3559)(2310,2870,3561)(2313,2872,3564)(2314,2873,3566)(2316,2875,3569)
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