bin1 := (1,3,5)(4,6,9)(7,10,14)(8,11,16)(12,17,23)(13,18,25)(15,20,28)(19,26,35)
     (21,29,39)(22,30,41)(24,32,44)(27,36,49)(31,42,56)(33,45,60)(34,46,62)
     (37,50,67)(38,51,69)(40,53,72)(43,57,77)(47,63,84)(48,64,86)(52,70,93)
     (54,73,97)(55,74,99)(58,78,104)(59,79,106)(61,81,109)(65,87,116)(66,88,
     118)(68,90,121)(71,94,126)(75,100,133)(76,101,135)(80,107,142)(82,110,
     146)(83,111,148)(85,113,151)(89,119,158)(91,122,162)(92,123,164)(95,127,
     169)(96,128,171)(98,130,174)(102,136,181)(103,137,183)(105,139,186)(108,
     143,191)(112,149,198)(114,152,202)(115,153,204)(117,155,207)(120,159,212)
     (124,165,219)(125,166,221)(129,172,228)(131,175,232)(132,176,234)(134,
     178,237)(138,184,244)(140,187,248)(141,188,250)(144,192,255)(145,193,257)
     (147,195,260)(150,199,265)(154,205,272)(156,208,276)(157,209,278)(160,
     213,283)(161,214,285)(163,216,288)(167,222,295)(168,223,297)(170,225,300)
     (173,229,304)(177,235,311)(179,238,315)(180,239,317)(182,241,320)(185,
     245,325)(189,251,332)(190,252,334)(194,258,341)(196,261,345)(197,262,347)
     (200,266,351)(201,267,353)(203,269,356)(206,273,361)(210,279,368)(211,
     280,370)(215,286,377)(217,289,381)(218,290,383)(220,292,386)(224,298,393)
     (226,247,327)(227,301,397)(230,305,402)(231,306,404)(233,308,407)(236,
     312,412)(240,318,419)(242,321,423)(243,322,425)(246,326,429)(249,329,433)
     (253,335,440)(254,336,442)(256,338,445)(259,342,450)(264,348,457)(268,
     354,464)(270,357,468)(271,358,469)(274,362,474)(275,363,476)(277,365,479)
     (281,371,486)(282,372,488)(284,374,491)(287,378,496)(291,384,503)(293,
     387,507)(294,388,509)(296,390,512)(299,394,517)(302,398,522)(303,399,524)
     (307,405,531)(309,408,535)(310,409,537)(313,413,542)(314,414,544)(316,
     416,547)(319,420,552)(323,426,559)(324,427,561)(328,431,566)(330,434,570)
     (331,435,572)(333,437,575)(337,443,582)(339,446,585)(340,447,587)(343,
     451,592)(344,452,594)(346,454,597)(349,458,602)(350,459,604)(352,461,607)
     (355,465,612)(359,470,618)(360,471,620)(364,477,627)(366,480,631)(367,
     481,633)(369,483,636)(373,489,643)(375,492,646)(376,493,648)(379,497,653)
     (380,498,655)(382,500,658)(385,504,663)(389,510,670)(391,513,674)(392,
     514,676)(395,518,681)(396,519,683)(400,525,690)(401,526,692)(403,528,695)
     (406,532,700)(410,538,707)(411,539,709)(415,545,716)(417,548,720)(418,
     549,722)(421,553,727)(422,554,729)(424,556,732)(428,562,739)(430,564,742)
     (432,567,746)(436,573,753)(438,576,757)(439,577,759)(441,579,762)(444,
     583,767)(448,588,773)(449,589,775)(453,595,782)(455,598,786)(456,599,788)
     (460,605,795)(462,608,799)(463,609,801)(466,613,806)(467,614,808)(472,
     621,816)(473,622,818)(475,624,821)(478,628,826)(482,634,833)(484,637,837)
     (485,638,839)(487,640,842)(490,644,847)(494,649,853)(495,650,855)(499,
     656,862)(501,659,866)(502,660,868)(505,664,873)(506,665,875)(508,667,878)
     (511,671,883)(515,677,890)(516,678,892)(520,684,899)(521,685,901)(523,
     687,904)(527,693,911)(529,696,914)(530,697,916)(533,701,921)(534,702,923)
     (536,704,926)(540,710,933)(541,711,935)(543,713,938)(546,717,943)(550,
     723,950)(551,724,952)(555,730,959)(557,733,963)(558,734,965)(560,736,968)
     (563,740,973)(565,743,977)(568,747,982)(569,748,984)(571,750,987)(574,
     754,992)(578,760,999)(580,763,1003)(581,764,1005)(584,768,1010)(586,770,
     1013)(590,776,1020)(591,777,1022)(593,779,1025)(596,783,1030)(600,789,
     1036)(601,790,1038)(603,792,1041)(606,796,1046)(610,802,1053)(611,803,
     1055)(615,809,1062)(616,810,1064)(617,811,1066)(619,813,1069)(623,819,
     1076)(625,822,1079)(626,823,1081)(629,827,1086)(630,828,1088)(632,830,
     1091)(635,834,1096)(639,840,1103)(641,843,1107)(642,844,1109)(645,848,
     1114)(647,850,1117)(651,856,1124)(652,857,1126)(654,859,1129)(657,863,
     1134)(661,869,1141)(662,870,1143)(666,876,1150)(668,879,1154)(669,880,
     1156)(672,884,1161)(673,885,1163)(675,887,1166)(679,893,1173)(680,894,
     1175)(682,896,1178)(686,902,1185)(688,905,1189)(689,906,1191)(691,908,
     1194)(694,912,1199)(698,917,1205)(699,918,1207)(703,924,1214)(705,927,
     1218)(706,928,1220)(708,930,1223)(712,936,1230)(714,939,1234)(715,940,
     1236)(718,944,1241)(719,945,1243)(721,947,1246)(725,953,1253)(726,954,
     1255)(728,956,1258)(731,960,1263)(735,966,1270)(737,969,1274)(738,970,
     1276)(741,974,1281)(744,978,1286)(745,979,1288)(749,985,1295)(751,988,
     1299)(752,989,1301)(755,993,1306)(756,994,1308)(758,996,1311)(761,1000,
     1316)(765,1006,1323)(766,1007,1325)(769,1011,1330)(771,1014,1334)(772,
     1015,1336)(774,1017,1339)(778,1023,1346)(780,1026,1349)(781,1027,1351)
     (784,1031,1356)(785,1032,1358)(787,1033,1359)(791,1039,1366)(793,1042,
     1370)(794,1043,1372)(797,1047,1377)(798,1048,1379)(800,1050,1382)(804,
     1056,1389)(805,1057,1391)(807,1059,1394)(812,1067,1403)(814,1070,1407)
     (815,1071,1409)(817,1073,1412)(820,1077,1417)(824,1082,1423)(825,1083,
     1425)(829,1089,1432)(831,1092,1436)(832,1093,1438)(835,1097,1443)(836,
     1098,1445)(838,1100,1448)(841,1104,1453)(845,1110,1460)(846,1111,1462)
     (849,1115,1467)(851,1118,1471)(852,1119,1473)(854,1121,1476)(858,1127,
     1483)(860,1130,1486)(861,1131,1488)(864,1135,1492)(865,1136,1494)(867,
     1138,1497)(871,1144,1504)(872,1145,1506)(874,1147,1509)(877,1151,1514)
     (881,1157,1521)(882,1158,1523)(886,1164,1530)(888,1167,1534)(889,1168,
     1536)(891,1170,1539)(895,1176,1546)(897,1179,1550)(898,1180,1552)(900,
     1182,1555)(903,1186,1560)(907,1192,1567)(909,1195,1571)(910,1196,1573)
     (913,1200,1578)(915,1202,1581)(919,1208,1586)(920,1209,1588)(922,1211,
     1591)(925,1215,1596)(929,1221,1603)(931,1224,1607)(932,1225,1609)(934,
     1227,1612)(937,1231,1617)(941,1237,1624)(942,1238,1626)(946,1244,1633)
     (948,1247,1204)(949,1248,1638)(951,1250,1641)(955,1256,1648)(957,1259,
     1651)(958,1260,1653)(961,1264,1658)(962,1265,1660)(964,1267,1663)(967,
     1271,1668)(971,1277,1675)(972,1278,1677)(975,1282,1682)(976,1283,1684)
     (980,1289,1691)(981,1290,1693)(983,1292,1696)(986,1296,1701)(990,1302,
     1708)(991,1303,1710)(995,1309,1717)(997,1312,1721)(998,1313,1723)(1001,
     1317,1728)(1002,1318,1730)(1004,1320,1733)(1008,1326,1740)(1009,1327,
     1742)(1012,1331,1747)(1016,1337,1754)(1018,1340,1758)(1019,1341,1760)
     (1021,1343,1763)(1024,1347,1768)(1028,1352,1774)(1029,1353,1776)(1034,
     1360,1784)(1035,1361,1786)(1037,1363,1789)(1040,1367,1794)(1044,1373,
     1801)(1045,1374,1803)(1049,1380,1810)(1051,1383,1814)(1052,1384,1816)
     (1054,1386,1819)(1058,1392,1826)(1060,1395,1829)(1061,1396,1831)(1063,
     1398,1834)(1065,1400,1837)(1068,1404,1842)(1072,1410,1849)(1074,1413,
     1853)(1075,1414,1855)(1078,1418,1860)(1080,1420,1863)(1084,1426,1870)
     (1085,1427,1872)(1087,1429,1875)(1090,1433,1880)(1094,1439,1887)(1095,
     1440,1889)(1099,1446,1896)(1101,1449,1900)(1102,1450,1902)(1105,1454,
     1907)(1106,1455,1909)(1108,1457,1912)(1112,1463,1919)(1113,1464,1921)
     (1116,1468,1926)(1120,1474,1933)(1122,1477,1937)(1123,1478,1939)(1125,
     1480,1942)(1128,1484,1947)(1132,1489,1953)(1133,1490,1955)(1137,1495,
     1961)(1139,1498,1965)(1140,1499,1967)(1142,1501,1970)(1146,1507,1977)
     (1148,1510,1981)(1149,1511,1983)(1152,1515,1988)(1153,1516,1990)(1155,
     1518,1993)(1159,1524,2000)(1160,1525,2002)(1162,1527,2005)(1165,1531,
     2010)(1169,1537,2017)(1171,1540,2021)(1172,1541,2023)(1174,1543,2026)
     (1177,1547,2031)(1181,1553,2038)(1183,1556,2042)(1184,1557,2044)(1187,
     1561,2049)(1188,1562,2051)(1190,1564,2054)(1193,1568,2059)(1197,1574,
     2066)(1198,1575,2068)(1201,1579,2073)(1203,1582,2077)(1206,1584,2080)
     (1210,1589,2086)(1212,1592,2089)(1213,1593,2091)(1216,1597,2096)(1217,
     1598,2098)(1219,1600,2101)(1222,1604,2106)(1226,1610,2113)(1228,1613,
     2117)(1229,1614,2119)(1232,1618,2124)(1233,1619,2126)(1235,1621,2129)
     (1239,1627,2136)(1240,1628,2138)(1242,1630,2141)(1245,1634,2146)(1249,
     1639,2152)(1251,1642,2156)(1252,1643,2158)(1254,1645,2161)(1257,1649,
     2166)(1261,1654,2172)(1262,1655,2174)(1266,1661,2181)(1268,1664,2185)
     (1269,1665,2187)(1272,1669,2192)(1273,1670,2194)(1275,1672,2197)(1279,
     1678,2204)(1280,1679,2206)(1284,1685,2213)(1285,1686,2215)(1287,1688,
     2218)(1291,1694,2225)(1293,1697,2228)(1294,1698,2230)(1297,1702,2235)
     (1298,1703,2237)(1300,1705,2240)(1304,1711,2247)(1305,1712,2248)(1307,
     1714,2251)(1310,1718,2256)(1314,1724,2263)(1315,1725,2265)(1319,1731,
     2272)(1321,1734,2276)(1322,1735,2278)(1324,1737,2281)(1328,1743,2288)
     (1329,1744,2290)(1332,1748,2295)(1333,1749,2297)(1335,1751,2300)(1338,
     1755,2305)(1342,1761,2312)(1344,1764,2316)(1345,1765,2318)(1348,1769,
     2323)(1350,1771,2326)(1354,1777,2333)(1355,1778,2335)(1357,1780,2338)
     (1362,1787,2346)(1364,1790,2350)(1365,1791,2352)(1368,1795,2357)(1369,
     1796,2359)(1371,1798,2362)(1375,1804,2369)(1376,1805,2371)(1378,1807,
     2374)(1381,1811,2379)(1385,1817,2384)(1387,1820,2388)(1388,1821,2390)
     (1390,1823,2393)(1393,1827,2398)(1397,1832,2404)(1399,1835,2408)(1401,
     1838,2412)(1402,1839,2414)(1405,1843,2419)(1406,1844,2421)(1408,1846,
     2424)(1411,1850,2429)(1415,1856,2436)(1416,1857,2438)(1419,1861,2443)
     (1421,1864,2447)(1422,1865,2449)(1424,1867,2452)(1428,1873,2459)(1430,
     1876,2462)(1431,1877,2464)(1434,1881,2469)(1435,1882,2471)(1437,1884,
     2474)(1441,1890,2480)(1442,1891,2482)(1444,1893,2485)(1447,1897,2490)
     (1451,1903,2497)(1452,1904,2499)(1456,1910,2506)(1458,1913,2510)(1459,
     1914,2512)(1461,1916,2515)(1465,1922,2522)(1466,1923,2524)(1469,1927,
     2529)(1470,1928,2531)(1472,1930,2533)(1475,1934,2538)(1479,1940,2545)
     (1481,1943,2549)(1482,1944,2551)(1485,1948,2556)(1487,1950,2558)(1491,
     1956,2565)(1493,1958,2568)(1496,1962,2573)(1500,1968,2579)(1502,1971,
     2583)(1503,1972,2585)(1505,1974,2588)(1508,1978,2593)(1512,1984,2600)
     (1513,1985,2602)(1517,1991,2609)(1519,1994,2613)(1520,1995,2615)(1522,
     1997,2618)(1526,2003,2625)(1528,2006,2628)(1529,2007,2630)(1532,2011,
     2635)(1533,2012,2637)(1535,2014,2639)(1538,2018,2644)(1542,2024,2649)
     (1544,2027,2653)(1545,2028,2655)(1548,2032,2660)(1549,2033,2662)(1551,
     2035,2665)(1554,2039,2670)(1558,2045,2677)(1559,2046,2679)(1563,2052,
     2686)(1565,2055,2690)(1566,2056,2692)(1569,2060,2697)(1570,2061,2699)
     (1572,2063,2702)(1576,2069,2709)(1577,2070,2711)(1580,2074,2716)(1583,
     2078,2721)(1585,2081,2725)(1587,2083,2728)(1590,2087,2733)(1594,2092,
     2738)(1595,2093,2740)(1599,2099,2747)(1601,2102,2751)(1602,2103,2753)
     (1605,2107,2758)(1606,2108,2760)(1608,2110,2763)(1611,2114,2768)(1615,
     2120,2775)(1616,2121,2777)(1620,2127,2784)(1622,2130,2788)(1623,2131,
     2790)(1625,2133,2793)(1629,2139,2800)(1631,2142,2803)(1632,2143,2805)
     (1635,2147,2810)(1636,2148,2812)(1637,2149,2814)(1640,2153,2819)(1644,
     2159,2826)(1646,2162,2830)(1647,2163,2832)(1650,2167,2837)(1652,2169,
     2840)(1656,2175,2847)(1657,2176,2849)(1659,2178,2852)(1662,2182,2857)
     (1666,2188,2864)(1667,2189,2866)(1671,2195,2873)(1673,2198,2877)(1674,
     2199,2879)(1676,2201,2882)(1680,2207,2889)(1681,2208,2891)(1683,2210,
     2643)(1687,2216,2899)(1689,2219,2903)(1690,2220,2905)(1692,2222,2908)
     (1695,2226,2913)(1699,2231,2919)(1700,2232,2921)(1704,2238,2927)(1706,
     2241,2931)(1707,2242,2933)(1709,2244,2936)(1713,2249,2942)(1715,2252,
     2946)(1716,2253,2948)(1719,2257,2953)(1720,2258,2955)(1722,2260,2958)
     (1726,2266,2965)(1727,2267,2967)(1729,2269,2970)(1732,2273,2975)(1736,
     2279,2981)(1738,2282,2985)(1739,2283,2987)(1741,2285,2990)(1745,2291,
     2997)(1746,2292,2999)(1750,2298,3006)(1752,2301,3010)(1753,2302,3012)
     (1756,2306,3017)(1757,2307,3019)(1759,2309,3022)(1762,2313,3027)(1766,
     2319,3034)(1767,2320,3036)(1770,2324,3041)(1772,2327,3045)(1773,2328,
     3047)(1775,2330,3050)(1779,2336,3057)(1781,2339,3060)(1782,2340,3062)
     (1783,2341,3064)(1785,2343,3066)(1788,2347,3071)(1792,2353,3078)(1793,
     2354,3080)(1797,2360,3087)(1799,2363,3090)(1800,2364,3092)(1802,2366,
     3095)(1806,2372,3102)(1808,2375,3105)(1809,2376,3107)(1812,2380,3112)
     (1813,2381,3114)(1815,2382,3116)(1818,2385,3120)(1822,2391,3126)(1824,
     2394,3130)(1825,2395,3132)(1828,2399,3137)(1830,2401,3140)(1833,2405,
     3145)(1836,2409,3150)(1840,2415,3156)(1841,2416,3158)(1845,2422,3165)
     (1847,2425,3169)(1848,2426,3171)(1851,2430,3176)(1852,2431,3178)(1854,
     2433,3181)(1858,2439,2274)(1859,2440,3189)(1862,2444,3194)(1866,2450,
     3201)(1868,2453,3205)(1869,2454,3207)(1871,2456,3210)(1874,2460,3215)
     (1878,2465,3221)(1879,2466,3223)(1883,2472,3230)(1885,2475,3234)(1886,
     2476,3236)(1888,2478,3239)(1892,2483,3245)(1894,2486,3249)(1895,2487,
     3251)(1898,2491,3256)(1899,2492,3258)(1901,2494,3261)(1905,2500,3267)
     (1906,2501,3269)(1908,2503,3272)(1911,2507,3277)(1915,2513,3284)(1917,
     2516,3288)(1918,2517,3290)(1920,2519,3293)(1924,2525,3300)(1925,2526,
     3302)(1931,2534,3311)(1932,2535,3313)(1935,2539,3318)(1936,2540,3320)
     (1938,2542,3323)(1941,2546,3328)(1945,2552,3335)(1946,2553,3337)(1949,
     2557,3342)(1951,2559,3344)(1952,2560,3346)(1954,2562,3349)(1957,2566,
     3354)(1959,2569,3357)(1960,2570,3359)(1963,2574,3364)(1964,2575,3366)
     (1966,2577,3369)(1969,2580,3373)(1973,2586,3380)(1975,2589,3384)(1976,
     2590,3386)(1979,2594,3391)(1980,2595,3393)(1982,2597,3395)(1986,2603,
     3402)(1987,2604,3404)(1989,2606,3407)(1992,2610,3412)(1996,2616,3419)
     (1998,2619,3423)(1999,2620,3425)(2001,2622,3428)(2004,2626,3433)(2008,
     2631,3439)(2009,2632,3441)(2013,2638,3448)(2015,2640,3451)(2016,2641,
     3453)(2019,2205,2886)(2020,2645,3457)(2022,2646,3459)(2025,2650,3464)
     (2029,2656,3470)(2030,2657,3472)(2034,2663,3479)(2036,2666,3482)(2037,
     2667,3484)(2040,2671,3489)(2041,2672,3491)(2043,2674,3494)(2047,2680,
     3501)(2048,2681,3503)(2050,2683,3506)(2053,2687,3511)(2057,2693,3518)
     (2058,2694,3520)(2062,2700,3527)(2064,2703,3531)(2065,2704,3533)(2067,
     2706,3536)(2071,2712,3542)(2072,2713,3544)(2075,2717,3549)(2076,2718,
     3551)(2079,2722,3556)(2082,2726,3561)(2084,2729,3565)(2085,2730,3567)
     (2088,2734,3571)(2090,2736,3574)(2094,2741,3580)(2095,2742,3582)(2097,
     2744,3585)(2100,2748,3590)(2104,2754,3596)(2105,2755,3598)(2109,2761,
     3605)(2111,2764,3609)(2112,2765,3611)(2115,2769,3616)(2116,2770,3618)
     (2118,2772,3621)(2122,2778,3628)(2123,2779,3630)(2125,2781,3100)(2128,
     2785,3637)(2132,2791,3644)(2134,2794,3648)(2135,2795,3650)(2137,2797,
     3652)(2140,2801,3656)(2144,2806,3662)(2145,2807,3664)(2150,2815,3673)
     (2151,2816,3675)(2154,2820,3680)(2155,2821,3682)(2157,2823,3685)(2160,
     2827,3690)(2164,2833,3697)(2165,2834,3699)(2168,2838,3704)(2170,2841,
     3708)(2171,2842,3710)(2173,2844,3713)(2177,2850,3720)(2179,2853,3723)
     (2180,2854,3725)(2183,2858,3730)(2184,2859,3732)(2186,2861,3735)(2190,
     2867,3742)(2191,2868,3744)(2193,2870,3747)(2196,2874,3752)(2200,2880,
     3759)(2202,2883,3763)(2203,2884,3765)(2209,2892,3774)(2211,2894,3777)
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