bin1 := (1,3,6)(2,4,8)(5,9,13)(7,10,15)(11,16,22)(12,17,24)(14,19,27)(18,25,34)
     (20,28,38)(21,29,40)(23,31,43)(26,35,46)(30,41,53)(32,44,57)(33,45,59)
     (36,47,62)(37,48,64)(39,50,67)(42,54,70)(49,65,82)(51,68,86)(52,69,88)
     (55,71,91)(56,72,93)(58,74,95)(60,76,98)(61,77,100)(63,79,103)(66,83,106)
     (73,94,118)(75,96,120)(78,101,125)(80,104,129)(81,105,131)(84,107,134)
     (85,108,136)(87,110,139)(89,112,142)(90,113,144)(92,115,147)(97,121,153)
     (99,122,154)(102,126,157)(109,137,169)(111,140,173)(114,145,179)(116,148,
     183)(117,149,185)(119,150,187)(123,155,192)(124,156,194)(127,158,197)
     (128,159,199)(130,161,202)(132,163,204)(133,164,206)(135,166,209)(138,
     170,212)(141,174,217)(143,176,220)(146,180,223)(151,188,232)(152,189,233)
     (160,200,245)(162,203,249)(165,207,254)(167,210,258)(168,211,260)(171,
     213,263)(172,214,265)(175,218,270)(177,221,274)(178,222,276)(181,224,279)
     (182,225,281)(184,227,284)(186,229,287)(190,234,292)(191,235,294)(193,
     237,297)(195,239,300)(196,240,302)(198,242,305)(201,246,308)(205,251,314)
     (208,255,317)(215,266,329)(216,267,330)(219,271,333)(226,282,345)(228,
     285,286)(230,288,351)(231,289,353)(236,295,360)(238,298,364)(241,303,370)
     (243,306,374)(244,307,376)(247,309,379)(248,310,381)(250,312,384)(252,
     315,388)(253,316,390)(256,318,393)(257,319,395)(259,321,398)(261,323,400)
     (262,324,402)(264,326,405)(268,331,410)(269,332,412)(272,334,415)(273,
     335,417)(275,337,420)(277,339,423)(278,340,425)(280,342,428)(283,346,431)
     (290,354,440)(291,355,442)(293,357,445)(296,361,448)(299,365,453)(301,
     367,456)(304,371,458)(311,382,383)(313,385,470)(320,396,481)(322,399,485)
     (325,403,488)(327,406,492)(328,407,494)(336,418,505)(338,421,509)(341,
     426,515)(343,429,519)(344,430,520)(347,432,523)(348,433,525)(349,434,527)
     (350,435,529)(352,437,532)(356,443,538)(358,446,542)(359,447,544)(362,
     449,547)(363,450,549)(366,454,554)(368,457,369)(372,459,560)(373,460,562)
     (375,462,565)(377,464,568)(378,465,570)(380,467,573)(386,471,578)(387,
     472,580)(389,474,583)(391,476,586)(392,477,588)(394,479,590)(397,482,592)
     (401,484,594)(404,489,598)(408,495,605)(409,496,607)(411,498,610)(413,
     499,612)(414,500,478)(416,502,616)(419,506,619)(422,510,624)(424,512,627)
     (427,516,630)(436,530,645)(438,503,617)(439,533,649)(441,535,652)(444,
     539,655)(451,550,667)(452,551,668)(455,555,671)(461,563,680)(463,566,684)
     (466,571,690)(468,574,694)(469,575,696)(473,581,703)(475,584,707)(480,
     591,714)(483,593,717)(486,596,595)(487,597,713)(490,599,722)(491,600,724)
     (493,602,727)(497,608,734)(501,614,741)(504,618,746)(507,620,749)(508,
     621,751)(511,625,756)(513,628,760)(514,629,762)(517,631,765)(518,632,767)
     (521,635,771)(522,636,773)(524,638,776)(526,640,779)(528,642,782)(531,
     646,785)(534,650,651)(536,653,792)(537,654,794)(540,656,797)(541,657,799)
     (543,659,802)(545,661,805)(546,662,807)(548,664,810)(552,669,814)(553,
     670,816)(556,672,819)(557,673,821)(558,674,823)(559,675,825)(561,677,828)
     (564,681,831)(567,685,835)(569,687,838)(572,691,841)(576,697,848)(577,
     698,850)(579,700,853)(582,704,856)(585,708,861)(587,710,864)(589,613,739)
     (601,725,879)(603,728,883)(604,729,885)(606,731,888)(609,735,891)(611,
     737,894)(615,742,898)(622,752,908)(623,753,909)(626,757,912)(633,768,924)
     (634,769,925)(637,774,931)(639,777,935)(641,780,939)(643,783,943)(644,
     784,945)(647,786,745)(648,787,949)(658,800,963)(660,803,920)(663,808,971)
     (665,733,890)(666,811,975)(676,826,991)(678,829,995)(679,830,997)(682,
     748,903)(683,832,999)(686,836,1004)(688,839,1008)(689,840,1010)(692,842,
     1013)(693,843,1015)(695,845,1018)(699,851,1025)(701,854,1029)(702,855,
     1031)(705,857,1034)(706,858,1036)(709,862,1041)(711,865,1045)(712,866,
     1047)(715,868,1050)(716,869,1052)(718,871,1055)(719,872,1057)(720,873,
     1059)(721,874,1061)(723,876,1064)(726,880,1067)(730,886,1074)(732,889,
     1078)(736,892,893)(738,895,1084)(740,897,1087)(743,899,1090)(744,900,948)
     (747,902,1094)(750,905,1098)(754,910,1103)(755,911,1105)(758,913,1108)
     (759,914,1110)(761,916,968)(763,918,1115)(764,919,1117)(766,921,1119)
     (770,926,1124)(772,928,1127)(775,932,1130)(778,936,1135)(781,940,1138)
     (788,950,1148)(789,951,1150)(790,952,1152)(791,953,1154)(793,955,1157)
     (795,957,1160)(796,958,1162)(798,960,1165)(801,964,1168)(804,967,1171)
     (806,969,1173)(809,972,1175)(812,976,1180)(813,977,1182)(815,979,1185)
     (817,981,1188)(818,982,1190)(820,984,1193)(822,986,1196)(824,988,1199)
     (827,992,1202)(833,1000,1210)(834,1001,1211)(837,1005,1214)(844,1016,
     1226)(846,1019,1230)(847,1020,1232)(849,1022,1235)(852,1026,1238)(859,
     1037,1249)(860,1038,1250)(863,1042,1253)(867,1048,1260)(870,1053,1266)
     (875,1062,1276)(877,1065,1280)(878,1066,1282)(881,1068,1285)(882,1069,
     1287)(884,1071,1290)(887,1075,1293)(896,1085,1302)(901,1092,1309)(904,
     1096,1313)(906,1099,1317)(907,1100,1318)(915,1111,1330)(917,1113,1333)
     (922,1120,1339)(923,1121,1341)(927,1125,1345)(929,1128,1349)(930,1129,
     1351)(933,1131,1354)(934,1132,1356)(937,1136,1360)(938,1137,1362)(941,
     1139,1365)(942,1140,1367)(944,1142,1370)(946,1144,1373)(947,1145,1375)
     (954,1155,1385)(956,1158,1389)(959,1163,1395)(961,1166,1399)(962,1167,
     1401)(965,1169,1404)(966,1170,1118)(970,1174,1409)(973,1176,1412)(974,
     1177,1414)(978,1183,1420)(980,1186,1424)(983,1191,1430)(985,1194,1434)
     (987,1197,1438)(989,1200,1442)(990,1201,1247)(993,1203,1446)(994,1204,
     1448)(996,1206,1451)(998,1207,1453)(1002,1212,1458)(1003,1213,1460)(1006,
     1215,1463)(1007,1216,1465)(1009,1218,1468)(1011,1220,1471)(1012,1221,
     1473)(1014,1223,1475)(1017,1227,1478)(1021,1233,1483)(1023,1236,1487)
     (1024,1237,1178)(1027,1239,1491)(1028,1240,1493)(1030,1242,1496)(1032,
     1244,1499)(1033,1093,1310)(1035,1246,1502)(1039,1251,1505)(1040,1252,
     1507)(1043,1254,1510)(1044,1255,1512)(1046,1257,1515)(1049,1261,1350)
     (1051,1263,1522)(1054,1267,1525)(1056,1269,1528)(1058,1271,1530)(1060,
     1273,1533)(1063,1277,1536)(1070,1288,1289)(1072,1291,1550)(1073,1292,
     1552)(1076,1294,1555)(1077,1295,1556)(1079,1297,1559)(1080,1298,1561)
     (1081,1299,1563)(1082,1300,1565)(1083,1301,1567)(1086,1256,1513)(1088,
     1304,1571)(1089,1305,1573)(1091,1307,1576)(1095,1312,1581)(1097,1314,
     1582)(1101,1319,1587)(1102,1320,1589)(1104,1322,1592)(1106,1324,1595)
     (1107,1325,1597)(1109,1327,1600)(1112,1331,1172)(1114,1334,1606)(1116,
     1336,1609)(1122,1279,1538)(1123,1342,1615)(1126,1346,1618)(1133,1357,
     1134)(1141,1368,1639)(1143,1371,1643)(1146,1376,1648)(1147,1377,1649)
     (1149,1379,1651)(1151,1381,1654)(1153,1383,1657)(1156,1386,1659)(1159,
     1390,1663)(1161,1392,1666)(1164,1396,1669)(1179,1415,1688)(1181,1417,
     1691)(1184,1421,1694)(1187,1425,1699)(1189,1427,1702)(1192,1431,1705)
     (1195,1435,1708)(1198,1439,1710)(1205,1449,1719)(1208,1454,1723)(1209,
     1455,1725)(1217,1466,1737)(1219,1469,1741)(1222,1441,1711)(1224,1476,
     1748)(1225,1477,1750)(1228,1443,1713)(1229,1479,1752)(1231,1480,1753)
     (1234,1484,1756)(1241,1494,1767)(1243,1497,1771)(1245,1500,1774)(1248,
     1503,1777)(1258,1516,1529)(1259,1517,1792)(1262,1520,1795)(1264,1523,
     1799)(1265,1524,1801)(1268,1526,1803)(1270,1422,1695)(1272,1531,1808)
     (1274,1534,1812)(1275,1535,1814)(1278,1537,1817)(1281,1540,1820)(1283,
     1542,1823)(1284,1543,1825)(1286,1545,1828)(1296,1557,1840)(1303,1569,
     1851)(1306,1574,1857)(1308,1577,1861)(1311,1498,1772)(1315,1583,1866)
     (1316,1584,1868)(1321,1590,1875)(1323,1593,1879)(1326,1598,1885)(1328,
     1601,1889)(1329,1602,1891)(1332,1603,1893)(1335,1607,1897)(1337,1610,
     1901)(1338,1611,1903)(1340,1613,1905)(1343,1616,1908)(1344,1617,1910)
     (1347,1619,1913)(1348,1620,1915)(1352,1622,1918)(1353,1623,1919)(1355,
     1625,1922)(1358,1628,1926)(1359,1629,1928)(1361,1631,1931)(1363,1633,
     1934)(1364,1634,1935)(1366,1636,1937)(1369,1640,1940)(1372,1644,1436)
     (1374,1646,1947)(1378,1650,1779)(1380,1652,1953)(1382,1655,1957)(1384,
     1658,1961)(1387,1660,1964)(1388,1661,1966)(1391,1664,1969)(1393,1667,
     1973)(1394,1668,1975)(1397,1670,1718)(1398,1671,1978)(1400,1673,1981)
     (1402,1675,1984)(1403,1676,1986)(1405,1678,1989)(1406,1679,1991)(1407,
     1680,1993)(1408,1681,1994)(1410,1683,1996)(1411,1684,1998)(1413,1686,
     2000)(1416,1689,2004)(1418,1692,2008)(1419,1693,2010)(1423,1696,2014)
     (1426,1700,2018)(1428,1703,2022)(1429,1704,2024)(1432,1706,2027)(1433,
     1707,2029)(1437,1709,2032)(1440,1621,1916)(1444,1714,2036)(1445,1715,
     2038)(1447,1717,2041)(1450,1720,2042)(1452,1721,2043)(1456,1726,2049)
     (1457,1727,2051)(1459,1729,2054)(1461,1731,2056)(1462,1732,2058)(1464,
     1734,2061)(1467,1738,2064)(1470,1742,1838)(1472,1743,2069)(1474,1745,
     2071)(1481,1754,2080)(1482,1755,2081)(1485,1757,2082)(1486,1758,2084)
     (1488,1760,2087)(1489,1761,2088)(1490,1762,2090)(1492,1764,2093)(1495,
     1768,2096)(1501,1775,2101)(1504,1778,2105)(1506,1780,2107)(1508,1782,
     2110)(1509,1783,2112)(1511,1785,2115)(1514,1788,2119)(1518,1793,2124)
     (1519,1794,2026)(1521,1796,2125)(1527,1804,2132)(1532,1809,2135)(1539,
     1818,2143)(1541,1821,2147)(1544,1826,2153)(1546,1829,2157)(1547,1830,
     2159)(1548,1831,2161)(1549,1832,2074)(1551,1834,2165)(1553,1835,2167)
     (1554,1836,2169)(1558,1841,2172)(1560,1685,1999)(1562,1843,2175)(1564,
     1845,2178)(1566,1847,2181)(1568,1849,2184)(1570,1852,2188)(1572,1854,
     2191)(1575,1858,2194)(1578,1862,2199)(1579,1863,2200)(1580,1864,2201)
     (1585,1869,2207)(1586,1870,2208)(1588,1872,2211)(1591,1876,2214)(1594,
     1880,2219)(1596,1882,2222)(1599,1886,2225)(1604,1894,2233)(1605,1895,
     2234)(1608,1898,1662)(1612,1904,2238)(1614,1906,2241)(1624,1920,2255)
     (1626,1923,2259)(1627,1924,2261)(1630,1929,2267)(1632,1932,2271)(1635,
     1936,2275)(1637,1938,2277)(1638,1939,2279)(1641,1941,2282)(1642,1942,
     2284)(1645,1945,2288)(1647,1948,2068)(1653,1954,2293)(1656,1958,2295)
     (1665,1970,2305)(1672,1979,2315)(1674,1982,2318)(1677,1987,2324)(1682,
     1730,1995)(1687,2001,2334)(1690,2005,2337)(1697,2015,2347)(1698,2016,
     2348)(1701,2019,2350)(1712,2034,2363)(1716,2039,2369)(1722,2044,2374)
     (1724,2046,2377)(1728,2052,2383)(1733,2059,2390)(1735,2062,2393)(1736,
     2063,2395)(1739,2065,1740)(1744,2070,2402)(1746,2072,2405)(1747,2073,
     2407)(1749,2075,2409)(1751,2077,2412)(1759,2085,2419)(1763,2091,2425)
     (1765,2094,2310)(1766,2095,2430)(1769,2097,2433)(1770,2098,2435)(1773,
     2100,2437)(1776,2102,2365)(1781,2108,2445)(1784,2113,2451)(1786,2116,
     2455)(1787,2117,2457)(1789,1859,2195)(1790,2120,2460)(1791,2121,2462)
     (1797,2126,2466)(1798,2127,2468)(1800,2129,2471)(1802,2131,2166)(1805,
     1956,2013)(1806,2133,2475)(1807,2134,2477)(1810,2136,2480)(1811,2137,
     2482)(1813,2138,2484)(1815,2140,1959)(1816,2141,2488)(1819,2144,2490)
     (1822,2148,2494)(1824,2150,2497)(1827,2154,2500)(1833,2163,2509)(1837,
     2170,2516)(1839,2171,2518)(1842,2173,2521)(1844,2176,2525)(1846,2179,
     2529)(1848,2182,2533)(1850,2185,2536)(1853,2189,2541)(1855,2192,2545)
     (1856,2193,2547)(1860,2196,2550)(1865,2202,2556)(1867,2204,2559)(1871,
     2209,2563)(1873,2212,2567)(1874,2213,2524)(1877,2215,2571)(1878,2216,
     2573)(1881,2220,2577)(1883,2223,2580)(1884,2224,2581)(1887,2226,2583)
     (1888,2227,2584)(1890,2109,2446)(1892,2230,2587)(1896,2235,2592)(1899,
     2236,2594)(1900,1997,2331)(1902,2237,2595)(1907,2242,2598)(1909,2244,
     2601)(1911,2246,2604)(1912,2247,2606)(1914,2249,2609)(1917,2033,2361)
     (1921,2256,2614)(1925,2262,2621)(1927,2264,2624)(1930,2268,2627)(1933,
     2272,2632)(1943,2285,2643)(1944,2286,2644)(1946,2289,2646)(1949,2290,
     2647)(1950,2291,2106)(1951,2292,1952)(1955,2294,2651)(1960,2296,2654)
     (1962,2298,2657)(1963,2299,2659)(1965,2301,2662)(1967,2303,2665)(1968,
     2304,2666)(1971,2306,2669)(1972,2307,2671)(1974,2309,2674)(1976,2311,
     2328)(1977,2312,2677)(1980,2316,2680)(1983,2319,2683)(1985,2321,2686)
     (1988,2325,2689)(1990,2314,2679)(1992,2327,2691)(2002,2335,2695)(2003,
     2336,2697)(2006,2338,2700)(2007,2339,2030)(2009,2341,2704)(2011,2343,
     2431)(2012,2344,2461)(2017,2349,2711)(2020,2351,2274)(2021,2273,2576)
     (2023,2353,2714)(2025,2355,2251)(2028,2357,2718)(2031,2359,2721)(2035,
     2364,2725)(2037,2366,2727)(2040,2370,2730)(2045,2375,2736)(2047,2378,
     2740)(2048,2379,2741)(2050,2381,2744)(2053,2384,2746)(2055,2329,2675)
     (2057,2387,2748)(2060,2391,2483)(2066,2398,2758)(2067,2399,2759)(2076,
     2410,2769)(2078,2413,2773)(2079,2414,2775)(2083,2417,2778)(2086,2420,
     2780)(2089,2422,2783)(2092,2426,2786)(2099,2385,2554)(2103,2440,2797)
     (2104,2441,2799)(2111,2448,2806)(2114,2452,2809)(2118,2458,2814)(2122,
     2463,2819)(2123,2183,2534)(2128,2469,2824)(2130,2472,2582)(2139,2485,
     2839)(2142,2489,2597)(2145,2491,2845)(2146,2492,2847)(2149,2495,2849)
     (2151,2498,2852)(2152,2499,2854)(2155,2501,2857)(2156,2502,2859)(2158,
     2504,2862)(2160,2505,2863)(2162,2507,2408)(2164,2510,2867)(2168,2513,
     2871)(2174,2522,2877)(2177,2526,2881)(2180,2530,2436)(2186,2537,2889)
     (2187,2538,2890)(2190,2542,2892)(2197,2551,2901)(2198,2552,2903)(2203,
     2557,2908)(2205,2401,2761)(2206,2560,2911)(2210,2564,2913)(2217,2574,
     2923)(2218,2575,2924)(2221,2578,2415)(2228,2585,2447)(2229,2586,2931)
     (2231,2588,2934)(2232,2589,2936)(2239,2382,2745)(2240,2596,2682)(2243,
     2599,2944)(2245,2602,2948)(2248,2607,2953)(2250,2610,2957)(2252,2611,
     2943)(2253,2612,2959)(2254,2613,2961)(2257,2615,2964)(2258,2616,2966)
     (2260,2618,2968)(2263,2622,2973)(2265,2625,2977)(2266,2626,2979)(2269,
     2628,2694)(2270,2629,2982)(2276,2633,2986)(2278,2635,2989)(2280,2637,
     2992)(2281,2638,2994)(2283,2640,2996)(2287,2645,3001)(2297,2655,2656)
     (2300,2660,3015)(2302,2663,3019)(2308,2672,3027)(2313,2678,3032)(2317,
     2681,3034)(2320,2684,3037)(2322,2687,3041)(2323,2688,2826)(2326,2690,
     3045)(2330,2692,2940)(2332,2693,2515)(2333,2514,2872)(2340,2702,3054)
     (2342,2705,3058)(2345,2707,3061)(2346,2708,3063)(2352,2712,3067)(2354,
     2715,2906)(2356,2717,2927)(2358,2719,3074)(2360,2722,3076)(2362,2724,
     3079)(2367,2728,3082)(2368,2729,3084)(2371,2731,3087)(2372,2732,3089)
     (2373,2733,3091)(2376,2737,3094)(2380,2742,3099)(2386,2428,2788)(2388,
     2749,3106)(2389,2750,3108)(2392,2751,3110)(2394,2753,3113)(2396,2755,
     3116)(2397,2756,3117)(2400,2760,3120)(2403,2716,3070)(2404,2763,3124)
     (2406,2765,3127)(2411,2770,3132)(2416,2776,3137)(2418,2779,3141)(2421,
     2781,3143)(2423,2784,3146)(2424,2785,3148)(2427,2787,3151)(2429,2789,
     3152)(2432,2790,3154)(2434,2792,3157)(2438,2794,3160)(2439,2795,2726)
     (2442,2800,3166)(2443,2801,3168)(2444,2802,3170)(2449,2807,3175)(2450,
     2808,3177)(2453,2810,2543)(2454,2811,3180)(2456,2813,2493)(2459,2815,
     3185)(2464,2820,3190)(2465,2821,3192)(2467,2823,3195)(2470,2825,3097)
     (2473,2827,3197)(2474,2828,3199)(2476,2830,3202)(2478,2832,3205)(2479,
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