D₆₂₄₇⋊C₃ #49154136

order	37482
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	D₆₂₄₇⋊C₃
unambiguous semidirect product	(C₆₂₄₇⋊C₃)⋊C₂

Splittings

Fitting, socle, derived, Sylow	C₆₂₄₇ ⋊ C₂×C₃
Hall	C₆₂₄₇⋊C₃ ⋊ C₂
Hall	D₆₂₄₇ ⋊ C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₂₄₇	C₂×C₃
LCS	G ▷ C₆₂₄₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 6247
transitive degree	μ_t(G) = 6247

A minimal faithful permutation representation — 2 generators on 6247 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,269)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,234,235,189,190,209)(156,241,242,196,197,204)(161,248,246,201,202,199)(165,253,239,206,207,193)(168,258,232,210,211,186)(179,274,275,224,225,328)(181,272,273,227,223,266)(184,217,271,229,230,267)(191,287,288,236,237,262)(198,294,295,243,244,257)(203,301,302,249,250,252)(208,307,299,254,255,247)(212,312,292,259,260,240)(215,317,285,263,264,233)(226,333,334,277,278,393)(228,331,332,280,276,325)(231,270,330,282,283,326)(238,346,347,289,290,321)(245,353,354,296,297,316)(251,360,361,303,304,311)(256,367,365,308,309,306)(261,372,358,313,314,300)(265,377,351,318,319,293)(268,382,344,322,323,286)(279,398,399,336,337,464)(281,396,397,339,335,390)(284,329,395,341,342,391)(291,411,412,348,349,386)(298,418,419,355,356,381)(305,425,426,362,363,376)(310,432,433,368,369,371)(315,438,430,373,374,366)(320,443,423,378,379,359)(324,448,416,383,384,352)(327,453,409,387,388,345)(338,469,470,401,402,541)(340,467,468,404,400,461)(343,394,466,406,407,462)(350,482,483,413,414,457)(357,489,490,420,421,452)(364,496,497,427,428,447)(370,503,504,434,435,442)(375,510,508,439,440,437)(380,515,501,444,445,431)(385,520,494,449,450,424)(389,525,487,454,455,417)(392,530,480,458,459,410)(403,546,547,472,473,624)(405,544,545,475,471,538)(408,465,543,477,478,539)(415,559,560,484,485,534)(422,566,567,491,492,529)(429,573,574,498,499,524)(436,580,581,505,506,519)(441,587,588,511,512,514)(446,593,585,516,517,509)(451,598,578,521,522,502)(456,603,571,526,527,495)(460,608,564,531,532,488)(463,613,557,535,536,481)(474,629,630,549,550,713)(476,627,628,552,548,621)(479,542,626,554,555,622)(486,642,643,561,562,617)(493,649,650,568,569,612)(500,656,657,575,576,607)(507,663,664,582,583,602)(513,670,671,589,590,597)(518,677,675,594,595,592)(523,682,668,599,600,586)(528,687,661,604,605,579)(533,692,654,609,610,572)(537,697,647,614,615,565)(540,702,640,618,619,558)(551,718,719,632,633,808)(553,716,717,635,631,710)(556,625,715,637,638,711)(563,731,732,644,645,706)(570,738,739,651,652,701)(577,745,746,658,659,696)(584,752,753,665,666,691)(591,759,760,672,673,686)(596,766,767,678,679,681)(601,772,764,683,684,676)(606,777,757,688,689,669)(611,782,750,693,694,662)(616,787,743,698,699,655)(620,792,736,703,704,648)(623,797,729,707,708,641)(634,813,814,721,722,909)(636,811,812,724,720,805)(639,714,810,726,727,806)(646,826,827,733,734,801)(653,833,834,740,741,796)(660,840,841,747,748,791)(667,847,848,754,755,786)(674,854,855,761,762,781)(680,861,862,768,769,776)(685,868,866,773,774,771)(690,873,859,778,779,765)(695,878,852,783,784,758)(700,883,845,788,789,751)(705,888,838,793,794,744)(709,893,831,798,799,737)(712,898,824,802,803,730)(723,914,915,816,817,1016)(725,912,913,819,815,906)(728,809,911,821,822,907)(735,927,928,828,829,902)(742,934,935,835,836,897)(749,941,942,842,843,892)(756,948,949,849,850,887)(763,955,956,856,857,882)(770,962,963,863,864,877)(775,969,970,869,870,872)(780,975,967,874,875,867)(785,980,960,879,880,860)(790,985,953,884,885,853)(795,990,946,889,890,846)(800,995,939,894,895,839)(804,1000,932,899,900,832)(807,1005,925,903,904,825)(818,1021,1022,917,918,1129)(820,1019,1020,920,916,1013)(823,910,1018,922,923,1014)(830,1034,1035,929,930,1009)(837,1041,1042,936,937,1004)(844,1048,1049,943,944,999)(851,1055,1056,950,951,994)(858,1062,1063,957,958,989)(865,1069,1070,964,965,984)(871,1076,1077,971,972,979)(876,1083,1081,976,977,974)(881,1088,1074,981,982,968)(886,1093,1067,986,987,961)(891,1098,1060,991,992,954)(896,1103,1053,996,997,947)(901,1108,1046,1001,1002,940)(905,1113,1039,1006,1007,933)(908,1118,1032,1010,1011,926)(919,1134,1135,1024,1025,1248)(921,1132,1133,1027,1023,1126)(924,1017,1131,1029,1030,1127)(931,1147,1148,1036,1037,1122)(938,1154,1155,1043,1044,1117)(945,1161,1162,1050,1051,1112)(952,1168,1169,1057,1058,1107)(959,1175,1176,1064,1065,1102)(966,1182,1183,1071,1072,1097)(973,1189,1190,1078,1079,1092)(978,1196,1197,1084,1085,1087)(983,1202,1194,1089,1090,1082)(988,1207,1187,1094,1095,1075)(993,1212,1180,1099,1100,1068)(998,1217,1173,1104,1105,1061)(1003,1222,1166,1109,1110,1054)(1008,1227,1159,1114,1115,1047)(1012,1232,1152,1119,1120,1040)(1015,1237,1145,1123,1124,1033)(1026,1253,1254,1137,1138,1373)(1028,1251,1252,1140,1136,1245)(1031,1130,1250,1142,1143,1246)(1038,1266,1267,1149,1150,1241)(1045,1273,1274,1156,1157,1236)(1052,1280,1281,1163,1164,1231)(1059,1287,1288,1170,1171,1226)(1066,1294,1295,1177,1178,1221)(1073,1301,1302,1184,1185,1216)(1080,1308,1309,1191,1192,1211)(1086,1315,1316,1198,1199,1206)(1091,1322,1320,1203,1204,1201)(1096,1327,1313,1208,1209,1195)(1101,1332,1306,1213,1214,1188)(1106,1337,1299,1218,1219,1181)(1111,1342,1292,1223,1224,1174)(1116,1347,1285,1228,1229,1167)(1121,1352,1278,1233,1234,1160)(1125,1357,1271,1238,1239,1153)(1128,1362,1264,1242,1243,1146)(1139,1378,1379,1256,1257,1504)(1141,1376,1377,1259,1255,1370)(1144,1249,1375,1261,1262,1371)(1151,1391,1392,1268,1269,1366)(1158,1398,1399,1275,1276,1361)(1165,1405,1406,1282,1283,1356)(1172,1412,1413,1289,1290,1351)(1179,1419,1420,1296,1297,1346)(1186,1426,1427,1303,1304,1341)(1193,1433,1434,1310,1311,1336)(1200,1440,1441,1317,1318,1331)(1205,1447,1448,1323,1324,1326)(1210,1453,1445,1328,1329,1321)(1215,1458,1438,1333,1334,1314)(1220,1463,1431,1338,1339,1307)(1225,1468,1424,1343,1344,1300)(1230,1473,1417,1348,1349,1293)(1235,1478,1410,1353,1354,1286)(1240,1483,1403,1358,1359,1279)(1244,1488,1396,1363,1364,1272)(1247,1493,1389,1367,1368,1265)(1258,1509,1510,1381,1382,1641)(1260,1507,1508,1384,1380,1501)(1263,1374,1506,1386,1387,1502)(1270,1522,1523,1393,1394,1497)(1277,1529,1530,1400,1401,1492)(1284,1536,1537,1407,1408,1487)(1291,1543,1544,1414,1415,1482)(1298,1550,1551,1421,1422,1477)(1305,1557,1558,1428,1429,1472)(1312,1564,1565,1435,1436,1467)(1319,1571,1572,1442,1443,1462)(1325,1578,1579,1449,1450,1457)(1330,1585,1583,1454,1455,1452)(1335,1590,1576,1459,1460,1446)(1340,1595,1569,1464,1465,1439)(1345,1600,1562,1469,1470,1432)(1350,1605,1555,1474,1475,1425)(1355,1610,1548,1479,1480,1418)(1360,1615,1541,1484,1485,1411)(1365,1620,1534,1489,1490,1404)(1369,1625,1527,1494,1495,1397)(1372,1630,1520,1498,1499,1390)(1383,1646,1647,1512,1513,1784)(1385,1644,1645,1515,1511,1638)(1388,1505,1643,1517,1518,1639)(1395,1659,1660,1524,1525,1634)(1402,1666,1667,1531,1532,1629)(1409,1673,1674,1538,1539,1624)(1416,1680,1681,1545,1546,1619)(1423,1687,1688,1552,1553,1614)(1430,1694,1695,1559,1560,1609)(1437,1701,1702,1566,1567,1604)(1444,1708,1709,1573,1574,1599)(1451,1715,1716,1580,1581,1594)(1456,1722,1723,1586,1587,1589)(1461,1728,1720,1591,1592,1584)(1466,1733,1713,1596,1597,1577)(1471,1738,1706,1601,1602,1570)(1476,1743,1699,1606,1607,1563)(1481,1748,1692,1611,1612,1556)(1486,1753,1685,1616,1617,1549)(1491,1758,1678,1621,1622,1542)(1496,1763,1671,1626,1627,1535)(1500,1768,1664,1631,1632,1528)(1503,1773,1657,1635,1636,1521)(1514,1789,1790,1649,1650,1933)(1516,1787,1788,1652,1648,1781)(1519,1642,1786,1654,1655,1782)(1526,1802,1803,1661,1662,1777)(1533,1809,1810,1668,1669,1772)(1540,1816,1817,1675,1676,1767)(1547,1823,1824,1682,1683,1762)(1554,1830,1831,1689,1690,1757)(1561,1837,1838,1696,1697,1752)(1568,1844,1845,1703,1704,1747)(1575,1851,1852,1710,1711,1742)(1582,1858,1859,1717,1718,1737)(1588,1865,1866,1724,1725,1732)(1593,1872,1870,1729,1730,1727)(1598,1877,1863,1734,1735,1721)(1603,1882,1856,1739,1740,1714)(1608,1887,1849,1744,1745,1707)(1613,1892,1842,1749,1750,1700)(1618,1897,1835,1754,1755,1693)(1623,1902,1828,1759,1760,1686)(1628,1907,1821,1764,1765,1679)(1633,1912,1814,1769,1770,1672)(1637,1917,1807,1774,1775,1665)(1640,1922,1800,1778,1779,1658)(1651,1938,1939,1792,1793,2088)(1653,1936,1937,1795,1791,1930)(1656,1785,1935,1797,1798,1931)(1663,1951,1952,1804,1805,1926)(1670,1958,1959,1811,1812,1921)(1677,1965,1966,1818,1819,1916)(1684,1972,1973,1825,1826,1911)(1691,1979,1980,1832,1833,1906)(1698,1986,1987,1839,1840,1901)(1705,1993,1994,1846,1847,1896)(1712,2000,2001,1853,1854,1891)(1719,2007,2008,1860,1861,1886)(1726,2014,2015,1867,1868,1881)(1731,2021,2022,1873,1874,1876)(1736,2027,2019,1878,1879,1871)(1741,2032,2012,1883,1884,1864)(1746,2037,2005,1888,1889,1857)(1751,2042,1998,1893,1894,1850)(1756,2047,1991,1898,1899,1843)(1761,2052,1984,1903,1904,1836)(1766,2057,1977,1908,1909,1829)(1771,2062,1970,1913,1914,1822)(1776,2067,1963,1918,1919,1815)(1780,2072,1956,1923,1924,1808)(1783,2077,1949,1927,1928,1801)(1794,2093,2094,1941,1942,2249)(1796,2091,2092,1944,1940,2085)(1799,1934,2090,1946,1947,2086)(1806,2106,2107,1953,1954,2081)(1813,2113,2114,1960,1961,2076)(1820,2120,2121,1967,1968,2071)(1827,2127,2128,1974,1975,2066)(1834,2134,2135,1981,1982,2061)(1841,2141,2142,1988,1989,2056)(1848,2148,2149,1995,1996,2051)(1855,2155,2156,2002,2003,2046)(1862,2162,2163,2009,2010,2041)(1869,2169,2170,2016,2017,2036)(1875,2176,2177,2023,2024,2031)(1880,2183,2181,2028,2029,2026)(1885,2188,2174,2033,2034,2020)(1890,2193,2167,2038,2039,2013)(1895,2198,2160,2043,2044,2006)(1900,2203,2153,2048,2049,1999)(1905,2208,2146,2053,2054,1992)(1910,2213,2139,2058,2059,1985)(1915,2218,2132,2063,2064,1978)(1920,2223,2125,2068,2069,1971)(1925,2228,2118,2073,2074,1964)(1929,2233,2111,2078,2079,1957)(1932,2238,2104,2082,2083,1950)(1943,2254,2255,2096,2097,2416)(1945,2252,2253,2099,2095,2246)(1948,2089,2251,2101,2102,2247)(1955,2267,2268,2108,2109,2242)(1962,2274,2275,2115,2116,2237)(1969,2281,2282,2122,2123,2232)(1976,2288,2289,2129,2130,2227)(1983,2295,2296,2136,2137,2222)(1990,2302,2303,2143,2144,2217)(1997,2309,2310,2150,2151,2212)(2004,2316,2317,2157,2158,2207)(2011,2323,2324,2164,2165,2202)(2018,2330,2331,2171,2172,2197)(2025,2337,2338,2178,2179,2192)(2030,2344,2345,2184,2185,2187)(2035,2350,2342,2189,2190,2182)(2040,2355,2335,2194,2195,2175)(2045,2360,2328,2199,2200,2168)(2050,2365,2321,2204,2205,2161)(2055,2370,2314,2209,2210,2154)(2060,2375,2307,2214,2215,2147)(2065,2380,2300,2219,2220,2140)(2070,2385,2293,2224,2225,2133)(2075,2390,2286,2229,2230,2126)(2080,2395,2279,2234,2235,2119)(2084,2400,2272,2239,2240,2112)(2087,2405,2265,2243,2244,2105)(2098,2421,2422,2257,2258,2589)(2100,2419,2420,2260,2256,2413)(2103,2250,2418,2262,2263,2414)(2110,2434,2435,2269,2270,2409)(2117,2441,2442,2276,2277,2404)(2124,2448,2449,2283,2284,2399)(2131,2455,2456,2290,2291,2394)(2138,2462,2463,2297,2298,2389)(2145,2469,2470,2304,2305,2384)(2152,2476,2477,2311,2312,2379)(2159,2483,2484,2318,2319,2374)(2166,2490,2491,2325,2326,2369)(2173,2497,2498,2332,2333,2364)(2180,2504,2505,2339,2340,2359)(2186,2511,2512,2346,2347,2354)(2191,2518,2516,2351,2352,2349)(2196,2523,2509,2356,2357,2343)(2201,2528,2502,2361,2362,2336)(2206,2533,2495,2366,2367,2329)(2211,2538,2488,2371,2372,2322)(2216,2543,2481,2376,2377,2315)(2221,2548,2474,2381,2382,2308)(2226,2553,2467,2386,2387,2301)(2231,2558,2460,2391,2392,2294)(2236,2563,2453,2396,2397,2287)(2241,2568,2446,2401,2402,2280)(2245,2573,2439,2406,2407,2273)(2248,2578,2432,2410,2411,2266)(2259,2594,2595,2424,2425,2768)(2261,2592,2593,2427,2423,2586)(2264,2417,2591,2429,2430,2587)(2271,2607,2608,2436,2437,2582)(2278,2614,2615,2443,2444,2577)(2285,2621,2622,2450,2451,2572)(2292,2628,2629,2457,2458,2567)(2299,2635,2636,2464,2465,2562)(2306,2642,2643,2471,2472,2557)(2313,2649,2650,2478,2479,2552)(2320,2656,2657,2485,2486,2547)(2327,2663,2664,2492,2493,2542)(2334,2670,2671,2499,2500,2537)(2341,2677,2678,2506,2507,2532)(2348,2684,2685,2513,2514,2527)(2353,2691,2692,2519,2520,2522)(2358,2697,2689,2524,2525,2517)(2363,2702,2682,2529,2530,2510)(2368,2707,2675,2534,2535,2503)(2373,2712,2668,2539,2540,2496)(2378,2717,2661,2544,2545,2489)(2383,2722,2654,2549,2550,2482)(2388,2727,2647,2554,2555,2475)(2393,2732,2640,2559,2560,2468)(2398,2737,2633,2564,2565,2461)(2403,2742,2626,2569,2570,2454)(2408,2747,2619,2574,2575,2447)(2412,2752,2612,2579,2580,2440)(2415,2757,2605,2583,2584,2433)(2426,2773,2774,2597,2598,2953)(2428,2771,2772,2600,2596,2765)(2431,2590,2770,2602,2603,2766)(2438,2786,2787,2609,2610,2761)(2445,2793,2794,2616,2617,2756)(2452,2800,2801,2623,2624,2751)(2459,2807,2808,2630,2631,2746)(2466,2814,2815,2637,2638,2741)(2473,2821,2822,2644,2645,2736)(2480,2828,2829,2651,2652,2731)(2487,2835,2836,2658,2659,2726)(2494,2842,2843,2665,2666,2721)(2501,2849,2850,2672,2673,2716)(2508,2856,2857,2679,2680,2711)(2515,2863,2864,2686,2687,2706)(2521,2870,2871,2693,2694,2701)(2526,2877,2875,2698,2699,2696)(2531,2882,2868,2703,2704,2690)(2536,2887,2861,2708,2709,2683)(2541,2892,2854,2713,2714,2676)(2546,2897,2847,2718,2719,2669)(2551,2902,2840,2723,2724,2662)(2556,2907,2833,2728,2729,2655)(2561,2912,2826,2733,2734,2648)(2566,2917,2819,2738,2739,2641)(2571,2922,2812,2743,2744,2634)(2576,2927,2805,2748,2749,2627)(2581,2932,2798,2753,2754,2620)(2585,2937,2791,2758,2759,2613)(2588,2942,2784,2762,2763,2606)(2599,2958,2959,2776,2777,3144)(2601,2956,2957,2779,2775,2950)(2604,2769,2955,2781,2782,2951)(2611,2971,2972,2788,2789,2946)(2618,2978,2979,2795,2796,2941)(2625,2985,2986,2802,2803,2936)(2632,2992,2993,2809,2810,2931)(2639,2999,3000,2816,2817,2926)(2646,3006,3007,2823,2824,2921)(2653,3013,3014,2830,2831,2916)(2660,3020,3021,2837,2838,2911)(2667,3027,3028,2844,2845,2906)(2674,3034,3035,2851,2852,2901)(2681,3041,3042,2858,2859,2896)(2688,3048,3049,2865,2866,2891)(2695,3055,3056,2872,2873,2886)(2700,3062,3063,2878,2879,2881)(2705,3068,3060,2883,2884,2876)(2710,3073,3053,2888,2889,2869)(2715,3078,3046,2893,2894,2862)(2720,3083,3039,2898,2899,2855)(2725,3088,3032,2903,2904,2848)(2730,3093,3025,2908,2909,2841)(2735,3098,3018,2913,2914,2834)(2740,3103,3011,2918,2919,2827)(2745,3108,3004,2923,2924,2820)(2750,3113,2997,2928,2929,2813)(2755,3118,2990,2933,2934,2806)(2760,3123,2983,2938,2939,2799)(2764,3128,2976,2943,2944,2792)(2767,3133,2969,2947,2948,2785)(2778,3149,3150,2961,2962,3341)(2780,3147,3148,2964,2960,3141)(2783,2954,3146,2966,2967,3142)(2790,3162,3163,2973,2974,3137)(2797,3169,3170,2980,2981,3132)(2804,3176,3177,2987,2988,3127)(2811,3183,3184,2994,2995,3122)(2818,3190,3191,3001,3002,3117)(2825,3197,3198,3008,3009,3112)(2832,3204,3205,3015,3016,3107)(2839,3211,3212,3022,3023,3102)(2846,3218,3219,3029,3030,3097)(2853,3225,3226,3036,3037,3092)(2860,3232,3233,3043,3044,3087)(2867,3239,3240,3050,3051,3082)(2874,3246,3247,3057,3058,3077)(2880,3253,3254,3064,3065,3072)(2885,3260,3258,3069,3070,3067)(2890,3265,3251,3074,3075,3061)(2895,3270,3244,3079,3080,3054)(2900,3275,3237,3084,3085,3047)(2905,3280,3230,3089,3090,3040)(2910,3285,3223,3094,3095,3033)(2915,3290,3216,3099,3100,3026)(2920,3295,3209,3104,3105,3019)(2925,3300,3202,3109,3110,3012)(2930,3305,3195,3114,3115,3005)(2935,3310,3188,3119,3120,2998)(2940,3315,3181,3124,3125,2991)(2945,3320,3174,3129,3130,2984)(2949,3325,3167,3134,3135,2977)(2952,3330,3160,3138,3139,2970)(2963,3346,3347,3152,3153,3544)(2965,3344,3345,3155,3151,3338)(2968,3145,3343,3157,3158,3339)(2975,3359,3360,3164,3165,3334)(2982,3366,3367,3171,3172,3329)(2989,3373,3374,3178,3179,3324)(2996,3380,3381,3185,3186,3319)(3003,3387,3388,3192,3193,3314)(3010,3394,3395,3199,3200,3309)(3017,3401,3402,3206,3207,3304)(3024,3408,3409,3213,3214,3299)(3031,3415,3416,3220,3221,3294)(3038,3422,3423,3227,3228,3289)(3045,3429,3430,3234,3235,3284)(3052,3436,3437,3241,3242,3279)(3059,3443,3444,3248,3249,3274)(3066,3450,3451,3255,3256,3269)(3071,3457,3458,3261,3262,3264)(3076,3463,3455,3266,3267,3259)(3081,3468,3448,3271,3272,3252)(3086,3473,3441,3276,3277,3245)(3091,3478,3434,3281,3282,3238)(3096,3483,3427,3286,3287,3231)(3101,3488,3420,3291,3292,3224)(3106,3493,3413,3296,3297,3217)(3111,3498,3406,3301,3302,3210)(3116,3503,3399,3306,3307,3203)(3121,3508,3392,3311,3312,3196)(3126,3513,3385,3316,3317,3189)(3131,3518,3378,3321,3322,3182)(3136,3523,3371,3326,3327,3175)(3140,3528,3364,3331,3332,3168)(3143,3533,3357,3335,3336,3161)(3154,3549,3550,3349,3350,3753)(3156,3547,3548,3352,3348,3541)(3159,3342,3546,3354,3355,3542)(3166,3562,3563,3361,3362,3537)(3173,3569,3570,3368,3369,3532)(3180,3576,3577,3375,3376,3527)(3187,3583,3584,3382,3383,3522)(3194,3590,3591,3389,3390,3517)(3201,3597,3598,3396,3397,3512)(3208,3604,3605,3403,3404,3507)(3215,3611,3612,3410,3411,3502)(3222,3618,3619,3417,3418,3497)(3229,3625,3626,3424,3425,3492)(3236,3632,3633,3431,3432,3487)(3243,3639,3640,3438,3439,3482)(3250,3646,3647,3445,3446,3477)(3257,3653,3654,3452,3453,3472)(3263,3660,3661,3459,3460,3467)(3268,3667,3665,3464,3465,3462)(3273,3672,3658,3469,3470,3456)(3278,3677,3651,3474,3475,3449)(3283,3682,3644,3479,3480,3442)(3288,3687,3637,3484,3485,3435)(3293,3692,3630,3489,3490,3428)(3298,3697,3623,3494,3495,3421)(3303,3702,3616,3499,3500,3414)(3308,3707,3609,3504,3505,3407)(3313,3712,3602,3509,3510,3400)(3318,3717,3595,3514,3515,3393)(3323,3722,3588,3519,3520,3386)(3328,3727,3581,3524,3525,3379)(3333,3732,3574,3529,3530,3372)(3337,3737,3567,3534,3535,3365)(3340,3742,3560,3538,3539,3358)(3351,3758,3759,3552,3553,3968)(3353,3756,3757,3555,3551,3750)(3356,3545,3755,3557,3558,3751)(3363,3771,3772,3564,3565,3746)(3370,3778,3779,3571,3572,3741)(3377,3785,3786,3578,3579,3736)(3384,3792,3793,3585,3586,3731)(3391,3799,3800,3592,3593,3726)(3398,3806,3807,3599,3600,3721)(3405,3813,3814,3606,3607,3716)(3412,3820,3821,3613,3614,3711)(3419,3827,3828,3620,3621,3706)(3426,3834,3835,3627,3628,3701)(3433,3841,3842,3634,3635,3696)(3440,3848,3849,3641,3642,3691)(3447,3855,3856,3648,3649,3686)(3454,3862,3863,3655,3656,3681)(3461,3869,3870,3662,3663,3676)(3466,3876,3877,3668,3669,3671)(3471,3882,3874,3673,3674,3666)(3476,3887,3867,3678,3679,3659)(3481,3892,3860,3683,3684,3652)(3486,3897,3853,3688,3689,3645)(3491,3902,3846,3693,3694,3638)(3496,3907,3839,3698,3699,3631)(3501,3912,3832,3703,3704,3624)(3506,3917,3825,3708,3709,3617)(3511,3922,3818,3713,3714,3610)(3516,3927,3811,3718,3719,3603)(3521,3932,3804,3723,3724,3596)(3526,3937,3797,3728,3729,3589)(3531,3942,3790,3733,3734,3582)(3536,3947,3783,3738,3739,3575)(3540,3952,3776,3743,3744,3568)(3543,3957,3769,3747,3748,3561)(3554,3973,3974,3761,3762,4189)(3556,3971,3972,3764,3760,3965)(3559,3754,3970,3766,3767,3966)(3566,3986,3987,3773,3774,3961)(3573,3993,3994,3780,3781,3956)(3580,4000,4001,3787,3788,3951)(3587,4007,4008,3794,3795,3946)(3594,4014,4015,3801,3802,3941)(3601,4021,4022,3808,3809,3936)(3608,4028,4029,3815,3816,3931)(3615,4035,4036,3822,3823,3926)(3622,4042,4043,3829,3830,3921)(3629,4049,4050,3836,3837,3916)(3636,4056,4057,3843,3844,3911)(3643,4063,4064,3850,3851,3906)(3650,4070,4071,3857,3858,3901)(3657,4077,4078,3864,3865,3896)(3664,4084,4085,3871,3872,3891)(3670,4091,4092,3878,3879,3886)(3675,4098,4096,3883,3884,3881)(3680,4103,4089,3888,3889,3875)(3685,4108,4082,3893,3894,3868)(3690,4113,4075,3898,3899,3861)(3695,4118,4068,3903,3904,3854)(3700,4123,4061,3908,3909,3847)(3705,4128,4054,3913,3914,3840)(3710,4133,4047,3918,3919,3833)(3715,4138,4040,3923,3924,3826)(3720,4143,4033,3928,3929,3819)(3725,4148,4026,3933,3934,3812)(3730,4153,4019,3938,3939,3805)(3735,4158,4012,3943,3944,3798)(3740,4163,4005,3948,3949,3791)(3745,4168,3998,3953,3954,3784)(3749,4173,3991,3958,3959,3777)(3752,4178,3984,3962,3963,3770)(3763,4194,4195,3976,3977,4416)(3765,4192,4193,3979,3975,4186)(3768,3969,4191,3981,3982,4187)(3775,4207,4208,3988,3989,4182)(3782,4214,4215,3995,3996,4177)(3789,4221,4222,4002,4003,4172)(3796,4228,4229,4009,4010,4167)(3803,4235,4236,4016,4017,4162)(3810,4242,4243,4023,4024,4157)(3817,4249,4250,4030,4031,4152)(3824,4256,4257,4037,4038,4147)(3831,4263,4264,4044,4045,4142)(3838,4270,4271,4051,4052,4137)(3845,4277,4278,4058,4059,4132)(3852,4284,4285,4065,4066,4127)(3859,4291,4292,4072,4073,4122)(3866,4298,4299,4079,4080,4117)(3873,4305,4306,4086,4087,4112)(3880,4312,4313,4093,4094,4107)(3885,4319,4320,4099,4100,4102)(3890,4325,4317,4104,4105,4097)(3895,4330,4310,4109,4110,4090)(3900,4335,4303,4114,4115,4083)(3905,4340,4296,4119,4120,4076)(3910,4345,4289,4124,4125,4069)(3915,4350,4282,4129,4130,4062)(3920,4355,4275,4134,4135,4055)(3925,4360,4268,4139,4140,4048)(3930,4365,4261,4144,4145,4041)(3935,4370,4254,4149,4150,4034)(3940,4375,4247,4154,4155,4027)(3945,4380,4240,4159,4160,4020)(3950,4385,4233,4164,4165,4013)(3955,4390,4226,4169,4170,4006)(3960,4395,4219,4174,4175,3999)(3964,4400,4212,4179,4180,3992)(3967,4405,4205,4183,4184,3985)(3978,4421,4422,4197,4198,4649)(3980,4419,4420,4200,4196,4413)(3983,4190,4418,4202,4203,4414)(3990,4434,4435,4209,4210,4409)(3997,4441,4442,4216,4217,4404)(4004,4448,4449,4223,4224,4399)(4011,4455,4456,4230,4231,4394)(4018,4462,4463,4237,4238,4389)(4025,4469,4470,4244,4245,4384)(4032,4476,4477,4251,4252,4379)(4039,4483,4484,4258,4259,4374)(4046,4490,4491,4265,4266,4369)(4053,4497,4498,4272,4273,4364)(4060,4504,4505,4279,4280,4359)(4067,4511,4512,4286,4287,4354)(4074,4518,4519,4293,4294,4349)(4081,4525,4526,4300,4301,4344)(4088,4532,4533,4307,4308,4339)(4095,4539,4540,4314,4315,4334)(4101,4546,4547,4321,4322,4329)(4106,4553,4551,4326,4327,4324)(4111,4558,4544,4331,4332,4318)(4116,4563,4537,4336,4337,4311)(4121,4568,4530,4341,4342,4304)(4126,4573,4523,4346,4347,4297)(4131,4578,4516,4351,4352,4290)(4136,4583,4509,4356,4357,4283)(4141,4588,4502,4361,4362,4276)(4146,4593,4495,4366,4367,4269)(4151,4598,4488,4371,4372,4262)(4156,4603,4481,4376,4377,4255)(4161,4608,4474,4381,4382,4248)(4166,4613,4467,4386,4387,4241)(4171,4618,4460,4391,4392,4234)(4176,4623,4453,4396,4397,4227)(4181,4628,4446,4401,4402,4220)(4185,4633,4439,4406,4407,4213)(4188,4638,4432,4410,4411,4206)(4199,4654,4655,4424,4425,4888)(4201,4652,4653,4427,4423,4646)(4204,4417,4651,4429,4430,4647)(4211,4667,4668,4436,4437,4642)(4218,4674,4675,4443,4444,4637)(4225,4681,4682,4450,4451,4632)(4232,4688,4689,4457,4458,4627)(4239,4695,4696,4464,4465,4622)(4246,4702,4703,4471,4472,4617)(4253,4709,4710,4478,4479,4612)(4260,4716,4717,4485,4486,4607)(4267,4723,4724,4492,4493,4602)(4274,4730,4731,4499,4500,4597)(4281,4737,4738,4506,4507,4592)(4288,4744,4745,4513,4514,4587)(4295,4751,4752,4520,4521,4582)(4302,4758,4759,4527,4528,4577)(4309,4765,4766,4534,4535,4572)(4316,4772,4773,4541,4542,4567)(4323,4779,4780,4548,4549,4562)(4328,4786,4787,4554,4555,4557)(4333,4792,4784,4559,4560,4552)(4338,4797,4777,4564,4565,4545)(4343,4802,4770,4569,4570,4538)(4348,4807,4763,4574,4575,4531)(4353,4812,4756,4579,4580,4524)(4358,4817,4749,4584,4585,4517)(4363,4822,4742,4589,4590,4510)(4368,4827,4735,4594,4595,4503)(4373,4832,4728,4599,4600,4496)(4378,4837,4721,4604,4605,4489)(4383,4842,4714,4609,4610,4482)(4388,4847,4707,4614,4615,4475)(4393,4852,4700,4619,4620,4468)(4398,4857,4693,4624,4625,4461)(4403,4862,4686,4629,4630,4454)(4408,4867,4679,4634,4635,4447)(4412,4872,4672,4639,4640,4440)(4415,4877,4665,4643,4644,4433)(4426,4893,4894,4657,4658,5133)(4428,4891,4892,4660,4656,4885)(4431,4650,4890,4662,4663,4886)(4438,4906,4907,4669,4670,4881)(4445,4913,4914,4676,4677,4876)(4452,4920,4921,4683,4684,4871)(4459,4927,4928,4690,4691,4866)(4466,4934,4935,4697,4698,4861)(4473,4941,4942,4704,4705,4856)(4480,4948,4949,4711,4712,4851)(4487,4955,4956,4718,4719,4846)(4494,4962,4963,4725,4726,4841)(4501,4969,4970,4732,4733,4836)(4508,4976,4977,4739,4740,4831)(4515,4983,4984,4746,4747,4826)(4522,4990,4991,4753,4754,4821)(4529,4997,4998,4760,4761,4816)(4536,5004,5005,4767,4768,4811)(4543,5011,5012,4774,4775,4806)(4550,5018,5019,4781,4782,4801)(4556,5025,5026,4788,4789,4796)(4561,5032,5030,4793,4794,4791)(4566,5037,5023,4798,4799,4785)(4571,5042,5016,4803,4804,4778)(4576,5047,5009,4808,4809,4771)(4581,5052,5002,4813,4814,4764)(4586,5057,4995,4818,4819,4757)(4591,5062,4988,4823,4824,4750)(4596,5067,4981,4828,4829,4743)(4601,5072,4974,4833,4834,4736)(4606,5077,4967,4838,4839,4729)(4611,5082,4960,4843,4844,4722)(4616,5087,4953,4848,4849,4715)(4621,5092,4946,4853,4854,4708)(4626,5097,4939,4858,4859,4701)(4631,5102,4932,4863,4864,4694)(4636,5107,4925,4868,4869,4687)(4641,5112,4918,4873,4874,4680)(4645,5117,4911,4878,4879,4673)(4648,5122,4904,4882,4883,4666)(4659,5138,5139,4896,4897,5384)(4661,5136,5137,4899,4895,5130)(4664,4889,5135,4901,4902,5131)(4671,5151,5152,4908,4909,5126)(4678,5158,5159,4915,4916,5121)(4685,5165,5166,4922,4923,5116)(4692,5172,5173,4929,4930,5111)(4699,5179,5180,4936,4937,5106)(4706,5186,5187,4943,4944,5101)(4713,5193,5194,4950,4951,5096)(4720,5200,5201,4957,4958,5091)(4727,5207,5208,4964,4965,5086)(4734,5214,5215,4971,4972,5081)(4741,5221,5222,4978,4979,5076)(4748,5228,5229,4985,4986,5071)(4755,5235,5236,4992,4993,5066)(4762,5242,5243,4999,5000,5061)(4769,5249,5250,5006,5007,5056)(4776,5256,5257,5013,5014,5051)(4783,5263,5264,5020,5021,5046)(4790,5270,5271,5027,5028,5041)(4795,5277,5278,5033,5034,5036)(4800,5283,5275,5038,5039,5031)(4805,5288,5268,5043,5044,5024)(4810,5293,5261,5048,5049,5017)(4815,5298,5254,5053,5054,5010)(4820,5303,5247,5058,5059,5003)(4825,5308,5240,5063,5064,4996)(4830,5313,5233,5068,5069,4989)(4835,5318,5226,5073,5074,4982)(4840,5323,5219,5078,5079,4975)(4845,5328,5212,5083,5084,4968)(4850,5333,5205,5088,5089,4961)(4855,5338,5198,5093,5094,4954)(4860,5343,5191,5098,5099,4947)(4865,5348,5184,5103,5104,4940)(4870,5353,5177,5108,5109,4933)(4875,5358,5170,5113,5114,4926)(4880,5363,5163,5118,5119,4919)(4884,5368,5156,5123,5124,4912)(4887,5373,5149,5127,5128,4905)(4898,5389,5390,5141,5142,5641)(4900,5387,5388,5144,5140,5381)(4903,5134,5386,5146,5147,5382)(4910,5402,5403,5153,5154,5377)(4917,5409,5410,5160,5161,5372)(4924,5416,5417,5167,5168,5367)(4931,5423,5424,5174,5175,5362)(4938,5430,5431,5181,5182,5357)(4945,5437,5438,5188,5189,5352)(4952,5444,5445,5195,5196,5347)(4959,5451,5452,5202,5203,5342)(4966,5458,5459,5209,5210,5337)(4973,5465,5466,5216,5217,5332)(4980,5472,5473,5223,5224,5327)(4987,5479,5480,5230,5231,5322)(4994,5486,5487,5237,5238,5317)(5001,5493,5494,5244,5245,5312)(5008,5500,5501,5251,5252,5307)(5015,5507,5508,5258,5259,5302)(5022,5514,5515,5265,5266,5297)(5029,5521,5522,5272,5273,5292)(5035,5528,5529,5279,5280,5287)(5040,5535,5533,5284,5285,5282)(5045,5540,5526,5289,5290,5276)(5050,5545,5519,5294,5295,5269)(5055,5550,5512,5299,5300,5262)(5060,5555,5505,5304,5305,5255)(5065,5560,5498,5309,5310,5248)(5070,5565,5491,5314,5315,5241)(5075,5570,5484,5319,5320,5234)(5080,5575,5477,5324,5325,5227)(5085,5580,5470,5329,5330,5220)(5090,5585,5463,5334,5335,5213)(5095,5590,5456,5339,5340,5206)(5100,5595,5449,5344,5345,5199)(5105,5600,5442,5349,5350,5192)(5110,5605,5435,5354,5355,5185)(5115,5610,5428,5359,5360,5178)(5120,5615,5421,5364,5365,5171)(5125,5620,5414,5369,5370,5164)(5129,5625,5407,5374,5375,5157)(5132,5630,5400,5378,5379,5150)(5143,5646,5647,5392,5393,5874)(5145,5644,5645,5395,5391,5638)(5148,5385,5643,5397,5398,5639)(5155,5657,5658,5404,5405,5634)(5162,5664,5665,5411,5412,5629)(5169,5671,5672,5418,5419,5624)(5176,5678,5679,5425,5426,5619)(5183,5685,5686,5432,5433,5614)(5190,5692,5693,5439,5440,5609)(5197,5699,5700,5446,5447,5604)(5204,5706,5707,5453,5454,5599)(5211,5713,5714,5460,5461,5594)(5218,5720,5721,5467,5468,5589)(5225,5727,5728,5474,5475,5584)(5232,5734,5735,5481,5482,5579)(5239,5741,5742,5488,5489,5574)(5246,5746,5747,5495,5496,5569)(5253,5751,5752,5502,5503,5564)(5260,5756,5757,5509,5510,5559)(5267,5761,5762,5516,5517,5554)(5274,5766,5767,5523,5524,5549)(5281,5771,5772,5530,5531,5544)(5286,5776,5777,5536,5537,5539)(5291,5780,5774,5541,5542,5534)(5296,5783,5769,5546,5547,5527)(5301,5786,5764,5551,5552,5520)(5306,5789,5759,5556,5557,5513)(5311,5792,5754,5561,5562,5506)(5316,5795,5749,5566,5567,5499)(5321,5798,5744,5571,5572,5492)(5326,5803,5739,5576,5577,5485)(5331,5808,5732,5581,5582,5478)(5336,5813,5725,5586,5587,5471)(5341,5818,5718,5591,5592,5464)(5346,5823,5711,5596,5597,5457)(5351,5828,5704,5601,5602,5450)(5356,5833,5697,5606,5607,5443)(5361,5838,5690,5611,5612,5436)(5366,5843,5683,5616,5617,5429)(5371,5848,5676,5621,5622,5422)(5376,5853,5669,5626,5627,5415)(5380,5858,5662,5631,5632,5408)(5383,5863,5655,5635,5636,5401)(5394,5796,5755,5568,5649,5950)(5396,5877,5878,5650,5648,5871)(5399,5642,5876,5652,5653,5872)(5406,5883,5884,5659,5660,5867)(5413,5888,5889,5666,5667,5862)(5420,5893,5894,5673,5674,5857)(5427,5898,5899,5680,5681,5852)(5434,5903,5904,5687,5688,5847)(5441,5908,5909,5694,5695,5842)(5448,5913,5914,5701,5702,5837)(5455,5918,5919,5708,5709,5832)(5462,5923,5924,5715,5716,5827)(5469,5928,5929,5722,5723,5822)(5476,5933,5934,5729,5730,5817)(5483,5938,5939,5736,5737,5812)(5490,5940,5943,5738,5743,5807)(5497,5935,5946,5731,5748,5802)(5504,5930,5949,5724,5753,5797)(5511,5925,5952,5717,5758,5794)(5518,5920,5954,5710,5763,5791)(5525,5915,5956,5703,5768,5788)(5532,5910,5958,5696,5773,5785)(5538,5905,5960,5689,5778,5782)(5543,5900,5961,5682,5781,5779)(5548,5895,5959,5675,5784,5775)(5553,5890,5957,5668,5787,5770)(5558,5885,5955,5661,5790,5765)(5563,5879,5953,5651,5793,5760)(5573,5962,5947,5799,5800,5750)(5578,5963,5944,5804,5805,5745)(5583,5967,5941,5809,5810,5740)(5588,5971,5936,5814,5815,5733)(5593,5975,5931,5819,5820,5726)(5598,5979,5926,5824,5825,5719)(5603,5983,5921,5829,5830,5712)(5608,5987,5916,5834,5835,5705)(5613,5991,5911,5839,5840,5698)(5618,5995,5906,5844,5845,5691)(5623,5999,5901,5849,5850,5684)(5628,6003,5896,5854,5855,5677)(5633,6007,5891,5859,5860,5670)(5637,6011,5886,5864,5865,5663)(5640,6015,5881,5868,5869,5656)(5654,5875,5951,5801,5880,6022)(5806,6052,6049,5964,5965,5948)(5811,6053,6047,5968,5969,5945)(5816,6054,6045,5972,5973,5942)(5821,6058,6043,5976,5977,5937)(5826,6062,6041,5980,5981,5932)(5831,6066,6039,5984,5985,5927)(5836,6070,6037,5988,5989,5922)(5841,6074,6035,5992,5993,5917)(5846,6078,6033,5996,5997,5912)(5851,6082,6031,6000,6001,5907)(5856,6086,6029,6004,6005,5902)(5861,6090,6027,6008,6009,5897)(5866,6094,6025,6012,6013,5892)(5870,6098,6023,6016,6017,5887)(5873,6051,5966,6019,6020,5882)(5970,6102,6103,6024,6021,6050)(5974,6127,6124,6055,6056,6048)(5978,6128,6122,6059,6060,6046)(5982,6129,6120,6063,6064,6044)(5986,6133,6118,6067,6068,6042)(5990,6137,6116,6071,6072,6040)(5994,6141,6114,6075,6076,6038)(5998,6145,6112,6079,6080,6036)(6002,6149,6110,6083,6084,6034)(6006,6153,6108,6087,6088,6032)(6010,6157,6106,6091,6092,6030)(6014,6161,6104,6095,6096,6028)(6018,6126,6057,6099,6100,6026)(6061,6165,6166,6105,6101,6125)(6065,6184,6181,6130,6131,6123)(6069,6185,6179,6134,6135,6121)(6073,6186,6177,6138,6139,6119)(6077,6190,6175,6142,6143,6117)(6081,6194,6173,6146,6147,6115)(6085,6198,6171,6150,6151,6113)(6089,6202,6169,6154,6155,6111)(6093,6206,6167,6158,6159,6109)(6097,6183,6132,6162,6163,6107)(6136,6210,6211,6168,6164,6182)(6140,6223,6220,6187,6188,6180)(6144,6224,6218,6191,6192,6178)(6148,6225,6216,6195,6196,6176)(6152,6229,6214,6199,6200,6174)(6156,6233,6212,6203,6204,6172)(6160,6222,6189,6207,6208,6170)(6193,6237,6238,6213,6209,6221)(6197,6244,6241,6226,6227,6219)(6201,6245,6239,6230,6231,6217)(6205,6243,6228,6234,6235,6215)(6232,6246,6247,6240,6236,6242);(1,2,5,11,19,32,51,74,103,138,179,226,279,338,403,474,551,634,723,818,919,1026,1139,1258,1383,1514,1651,1794,1943,2098,2259,2426,2599,2778,2963,3154,3351,3554,3763,3978,4199,4426,4659,4898,5143,5394,5566,5314,5068,4828,4594,4366,4144,3928,3718,3514,3316,3124,2938,2758,2583,2263,1942,2095,2109,2116,2123,2130,2137,2144,2151,2158,2165,2172,2179,2185,2190,2195,2200,2205,2210,2215,2220,2225,2230,2235,2240,2244,2247,2249,2413,2582,2756,2936,3122,3314,3512,3716,3926,4142,4364,4592,4826,5066,5312,5564,5794,5919,5700,5438,5180,4928,4682,4442,4208,3972,3550,3755,3957,3952,3947,3942,3937,3932,3927,3922,3917,3912,3907,3902,3897,3892,3887,3882,3876,3869,3862,3855,3848,3841,3834,3827,3820,3813,3806,3799,3792,3785,3778,3771,3756,3549,3754,3967,4185,4408,4636,4870,5110,5356,5608,5836,5990,6073,6140,6189,6169,6110,6033,5911,5697,5442,5191,4946,4707,4474,4247,4026,3811,3602,3399,3202,3011,2826,2647,2474,2307,2146,1991,1842,1699,1562,1431,1306,1187,1074,967,866,767,671,581,497,419,347,273,175,218,258,253,248,241,234,219,174,217,268,324,385,451,523,601,685,775,871,973,1080,1193,1312,1437,1568,1705,1848,1997,2152,2313,2480,2653,2832,3017,3208,3405,3608,3817,4032,4253,4480,4713,4952,5197,5448,5703,5523,5272,5027,4788,4554,4326,4104,3888,3678,3474,3276,3084,2898,2718,2544,2376,2214,2058,1908,1764,1626,1494,1367,1143,918,1023,1037,1044,1051,1058,1065,1072,1079,1085,1090,1095,1100,1105,1110,1115,1120,1124,1127,1129,1245,1366,1492,1624,1762,1906,2056,2212,2374,2542,2716,2896,3082,3274,3472,3676,3886,4102,4324,4552,4785,5024,5269,5520,5765,5878,5390,5643,5863,5858,5853,5848,5843,5838,5833,5828,5823,5818,5813,5808,5803,5798,5795,5792,5789,5786,5783,5780,5776,5771,5766,5761,5756,5751,5746,5741,5734,5727,5720,5713,5706,5699,5692,5685,5678,5671,5664,5657,5644,5389,5642,5873,6021,6056,6060,6064,6068,6072,6076,6080,6084,6088,6092,6096,6100,6103,6049,5947,5749,5498,5247,5002,4763,4530,4303,4082,3867,3658,3455,3258,3063,2871,2685,2505,2331,2163,2001,1845,1695,1551,1413,1281,1155,1035,913,719,810,898,893,888,883,878,873,868,861,854,847,840,833,826,811,718,809,908,1012,1121,1235,1355,1481,1613,1751,1895,2045,2201,2363,2531,2705,2885,3071,3263,3461,3664,3873,4088,4309,4536,4769,5008,5253,5504,5722,5467,5216,4971,4732,4499,4272,4051,3836,3627,3424,3227,3036,2851,2672,2499,2332,2171,2016,1867,1724,1586,1454,1328,1208,1094,986,884,788,698,614,535,407,278,335,349,356,363,369,374,379,384,388,391,393,461,534,612,696,786,882,984,1092,1206,1326,1452,1584,1721,1864,2013,2168,2329,2496,2669,2848,3033,3224,3421,3624,3833,4048,4269,4496,4729,4968,5213,5464,5719,5927,6040,6117,6176,6217,6240,6230,6199,6150,6083,6000,5849,5621,5369,5123,4882,4430,3977,4196,4210,4217,4224,4231,4238,4245,4252,4259,4266,4273,4280,4287,4294,4301,4308,4315,4322,4327,4332,4337,4342,4347,4352,4357,4362,4367,4372,4377,4382,4387,4392,4397,4402,4407,4411,4414,4416,4646,4881,5121,5367,5619,5847,5958,5767,5515,5257,5005,4759,4519,4285,4057,3835,3619,3409,3205,3007,2815,2629,2449,2275,2107,1937,1647,1786,1922,1917,1912,1907,1902,1897,1892,1887,1882,1877,1872,1865,1858,1851,1844,1837,1830,1823,1816,1809,1802,1787,1646,1785,1932,2084,2241,2403,2571,2745,2925,3111,3303,3501,3705,3915,4131,4353,4581,4815,5055,5301,5553,5666,5411,5160,4915,4676,4443,4216,3995,3780,3571,3368,3171,2980,2795,2616,2443,2276,2115,1960,1811,1668,1531,1400,1275,1156,1043,936,835,740,651,568,491,420,355,296,243,196,154,118,87,55,18,29,39,41,61,86,116,152,193,240,293,352,417,488,565,648,737,832,933,1040,1153,1272,1397,1528,1665,1808,1957,2112,2273,2440,2613,2792,2977,3168,3365,3568,3777,3992,4213,4440,4673,4912,5157,5408,5663,5887,6024,5968,5809,5581,5329,5083,4843,4609,4381,4159,3943,3733,3529,3331,3138,2782,2425,2596,2610,2617,2624,2631,2638,2645,2652,2659,2666,2673,2680,2687,2694,2699,2704,2709,2714,2719,2724,2729,2734,2739,2744,2749,2754,2759,2763,2766,2768,2950,3137,3329,3527,3731,3941,4157,4379,4607,4841,5081,5327,5579,5807,5934,5721,5459,5201,4949,4703,4463,4229,4001,3779,3563,3345,2959,3146,3330,3325,3320,3315,3310,3305,3300,3295,3290,3285,3280,3275,3270,3265,3260,3253,3246,3239,3232,3225,3218,3211,3204,3197,3190,3183,3176,3169,3162,3147,2958,3145,3340,3540,3745,3955,4171,4393,4621,4855,5095,5341,5593,5821,5978,6061,6104,6027,5896,5676,5421,5170,4925,4686,4453,4226,4005,3790,3581,3378,3181,2990,2805,2626,2453,2286,2125,1970,1821,1678,1541,1410,1285,1166,1053,946,845,750,661,578,501,430,365,302,242,188,132,70,95,117,111,96,69,94,127,165,208,256,310,370,436,507,584,667,756,851,952,1059,1172,1291,1416,1547,1684,1827,1976,2131,2292,2459,2632,2811,2996,3187,3384,3587,3796,4011,4232,4459,4692,4931,5176,5427,5682,5541,5289,5043,4803,4569,4341,4119,3903,3693,3489,3291,3099,2913,2733,2559,2391,2229,2073,1923,1778,1518,1257,1380,1394,1401,1408,1415,1422,1429,1436,1443,1450,1455,1460,1465,1470,1475,1480,1485,1490,1495,1499,1502,1504,1638,1777,1921,2071,2227,2389,2557,2731,2911,3097,3289,3487,3691,3901,4117,4339,4567,4801,5041,5287,5539,5779,5894,5665,5403,5137,4655,4890,5122,5117,5112,5107,5102,5097,5092,5087,5082,5077,5072,5067,5062,5057,5052,5047,5042,5037,5032,5025,5018,5011,5004,4997,4990,4983,4976,4969,4962,4955,4948,4941,4934,4927,4920,4913,4906,4891,4654,4889,5132,5380,5633,5861,6010,6093,6160,6209,6227,6231,6235,6238,6220,6179,6120,6043,5936,5732,5477,5226,4981,4742,4509,4282,4061,3846,3637,3434,3237,3046,2861,2682,2509,2342,2181,2022,1866,1716,1572,1434,1302,1176,1056,942,834,732,628,470,543,613,608,603,598,593,587,580,573,566,559,544,469,542,623,709,800,896,998,1106,1220,1340,1466,1598,1736,1880,2030,2186,2348,2515,2688,2867,3052,3243,3440,3643,3852,4067,4288,4515,4748,4987,5232,5483,5738,5488,5237,4992,4753,4520,4293,4072,3857,3648,3445,3248,3057,2872,2693,2519,2351,2189,2033,1883,1739,1601,1469,1343,1223,1109,1001,899,802,638,473,548,562,569,576,583,590,595,600,605,610,615,619,622,624,710,801,897,999,1107,1221,1341,1467,1599,1737,1881,2031,2187,2349,2517,2690,2869,3054,3245,3442,3645,3854,4069,4290,4517,4750,4989,5234,5485,5740,5942,6046,6123,6182,6222,6233,6229,6225,6224,6223,6210,6162,6095,6012,5864,5635,5147,4658,4895,4909,4916,4923,4930,4937,4944,4951,4958,4965,4972,4979,4986,4993,5000,5007,5014,5021,5028,5034,5039,5044,5049,5054,5059,5064,5069,5074,5079,5084,5089,5094,5099,5104,5109,5114,5119,5124,5128,5131,5133,5381,5634,5862,5959,5774,5533,5278,5026,4780,4540,4306,4078,3856,3640,3430,3226,3028,2836,2650,2470,2296,2128,1966,1810,1660,1508,1254,1375,1493,1488,1483,1478,1473,1468,1463,1458,1453,1447,1440,1433,1426,1419,1412,1405,1398,1391,1376,1253,1374,1503,1637,1776,1920,2070,2226,2388,2556,2730,2910,3096,3288,3486,3690,3900,4116,4338,4566,4800,5040,5286,5538,5687,5432,5181,4936,4697,4464,4237,4016,3801,3592,3389,3192,3001,2816,2637,2464,2297,2136,1981,1832,1689,1552,1421,1296,1177,1064,957,856,761,672,589,511,439,373,313,259,210,142,73,100,114,119,123,126,128,166,209,257,311,371,437,509,586,669,758,853,954,1061,1174,1293,1418,1549,1686,1829,1978,2133,2294,2461,2634,2813,2998,3189,3386,3589,3798,4013,4234,4461,4694,4933,5178,5429,5684,5902,6030,6107,6130,6063,5980,5824,5596,5344,5098,4858,4624,4396,4174,3958,3747,3355,2962,3151,3165,3172,3179,3186,3193,3200,3207,3214,3221,3228,3235,3242,3249,3256,3262,3267,3272,3277,3282,3287,3292,3297,3302,3307,3312,3317,3322,3327,3332,3336,3339,3341,3541,3746,3956,4172,4394,4622,4856,5096,5342,5594,5822,5946,5742,5480,5222,4970,4724,4484,4250,4022,3800,3584,3374,3170,2972,2772,2422,2591,2757,2752,2747,2742,2737,2732,2727,2722,2717,2712,2707,2702,2697,2691,2684,2677,2670,2663,2656,2649,2642,2635,2628,2621,2614,2607,2592,2421,2590,2767,2949,3136,3328,3526,3730,3940,4156,4378,4606,4840,5080,5326,5578,5806,5966,5881,5655,5400,5149,4904,4665,4432,4205,3984,3769,3560,3357,3160,2969,2784,2605,2432,2265,2104,1949,1800,1657,1520,1389,1264,1145,1032,925,824,729,640,557,480,409,344,285,232,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,238,291,350,415,486,563,646,735,830,931,1038,1151,1270,1395,1526,1663,1806,1955,2110,2271,2438,2611,2790,2975,3166,3363,3566,3775,3990,4211,4438,4671,4910,5155,5406,5661,5556,5304,5058,4818,4584,4356,4134,3918,3708,3504,3306,3114,2928,2748,2574,2406,2243,1947,1650,1791,1805,1812,1819,1826,1833,1840,1847,1854,1861,1868,1874,1879,1884,1889,1894,1899,1904,1909,1914,1919,1924,1928,1931,1933,2085,2242,2404,2572,2746,2926,3112,3304,3502,3706,3916,4132,4354,4582,4816,5056,5302,5554,5788,5909,5686,5424,5166,4914,4668,4420,3974,4191,4405,4400,4395,4390,4385,4380,4375,4370,4365,4360,4355,4350,4345,4340,4335,4330,4325,4319,4312,4305,4298,4291,4284,4277,4270,4263,4256,4249,4242,4235,4228,4221,4214,4207,4192,3973,4190,4415,4645,4880,5120,5366,5618,5846,5998,6081,6148,6197,6228,6214,6173,6114,6037,5921,5711,5456,5205,4960,4721,4488,4261,4040,3825,3616,3413,3216,3025,2840,2661,2488,2321,2160,2005,1856,1713,1576,1445,1320,1197,1077,963,855,753,657,567,483,397,275,330,382,377,372,367,360,353,346,331,274,329,392,460,533,611,695,785,881,983,1091,1205,1325,1451,1582,1719,1862,2011,2166,2327,2494,2667,2846,3031,3222,3419,3622,3831,4046,4267,4494,4727,4966,5211,5462,5717,5509,5258,5013,4774,4541,4314,4093,3878,3668,3464,3266,3074,2888,2708,2534,2366,2204,2048,1898,1754,1616,1484,1358,1238,1123,923,722,815,829,836,843,850,857,864,870,875,880,885,890,895,900,904,907,909,1013,1122,1236,1356,1482,1614,1752,1896,2046,2202,2364,2532,2706,2886,3072,3264,3462,3666,3875,4090,4311,4538,4771,5010,5255,5506,5755,5951,6051,6098,6094,6090,6086,6082,6078,6074,6070,6066,6062,6058,6054,6053,6052,5880,5393,5648,5660,5667,5674,5681,5688,5695,5702,5709,5716,5723,5730,5737,5743,5748,5753,5758,5763,5768,5773,5778,5781,5784,5787,5790,5793,5796,5800,5805,5810,5815,5820,5825,5830,5835,5840,5845,5850,5855,5860,5865,5869,5872,5874,5953,5759,5512,5261,5016,4777,4544,4317,4096,3877,3661,3451,3247,3049,2857,2671,2491,2317,2149,1987,1831,1681,1537,1399,1267,1133,915,1018,1118,1113,1108,1103,1098,1093,1088,1083,1076,1069,1062,1055,1048,1041,1034,1019,914,1017,1128,1244,1365,1491,1623,1761,1905,2055,2211,2373,2541,2715,2895,3081,3273,3471,3675,3885,4101,4323,4550,4783,5022,5267,5518,5708,5453,5202,4957,4718,4485,4258,4037,3822,3613,3410,3213,3022,2837,2658,2485,2318,2157,2002,1853,1710,1573,1442,1317,1198,1084,976,874,778,688,604,526,454,387,283,178,223,237,244,250,255,260,264,267,269,325,386,452,524,602,686,776,872,974,1082,1195,1314,1439,1570,1707,1850,1999,2154,2315,2482,2655,2834,3019,3210,3407,3610,3819,4034,4255,4482,4715,4954,5199,5450,5705,5917,6036,6113,6172,6213,6191,6142,6075,5992,5839,5611,5359,5113,4873,4639,4410,3982,3553,3760,3774,3781,3788,3795,3802,3809,3816,3823,3830,3837,3844,3851,3858,3865,3872,3879,3884,3889,3894,3899,3904,3909,3914,3919,3924,3929,3934,3939,3944,3949,3954,3959,3963,3966,3968,4186,4409,4637,4871,5111,5357,5609,5837,5954,5757,5501,5243,4991,4745,4505,4271,4043,3821,3605,3395,3191,2993,2801,2615,2435,2253,1939,2090,2238,2233,2228,2223,2218,2213,2208,2203,2198,2193,2188,2183,2176,2169,2162,2155,2148,2141,2134,2127,2120,2113,2106,2091,1938,2089,2248,2412,2581,2755,2935,3121,3313,3511,3715,3925,4141,4363,4591,4825,5065,5311,5563,5650,5395,5144,4899,4660,4427,4200,3979,3764,3555,3352,3155,2964,2779,2600,2427,2260,2099,1944,1795,1652,1515,1384,1259,1140,1027,920,819,724,635,552,475,404,339,280,227,180,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,184,231,284,343,408,479,556,639,728,823,924,1031,1144,1263,1388,1519,1656,1799,1948,2103,2264,2431,2604,2783,2968,3159,3356,3559,3768,3983,4204,4431,4664,4903,5148,5399,5654,5799,5571,5319,5073,4833,4599,4371,4149,3933,3723,3519,3321,3129,2943,2762,2430,2097,2256,2270,2277,2284,2291,2298,2305,2312,2319,2326,2333,2340,2347,2352,2357,2362,2367,2372,2377,2382,2387,2392,2397,2402,2407,2411,2414,2416,2586,2761,2941,3127,3319,3517,3721,3931,4147,4369,4597,4831,5071,5317,5569,5797,5924,5707,5445,5187,4935,4689,4449,4215,3987,3757,3347,3546,3742,3737,3732,3727,3722,3717,3712,3707,3702,3697,3692,3687,3682,3677,3672,3667,3660,3653,3646,3639,3632,3625,3618,3611,3604,3597,3590,3583,3576,3569,3562,3547,3346,3545,3752,3964,4181,4403,4631,4865,5105,5351,5603,5831,5986,6069,6136,6167,6108,6031,5906,5690,5435,5184,4939,4700,4467,4240,4019,3804,3595,3392,3195,3004,2819,2640,2467,2300,2139,1984,1835,1692,1555,1424,1299,1180,1067,960,859,764,675,588,504,426,354,288,220,134,171,205,200,194,187,172,133,170,215,265,320,380,446,518,596,680,770,865,966,1073,1186,1305,1430,1561,1698,1841,1990,2145,2306,2473,2646,2825,3010,3201,3398,3601,3810,4025,4246,4473,4706,4945,5190,5441,5696,5530,5279,5033,4793,4559,4331,4109,3893,3683,3479,3281,3089,2903,2723,2549,2381,2219,2063,1913,1769,1631,1498,1262,1025,1136,1150,1157,1164,1171,1178,1185,1192,1199,1204,1209,1214,1219,1224,1229,1234,1239,1243,1246,1248,1370,1497,1629,1767,1911,2061,2217,2379,2547,2721,2901,3087,3279,3477,3681,3891,4107,4329,4557,4791,5031,5276,5527,5770,5884,5645,5139,5386,5630,5625,5620,5615,5610,5605,5600,5595,5590,5585,5580,5575,5570,5565,5560,5555,5550,5545,5540,5535,5528,5521,5514,5507,5500,5493,5486,5479,5472,5465,5458,5451,5444,5437,5430,5423,5416,5409,5402,5387,5138,5385,5640,5870,6018,6101,6131,6135,6139,6143,6147,6151,6155,6159,6163,6166,6124,6047,5944,5744,5491,5240,4995,4756,4523,4296,4075,3860,3651,3448,3251,3060,2875,2692,2512,2338,2170,2008,1852,1702,1558,1420,1288,1162,1042,928,812,630,715,797,792,787,782,777,772,766,759,752,745,738,731,716,629,714,807,905,1008,1116,1230,1350,1476,1608,1746,1890,2040,2196,2358,2526,2700,2880,3066,3257,3454,3657,3866,4081,4302,4529,4762,5001,5246,5497,5729,5474,5223,4978,4739,4506,4279,4058,3843,3634,3431,3234,3043,2858,2679,2506,2339,2178,2023,1873,1729,1591,1459,1333,1213,1099,991,889,793,703,618,478,337,400,414,421,428,435,440,445,450,455,459,462,464,538,617,701,791,887,989,1097,1211,1331,1457,1589,1727,1871,2020,2175,2336,2503,2676,2855,3040,3231,3428,3631,3840,4055,4276,4503,4736,4975,5220,5471,5726,5932,6042,6119,6178,6219,6242,6246,6234,6203,6154,6087,6004,5854,5626,5374,5127,4663,4198,4423,4437,4444,4451,4458,4465,4472,4479,4486,4493,4500,4507,4514,4521,4528,4535,4542,4549,4555,4560,4565,4570,4575,4580,4585,4590,4595,4600,4605,4610,4615,4620,4625,4630,4635,4640,4644,4647,4649,4885,5126,5372,5624,5852,5960,5772,5522,5264,5012,4766,4526,4292,4064,3842,3626,3416,3212,3014,2822,2636,2456,2282,2114,1952,1788,1510,1643,1773,1768,1763,1758,1753,1748,1743,1738,1733,1728,1722,1715,1708,1701,1694,1687,1680,1673,1666,1659,1644,1509,1642,1783,1929,2080,2236,2398,2566,2740,2920,3106,3298,3496,3700,3910,4126,4348,4576,4810,5050,5296,5548,5673,5418,5167,4922,4683,4450,4223,4002,3787,3578,3375,3178,2987,2802,2623,2450,2283,2122,1967,1818,1675,1538,1407,1282,1163,1050,943,842,747,658,575,498,427,362,303,249,201,159,122,78,31,48,59,62,64,90,121,157,199,247,300,359,424,495,572,655,744,839,940,1047,1160,1279,1404,1535,1672,1815,1964,2119,2280,2447,2620,2799,2984,3175,3372,3575,3784,3999,4220,4447,4680,4919,5164,5415,5670,5892,6026,6055,5972,5814,5586,5334,5088,4848,4614,4386,4164,3948,3738,3534,3335,2967,2598,2775,2789,2796,2803,2810,2817,2824,2831,2838,2845,2852,2859,2866,2873,2879,2884,2889,2894,2899,2904,2909,2914,2919,2924,2929,2934,2939,2944,2948,2951,2953,3141,3334,3532,3736,3946,4162,4384,4612,4846,5086,5332,5584,5812,5939,5728,5466,5208,4956,4710,4470,4236,4008,3786,3570,3360,3148,2774,2955,3133,3128,3123,3118,3113,3108,3103,3098,3093,3088,3083,3078,3073,3068,3062,3055,3048,3041,3034,3027,3020,3013,3006,2999,2992,2985,2978,2971,2956,2773,2954,3143,3337,3536,3740,3950,4166,4388,4616,4850,5090,5336,5588,5816,5974,6057,6025,5891,5669,5414,5163,4918,4679,4446,4219,3998,3783,3574,3371,3174,2983,2798,2619,2446,2279,2118,1963,1814,1671,1534,1403,1278,1159,1046,939,838,743,654,571,494,423,358,299,246,195,147,97,47,66,82,67,46,65,92,124,161,203,251,305,364,429,500,577,660,749,844,945,1052,1165,1284,1409,1540,1677,1820,1969,2124,2285,2452,2625,2804,2989,3180,3377,3580,3789,4004,4225,4452,4685,4924,5169,5420,5675,5546,5294,5048,4808,4574,4346,4124,3908,3698,3494,3296,3104,2918,2738,2564,2396,2234,2078,1927,1655,1382,1511,1525,1532,1539,1546,1553,1560,1567,1574,1581,1587,1592,1597,1602,1607,1612,1617,1622,1627,1632,1636,1639,1641,1781,1926,2076,2232,2394,2562,2736,2916,3102,3294,3492,3696,3906,4122,4344,4572,4806,5046,5292,5544,5782,5899,5672,5410,5152,4892,4422,4651,4877,4872,4867,4862,4857,4852,4847,4842,4837,4832,4827,4822,4817,4812,4807,4802,4797,4792,4786,4779,4772,4765,4758,4751,4744,4737,4730,4723,4716,4709,4702,4695,4688,4681,4674,4667,4652,4421,4650,4887,5129,5376,5628,5856,6006,6089,6156,6205,6236,6247,6241,6218,6177,6118,6041,5931,5725,5470,5219,4974,4735,4502,4275,4054,3839,3630,3427,3230,3039,2854,2675,2502,2335,2174,2019,1870,1723,1579,1441,1309,1183,1063,949,841,739,643,545,399,466,530,525,520,515,510,503,496,489,482,467,398,465,540,620,705,795,891,993,1101,1215,1335,1461,1593,1731,1875,2025,2180,2341,2508,2681,2860,3045,3236,3433,3636,3845,4060,4281,4508,4741,4980,5225,5476,5731,5495,5244,4999,4760,4527,4300,4079,3864,3655,3452,3255,3064,2878,2698,2524,2356,2194,2038,1888,1744,1606,1474,1348,1228,1114,1006,903,727,550,631,645,652,659,666,673,679,684,689,694,699,704,708,711,713,805,902,1004,1112,1226,1346,1472,1604,1742,1886,2036,2192,2354,2522,2696,2876,3061,3252,3449,3652,3861,4076,4297,4524,4757,4996,5241,5492,5745,5945,6048,6125,6183,6206,6202,6198,6194,6190,6186,6185,6184,6165,6099,6016,5868,5398,4897,5140,5154,5161,5168,5175,5182,5189,5196,5203,5210,5217,5224,5231,5238,5245,5252,5259,5266,5273,5280,5285,5290,5295,5300,5305,5310,5315,5320,5325,5330,5335,5340,5345,5350,5355,5360,5365,5370,5375,5379,5382,5384,5638,5867,5957,5769,5526,5275,5030,4787,4547,4313,4085,3863,3647,3437,3233,3035,2843,2657,2477,2303,2135,1973,1817,1667,1523,1377,1135,1250,1362,1357,1352,1347,1342,1337,1332,1327,1322,1315,1308,1301,1294,1287,1280,1273,1266,1251,1134,1249,1372,1500,1633,1771,1915,2065,2221,2383,2551,2725,2905,3091,3283,3481,3685,3895,4111,4333,4561,4795,5035,5281,5532,5694,5439,5188,4943,4704,4471,4244,4023,3808,3599,3396,3199,3008,2823,2644,2471,2304,2143,1988,1839,1696,1559,1428,1303,1184,1071,964,863,768,678,594,516,444,378,318,263,183,102,135,149,155,160,164,167,169,213,262,316,376,442,514,592,676,765,860,961,1068,1181,1300,1425,1556,1693,1836,1985,2140,2301,2468,2641,2820,3005,3196,3393,3596,3805,4020,4241,4468,4701,4940,5185,5436,5691,5907,6032,6109,6168,6134,6067,5984,5829,5601,5349,5103,4863,4629,4401,4179,3962,3558,3153,3348,3362,3369,3376,3383,3390,3397,3404,3411,3418,3425,3432,3439,3446,3453,3460,3465,3470,3475,3480,3485,3490,3495,3500,3505,3510,3515,3520,3525,3530,3535,3539,3542,3544,3750,3961,4177,4399,4627,4861,5101,5347,5599,5827,5949,5747,5487,5229,4977,4731,4491,4257,4029,3807,3591,3381,3177,2979,2787,2593,2255,2418,2578,2573,2568,2563,2558,2553,2548,2543,2538,2533,2528,2523,2518,2511,2504,2497,2490,2483,2476,2469,2462,2455,2448,2441,2434,2419,2254,2417,2588,2764,2945,3131,3323,3521,3725,3935,4151,4373,4601,4835,5075,5321,5573,5801,5652,5397,5146,4901,4662,4429,4202,3981,3766,3557,3354,3157,2966,2781,2602,2429,2262,2101,1946,1797,1654,1517,1386,1261,1142,1029,922,821,726,637,554,477,406,341,282,229,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,228,281,340,405,476,553,636,725,820,921,1028,1141,1260,1385,1516,1653,1796,1945,2100,2261,2428,2601,2780,2965,3156,3353,3556,3765,3980,4201,4428,4661,4900,5145,5396,5651,5561,5309,5063,4823,4589,4361,4139,3923,3713,3509,3311,3119,2933,2753,2579,2410,2102,1793,1940,1954,1961,1968,1975,1982,1989,1996,2003,2010,2017,2024,2029,2034,2039,2044,2049,2054,2059,2064,2069,2074,2079,2083,2086,2088,2246,2409,2577,2751,2931,3117,3309,3507,3711,3921,4137,4359,4587,4821,5061,5307,5559,5791,5914,5693,5431,5173,4921,4675,4435,4193,3759,3970,4178,4173,4168,4163,4158,4153,4148,4143,4138,4133,4128,4123,4118,4113,4108,4103,4098,4091,4084,4077,4070,4063,4056,4049,4042,4035,4028,4021,4014,4007,4000,3993,3986,3971,3758,3969,4188,4412,4641,4875,5115,5361,5613,5841,5994,6077,6144,6193,6212,6171,6112,6035,5916,5704,5449,5198,4953,4714,4481,4254,4033,3818,3609,3406,3209,3018,2833,2654,2481,2314,2153,1998,1849,1706,1569,1438,1313,1194,1081,970,862,760,664,574,490,412,332,222,271,317,312,307,301,294,287,272,221,270,327,389,456,528,606,690,780,876,978,1086,1200,1319,1444,1575,1712,1855,2004,2159,2320,2487,2660,2839,3024,3215,3412,3615,3824,4039,4260,4487,4720,4959,5204,5455,5710,5516,5265,5020,4781,4548,4321,4099,3883,3673,3469,3271,3079,2893,2713,2539,2371,2209,2053,1903,1759,1621,1489,1363,1242,1030,817,916,930,937,944,951,958,965,972,977,982,987,992,997,1002,1007,1011,1014,1016,1126,1241,1361,1487,1619,1757,1901,2051,2207,2369,2537,2711,2891,3077,3269,3467,3671,3881,4097,4318,4545,4778,5017,5262,5513,5760,5647,5876,6015,6011,6007,6003,5999,5995,5991,5987,5983,5979,5975,5971,5967,5963,5962,5649,5879,5885,5890,5895,5900,5905,5910,5915,5920,5925,5930,5935,5940,5938,5933,5928,5923,5918,5913,5908,5903,5898,5893,5888,5883,5877,5646,5875,5965,5969,5973,5977,5981,5985,5989,5993,5997,6001,6005,6009,6013,6017,6020,6022,5950,5754,5505,5254,5009,4770,4537,4310,4089,3874,3665,3458,3254,3056,2864,2678,2498,2324,2156,1994,1838,1688,1544,1406,1274,1148,1020,814,911,1005,1000,995,990,985,980,975,969,962,955,948,941,934,927,912,813,910,1015,1125,1240,1360,1486,1618,1756,1900,2050,2206,2368,2536,2710,2890,3076,3268,3466,3670,3880,4095,4316,4543,4776,5015,5260,5511,5715,5460,5209,4964,4725,4492,4265,4044,3829,3620,3417,3220,3029,2844,2665,2492,2325,2164,2009,1860,1717,1580,1449,1323,1203,1089,981,879,783,693,609,531,458,342,225,276,290,297,304,309,314,319,323,326,328,390,457,529,607,691,781,877,979,1087,1201,1321,1446,1577,1714,1857,2006,2161,2322,2489,2662,2841,3026,3217,3414,3617,3826,4041,4262,4489,4722,4961,5206,5457,5712,5922,6038,6115,6174,6215,6226,6195,6146,6079,5996,5844,5616,5364,5118,4878,4643,4203,3762,3975,3989,3996,4003,4010,4017,4024,4031,4038,4045,4052,4059,4066,4073,4080,4087,4094,4100,4105,4110,4115,4120,4125,4130,4135,4140,4145,4150,4155,4160,4165,4170,4175,4180,4184,4187,4189,4413,4642,4876,5116,5362,5614,5842,5956,5762,5508,5250,4998,4752,4512,4278,4050,3828,3612,3402,3198,3000,2808,2622,2442,2268,2092,1790,1935,2077,2072,2067,2062,2057,2052,2047,2042,2037,2032,2027,2021,2014,2007,2000,1993,1986,1979,1972,1965,1958,1951,1936,1789,1934,2087,2245,2408,2576,2750,2930,3116,3308,3506,3710,3920,4136,4358,4586,4820,5060,5306,5558,5659,5404,5153,4908,4669,4436,4209,3988,3773,3564,3361,3164,2973,2788,2609,2436,2269,2108,1953,1804,1661,1524,1393,1268,1149,1036,929,828,733,644,561,484,413,348,289,236,189,148,113,83,58,36,10,16,24,38,57,81,110,145,186,233,286,345,410,481,558,641,730,825,926,1033,1146,1265,1390,1521,1658,1801,1950,2105,2266,2433,2606,2785,2970,3161,3358,3561,3770,3985,4206,4433,4666,4905,5150,5401,5656,5882,5964,5804,5576,5324,5078,4838,4604,4376,4154,3938,3728,3524,3326,3134,2947,2603,2258,2423,2437,2444,2451,2458,2465,2472,2479,2486,2493,2500,2507,2514,2520,2525,2530,2535,2540,2545,2550,2555,2560,2565,2570,2575,2580,2584,2587,2589,2765,2946,3132,3324,3522,3726,3936,4152,4374,4602,4836,5076,5322,5574,5802,5929,5714,5452,5194,4942,4696,4456,4222,3994,3772,3548,3150,3343,3533,3528,3523,3518,3513,3508,3503,3498,3493,3488,3483,3478,3473,3468,3463,3457,3450,3443,3436,3429,3422,3415,3408,3401,3394,3387,3380,3373,3366,3359,3344,3149,3342,3543,3749,3960,4176,4398,4626,4860,5100,5346,5598,5826,5982,6065,6132,6106,6029,5901,5683,5428,5177,4932,4693,4460,4233,4012,3797,3588,3385,3188,2997,2812,2633,2460,2293,2132,1977,1828,1685,1548,1417,1292,1173,1060,953,852,757,668,585,508,433,361,295,235,173,99,130,158,153,146,131,98,129,168,212,261,315,375,441,513,591,674,763,858,959,1066,1179,1298,1423,1554,1691,1834,1983,2138,2299,2466,2639,2818,3003,3194,3391,3594,3803,4018,4239,4466,4699,4938,5183,5434,5689,5536,5284,5038,4798,4564,4336,4114,3898,3688,3484,3286,3094,2908,2728,2554,2386,2224,2068,1918,1774,1635,1387,1138,1255,1269,1276,1283,1290,1297,1304,1311,1318,1324,1329,1334,1339,1344,1349,1354,1359,1364,1368,1371,1373,1501,1634,1772,1916,2066,2222,2384,2552,2726,2906,3092,3284,3482,3686,3896,4112,4334,4562,4796,5036,5282,5534,5775,5889,5658,5388,4894,5135,5373,5368,5363,5358,5353,5348,5343,5338,5333,5328,5323,5318,5313,5308,5303,5298,5293,5288,5283,5277,5270,5263,5256,5249,5242,5235,5228,5221,5214,5207,5200,5193,5186,5179,5172,5165,5158,5151,5136,4893,5134,5383,5637,5866,6014,6097,6164,6188,6192,6196,6200,6204,6208,6211,6181,6122,6045,5941,5739,5484,5233,4988,4749,4516,4289,4068,3853,3644,3441,3244,3053,2868,2689,2516,2345,2177,2015,1859,1709,1565,1427,1295,1169,1049,935,827,717,547,626,702,697,692,687,682,677,670,663,656,649,642,627,546,625,712,804,901,1003,1111,1225,1345,1471,1603,1741,1885,2035,2191,2353,2521,2695,2874,3059,3250,3447,3650,3859,4074,4295,4522,4755,4994,5239,5490,5736,5481,5230,4985,4746,4513,4286,4065,3850,3641,3438,3241,3050,2865,2686,2513,2346,2184,2028,1878,1734,1596,1464,1338,1218,1104,996,894,798,707,555,402,471,485,492,499,506,512,517,522,527,532,536,539,541,621,706,796,892,994,1102,1216,1336,1462,1594,1732,1876,2026,2182,2343,2510,2683,2862,3047,3238,3435,3638,3847,4062,4283,4510,4743,4982,5227,5478,5733,5937,6044,6121,6180,6221,6243,6245,6244,6237,6207,6158,6091,6008,5859,5631,5378,4902,4425,4656,4670,4677,4684,4691,4698,4705,4712,4719,4726,4733,4740,4747,4754,4761,4768,4775,4782,4789,4794,4799,4804,4809,4814,4819,4824,4829,4834,4839,4844,4849,4854,4859,4864,4869,4874,4879,4883,4886,4888,5130,5377,5629,5857,5961,5777,5529,5271,5019,4773,4533,4299,4071,3849,3633,3423,3219,3021,2829,2643,2463,2289,2121,1959,1803,1645,1379,1506,1630,1625,1620,1615,1610,1605,1600,1595,1590,1585,1578,1571,1564,1557,1550,1543,1536,1529,1522,1507,1378,1505,1640,1780,1925,2075,2231,2393,2561,2735,2915,3101,3293,3491,3695,3905,4121,4343,4571,4805,5045,5291,5543,5680,5425,5174,4929,4690,4457,4230,4009,3794,3585,3382,3185,2994,2809,2630,2457,2290,2129,1974,1825,1682,1545,1414,1289,1170,1057,950,849,754,665,582,505,434,368,308,254,206,163,107,50,71,84,88,91,93,125,162,204,252,306,366,431,502,579,662,751,846,947,1054,1167,1286,1411,1542,1679,1822,1971,2126,2287,2454,2627,2806,2991,3182,3379,3582,3791,4006,4227,4454,4687,4926,5171,5422,5677,5897,6028,6105,6059,5976,5819,5591,5339,5093,4853,4619,4391,4169,3953,3743,3538,3158,2777,2960,2974,2981,2988,2995,3002,3009,3016,3023,3030,3037,3044,3051,3058,3065,3070,3075,3080,3085,3090,3095,3100,3105,3110,3115,3120,3125,3130,3135,3139,3142,3144,3338,3537,3741,3951,4167,4389,4617,4851,5091,5337,5589,5817,5943,5735,5473,5215,4963,4717,4477,4243,4015,3793,3577,3367,3163,2957,2595,2770,2942,2937,2932,2927,2922,2917,2912,2907,2902,2897,2892,2887,2882,2877,2870,2863,2856,2849,2842,2835,2828,2821,2814,2807,2800,2793,2786,2771,2594,2769,2952,3140,3333,3531,3735,3945,4161,4383,4611,4845,5085,5331,5583,5811,5970,6023,5886,5662,5407,5156,4911,4672,4439,4212,3991,3776,3567,3364,3167,2976,2791,2612,2439,2272,2111,1956,1807,1664,1527,1396,1271,1152,1039,932,831,736,647,564,487,416,351,292,239,192,151,112,68,28,43,44,27,42,63,89,120,156,198,245,298,357,422,493,570,653,742,837,938,1045,1158,1277,1402,1533,1670,1813,1962,2117,2278,2445,2618,2797,2982,3173,3370,3573,3782,3997,4218,4445,4678,4917,5162,5413,5668,5551,5299,5053,4813,4579,4351,4129,3913,3703,3499,3301,3109,2923,2743,2569,2401,2239,2082,1798,1513,1648,1662,1669,1676,1683,1690,1697,1704,1711,1718,1725,1730,1735,1740,1745,1750,1755,1760,1765,1770,1775,1779,1782,1784,1930,2081,2237,2399,2567,2741,2921,3107,3299,3497,3701,3911,4127,4349,4577,4811,5051,5297,5549,5785,5904,5679,5417,5159,4907,4653,4195,4418,4638,4633,4628,4623,4618,4613,4608,4603,4598,4593,4588,4583,4578,4573,4568,4563,4558,4553,4546,4539,4532,4525,4518,4511,4504,4497,4490,4483,4476,4469,4462,4455,4448,4441,4434,4419,4194,4417,4648,4884,5125,5371,5623,5851,6002,6085,6152,6201,6232,6239,6216,6175,6116,6039,5926,5718,5463,5212,4967,4728,4495,4268,4047,3832,3623,3420,3223,3032,2847,2668,2495,2328,2167,2012,1863,1720,1583,1448,1316,1190,1070,956,848,746,650,560,468,334,395,453,448,443,438,432,425,418,411,396,333,394,463,537,616,700,790,886,988,1096,1210,1330,1456,1588,1726,1869,2018,2173,2334,2501,2674,2853,3038,3229,3426,3629,3838,4053,4274,4501,4734,4973,5218,5469,5724,5502,5251,5006,4767,4534,4307,4086,3871,3662,3459,3261,3069,2883,2703,2529,2361,2199,2043,1893,1749,1611,1479,1353,1233,1119,1010,822,633,720,734,741,748,755,762,769,774,779,784,789,794,799,803,806,808,906,1009,1117,1231,1351,1477,1609,1747,1891,2041,2197,2359,2527,2701,2881,3067,3259,3456,3659,3868,4083,4304,4531,4764,5003,5248,5499,5750,5948,6050,6126,6161,6157,6153,6149,6145,6141,6137,6133,6129,6128,6127,6102,6019,5653,5142,5391,5405,5412,5419,5426,5433,5440,5447,5454,5461,5468,5475,5482,5489,5496,5503,5510,5517,5524,5531,5537,5542,5547,5552,5557,5562,5567,5572,5577,5582,5587,5592,5597,5602,5607,5612,5617,5622,5627,5632,5636,5639,5641,5871,5955,5764,5519,5268,5023,4784,4551,4320,4092,3870,3654,3444,3240,3042,2850,2664,2484,2310,2142,1980,1824,1674,1530,1392,1252,1022,1131,1237,1232,1227,1222,1217,1212,1207,1202,1196,1189,1182,1175,1168,1161,1154,1147,1132,1021,1130,1247,1369,1496,1628,1766,1910,2060,2216,2378,2546,2720,2900,3086,3278,3476,3680,3890,4106,4328,4556,4790,5029,5274,5525,5701,5446,5195,4950,4711,4478,4251,4030,3815,3606,3403,3206,3015,2830,2651,2478,2311,2150,1995,1846,1703,1566,1435,1310,1191,1078,971,869,773,683,599,521,449,383,322,230,137,176,190,197,202,207,211,214,216,266,321,381,447,519,597,681,771,867,968,1075,1188,1307,1432,1563,1700,1843,1992,2147,2308,2475,2648,2827,3012,3203,3400,3603,3812,4027,4248,4475,4708,4947,5192,5443,5698,5912,6034,6111,6170,6187,6138,6071,5988,5834,5606,5354,5108,4868,4634,4406,4183,3767,3350,3551,3565,3572,3579,3586,3593,3600,3607,3614,3621,3628,3635,3642,3649,3656,3663,3669,3674,3679,3684,3689,3694,3699,3704,3709,3714,3719,3724,3729,3734,3739,3744,3748,3751,3753,3965,4182,4404,4632,4866,5106,5352,5604,5832,5952,5752,5494,5236,4984,4738,4498,4264,4036,3814,3598,3388,3184,2986,2794,2608,2420,2094,2251,2405,2400,2395,2390,2385,2380,2375,2370,2365,2360,2355,2350,2344,2337,2330,2323,2316,2309,2302,2295,2288,2281,2274,2267,2252,2093,2250,2415,2585,2760,2940,3126,3318,3516,3720,3930,4146,4368,4596,4830,5070,5316,5568,5392,5141,4896,4657,4424,4197,3976,3761,3552,3349,3152,2961,2776,2597,2424,2257,2096,1941,1792,1649,1512,1381,1256,1137,1024,917,816,721,632,549,472,401,336,277,224,177,136,101,72,49,30,17,9,3)

Polycyclic presentation:

2,3,6247|c^a=c^6246,c^b=c^2316

Conjugacy classes & character table

1047 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37482, 1);

D6247⋊C3 #49154136