HNG11 := (2,3)(4,6)(5,7)(8,11)(9,12)(10,14)(13,18)(15,20)(16,21)(17,23)(19,26)
     (22,30)(24,32)(25,33)(27,36)(28,37)(29,39)(31,42)(34,46)(35,47)(38,51)
     (40,53)(41,54)(43,57)(44,58)(45,60)(48,64)(49,65)(50,67)(52,70)(55,74)
     (56,75)(59,79)(61,81)(62,82)(63,84)(66,88)(68,90)(69,91)(71,94)(73,96)
     (76,100)(77,101)(78,103)(80,106)(83,110)(85,112)(86,113)(87,115)(89,118)
     (92,122)(93,123)(95,126)(97,128)(98,129)(99,131)(102,135)(105,137)(107,
     140)(108,120)(109,142)(111,145)(114,149)(116,151)(117,152)(119,155)(121,
     157)(124,161)(125,162)(127,165)(130,169)(132,171)(133,172)(134,174)(136,
     177)(138,180)(139,181)(141,184)(143,186)(144,187)(146,190)(147,191)(148,
     193)(150,196)(153,200)(154,201)(158,205)(159,206)(160,208)(163,212)(164,
     213)(166,216)(167,198)(168,218)(170,221)(173,225)(175,227)(176,228)(178,
     231)(179,232)(182,236)(183,237)(185,240)(188,244)(189,245)(192,249)(194,
     251)(195,252)(197,255)(199,257)(202,261)(203,262)(204,264)(207,268)(209,
     270)(210,271)(211,273)(214,277)(215,278)(217,281)(219,283)(220,284)(222,
     287)(223,288)(224,290)(226,293)(229,297)(230,298)(233,302)(234,303)(235,
     305)(238,309)(239,310)(241,313)(242,295)(243,315)(246,319)(247,320)(248,
     322)(250,325)(253,329)(254,330)(256,333)(258,335)(259,336)(260,338)(263,
     342)(265,344)(266,327)(267,346)(269,349)(272,353)(274,355)(275,356)(276,
     358)(279,362)(280,363)(282,366)(285,370)(286,371)(289,375)(291,377)(292,
     378)(294,381)(296,383)(299,387)(300,388)(301,390)(304,394)(306,396)(307,
     397)(308,399)(311,403)(312,404)(314,407)(316,409)(317,410)(318,412)(321,
     416)(323,418)(324,419)(326,422)(328,424)(331,428)(332,429)(334,432)(337,
     436)(339,438)(341,440)(343,443)(345,446)(347,448)(348,449)(350,452)(351,
     453)(352,455)(354,458)(357,462)(359,464)(360,465)(361,467)(364,471)(365,
     472)(367,475)(368,460)(369,477)(372,481)(373,482)(374,484)(376,487)(379,
     491)(380,492)(382,495)(384,497)(385,498)(386,500)(389,504)(391,506)(392,
     489)(393,508)(395,511)(398,515)(400,517)(401,518)(402,520)(405,524)(406,
     525)(408,528)(411,532)(413,534)(414,535)(415,537)(417,540)(420,544)(421,
     545)(423,548)(425,550)(426,551)(427,553)(430,557)(431,558)(433,561)(434,
     542)(435,563)(437,566)(439,569)(441,571)(442,572)(444,575)(445,576)(447,
     579)(450,583)(451,584)(454,588)(456,590)(457,591)(459,594)(461,596)(463,
     599)(466,603)(468,605)(469,606)(470,608)(473,612)(474,613)(476,616)(478,
     618)(479,619)(480,621)(483,625)(485,627)(486,628)(488,631)(490,633)(493,
     637)(494,638)(496,641)(499,645)(501,647)(502,648)(503,650)(505,653)(507,
     656)(509,658)(510,659)(512,662)(513,663)(514,665)(516,668)(519,672)(521,
     674)(522,675)(523,677)(526,681)(527,682)(529,685)(530,670)(531,687)(533,
     690)(536,694)(538,696)(539,697)(541,700)(546,705)(547,706)(549,709)(552,
     713)(554,715)(555,716)(556,718)(559,722)(560,723)(562,726)(564,728)(565,
     729)(567,732)(568,733)(570,736)(573,740)(574,741)(577,745)(578,746)(580,
     749)(581,738)(582,751)(585,755)(586,756)(587,758)(589,761)(592,765)(593,
     766)(595,769)(597,771)(598,772)(600,775)(601,763)(604,779)(607,783)(609,
     785)(610,786)(611,788)(614,792)(615,793)(617,796)(620,800)(622,802)(623,
     803)(624,805)(626,808)(629,812)(630,813)(632,816)(634,818)(635,819)(636,
     821)(639,825)(640,826)(642,829)(643,810)(644,831)(646,834)(649,838)(651,
     840)(652,841)(654,844)(655,845)(657,848)(660,852)(661,853)(664,857)(666,
     859)(667,860)(669,863)(671,865)(673,868)(676,872)(678,874)(679,875)(680,
     877)(683,881)(684,882)(686,885)(688,887)(689,888)(691,891)(692,892)(693,
     894)(695,897)(698,901)(699,902)(701,905)(702,906)(703,907)(704,909)(707,
     913)(708,914)(710,917)(711,899)(712,919)(714,922)(719,927)(720,928)(721,
     930)(724,934)(725,935)(730,941)(731,942)(734,946)(735,947)(737,950)(739,
     952)(742,956)(743,957)(744,959)(747,963)(748,964)(750,967)(752,969)(753,
     970)(754,972)(757,976)(759,978)(760,979)(762,982)(764,984)(767,988)(768,
     989)(770,992)(773,996)(774,997)(776,1000)(777,1001)(778,1002)(780,1005)
     (781,1006)(782,1008)(784,1011)(787,1015)(789,1017)(790,1018)(794,1023)
     (795,1024)(797,1027)(798,1013)(799,1029)(801,1032)(804,1036)(806,1038)
     (807,1039)(809,1042)(811,1044)(814,1048)(815,1049)(817,1052)(820,1056)
     (822,1058)(823,1059)(824,1061)(827,1065)(828,1066)(830,1069)(832,1071)
     (833,1072)(835,1075)(836,1076)(837,1078)(839,1081)(842,1085)(843,1086)
     (846,1090)(847,1091)(849,1094)(850,1083)(851,1096)(854,1100)(855,1101)
     (856,1103)(858,1106)(861,1110)(862,1111)(864,1114)(866,1116)(867,1117)
     (869,1120)(870,1108)(871,1122)(873,1125)(876,1129)(878,1131)(879,1132)
     (880,1134)(883,1138)(884,1139)(886,1142)(889,1146)(890,1147)(893,1151)
     (895,1153)(896,1154)(898,1157)(900,1159)(903,1163)(904,1164)(908,1169)
     (910,1171)(911,1172)(912,1174)(915,1178)(916,1179)(918,1182)(920,1184)
     (921,1185)(923,1188)(924,1189)(925,1191)(926,1193)(929,1197)(931,1199)
     (932,1200)(933,1202)(936,1206)(937,1207)(938,1209)(939,1195)(940,1211)
     (943,1215)(944,1216)(945,1218)(948,1222)(949,1223)(951,1226)(953,1228)
     (954,1229)(955,1231)(958,1235)(960,1237)(961,1238)(962,1240)(965,1244)
     (966,1245)(968,1248)(971,1252)(973,1254)(974,1255)(975,1257)(977,1260)
     (980,1264)(981,1265)(983,1268)(985,1270)(986,1271)(987,1273)(991,1277)
     (993,1280)(994,1262)(995,1282)(998,1286)(999,1287)(1003,1292)(1004,1293)
     (1007,1297)(1009,1299)(1010,1300)(1012,1303)(1014,1305)(1016,1308)(1019,
     1312)(1020,1313)(1021,1314)(1022,1316)(1025,1320)(1026,1321)(1028,1324)
     (1030,1326)(1031,1327)(1033,1330)(1034,1331)(1035,1333)(1037,1336)(1040,
     1340)(1041,1341)(1043,1344)(1045,1346)(1046,1347)(1047,1349)(1050,1353)
     (1051,1219)(1053,1356)(1054,1338)(1055,1358)(1057,1361)(1060,1365)(1062,
     1367)(1063,1368)(1064,1370)(1067,1374)(1068,1375)(1070,1378)(1073,1382)
     (1074,1383)(1077,1387)(1080,1389)(1082,1392)(1084,1394)(1087,1398)(1088,
     1399)(1089,1401)(1092,1405)(1093,1406)(1095,1409)(1097,1411)(1098,1412)
     (1099,1414)(1102,1418)(1104,1420)(1105,1421)(1107,1424)(1109,1426)(1112,
     1430)(1113,1431)(1115,1434)(1118,1438)(1119,1439)(1121,1442)(1124,1444)
     (1126,1447)(1127,1448)(1128,1450)(1130,1453)(1133,1457)(1135,1459)(1136,
     1460)(1137,1462)(1140,1466)(1141,1467)(1143,1470)(1144,1455)(1145,1472)
     (1148,1476)(1149,1477)(1150,1479)(1152,1482)(1155,1486)(1156,1487)(1158,
     1490)(1160,1492)(1161,1493)(1162,1495)(1165,1499)(1166,1500)(1167,1484)
     (1168,1503)(1170,1506)(1173,1510)(1175,1512)(1176,1513)(1177,1515)(1180,
     1519)(1181,1520)(1183,1523)(1186,1527)(1187,1528)(1190,1532)(1192,1534)
     (1194,1536)(1196,1538)(1198,1541)(1201,1545)(1203,1547)(1204,1548)(1205,
     1550)(1208,1554)(1210,1556)(1212,1558)(1213,1559)(1214,1561)(1217,1565)
     (1220,1567)(1221,1569)(1224,1573)(1225,1574)(1227,1577)(1230,1581)(1232,
     1583)(1233,1584)(1234,1586)(1236,1589)(1239,1593)(1241,1595)(1242,1596)
     (1243,1598)(1246,1602)(1247,1603)(1249,1606)(1250,1591)(1251,1608)(1253,
     1611)(1256,1615)(1258,1617)(1259,1618)(1261,1621)(1263,1623)(1266,1627)
     (1267,1628)(1269,1631)(1272,1635)(1274,1637)(1275,1638)(1276,1640)(1278,
     1643)(1279,1644)(1281,1647)(1283,1649)(1284,1650)(1285,1652)(1288,1656)
     (1289,1657)(1291,1660)(1294,1664)(1295,1665)(1296,1667)(1298,1670)(1301,
     1674)(1302,1675)(1304,1678)(1306,1680)(1307,1681)(1309,1684)(1310,1672)
     (1311,1686)(1315,1691)(1317,1693)(1318,1694)(1319,1696)(1322,1700)(1323,
     1701)(1325,1704)(1328,1708)(1329,1709)(1332,1713)(1334,1715)(1335,1716)
     (1337,1719)(1339,1721)(1342,1725)(1343,1726)(1345,1729)(1348,1733)(1350,
     1735)(1351,1736)(1352,1738)(1354,1579)(1355,1741)(1357,1744)(1359,1746)
     (1360,1747)(1362,1750)(1363,1751)(1364,1753)(1366,1756)(1369,1760)(1371,
     1762)(1372,1763)(1373,1765)(1376,1769)(1377,1770)(1379,1773)(1380,1758)
     (1381,1775)(1384,1779)(1385,1780)(1386,1782)(1388,1785)(1390,1788)(1391,
     1789)(1393,1792)(1395,1794)(1396,1795)(1397,1797)(1400,1801)(1402,1803)
     (1403,1804)(1404,1806)(1407,1810)(1408,1811)(1410,1814)(1413,1818)(1415,
     1820)(1416,1821)(1417,1823)(1419,1826)(1422,1830)(1423,1831)(1425,1834)
     (1427,1836)(1428,1837)(1429,1839)(1432,1843)(1433,1844)(1435,1847)(1436,
     1828)(1437,1849)(1440,1853)(1441,1854)(1443,1857)(1445,1860)(1446,1861)
     (1449,1865)(1451,1867)(1452,1868)(1454,1871)(1456,1873)(1458,1876)(1461,
     1880)(1463,1882)(1464,1883)(1465,1885)(1468,1889)(1469,1890)(1471,1893)
     (1473,1895)(1474,1896)(1475,1898)(1478,1902)(1480,1904)(1481,1905)(1483,
     1908)(1485,1910)(1488,1914)(1489,1915)(1491,1918)(1494,1922)(1496,1924)
     (1497,1925)(1498,1927)(1501,1931)(1502,1932)(1504,1934)(1505,1935)(1507,
     1938)(1508,1939)(1509,1941)(1511,1944)(1514,1948)(1516,1950)(1517,1951)
     (1518,1953)(1521,1957)(1522,1958)(1524,1961)(1525,1946)(1526,1963)(1529,
     1967)(1531,1969)(1533,1972)(1535,1975)(1537,1978)(1539,1980)(1540,1981)
     (1542,1984)(1543,1974)(1544,1986)(1546,1989)(1549,1993)(1551,1995)(1552,
     1996)(1555,2000)(1557,2003)(1560,2007)(1562,2009)(1563,2010)(1564,2012)
     (1566,2015)(1568,2018)(1570,2020)(1571,2021)(1572,2023)(1575,2027)(1576,
     2028)(1578,2031)(1580,2033)(1582,2036)(1585,2040)(1587,2042)(1588,2043)
     (1590,2046)(1594,2050)(1597,2054)(1599,2056)(1600,2057)(1601,2059)(1604,
     2063)(1605,2064)(1607,2067)(1609,2069)(1610,1864)(1612,2072)(1613,2073)
     (1614,2075)(1616,2078)(1619,2082)(1620,2083)(1622,2086)(1624,2088)(1625,
     2089)(1626,2091)(1629,2095)(1630,2096)(1632,2099)(1633,2080)(1634,2101)
     (1636,2104)(1639,2108)(1641,2110)(1642,2111)(1645,2115)(1646,2116)(1648,
     2119)(1651,2123)(1653,2125)(1654,2126)(1655,2128)(1658,2132)(1659,2133)
     (1661,2135)(1662,2136)(1663,2138)(1666,2142)(1668,2144)(1669,2145)(1671,
     2148)(1673,2150)(1676,2154)(1677,2155)(1679,2158)(1682,2162)(1683,2163)
     (1685,2166)(1687,2168)(1688,2169)(1689,2171)(1690,2173)(1692,2176)(1695,
     2180)(1697,2182)(1698,2183)(1699,2185)(1702,2189)(1703,2190)(1705,2193)
     (1706,2178)(1707,2195)(1710,2199)(1711,2200)(1712,2202)(1714,2205)(1717,
     2209)(1718,2210)(1720,2213)(1722,2215)(1723,2216)(1724,2218)(1727,2222)
     (1728,2223)(1730,2226)(1731,2207)(1732,2228)(1734,2231)(1737,2235)(1739,
     2237)(1740,2238)(1742,2241)(1743,2242)(1745,2245)(1748,2249)(1749,2250)
     (1752,2254)(1754,2256)(1755,2257)(1757,2260)(1759,2262)(1761,2265)(1764,
     2269)(1766,2271)(1767,2272)(1768,2274)(1771,2278)(1772,2279)(1774,2282)
     (1776,2284)(1777,2285)(1778,2287)(1781,2291)(1783,2293)(1784,2294)(1786,
     2297)(1787,2298)(1790,2302)(1791,2303)(1793,2306)(1796,2310)(1798,2312)
     (1799,2313)(1800,2315)(1802,2318)(1805,2322)(1807,2324)(1808,2325)(1809,
     2327)(1812,2331)(1813,2332)(1815,2335)(1816,2320)(1817,2337)(1819,2340)
     (1822,2344)(1824,2346)(1825,2347)(1827,2350)(1829,2352)(1832,2356)(1833,
     2357)(1835,2360)(1838,2364)(1840,2366)(1841,2367)(1842,2369)(1845,2373)
     (1846,2374)(1848,2377)(1850,2379)(1851,2380)(1852,2382)(1855,2385)(1856,
     2386)(1858,2389)(1859,2390)(1862,2394)(1863,2395)(1866,2399)(1870,2403)
     (1874,2407)(1875,2408)(1877,2411)(1878,2401)(1879,2413)(1881,2416)(1884,
     2420)(1886,2422)(1887,2423)(1888,2425)(1891,2429)(1892,2430)(1894,2433)
     (1897,2437)(1899,2439)(1900,2440)(1901,2442)(1903,2445)(1906,2449)(1907,
     2450)(1909,2453)(1911,2455)(1912,2456)(1913,2458)(1916,2462)(1917,2463)
     (1919,2466)(1920,2447)(1921,2468)(1923,2471)(1926,2475)(1928,2477)(1929,
     2478)(1930,2480)(1933,2484)(1936,2488)(1937,2489)(1940,2493)(1942,2495)
     (1943,2496)(1945,2499)(1947,2501)(1949,2504)(1952,2508)(1954,2510)(1955,
     2511)(1956,2513)(1959,2517)(1960,2518)(1962,2521)(1964,2523)(1965,2524)
     (1966,2526)(1968,2529)(1970,2531)(1971,2532)(1973,2535)(1976,2538)(1977,
     2539)(1979,2542)(1982,2546)(1983,2547)(1985,2550)(1987,2552)(1988,2553)
     (1990,2556)(1991,2557)(1992,2559)(1994,2562)(1997,2566)(1998,2567)(1999,
     2568)(2001,2571)(2002,2572)(2004,2575)(2005,2564)(2006,2577)(2008,2580)
     (2011,2584)(2013,2586)(2014,2587)(2016,2590)(2017,2591)(2019,2594)(2022,
     2598)(2024,2600)(2025,2601)(2026,2603)(2029,2607)(2030,2608)(2032,2611)
     (2034,2613)(2035,2614)(2037,2617)(2038,2618)(2039,2620)(2041,2623)(2044,
     2627)(2045,2628)(2048,2631)(2049,2632)(2051,2635)(2052,2625)(2053,2637)
     (2055,2640)(2058,2644)(2060,2646)(2061,2647)(2062,2649)(2065,2653)(2066,
     2654)(2070,2659)(2071,2660)(2074,2664)(2076,2666)(2077,2667)(2079,2670)
     (2081,2672)(2084,2676)(2085,2677)(2087,2680)(2090,2684)(2092,2686)(2093,
     2687)(2094,2689)(2097,2693)(2098,2694)(2100,2697)(2102,2699)(2103,2700)
     (2105,2703)(2107,2705)(2109,2708)(2112,2712)(2113,2713)(2114,2715)(2117,
     2719)(2118,2720)(2120,2723)(2121,2710)(2122,2725)(2124,2728)(2127,2732)
     (2129,2734)(2130,2735)(2131,2737)(2134,2741)(2137,2745)(2139,2747)(2140,
     2748)(2141,2750)(2143,2753)(2146,2757)(2147,2758)(2149,2761)(2151,2763)
     (2152,2764)(2153,2766)(2156,2770)(2157,2771)(2159,2276)(2160,2755)(2161,
     2775)(2164,2779)(2165,2780)(2167,2783)(2170,2787)(2172,2789)(2174,2791)
     (2175,2792)(2177,2795)(2179,2797)(2181,2800)(2184,2804)(2186,2806)(2187,
     2807)(2188,2809)(2191,2813)(2192,2814)(2194,2817)(2196,2819)(2197,2820)
     (2198,2822)(2201,2826)(2203,2828)(2204,2829)(2206,2832)(2208,2834)(2211,
     2838)(2212,2839)(2214,2842)(2217,2846)(2219,2848)(2220,2849)(2221,2851)
     (2224,2855)(2225,2856)(2227,2859)(2229,2861)(2230,2862)(2232,2865)(2233,
     2866)(2234,2868)(2236,2871)(2239,2875)(2240,2876)(2243,2880)(2244,2881)
     (2246,2884)(2247,2873)(2248,2886)(2251,2890)(2252,2891)(2253,2893)(2255,
     2896)(2258,2900)(2259,2901)(2261,2904)(2263,2906)(2264,2907)(2266,2910)
     (2267,2898)(2268,2912)(2270,2915)(2273,2919)(2275,2921)(2277,2923)(2280,
     2927)(2281,2928)(2283,2931)(2286,2935)(2288,2937)(2289,2938)(2290,2940)
     (2292,2943)(2295,2947)(2296,2948)(2299,2952)(2300,2953)(2301,2955)(2304,
     2959)(2305,2960)(2307,2963)(2308,2945)(2309,2965)(2311,2968)(2314,2972)
     (2316,2974)(2317,2975)(2319,2978)(2321,2565)(2323,2982)(2326,2986)(2328,
     2988)(2329,2989)(2330,2991)(2333,2995)(2334,2996)(2336,2999)(2338,3001)
     (2339,3002)(2341,3005)(2342,3006)(2343,3008)(2345,3011)(2349,3015)(2351,
     3018)(2353,3020)(2354,3021)(2355,3023)(2358,3027)(2359,3028)(2361,3031)
     (2362,3013)(2365,3035)(2368,3039)(2370,3041)(2371,3042)(2372,3044)(2375,
     3048)(2376,3049)(2378,2860)(2381,3055)(2383,3057)(2384,3058)(2387,3062)
     (2388,3063)(2391,3067)(2392,3068)(2393,3070)(2396,3074)(2397,3075)(2398,
     3076)(2400,3079)(2402,3081)(2404,3084)(2405,3085)(2406,3087)(2409,3091)
     (2410,3092)(2412,3095)(2414,3097)(2415,3098)(2417,3101)(2418,3102)(2419,
     3104)(2421,3107)(2424,3111)(2426,3113)(2427,3114)(2428,3116)(2432,3120)
     (2434,3123)(2435,3109)(2436,3125)(2438,3128)(2441,3132)(2443,3134)(2444,
     3135)(2446,3138)(2448,2616)(2451,3143)(2452,3144)(2454,3147)(2457,3151)
     (2459,3153)(2460,3154)(2461,3156)(2464,3160)(2465,3161)(2467,3164)(2469,
     3166)(2470,3167)(2472,3170)(2473,3171)(2474,3173)(2476,3176)(2479,3180)
     (2481,3182)(2482,3183)(2483,3185)(2485,3188)(2486,3178)(2487,3190)(2490,
     3194)(2491,3195)(2492,3197)(2494,3200)(2497,3204)(2498,3205)(2500,3208)
     (2502,3210)(2503,3211)(2505,3214)(2506,3202)(2507,3216)(2509,3219)(2512,
     3223)(2514,3225)(2515,3226)(2516,3228)(2519,3232)(2520,3233)(2522,3236)
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