a21 := (1,3,6)(2,4,8)(5,9,14)(7,11,17)(10,15,22)(12,18,26)(13,19,28)(16,23,33)
     (20,29,40)(21,30,42)(24,34,47)(25,35,49)(27,37,52)(31,43,59)(32,44,61)
     (36,50,68)(38,53,72)(39,54,74)(41,56,77)(45,62,84)(46,63,86)(48,65,89)
     (51,69,94)(55,75,101)(57,78,105)(58,79,107)(60,81,110)(64,87,117)(66,90,
     121)(67,91,123)(70,95,128)(71,96,130)(73,98,133)(76,102,138)(80,108,145)
     (82,111,149)(83,112,151)(85,114,154)(88,118,159)(92,124,166)(93,125,168)
     (97,131,175)(99,134,179)(100,135,181)(103,139,186)(104,140,188)(106,142,
     191)(109,146,196)(113,152,203)(115,155,207)(116,156,209)(119,160,214)
     (120,161,216)(122,163,219)(126,169,226)(127,170,228)(129,172,231)(132,
     176,236)(136,182,243)(137,183,245)(141,189,252)(143,192,256)(144,193,258)
     (147,197,263)(148,198,265)(150,200,268)(153,204,273)(157,210,280)(158,
     211,282)(162,217,289)(164,220,293)(165,221,295)(167,223,298)(171,229,303)
     (173,232,307)(174,233,309)(177,237,314)(178,238,316)(180,240,319)(184,
     246,325)(185,247,327)(187,249,330)(190,253,335)(194,259,342)(195,260,344)
     (199,266,351)(201,269,355)(202,270,357)(205,274,362)(206,275,364)(208,
     277,367)(212,283,374)(213,284,376)(215,286,379)(218,290,384)(222,296,391)
     (224,299,227)(225,300,396)(230,304,401)(234,310,408)(235,311,410)(239,
     317,416)(241,320,420)(242,321,422)(244,322,424)(248,328,431)(250,331,434)
     (251,332,436)(254,336,441)(255,337,443)(257,339,446)(261,345,453)(262,
     346,455)(264,348,458)(267,352,463)(271,358,470)(272,359,472)(276,365,478)
     (278,368,482)(279,369,484)(281,371,487)(285,377,494)(287,380,497)(288,
     381,499)(291,385,504)(292,386,506)(294,388,509)(297,392,514)(301,397,452)
     (302,398,521)(305,402,526)(306,403,528)(308,405,531)(312,411,538)(313,
     412,540)(315,414,543)(318,417,547)(323,425,556)(324,426,558)(326,428,561)
     (329,432,566)(333,437,572)(334,438,574)(338,444,580)(340,447,584)(341,
     448,586)(343,450,589)(347,456,595)(349,459,599)(350,460,601)(353,464,606)
     (354,465,608)(356,467,611)(360,473,618)(361,474,620)(363,476,623)(366,
     479,627)(370,485,634)(372,488,638)(373,489,640)(375,491,643)(378,495,648)
     (382,500,654)(383,501,656)(387,507,662)(389,510,666)(390,511,668)(393,
     515,673)(394,516,675)(395,517,677)(399,522,683)(400,523,685)(404,529,691)
     (406,532,695)(407,533,697)(409,535,700)(413,541,707)(415,544,711)(418,
     548,716)(419,549,718)(421,551,721)(423,553,724)(427,559,731)(429,562,735)
     (430,563,737)(433,567,742)(435,569,745)(439,575,752)(440,576,754)(442,
     578,757)(445,581,761)(449,587,768)(451,590,772)(454,592,775)(457,596,780)
     (461,602,787)(462,603,789)(466,609,795)(468,612,799)(469,613,801)(471,
     615,804)(475,621,811)(477,624,815)(480,628,820)(481,629,822)(483,631,825)
     (486,635,830)(490,641,837)(492,644,841)(493,645,843)(496,649,848)(498,
     651,851)(502,657,858)(503,658,860)(505,660,863)(508,663,867)(512,669,874)
     (513,670,876)(518,678,885)(519,679,887)(520,680,888)(524,686,895)(525,
     687,897)(527,689,900)(530,692,904)(534,698,911)(536,701,915)(537,702,917)
     (539,704,920)(542,708,925)(545,712,930)(546,713,932)(550,719,938)(552,
     722,942)(554,725,946)(555,726,948)(557,728,951)(560,732,956)(564,738,963)
     (565,739,965)(568,743,970)(570,746,974)(571,747,976)(573,749,979)(577,
     755,986)(579,758,990)(582,762,995)(583,763,997)(585,765,1000)(588,769,
     1005)(591,773,1010)(593,776,1014)(594,777,1016)(597,781,1021)(598,782,
     1023)(600,784,1026)(604,790,1033)(605,791,1035)(607,793,1038)(610,796,
     1041)(614,802,1048)(616,805,1052)(617,806,1054)(619,808,1057)(622,812,
     1062)(625,816,1067)(626,817,1069)(630,823,1075)(632,826,1079)(633,827,
     1081)(636,831,1086)(637,832,1088)(639,834,1091)(642,838,1096)(646,844,
     1103)(647,845,1105)(650,849,1110)(652,852,1114)(653,853,1116)(655,855,
     1119)(659,861,1126)(661,864,1130)(664,868,1135)(665,869,1137)(667,871,
     1140)(671,877,1147)(672,878,1149)(674,880,1152)(676,882,1155)(681,889,
     1162)(682,890,1164)(684,892,1167)(688,898,1174)(690,901,1178)(693,905,
     1183)(694,906,1185)(696,908,1188)(699,912,1193)(703,918,1200)(705,921,
     1204)(706,922,1206)(709,926,1211)(710,927,1213)(714,933,1220)(715,934,
     1222)(717,936,1225)(720,939,1229)(723,943,1234)(727,949,1241)(729,952,
     1245)(730,953,1247)(733,957,1252)(734,958,1254)(736,960,1257)(740,966,
     1264)(741,967,1266)(744,971,1271)(748,977,1278)(750,980,1282)(751,981,
     1284)(753,983,1287)(756,987,1292)(759,991,1297)(760,992,1299)(764,998,
     1305)(766,1001,1309)(767,1002,1311)(770,1006,1316)(771,1007,1318)(774,
     1011,1323)(778,1017,1330)(779,1018,1332)(783,1024,1338)(785,1027,1342)
     (786,1028,1344)(788,1030,1347)(792,1036,1354)(794,1039,1358)(797,1042,
     1362)(798,1043,1364)(800,1045,1367)(803,1049,1372)(807,1055,1379)(809,
     1058,1383)(810,1059,1385)(813,1063,1390)(814,1064,1392)(818,1070,1399)
     (819,1071,1401)(821,1073,1404)(824,1076,1408)(828,1082,1415)(829,1083,
     1417)(833,1089,1424)(835,1092,1428)(836,1093,1430)(839,1097,1435)(840,
     1098,1437)(842,1100,1440)(846,1106,1447)(847,1107,1449)(850,1111,1454)
     (854,1117,1461)(856,1120,1465)(857,1121,1467)(859,1123,1470)(862,1127,
     1475)(865,1131,1480)(866,1132,1482)(870,1138,1488)(872,1141,1492)(873,
     1142,1494)(875,1144,1497)(879,1150,1504)(881,1153,1507)(883,1156,1511)
     (884,1157,1513)(886,1159,1516)(891,1165,1523)(893,1168,1527)(894,1169,
     1529)(896,1171,1532)(899,1175,1537)(902,1179,1542)(903,1180,1544)(907,
     1186,1550)(909,1189,1554)(910,1190,1556)(913,1194,1561)(914,1195,1563)
     (916,1197,1566)(919,1201,1571)(923,1207,1578)(924,1208,1580)(928,1214,
     1587)(929,1215,1589)(931,1217,1592)(935,1223,1599)(937,1226,1603)(940,
     1230,1607)(941,1231,1609)(944,1235,1614)(945,1236,1616)(947,1238,1619)
     (950,1242,1624)(954,1248,1631)(955,1249,1633)(959,1255,1638)(961,1258,
     1642)(962,1259,1644)(964,1261,1647)(968,1267,1654)(969,1268,1656)(972,
     1272,1661)(973,1273,1663)(975,1275,1666)(978,1279,1671)(982,1285,1678)
     (984,1288,1682)(985,1289,1684)(988,1293,1689)(989,1294,1691)(993,1300,
     1698)(994,1301,1700)(996,1303,1703)(999,1306,1707)(1003,1312,1714)(1004,
     1313,1716)(1008,1319,1723)(1009,1320,1725)(1012,1324,1730)(1013,1325,
     1732)(1015,1327,1735)(1019,1333,1742)(1020,1334,1744)(1022,1336,1747)
     (1025,1339,1751)(1029,1345,1758)(1031,1348,1762)(1032,1349,1764)(1034,
     1351,1767)(1037,1355,1772)(1040,1359,1777)(1044,1365,1783)(1046,1368,
     1787)(1047,1369,1789)(1050,1373,1794)(1051,1374,1796)(1053,1376,1799)
     (1056,1380,1804)(1060,1386,1811)(1061,1387,1813)(1065,1393,1820)(1066,
     1394,1822)(1068,1396,1825)(1072,1402,1832)(1074,1405,1836)(1077,1409,
     1841)(1078,1410,1843)(1080,1412,1846)(1084,1418,1853)(1085,1419,1855)
     (1087,1421,1858)(1090,1425,1863)(1094,1431,1870)(1095,1432,1872)(1099,
     1438,1878)(1101,1441,1882)(1102,1442,1884)(1104,1444,1887)(1108,1450,
     1743)(1109,1451,1895)(1112,1455,1900)(1113,1456,1902)(1115,1458,1905)
     (1118,1462,1910)(1122,1468,1917)(1124,1471,1921)(1125,1472,1923)(1128,
     1476,1928)(1129,1477,1930)(1133,1483,1937)(1134,1484,1939)(1136,1486,
     1942)(1139,1489,1946)(1143,1495,1953)(1145,1498,1957)(1146,1499,1959)
     (1148,1501,1962)(1151,1505,1967)(1154,1508,1971)(1158,1514,1977)(1160,
     1517,1981)(1161,1518,1983)(1163,1520,1986)(1166,1524,1991)(1170,1530,
     1998)(1172,1533,2002)(1173,1534,2004)(1176,1538,2009)(1177,1539,2011)
     (1181,1545,2018)(1182,1546,2020)(1184,1548,2023)(1187,1551,2027)(1191,
     1557,2034)(1192,1558,2036)(1196,1564,2043)(1198,1567,2047)(1199,1568,
     2049)(1202,1572,2054)(1203,1573,2056)(1205,1575,2059)(1209,1581,2066)
     (1210,1582,2068)(1212,1584,2071)(1216,1590,2078)(1218,1593,2082)(1219,
     1594,2084)(1221,1596,2087)(1224,1600,2092)(1227,1604,2097)(1228,1605,
     2099)(1232,1610,2104)(1233,1611,2106)(1237,1617,2113)(1239,1620,2117)
     (1240,1621,2119)(1243,1625,2124)(1244,1626,2126)(1246,1628,2129)(1250,
     1634,2135)(1251,1635,2137)(1253,1637,2140)(1256,1639,2143)(1260,1645,
     2150)(1262,1648,2154)(1263,1649,2156)(1265,1651,2159)(1269,1657,2166)
     (1270,1658,2168)(1274,1664,2174)(1276,1667,2178)(1277,1668,2180)(1280,
     1672,2185)(1281,1673,2187)(1283,1675,2190)(1286,1679,2195)(1290,1685,
     2201)(1291,1686,2203)(1295,1692,2210)(1296,1693,2212)(1298,1695,2215)
     (1302,1701,2222)(1304,1704,2226)(1307,1708,2231)(1308,1709,2233)(1310,
     1711,2236)(1314,1717,2243)(1315,1718,2245)(1317,1720,2248)(1321,1726,
     2255)(1322,1727,2257)(1326,1733,2263)(1328,1736,2267)(1329,1737,2269)
     (1331,1739,2272)(1335,1745,2278)(1337,1748,2282)(1340,1752,2287)(1341,
     1753,1979)(1343,1755,2291)(1346,1759,2296)(1350,1765,2303)(1352,1768,
     2307)(1353,1769,2309)(1356,1773,2314)(1357,1774,2316)(1360,1778,2321)
     (1361,1779,2323)(1363,1781,2326)(1366,1784,2330)(1370,1790,2337)(1371,
     1791,2339)(1375,1797,2346)(1377,1800,2350)(1378,1801,2352)(1381,1805,
     2357)(1382,1806,2359)(1384,1808,2362)(1388,1814,2369)(1389,1815,2371)
     (1391,1817,2374)(1395,1823,2381)(1397,1826,2385)(1398,1827,2387)(1400,
     1829,2390)(1403,1833,2395)(1406,1837,2400)(1407,1838,2402)(1411,1844,
     2408)(1413,1847,2412)(1414,1848,2414)(1416,1850,2417)(1420,1856,2424)
     (1422,1859,2428)(1423,1860,2430)(1426,1864,2435)(1427,1865,2437)(1429,
     1867,2440)(1433,1873,2447)(1434,1874,2449)(1436,1876,2452)(1439,1879,
     2456)(1443,1885,2463)(1445,1888,2467)(1446,1889,2469)(1448,1891,2472)
     (1452,1896,2478)(1453,1897,2480)(1457,1903,2486)(1459,1906,2490)(1460,
     1907,2492)(1463,1911,2497)(1464,1912,2499)(1466,1914,2502)(1469,1918,
     2507)(1473,1924,2514)(1474,1925,2516)(1478,1931,2523)(1479,1932,2525)
     (1481,1934,2528)(1485,1940,2535)(1487,1943,2539)(1490,1947,2544)(1491,
     1948,2546)(1493,1950,2549)(1496,1954,2554)(1500,1960,2561)(1502,1963,
     2565)(1503,1964,2567)(1506,1968,2572)(1509,1972,2577)(1510,1973,2579)
     (1512,1975,2582)(1515,1978,2586)(1519,1984,2592)(1521,1987,2596)(1522,
     1988,2598)(1525,1992,2603)(1526,1993,2605)(1528,1995,2608)(1531,1999,
     2613)(1535,2005,2620)(1536,2006,2622)(1540,2012,2629)(1541,2013,2631)
     (1543,2015,2634)(1547,2021,2641)(1549,2024,2645)(1552,2028,2650)(1553,
     2029,2652)(1555,2031,2655)(1559,2037,2662)(1560,2038,2664)(1562,2040,
     2667)(1565,2044,2672)(1569,2050,2679)(1570,2051,2681)(1574,2057,2687)
     (1576,2060,2691)(1577,2061,2693)(1579,2063,2696)(1583,2069,2703)(1585,
     2072,2707)(1586,2073,2709)(1588,2075,2711)(1591,2079,2716)(1595,2085,
     2723)(1597,2088,2727)(1598,2089,2729)(1601,2093,2734)(1602,2094,2736)
     (1606,2100,2743)(1608,2102,2746)(1612,2107,2752)(1613,2108,2754)(1615,
     2110,2757)(1618,2114,2762)(1622,2120,2769)(1623,2121,2771)(1627,2127,
     2777)(1629,2130,2781)(1630,2131,2783)(1632,2133,2786)(1636,2138,2792)
     (1640,2144,2799)(1641,2145,2801)(1643,2147,2804)(1646,2151,2809)(1650,
     2157,2816)(1652,2160,2820)(1653,2161,2822)(1655,2163,2825)(1659,2169,
     2832)(1660,2170,2834)(1662,2172,2837)(1665,2175,2841)(1669,2181,2847)
     (1670,2182,2849)(1674,2188,2856)(1676,2191,2860)(1677,2192,2862)(1680,
     2196,2867)(1681,2197,2869)(1683,2198,2871)(1687,2204,2878)(1688,2205,
     2880)(1690,2207,2883)(1694,2213,2890)(1696,2216,2894)(1697,2217,2896)
     (1699,2219,2899)(1702,2223,2904)(1705,2227,2909)(1706,2228,2911)(1710,
     2234,2917)(1712,2237,2921)(1713,2238,2923)(1715,2240,2926)(1719,2246,
     2932)(1721,2249,2936)(1722,2250,2938)(1724,2252,2941)(1728,2258,2948)
     (1729,2259,2950)(1731,2261,2953)(1734,2264,2957)(1738,2270,2964)(1740,
     2273,2968)(1741,2274,2970)(1746,2279,2976)(1749,2283,2981)(1750,2284,
     2983)(1754,2289,2989)(1756,2292,2993)(1757,2293,2995)(1760,2297,3000)
     (1761,2298,3002)(1763,2300,3005)(1766,2304,3010)(1770,2310,3017)(1771,
     2311,3019)(1775,2317,3026)(1776,2318,3028)(1780,2324,3035)(1782,2327,
     3039)(1785,2331,3044)(1786,2332,3046)(1788,2334,3049)(1792,2340,3056)
     (1793,2341,3058)(1795,2343,3061)(1798,2347,3065)(1802,2353,3072)(1803,
     2354,3074)(1807,2360,3080)(1809,2363,3084)(1810,2364,3086)(1812,2366,
     3089)(1816,2372,3096)(1818,2375,3100)(1819,2376,3102)(1821,2378,3105)
     (1824,2382,3110)(1828,2388,3117)(1830,2391,3121)(1831,2392,3123)(1834,
     2396,3128)(1835,2397,3130)(1839,2403,3137)(1840,2404,3139)(1842,2406,
     3142)(1845,2409,3146)(1849,2415,3153)(1851,2418,3157)(1852,2419,3159)
     (1854,2421,3162)(1857,2425,3167)(1861,2431,3173)(1862,2432,3175)(1866,
     2438,3181)(1868,2441,3185)(1869,2442,3187)(1871,2444,3190)(1875,2450,
     3197)(1877,2453,3201)(1880,2457,3206)(1881,2458,3208)(1883,2460,3211)
     (1886,2464,3216)(1890,2470,3223)(1892,2473,3227)(1893,2474,3229)(1894,
     2475,3231)(1898,2481,3238)(1899,2482,3240)(1901,2484,3243)(1904,2487,
     3247)(1908,2493,3254)(1909,2494,3256)(1913,2500,3263)(1915,2503,3267)
     (1916,2504,3269)(1919,2508,3274)(1920,2509,3276)(1922,2511,3279)(1926,
     2517,3286)(1927,2518,3288)(1929,2520,3291)(1933,2526,3297)(1935,2529,
     3301)(1936,2530,3303)(1938,2532,3306)(1941,2536,3311)(1944,2540,3316)
     (1945,2541,3318)(1949,2547,3324)(1951,2550,3328)(1952,2551,3330)(1955,
     2555,3335)(1956,2556,3337)(1958,2558,3340)(1961,2562,3345)(1965,2568,
     3352)(1966,2569,3354)(1969,2573,3359)(1970,2574,3361)(1974,2580,3368)
     (1976,2583,3372)(1980,2587,3377)(1982,2589,3380)(1985,2593,3385)(1989,
     2599,3392)(1990,2600,3394)(1994,2606,3401)(1996,2609,3405)(1997,2610,
     3407)(2000,2614,3412)(2001,2615,3414)(2003,2617,3417)(2007,2623,3424)
     (2008,2624,3426)(2010,2626,3429)(2014,2632,3436)(2016,2635,3440)(2017,
     2636,3442)(2019,2638,3445)(2022,2642,3450)(2025,2646,3455)(2026,2647,
     3457)(2030,2653,3463)(2032,2656,3467)(2033,2657,3469)(2035,2659,3472)
     (2039,2665,3479)(2041,2668,3483)(2042,2669,3485)(2045,2673,3490)(2046,
     2674,3492)(2048,2676,3495)(2052,2682,3501)(2053,2683,3503)(2055,2685,
     3506)(2058,2688,3510)(2062,2694,3517)(2064,2697,3521)(2065,2698,3523)
     (2067,2700,3526)(2070,2704,3009)(2074,2710,3536)(2076,2712,3539)(2077,
     2713,3541)(2080,2717,3546)(2081,2718,3548)(2083,2720,3551)(2086,2724,
     3556)(2090,2730,3563)(2091,2731,3565)(2095,2737,3572)(2096,2738,3574)
     (2098,2740,3577)(2101,2744,3582)(2103,2747,3586)(2105,2749,3589)(2109,
     2755,3596)(2111,2758,3600)(2112,2759,3602)(2115,2763,3606)(2116,2764,
     3608)(2118,2766,3611)(2122,2772,3618)(2123,2773,3620)(2125,2775,3623)
     (2128,2778,3627)(2132,2784,3634)(2134,2787,3638)(2136,2789,3641)(2139,
     2793,3646)(2141,2795,3648)(2142,2796,3650)(2146,2802,3656)(2148,2805,
     3660)(2149,2806,3662)(2152,2810,3667)(2153,2811,3669)(2155,2813,3672)
     (2158,2817,3677)(2162,2823,3684)(2164,2826,3688)(2165,2827,3690)(2167,
     2829,3693)(2171,2835,3700)(2173,2838,3704)(2176,2842,3709)(2177,2843,
     3711)(2179,2845,3714)(2183,2850,3720)(2184,2851,3722)(2186,2853,3725)
     (2189,2857,3730)(2193,2863,3737)(2194,2864,3739)(2199,2872,3747)(2200,
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