q1 := (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)(162,217,288)(164,220,292)(165,221,222)(167,223,293)(171,229,298)
     (173,232,301)(174,233,303)(177,237,308)(178,238,310)(180,240,313)(184,
     246,320)(185,247,322)(187,249,325)(190,253,329)(194,259,336)(195,260,250)
     (199,266,342)(201,269,346)(202,270,348)(205,274,353)(206,275,355)(208,
     277,358)(212,283,365)(213,284,367)(215,286,370)(218,289,374)(224,294,380)
     (225,267,343)(227,296,383)(230,297,384)(234,304,391)(235,305,393)(239,
     311,400)(241,314,404)(242,315,406)(244,317,409)(248,323,416)(251,326,420)
     (254,330,424)(255,331,426)(257,333,429)(261,337,433)(262,338,435)(264,
     339,437)(271,349,448)(272,350,450)(276,356,457)(278,359,461)(279,360,463)
     (281,362,466)(285,368,473)(287,371,477)(290,375,482)(291,376,484)(295,
     381,490)(299,385,495)(300,386,497)(302,388,500)(306,394,507)(307,395,509)
     (309,397,512)(312,401,517)(316,407,408)(318,410,526)(319,411,528)(321,
     413,531)(324,417,536)(327,421,541)(332,427,548)(334,430,552)(335,431,554)
     (340,438,561)(341,439,563)(344,442,566)(345,443,567)(347,445,570)(351,
     451,577)(352,452,579)(354,454,582)(357,458,587)(361,464,465)(363,467,596)
     (364,468,598)(366,470,601)(369,474,605)(372,478,610)(373,479,612)(377,
     485,619)(378,486,621)(379,487,623)(382,491,628)(387,498,636)(389,501,640)
     (390,502,642)(392,504,645)(396,510,652)(398,513,654)(399,514,656)(402,
     518,661)(403,519,663)(405,521,666)(412,529,674)(414,532,677)(415,533,679)
     (418,537,684)(419,538,686)(422,542,689)(423,543,691)(425,545,694)(428,
     549,699)(432,555,706)(434,556,707)(436,558,710)(440,564,715)(441,565,717)
     (444,568,721)(446,571,725)(447,572,727)(449,574,730)(453,580,737)(455,
     583,740)(456,584,742)(459,588,746)(460,589,748)(462,591,751)(469,599,760)
     (471,481,614)(472,602,764)(475,606,768)(476,607,770)(480,613,777)(483,
     616,781)(488,624,789)(489,625,791)(492,629,796)(493,630,798)(494,631,800)
     (496,633,803)(499,637,808)(503,643,644)(505,646,559)(506,647,817)(508,
     649,820)(511,653,825)(515,657,830)(516,658,832)(520,664,839)(522,667,843)
     (523,668,845)(524,669,847)(525,638,809)(527,671,850)(530,540,688)(534,
     680,860)(535,681,862)(539,687,868)(544,692,874)(546,695,876)(547,696,878)
     (550,700,883)(551,701,885)(553,703,888)(557,708,894)(560,711,897)(562,
     712,898)(569,722,909)(573,728,729)(575,731,916)(576,732,918)(578,734,920)
     (581,738,925)(585,590,749)(586,743,813)(592,752,940)(593,753,942)(594,
     754,944)(595,755,946)(597,757,949)(600,761,953)(603,765,958)(604,766,960)
     (608,771,965)(609,772,967)(611,774,970)(615,779,976)(617,782,979)(618,
     783,980)(620,785,983)(622,787,986)(626,792,992)(627,793,994)(632,801,
     1003)(634,804,1006)(635,805,1008)(639,810,1014)(641,812,758)(648,818,
     1021)(650,821,1024)(651,822,1026)(655,827,1032)(659,833,1038)(660,834,
     1040)(662,836,1043)(665,840,1048)(670,848,1057)(672,851,1061)(673,852,
     1063)(675,854,1066)(676,855,1068)(678,857,1071)(682,863,1078)(683,756,
     947)(685,865,1081)(690,871,1088)(693,713,899)(697,879,1096)(698,880,1098)
     (702,886,1105)(704,889,1109)(705,890,1111)(709,895,1117)(714,900,1122)
     (716,902,1125)(718,904,1128)(719,905,1129)(720,906,1131)(723,736,922)
     (724,910,1136)(726,912,1139)(733,919,991)(735,921,1149)(739,926,1155)
     (741,928,1158)(744,931,1162)(745,932,1164)(747,934,1167)(750,937,1171)
     (759,950,1185)(762,954,1190)(763,955,1192)(767,961,1199)(769,963,1202)
     (773,968,969)(775,971,1208)(776,972,1161)(778,974,1212)(780,977,1216)
     (784,981,1220)(786,984,1224)(788,987,1228)(790,989,1231)(794,995,1237)
     (795,996,1002)(797,998,1241)(799,1000,1244)(802,1004,1247)(806,1009,1253)
     (807,1010,1255)(811,1015,1260)(814,872,1089)(815,1017,1263)(816,1018,
     1265)(819,1022,1270)(823,1027,1276)(824,1028,1278)(826,1030,1281)(828,
     1033,1285)(829,1034,1287)(831,1036,1290)(835,1041,1295)(837,1044,1011)
     (838,1045,1298)(841,1049,1303)(842,1050,1305)(844,1052,1308)(846,1054,
     1310)(849,1058,1314)(853,1064,1321)(856,1069,1326)(858,1072,1330)(859,
     1073,1332)(861,1075,1335)(864,1079,1339)(866,1082,1343)(867,1083,1345)
     (869,1085,1348)(870,1086,1349)(873,1090,1354)(875,1091,1356)(877,1093,
     1359)(881,1099,1366)(882,1100,1368)(884,1102,1371)(887,1106,1375)(891,
     1112,1382)(892,1113,1383)(893,1114,1385)(896,1118,1389)(901,1123,1124)
     (903,1126,1396)(907,1132,1403)(908,1133,1405)(911,1137,1410)(913,1140,
     1414)(914,1141,1415)(915,1142,1417)(917,1144,1420)(923,1151,1426)(924,
     1152,1428)(927,1156,1433)(929,1159,1437)(930,1160,1439)(933,1165,1442)
     (935,1168,1445)(936,1169,1438)(938,1172,1449)(939,1173,1451)(941,1175,
     1453)(943,1177,1456)(945,1179,1457)(948,1182,1460)(951,1186,1465)(952,
     1187,1467)(956,1193,1474)(957,1194,1476)(959,1196,1441)(962,1200,1116)
     (964,1203,1485)(966,1204,1487)(973,1210,1494)(975,1213,1498)(978,1217,
     1503)(982,1221,1508)(985,1225,1512)(988,1229,1517)(990,1232,1147)(993,
     1234,1522)(997,1239,1528)(999,1242,1491)(1001,1245,1533)(1005,1248,1537)
     (1007,1250,1540)(1012,1256,1547)(1013,1257,1549)(1016,1261,1553)(1019,
     1266,1558)(1020,1267,1560)(1023,1271,1565)(1025,1273,1568)(1029,1279,
     1575)(1031,1282,1577)(1035,1288,1289)(1037,1291,1264)(1039,1095,1361)
     (1042,1296,1590)(1046,1299,1594)(1047,1300,1596)(1051,1306,1603)(1053,
     1309,1607)(1055,1222,1509)(1056,1311,1610)(1059,1315,1615)(1060,1316,
     1616)(1062,1318,1351)(1065,1322,1621)(1067,1323,1580)(1070,1327,1627)
     (1074,1333,1334)(1076,1336,1636)(1077,1337,1638)(1080,1340,1642)(1084,
     1346,1648)(1087,1350,1393)(1092,1357,1659)(1094,1360,1663)(1097,1363,
     1667)(1101,1369,1673)(1103,1372,1676)(1104,1373,1678)(1107,1376,1681)
     (1108,1377,1682)(1110,1379,1684)(1115,1386,1692)(1119,1390,1696)(1120,
     1391,1697)(1121,1392,1699)(1127,1397,1702)(1130,1400,1706)(1134,1406,
     1711)(1135,1407,1713)(1138,1411,1717)(1143,1418,1723)(1145,1421,1727)
     (1146,1422,1728)(1148,1191,1471)(1150,1424,1731)(1153,1429,1737)(1154,
     1430,1739)(1157,1434,1743)(1163,1252,1542)(1166,1443,1748)(1170,1447,
     1751)(1174,1440,1747)(1176,1454,1759)(1178,1246,1534)(1180,1458,1764)
     (1181,1459,1766)(1183,1461,1769)(1184,1462,1771)(1188,1468,1777)(1189,
     1469,1779)(1195,1477,1478)(1197,1479,1789)(1198,1293,1586)(1201,1482,
     1364)(1205,1488,1798)(1206,1489,1800)(1207,1490,1802)(1209,1492,1804)
     (1211,1495,1808)(1214,1499,1811)(1215,1500,1431)(1218,1504,1816)(1219,
     1505,1818)(1223,1510,1823)(1226,1513,1827)(1227,1514,1829)(1230,1518,
     1833)(1233,1520,1521)(1235,1523,1838)(1236,1524,1672)(1238,1526,1842)
     (1240,1529,1846)(1243,1531,1849)(1249,1538,1856)(1251,1541,1859)(1254,
     1544,1496)(1258,1550,1865)(1259,1551,1867)(1262,1554,1280)(1268,1561,
     1876)(1269,1562,1878)(1272,1566,1882)(1274,1569,1463)(1275,1570,1887)
     (1277,1572,1890)(1283,1578,1897)(1284,1579,1898)(1286,1581,1900)(1292,
     1585,1905)(1294,1587,1908)(1297,1591,1913)(1301,1597,1920)(1302,1598,
     1921)(1304,1600,1923)(1307,1604,1928)(1312,1611,1935)(1313,1612,1937)
     (1317,1617,1941)(1319,1401,1444)(1320,1619,1943)(1324,1623,1946)(1325,
     1624,1948)(1328,1628,1952)(1329,1629,1954)(1331,1631,1957)(1338,1639,
     1966)(1341,1643,1970)(1342,1644,1972)(1344,1646,1975)(1347,1649,1907)
     (1352,1653,1981)(1353,1654,1982)(1355,1656,1985)(1358,1660,1990)(1362,
     1665,1666)(1365,1668,1996)(1367,1670,1999)(1370,1674,2003)(1374,1679,
     1497)(1378,1683,1641)(1380,1685,2015)(1381,1686,2017)(1384,1689,1746)
     (1387,1693,2023)(1388,1694,1933)(1394,1700,2029)(1395,1701,2030)(1398,
     1703,2031)(1399,1704,2033)(1402,1655,1983)(1404,1708,2036)(1408,1714,
     2042)(1409,1715,2044)(1412,1718,2048)(1413,1719,2050)(1416,1721,1609)
     (1419,1724,2056)(1423,1729,2061)(1425,1732,2064)(1427,1734,2067)(1432,
     1740,2074)(1435,1744,2077)(1436,1745,2079)(1446,1750,2082)(1448,1752,
     2084)(1450,1754,2087)(1452,1756,2090)(1455,1760,2095)(1464,1772,2106)
     (1466,1774,2109)(1470,1780,2116)(1472,1782,2118)(1473,1783,2120)(1475,
     1785,2122)(1480,1758,2092)(1481,1790,1614)(1483,1792,2126)(1484,1793,
     2128)(1486,1795,2129)(1493,1805,2139)(1501,1813,2147)(1502,1814,2149)
     (1506,1819,1507)(1511,1824,2159)(1515,1830,2165)(1516,1831,2167)(1519,
     1834,2171)(1525,1840,2177)(1527,1843,2180)(1530,1847,2185)(1532,1850,
     2189)(1535,1852,2192)(1536,1853,2194)(1539,1857,2198)(1543,1860,1861)
     (1545,1862,2201)(1546,1863,2203)(1548,1821,2155)(1552,1868,2209)(1555,
     1871,2213)(1556,1872,2215)(1557,1873,2217)(1559,1875,2219)(1563,1879,
     2224)(1564,1815,2150)(1567,1883,2229)(1571,1888,1889)(1573,1891,2232)
     (1574,1892,2234)(1576,1894,1647)(1582,1901,2240)(1583,1902,2242)(1584,
     1903,1707)(1588,1909,2247)(1589,1910,2248)(1592,1914,2251)(1593,1915,
     2253)(1595,1917,2256)(1599,1650,1978)(1601,1924,2262)(1602,1925,2263)
     (1605,1929,2267)(1606,1930,2269)(1608,1932,2272)(1613,1632,1958)(1618,
     1942,2072)(1620,1944,2283)(1622,1687,2018)(1625,1949,2287)(1626,1950,
     2289)(1630,1955,2294)(1633,1959,2298)(1634,1960,2299)(1635,1961,2300)
     (1637,1963,2303)(1640,1967,2013)(1645,1973,2227)(1651,1979,2314)(1652,
     1980,2316)(1657,1986,2320)(1658,1987,2322)(1661,1991,2327)(1662,1992,
     1788)(1664,1993,2105)(1669,1997,2333)(1671,2000,2169)(1675,2004,2339)
     (1677,2006,2342)(1680,2009,2345)(1688,2019,2355)(1690,2020,2356)(1691,
     2021,2358)(1695,2025,2363)(1698,1940,2278)(1705,2034,2371)(1709,2037,
     2375)(1710,2038,2376)(1712,2040,2378)(1716,2045,2383)(1720,2051,2389)
     (1722,2053,2392)(1725,2057,2397)(1726,2058,2399)(1730,2062,2233)(1733,
     2065,2066)(1735,2068,2409)(1736,2069,2411)(1738,2071,2414)(1741,2075,
     1794)(1742,2076,2418)(1749,2081,1947)(1753,2085,2427)(1755,2088,2200)
     (1757,2091,2432)(1761,2096,2437)(1762,2097,2438)(1763,2098,2440)(1765,
     2100,2443)(1767,2102,2446)(1768,2103,2049)(1770,2104,2449)(1773,2107,
     2108)(1775,2110,2453)(1776,2111,2455)(1778,2113,2114)(1781,2117,2460)
     (1784,2121,2465)(1786,2123,2467)(1791,2022,2359)(1796,2130,2472)(1797,
     2131,2474)(1799,2133,2476)(1801,2135,2478)(1803,2137,2480)(1806,2140,
     2483)(1807,2141,2485)(1809,1874,2218)(1810,2143,2487)(1812,2145,2490)
     (1817,2151,2494)(1820,2154,2498)(1822,2156,2501)(1825,2160,2505)(1826,
     1836,2173)(1828,2162,2506)(1832,2168,2512)(1835,2172,2515)(1837,2174,
     2518)(1839,2073,2415)(1841,2178,2523)(1844,2181,2527)(1845,2182,2529)
     (1848,2186,2534)(1851,2190,2537)(1854,2195,2542)(1855,2196,2543)(1858,
     2199,2546)(1864,2204,2514)(1866,2206,2551)(1869,2210,2556)(1870,2211,
     2558)(1877,2221,2565)(1880,2225,2568)(1881,2226,2570)(1884,2230,2245)
     (1885,2231,2574)(1886,2179,2524)(1893,2235,2578)(1895,2236,1939)(1896,
     2237,2580)(1899,2238,2582)(1904,2243,2587)(1906,2244,2589)(1911,2249,
     2594)(1912,2250,2595)(1916,2254,2255)(1918,2257,2601)(1919,2258,2492)
     (1926,2264,2607)(1927,2265,2567)(1931,2270,2305)(1934,2273,2517)(1936,
     2275,2617)(1938,2277,2620)(1945,2284,2373)(1951,2290,2223)(1953,2292,
     2634)(1956,2295,2638)(1962,2301,2369)(1964,2304,2647)(1965,2124,2468)
     (1968,2306,2649)(1969,2307,2642)(1971,2309,2652)(1974,2311,2654)(1976,
     2312,2386)(1977,2313,2656)(1984,2318,2661)(1988,2323,2665)(1989,2324,
     2667)(1994,2330,2674)(1995,2331,2547)(1998,2334,2405)(2001,2335,2678)
     (2002,2336,2680)(2005,2340,2683)(2007,2343,2008)(2010,2346,2689)(2011,
     2347,2690)(2012,2348,2187)(2014,2349,2693)(2016,2351,2163)(2024,2361,
     2705)(2026,2266,2609)(2027,2364,2708)(2028,2365,2709)(2032,2368,2712)
     (2035,2372,2716)(2039,2377,2720)(2041,2379,2723)(2043,2380,2454)(2046,
     2384,2729)(2047,2385,2655)(2052,2390,2735)(2054,2393,2738)(2055,2394,
     2740)(2059,2400,2745)(2060,2401,2747)(2063,2404,2751)(2070,2412,2758)
     (2078,2419,2764)(2080,2421,2766)(2083,2424,2768)(2086,2428,2771)(2089,
     2429,2773)(2093,2434,2777)(2094,2435,2779)(2099,2441,2784)(2101,2444,
     2786)(2112,2456,2132)(2115,2458,2798)(2119,2462,2801)(2125,2239,2583)
     (2127,2470,2807)(2134,2477,2813)(2136,2479,2533)(2138,2481,2815)(2142,
     2486,2310)(2144,2488,2489)(2146,2491,2822)(2148,2493,2824)(2152,2495,
     2827)(2153,2496,2550)(2157,2164,2507)(2158,2502,2834)(2161,2354,2698)
     (2166,2509,2841)(2170,2513,2845)(2175,2519,2849)(2176,2520,2851)(2183,
     2530,2625)(2184,2531,2426)(2188,2535,2864)(2191,2538,2867)(2193,2540,
     2870)(2197,2544,2319)(2202,2548,2876)(2205,2337,2681)(2207,2552,2880)
     (2208,2553,2881)(2212,2559,2884)(2214,2561,2886)(2216,2562,2744)(2220,
     2563,2564)(2222,2566,2890)(2228,2571,2279)(2241,2396,2395)(2246,2590,
     2908)(2252,2596,2912)(2260,2603,2918)(2261,2328,2671)(2268,2610,2924)
     (2271,2613,2714)(2274,2615,2616)(2276,2618,2664)(2280,2622,2817)(2281,
     2410,2755)(2282,2623,2934)(2285,2626,2826)(2286,2627,2937)(2288,2629,
     2939)(2291,2632,2943)(2293,2635,2736)(2296,2639,2949)(2297,2640,2950)
     (2302,2645,2953)(2308,2604,2919)(2315,2658,2657)(2317,2660,2814)(2321,
     2663,2832)(2325,2668,2969)(2326,2669,2971)(2329,2672,2974)(2332,2675,
     2977)(2338,2682,2982)(2341,2684,2985)(2344,2459,2466)(2350,2694,2992)
     (2352,2696,2994)(2353,2697,2996)(2357,2700,2998)(2360,2703,3002)(2362,
     2706,3005)(2366,2710,3008)(2367,2711,3010)(2370,2713,2391)(2374,2717,
     3014)(2381,2725,3017)(2382,2726,2560)(2387,2731,3022)(2388,2732,2692)
     (2398,2742,3030)(2402,2748,3034)(2403,2749,2407)(2406,2752,3038)(2408,
     2753,3039)(2413,2759,3045)(2416,2761,3048)(2417,2762,2557)(2420,2765,
     3052)(2422,2704,3003)(2423,2767,2976)(2425,2541,2804)(2430,2774,2719)
     (2431,2775,2770)(2433,2545,2873)(2436,2780,3058)(2439,2781,3064)(2442,
     2785,3068)(2445,2787,3071)(2447,2789,3073)(2448,2790,2829)(2450,2792,
     3077)(2451,2793,3079)(2452,2794,2593)(2457,2797,3063)(2461,2799,2916)
     (2463,2802,2577)(2464,2803,3086)(2469,2806,3088)(2471,2646,2878)(2473,
     2598,2914)(2475,2810,3092)(2482,2816,3096)(2484,2818,3097)(2497,2828,
     3104)(2499,2830,3106)(2500,2831,3076)(2503,2835,2688)(2504,2836,3110)
     (2508,2839,3113)(2510,2842,3115)(2511,2549,2877)(2516,2847,3118)(2521,
     2852,3123)(2522,2853,2679)(2525,2855,3125)(2526,2856,2997)(2528,2858,
     2699)(2532,2862,2875)(2536,2865,3135)(2539,2868,2644)(2554,2812,2555)
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