q1 := (1,2,3)(4,6,9)(5,8,13)(7,11,18)(10,16,27)(12,20,34)(14,23,40)(15,25,44)
     (17,29,51)(19,32,57)(21,36,64)(22,38,68)(24,42,75)(26,46,82)(28,49,88)
     (30,53,95)(31,55,99)(33,59,105)(35,62,109)(37,66,116)(39,70,123)(41,73,
     129)(43,77,136)(45,80,56)(47,84,148)(48,86,151)(50,90,158)(52,93,164)(54,
     97,171)(58,103,182)(60,107,189)(61,83,146)(63,111,196)(65,114,202)(67,
     118,209)(69,121,215)(71,125,222)(72,127,159)(74,131,232)(76,134,238)(78,
     138,244)(79,140,248)(81,143,254)(85,149,263)(87,153,269)(89,156,275)(91,
     160,281)(92,162,285)(94,166,292)(96,169,297)(98,173,304)(100,176,310)
     (101,178,314)(102,180,317)(104,184,324)(106,187,330)(108,191,337)(110,
     194,343)(112,198,350)(113,200,354)(115,204,225)(117,207,365)(119,211,371)
     (120,213,374)(122,217,380)(124,220,385)(126,224,392)(128,227,397)(130,
     230,402)(132,234,409)(133,236,413)(135,240,419)(137,242,423)(139,246,399)
     (141,250,434)(142,252,438)(144,255,443)(145,257,446)(147,260,442)(150,
     212,373)(152,267,461)(154,271,468)(155,273,472)(157,277,479)(161,283,490)
     (163,287,497)(165,290,502)(167,294,508)(168,296,512)(170,299,334)(172,
     302,522)(174,306,527)(175,308,529)(177,312,427)(179,315,540)(181,319,545)
     (183,322,469)(185,326,556)(186,328,559)(188,332,566)(190,335,571)(192,
     339,577)(193,341,581)(195,345,588)(197,348,593)(199,352,600)(201,355,605)
     (203,358,609)(205,361,615)(206,363,619)(208,367,623)(210,369,627)(214,
     375,634)(216,378,639)(218,381,644)(219,383,648)(221,387,654)(223,390,660)
     (226,395,667)(228,398,384)(229,400,673)(231,404,680)(233,407,686)(235,
     411,693)(237,414,698)(239,417,703)(241,421,709)(243,425,715)(245,428,720)
     (247,431,265)(249,432,727)(251,436,733)(253,440,736)(256,445,316)(258,
     448,746)(259,450,750)(261,453,415)(262,455,757)(264,458,364)(266,460,763)
     (268,463,768)(270,466,484)(272,470,777)(274,474,782)(276,477,787)(278,
     481,793)(279,483,796)(280,485,799)(282,488,803)(284,492,809)(286,495,437)
     (288,499,820)(289,467,774)(291,504,827)(293,506,831)(295,510,837)(298,
     515,845)(300,518,850)(301,520,854)(303,523,859)(305,526,864)(307,528,867)
     (309,531,872)(311,534,878)(313,537,884)(318,544,597)(320,546,895)(321,
     548,898)(323,551,903)(325,554,907)(327,558,913)(329,561,916)(331,564,922)
     (333,568,927)(336,573,936)(338,575,940)(340,579,946)(342,583,953)(344,
     586,958)(346,590,964)(347,591,966)(349,595,972)(351,598,977)(353,602,984)
     (356,454,756)(357,608,993)(359,611,998)(360,613,1002)(362,617,1009)(366,
     621,1015)(368,625,943)(370,629,1028)(372,631,1032)(376,422,711)(377,637,
     1040)(379,641,1045)(382,646,475)(386,652,1059)(388,656,945)(389,658,1068)
     (391,662,1074)(393,664,1077)(394,665,1078)(396,669,1084)(401,675,1092)
     (403,678,1097)(405,682,1102)(406,684,1106)(408,688,1112)(410,691,1118)
     (412,695,1124)(416,701,1132)(418,704,723)(420,707,1142)(424,713,642)(426,
     717,1157)(429,722,1164)(430,724,663)(433,728,1171)(435,731,1176)(439,734,
     594)(441,738,1186)(444,740,1190)(447,744,1198)(449,748,885)(451,751,1208)
     (452,753,1212)(456,758,1220)(457,760,1224)(459,762,719)(462,766,1232)
     (464,769,1236)(465,771,1239)(471,778,1250)(473,780,1254)(476,785,1262)
     (478,788,1267)(480,791,1273)(482,555,909)(486,800,539)(487,802,1286)(489,
     805,1290)(491,807,1294)(493,811,732)(494,813,1303)(496,816,1308)(498,818,
     552)(500,582,951)(501,823,1318)(503,825,1321)(505,829,1328)(507,833,1314)
     (509,836,1337)(511,839,1342)(513,841,1344)(514,843,1348)(516,846,1351)
     (517,848,1354)(519,852,1361)(521,856,1367)(524,861,1019)(525,821,1315)
     (530,870,1386)(532,874,1393)(533,876,1396)(535,880,1401)(536,882,1404)
     (538,886,877)(541,890,700)(542,887,1408)(543,891,1414)(547,897,1405)(549,
     900,1427)(553,905,618)(557,743,1196)(560,832,1332)(562,918,1447)(563,920,
     1451)(565,924,1458)(567,739,1188)(569,929,1465)(570,931,1469)(572,934,
     1473)(574,938,1479)(576,942,1486)(578,944,1489)(580,948,1493)(584,941,
     1484)(585,956,1504)(587,959,1509)(589,962,1514)(592,968,1523)(596,974,
     1532)(599,979,1540)(601,982,1544)(603,986,1550)(604,988,1554)(606,991,
     607)(610,996,1565)(612,1000,1570)(614,1004,1576)(616,1007,1579)(620,1013,
     1588)(622,1017,1593)(624,1020,1597)(626,1023,1601)(628,1026,1607)(630,
     1030,651)(632,1034,1383)(633,1036,1621)(635,1037,1623)(636,1039,863)(638,
     1041,1626)(640,1043,1630)(643,994,1561)(645,1050,1637)(647,849,1356)(649,
     1054,1644)(650,1056,1647)(653,1061,1466)(655,1064,1284)(657,1067,1663)
     (659,1069,1665)(661,1072,1669)(666,1080,1680)(668,1082,1683)(670,1086,
     1397)(671,696,1126)(672,1088,1690)(674,1090,1692)(676,1094,1697)(677,
     1096,1701)(679,1098,1703)(681,1101,1439)(683,1104,1538)(685,1108,1714)
     (687,742,1194)(689,1114,1725)(690,1116,1153)(692,1120,1733)(694,976,1536)
     (697,1128,1743)(699,1131,1747)(702,1134,881)(705,1138,1758)(706,1140,
     1761)(708,1144,1293)(710,1146,1771)(712,1149,1774)(714,1152,949)(716,
     1155,889)(718,1159,1785)(721,1162,1790)(725,1168,1799)(726,1169,1122)
     (729,1172,1803)(730,1174,853)(735,1181,1814)(737,1184,1820)(741,1192,
     1830)(745,1200,932)(747,1203,1845)(749,901,1429)(752,1210,1853)(754,1214,
     1859)(755,1216,1863)(759,1222,1866)(761,1226,1879)(764,1229,1884)(765,
     842,1346)(767,1233,1891)(770,892,1370)(772,1241,1901)(773,1243,1903)(775,
     1246,1909)(776,1248,1913)(779,1252,906)(781,1255,1922)(783,1258,1926)
     (784,1260,1929)(786,1264,1476)(789,1269,1921)(790,1271,1942)(792,1275,
     1948)(794,1278,1954)(795,1280,1958)(797,1281,1960)(798,1282,1962)(801,
     1115,1125)(804,1288,1970)(806,1292,1976)(808,1296,1981)(810,1298,875)
     (812,1301,1349)(814,1305,1991)(815,1307,1994)(817,1310,1998)(819,1195,
     1834)(822,1316,2006)(824,1319,2008)(826,1323,2012)(828,1326,2017)(830,
     1329,1508)(834,1333,2024)(835,1335,2027)(838,1340,1103)(840,1343,2039)
     (844,1225,1877)(847,1336,2029)(851,1359,2058)(855,1365,2066)(857,1369,
     1937)(858,1371,2074)(860,1374,2079)(862,1377,1283)(865,1380,2085)(866,
     1382,2087)(868,1384,1428)(869,1049,1256)(871,1388,2093)(873,1391,2098)
     (879,1399,2107)(883,1406,2114)(888,1410,1430)(893,1417,1947)(894,1419,
     2129)(896,1421,2050)(899,1425,2134)(902,1031,1614)(904,1431,1450)(908,
     1403,2111)(910,1435,2140)(911,1437,2088)(912,1141,1763)(914,1441,2148)
     (915,1165,1795)(917,1445,1611)(919,1449,2157)(921,1453,2161)(923,1456,
     2167)(925,1459,2170)(926,1461,2174)(928,1464,2178)(930,1467,1189)(933,
     1129,1745)(935,1474,978)(937,1477,2190)(939,1481,2196)(947,1491,2207)
     (950,1494,2209)(952,1497,1658)(954,1500,2214)(955,1502,1422)(957,1506,
     2223)(960,1511,2151)(961,1512,2228)(963,1516,2160)(965,1519,2238)(967,
     1522,1636)(969,1524,2243)(970,1525,2244)(971,1527,2248)(973,1530,2253)
     (975,1534,2258)(980,1541,1767)(981,1378,2083)(983,1546,2271)(985,1548,
     2274)(987,1552,2277)(989,1556,2280)(990,1557,2282)(992,1409,2118)(995,
     1563,1992)(997,1567,1446)(999,1012,1586)(1001,1572,2296)(1003,1503,2219)
     (1005,1578,1016)(1006,1251,1917)(1008,1580,2309)(1010,1582,2313)(1011,
     1584,2317)(1014,1589,1871)(1018,1594,1357)(1021,1555,2278)(1022,1599,
     2337)(1024,1603,2343)(1025,1605,2346)(1027,1609,2349)(1029,1612,2353)
     (1033,1617,2360)(1035,1620,1052)(1038,1487,1211)(1042,1628,2371)(1044,
     1312,2002)(1046,1632,2374)(1047,1634,2375)(1048,1201,1841)(1051,1639,
     1590)(1053,1642,1717)(1055,1646,1622)(1057,1649,2391)(1058,1651,2392)
     (1060,1654,2397)(1062,1656,2401)(1063,1657,2403)(1065,1659,2406)(1066,
     1661,2409)(1070,1667,2415)(1071,1238,1897)(1073,1671,2419)(1075,1674,
     2424)(1076,1676,2426)(1079,1558,2284)(1081,1682,1615)(1083,1685,2432)
     (1085,1687,2435)(1087,1689,2438)(1089,1691,2439)(1091,1694,2444)(1093,
     1696,2446)(1095,1699,2448)(1099,1705,2452)(1100,1707,2456)(1105,1711,
     2461)(1107,1471,1173)(1109,1716,2468)(1110,1718,2469)(1111,1720,2472)
     (1113,1723,2475)(1117,1729,2479)(1119,1731,2483)(1121,1734,2488)(1123,
     1737,2492)(1127,1648,2389)(1133,1750,2505)(1135,1752,2508)(1136,1754,
     2511)(1137,1756,2514)(1139,1759,2518)(1143,1766,2527)(1145,1769,1837)
     (1147,1772,2536)(1148,1553,1331)(1150,1775,2540)(1151,1776,2020)(1154,
     1777,2542)(1156,1780,2546)(1158,1783,2550)(1160,1616,2358)(1161,1788,
     1910)(1163,1792,2564)(1166,1797,2571)(1167,1177,1808)(1170,1801,2576)
     (1175,1228,1882)(1178,1810,2440)(1179,1811,1688)(1180,1812,2124)(1182,
     1816,2592)(1183,1818,1854)(1185,1821,2597)(1187,1824,2602)(1191,1828,
     2606)(1193,1831,1631)(1197,1836,2612)(1199,1838,2615)(1202,1843,2621)
     (1204,1675,2073)(1205,1846,2041)(1206,1847,2517)(1207,1849,2626)(1209,
     1438,1650)(1213,1857,2069)(1215,1861,2639)(1217,1865,1306)(1218,1867,
     2593)(1219,1869,2646)(1221,1872,1543)(1223,1874,2651)(1227,1880,2656)
     (1230,1886,1825)(1231,1888,2663)(1234,1893,2668)(1235,1894,2669)(1237,
     1624,2005)(1240,1899,2675)(1242,1902,2667)(1244,1905,1885)(1245,1907,
     1564)(1247,1911,2683)(1249,1914,1559)(1253,1920,2162)(1257,1924,2589)
     (1259,1480,2194)(1261,1931,2436)(1263,1782,2549)(1265,1935,2706)(1266,
     1936,2707)(1268,1939,2495)(1270,1823,2601)(1272,1943,1906)(1274,1946,
     2716)(1276,1950,2710)(1277,1952,1633)(1279,1956,2726)(1285,1966,2316)
     (1287,1968,2581)(1289,1971,2526)(1291,1974,1392)(1295,1979,1739)(1297,
     1982,2696)(1299,1984,2749)(1300,1679,1800)(1302,1826,2604)(1304,1989,
     2753)(1309,1996,2760)(1311,2000,2764)(1313,2004,2766)(1317,2007,2768)
     (1320,1793,2565)(1322,2010,2770)(1324,2014,2774)(1325,2015,2776)(1327,
     2019,2781)(1330,1608,2133)(1338,2032,2794)(1339,2034,2796)(1341,2037,
     2799)(1345,2042,2520)(1347,2045,2804)(1350,2048,1941)(1352,2051,2807)
     (1353,2052,1806)(1355,2053,2808)(1358,2056,2812)(1360,2059,2365)(1362,
     2062,2816)(1363,2064,1498)(1364,2065,2820)(1366,2067,2089)(1368,2070,
     2412)(1372,2075,1488)(1373,2077,1434)(1376,2082,2685)(1379,2084,2834)
     (1381,2086,2836)(1385,2091,1424)(1387,2092,1418)(1389,2095,2584)(1390,
     2097,2840)(1394,2100,2844)(1395,2102,2845)(1398,2105,2035)(1400,2108,
     2849)(1402,1786,2555)(1407,1815,2590)(1411,2120,2859)(1412,2122,1542)
     (1413,2123,2861)(1415,2125,2864)(1416,2126,2866)(1420,2131,2535)(1423,
     1517,2234)(1426,2136,2181)(1432,2110,1668)(1433,2138,1773)(1436,2142,
     2882)(1440,2146,2886)(1442,1444,2152)(1443,2150,2405)(1448,2155,2423)
     (1452,1988,2752)(1454,2163,2901)(1455,2165,2460)(1457,2168,2905)(1460,
     2172,2909)(1462,2175,2911)(1463,2177,2730)(1468,2183,2486)(1470,2185,
     2921)(1472,2144,1805)(1475,2187,2922)(1478,2192,2926)(1482,2198,2932)
     (1483,1686,2434)(1485,2201,2934)(1490,2205,2937)(1492,1583,2315)(1495,
     1993,2757)(1496,2212,1932)(1499,2213,2943)(1501,2216,2352)(1505,2061,
     2815)(1507,1765,2525)(1510,2182,2918)(1513,1762,2013)(1515,2232,1878)
     (1518,2236,2963)(1520,2239,2965)(1521,1581,2311)(1526,2246,2386)(1528,
     2250,2974)(1529,2252,2978)(1531,2254,2980)(1533,2257,2983)(1535,2260,
     2529)(1537,2263,2977)(1539,2266,2878)(1545,2269,2293)(1547,2272,2999)
     (1549,1896,1727)(1551,1833,2608)(1560,2287,3014)(1562,2290,2801)(1566,
     2292,2649)(1568,2295,2889)(1569,2294,1842)(1571,2028,2617)(1573,2298,
     3022)(1574,2300,2647)(1575,2302,3026)(1577,2305,3031)(1585,2319,2367)
     (1587,2322,1980)(1591,2215,2944)(1592,2327,3048)(1595,2331,2467)(1596,
     2333,3053)(1598,2335,3056)(1600,2339,2969)(1602,2341,3061)(1604,2344,
     1629)(1606,2347,3064)(1610,2350,1951)(1613,2355,3070)(1618,2362,2202)
     (1619,2364,2522)(1625,2264,2106)(1627,2369,2220)(1635,2377,2047)(1638,
     2380,2312)(1640,2383,1964)(1641,1963,1802)(1643,2385,3091)(1645,2387,
     2738)(1652,2394,3098)(1653,2396,3100)(1655,2399,3102)(1660,2408,3111)
     (1662,2410,2744)(1664,1728,2478)(1666,2414,2465)(1670,2417,1760)(1672,
     2420,3119)(1673,2422,3123)(1677,2427,1889)(1678,2429,3128)(1681,2249,
     2275)(1684,2078,2829)(1693,2442,3132)(1695,2268,2995)(1698,2447,3136)
     (1700,2449,2457)(1702,2451,2237)(1704,2071,2823)(1706,2454,3141)(1708,
     2458,2348)(1709,2459,3145)(1710,1813,2588)(1712,2463,3148)(1713,2464,
     3150)(1715,2251,2976)(1719,2470,3153)(1721,2473,3157)(1722,2474,3092)
     (1724,2477,3160)(1726,1912,2684)(1730,2481,3163)(1732,2485,2080)(1735,
     2147,1983)(1736,2490,3168)(1738,2493,3164)(1740,2491,2245)(1741,2496,
     2265)(1742,2498,3172)(1744,1876,2653)(1746,1868,2645)(1748,2501,3175)
     (1749,2503,3177)(1751,2507,2814)(1753,2510,3181)(1755,2513,2038)(1757,
     2515,3054)(1764,2523,3187)(1768,2530,3190)(1770,2533,2896)(1778,2543,
     3197)(1779,2544,3199)(1781,2547,3202)(1784,2552,2096)(1787,2556,3209)
     (1789,2559,3213)(1791,2562,2579)(1794,2567,3218)(1796,2569,3046)(1798,
     2573,2972)(1804,1945,2715)(1807,2370,3083)(1809,2583,2627)(1817,2090,
     2372)(1819,2595,3240)(1822,2599,2711)(1827,2605,3174)(1829,2607,3249)
     (1832,2288,2655)(1835,2610,1839)(1840,2618,2833)(1844,2622,2609)(1848,
     2060,1850)(1851,2629,3265)(1852,2631,3220)(1855,2357,2211)(1856,2633,
     3271)(1858,2635,2325)(1860,2638,2240)(1862,2640,3277)(1864,2642,3117)
     (1870,2487,3152)(1873,2650,2330)(1875,2072,2825)(1881,2188,2166)(1883,
     2659,2773)(1887,2445,3134)(1890,2665,2987)(1892,2139,1900)(1895,2671,
     3292)(1898,2673,2145)(1904,2679,3155)(1908,2682,3300)(1915,2687,3016)
     (1916,2688,3303)(1918,2690,2821)(1919,2691,3176)(1923,2695,3305)(1925,
     2697,2199)(1927,2256,2661)(1928,2699,3124)(1930,2701,3309)(1933,2704,
     3312)(1934,2705,2494)(1938,2169,2906)(1944,2714,2662)(1949,2718,3318)
     (1953,2722,2281)(1955,2724,3322)(1957,2728,3325)(1959,2731,2846)(1961,
     2733,3329)(1965,2600,2379)(1967,2676,3296)(1969,2400,2210)(1972,2741,
     2195)(1973,2743,3224)(1975,2267,2993)(1977,2001,2634)(1978,2746,3337)
     (1985,2693,3113)(1986,2750,3191)(1987,2751,2186)(1990,2754,2877)(1995,
     2759,3347)(1997,2761,2648)(1999,2762,3342)(2003,2113,2852)(2009,2717,
     2890)(2011,2771,3112)(2016,2777,2425)(2018,2779,2043)(2021,2783,2127)
     (2022,2784,2698)(2023,2702,2769)(2025,2787,3368)(2026,2789,3189)(2030,
     2791,3032)(2031,2792,3372)(2033,2795,2321)(2036,2798,2692)(2040,2800,
     3239)(2044,2803,3171)(2046,2806,3381)(2049,2428,3127)(2054,2810,3382)
     (2055,2554,3208)(2057,2404,3108)(2063,2818,3387)(2068,2418,3118)(2076,
     2826,2431)(2081,2830,2843)(2094,2203,2936)(2099,2842,3109)(2101,2736,
     3330)(2103,2484,2384)(2104,2164,2902)(2109,2824,3248)(2112,2851,3403)
     (2115,2853,3406)(2116,2855,2497)(2117,2856,3407)(2119,2158,2895)(2121,
     2809,3343)(2128,2867,2854)(2130,2869,3413)(2132,2871,2793)(2135,2873,
     3244)(2137,2876,3419)(2141,2880,2967)(2143,2255,2393)(2149,2611,3251)
     (2153,2499,2314)(2154,2892,2233)(2156,2894,3287)(2159,2897,2875)(2171,
     2908,3402)(2173,2813,3261)(2176,2912,3069)(2179,2915,2189)(2180,2775,
     3201)(2184,2920,3310)(2191,2925,3258)(2193,2519,3052)(2197,2930,3445)
     (2200,2898,3422)(2204,2839,2411)(2206,2938,3451)(2208,2940,3095)(2217,
     2946,3231)(2218,2819,3389)(2221,2948,3456)(2222,2949,3457)(2224,2951,
     3071)(2225,2952,3293)(2226,2954,2847)(2227,2956,3373)(2229,2959,2672)
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