z1 := (1,2,3)(4,6,11,20,13,7)(5,8,15,25,17,9)(10,18,29,49,31,19)(12,21,34,58, 36,22)(14,23,38,65,40,24)(16,26,43,74,45,27)(28,46,79,131,81,47)(30,50, 85,139,87,51)(32,53,70,41,69,54)(33,55,93,151,94,56)(35,59,98,157,100,60) (37,62,104,168,106,63)(39,66,109,175,111,67)(42,71,117,187,119,72)(44,75, 123,194,125,76)(48,82,135,215,137,83)(52,88,90,146,145,89)(57,95,153,147, 91,96)(61,101,162,260,164,102)(64,107,172,275,174,108)(68,112,114,182, 181,113)(73,120,190,183,115,121)(77,126,199,314,201,127)(78,128,202,319, 204,129)(80,132,209,331,211,133)(84,138,220,297,188,118)(86,140,223,352, 225,141)(92,148,236,370,238,149)(97,155,248,178,249,156)(99,158,252,391, 254,159)(103,165,265,412,267,166)(105,169,240,150,239,170)(110,176,281, 432,283,177)(116,184,291,332,210,185)(122,192,303,459,304,193)(124,195, 307,464,308,196)(130,205,324,491,326,206)(134,212,334,270,336,213)(136, 216,341,513,343,217)(142,226,357,534,358,227)(143,228,349,221,348,229) (144,230,299,189,298,231)(152,242,286,180,285,243)(154,245,376,241,375, 246)(160,255,395,592,397,256)(161,257,399,599,401,258)(163,261,405,305, 407,262)(167,268,417,626,419,269)(171,272,328,207,327,273)(173,276,425, 638,427,277)(179,208,329,279,429,284)(186,293,449,677,451,294)(191,301, 453,295,452,302)(197,309,467,699,469,310)(198,311,471,705,473,312)(200, 315,387,250,386,316)(203,320,483,723,485,321)(214,337,317,478,507,338) (218,344,287,439,518,345)(219,346,520,654,436,347)(222,350,524,782,525, 351)(224,353,481,720,529,354)(232,361,541,428,278,362)(233,363,543,808, 545,364)(234,365,547,812,549,366)(235,367,551,818,553,368)(237,371,558, 828,559,372)(244,379,313,474,570,380)(247,382,573,420,271,383)(251,388, 580,861,582,389)(253,392,587,613,410,264)(259,402,604,458,300,403)(263, 408,611,422,274,409)(266,413,618,915,620,414)(280,430,644,952,646,431) (282,433,649,958,651,434)(288,440,661,977,663,441)(289,442,665,981,667, 443)(290,444,669,986,671,445)(292,447,674,992,675,448)(296,454,381,571, 684,455)(306,461,691,1013,693,462)(318,479,717,1050,719,480)(322,486,660, 975,727,487)(323,488,729,1063,730,489)(325,492,476,712,735,493)(330,497, 740,978,662,498)(333,500,745,1080,747,501)(335,503,466,698,751,504)(339, 508,758,1101,760,509)(340,510,762,835,563,511)(342,514,766,1113,768,515) (355,530,790,1150,792,531)(356,532,794,1153,796,533)(359,536,537)(360, 538,801,1161,803,539)(369,554,822,1188,824,555)(373,560,831,741,574,384) (374,561,833,809,544,562)(377,565,838,1208,840,566)(378,567,841,1212,843, 568)(385,575,664,980,853,576)(390,583,865,982,666,584)(393,588,871,1250, 873,589)(394,590,875,1256,877,591)(396,593,878,1260,880,594)(398,596,884, 1172,810,597)(400,600,523,780,889,601)(404,605,896,1284,897,606)(406,608, 901,1290,902,609)(411,614,908,1299,910,615)(415,621,542,806,920,622)(416, 623,922,1316,923,624)(418,627,926,1321,928,628)(421,630,931,1329,933,631) (423,633,936,1336,938,634)(424,635,940,1000,680,636)(426,639,943,1344, 945,640)(435,652,963,1372,965,653)(437,655,832,1202,968,656)(438,657,970, 1380,972,658)(446,672,989,1404,991,673)(450,678,997,1412,999,679)(456, 685,1008,1072,738,495)(457,686,687)(460,688,546,811,1010,689)(463,694, 1017,813,548,695)(465,696,1019,1434,1021,697)(468,540,804,1166,1025,700) (470,702,1028,1392,979,703)(472,706,496,739,1033,707)(475,710,1039,1458, 1041,711)(477,713,1044,1464,1046,714)(482,721,1055,1476,1056,722)(484, 724,1057,1478,1059,725)(490,731,701,1026,1066,732)(494,736,925,1319,1070, 737)(499,742,781,1135,1076,743)(502,748,1085,1516,1087,749)(505,752,996, 1411,1092,753)(506,754,1094,942,1096,755)(512,763,1109,1413,998,764)(516, 769,1117,1538,1119,770)(517,771,1120,1556,1122,772)(519,774,1126,1091, 1128,775)(521,777,1131,1358,953,645)(522,778,1022,969,1133,779)(526,783, 1138,1408,993,784)(527,785,1141,1578,1143,786)(528,787,1145,1584,1147, 788)(535,798,1158,994,676,799)(550,815,1178,1620,1180,816)(552,819,1184, 1245,1186,820)(556,825,716,1049,1194,826)(557,827,1196,1417,1003,682) (564,643,950,852,834,836)(569,844,1215,1173,1217,845)(572,848,1222,1676, 1224,849)(577,854,1228,1684,1230,855)(578,856,1232,1154,795,857)(579,858, 1235,1613,1171,859)(581,862,1237,1566,1239,863)(585,866,1243,1311,918, 867)(586,868,612,906,1246,869)(595,881,850,924,625,882)(598,885,1269, 1730,1270,886)(602,890,874,1254,1277,891)(603,892,1279,1737,1280,893) (607,898,1286,1257,876,899)(610,903,1292,1031,1294,904)(616,911,860,1236, 1304,912)(617,913,1306,1767,1307,914)(619,916,1308,1769,1310,917)(629, 929,1325,1788,1327,930)(632,934,1112,765,1111,935)(637,941,1343,1322,927, 791)(641,946,1348,1816,1350,947)(642,948,1146,1532,1352,949)(647,954, 1360,1435,1020,955)(648,956,1069,1295,1363,957)(650,959,1365,1835,1367, 960)(659,973,1385,1390,1386,974)(668,984,1396,1866,1398,985)(670,987, 1401,1872,1403,988)(681,1001,1209,839,734,1002)(683,1004,1419,1231,1421, 1005)(690,1011,1429,1859,1391,1012)(692,1014,1430,1903,1432,1015)(704, 1029,1444,1919,1446,1030)(708,1034,793,1151,1451,1035)(709,1036,1453, 1741,1454,1037)(715,1047,1272,887,1271,1048)(718,1009,1427,1899,1470, 1051)(726,1016,1433,1907,1482,1060)(728,1061,1483,1954,1485,1062)(733, 1067,1490,1959,1492,1068)(744,1077,1503,1969,1505,1078)(746,1081,1509, 1977,1510,1082)(750,1088,1520,1985,1521,1089)(756,1097,805,1167,894,1098) (757,1099,1529,1881,1410,995)(759,1102,1533,1572,1136,1103)(761,1105, 1537,1873,1402,1106)(767,1114,1547,2009,1549,1115)(773,1123,846,1218,905, 1124)(776,1129,1371,1840,1565,1130)(789,1148,1586,2039,1588,1149)(797, 1156,1595,1933,1459,1040)(800,1018,1093,1524,1599,1159)(802,1162,1603, 2057,1604,1163)(807,1169,1610,2064,1612,1170)(814,1175,1176)(817,1181, 1369,961,1368,1182)(821,1187,1629,2049,1593,1155)(823,1189,1630,2085, 1632,1190)(829,1198,1644,1554,1646,1199)(830,1200,1647,2096,1649,1201) (837,1205,1655,2102,1657,1206)(842,1213,1667,2114,1668,1214)(847,1219, 1238,1628,1185,1220)(851,1225,1680,1949,1477,1226)(864,1240,1694,1312, 919,1241)(870,1247,1548,2010,1700,1248)(872,1251,1705,2149,1707,1252) (879,1261,1716,2016,1718,1262)(883,1265,1723,1830,1724,1266)(888,1273, 1244,1340,939,1274)(895,1281,1197,1642,1351,1282)(900,1287,1746,2186, 1748,1288)(907,1296,1754,2191,1756,1297)(909,1300,1760,2197,1762,1301) (921,1313,1774,2206,1775,1314)(932,1330,1794,2227,1796,1331)(937,1337, 1278,1736,1356,1338)(944,1345,1810,1638,1812,1346)(951,1354,1823,1918, 1598,1355)(962,1370,1839,2002,1539,1107)(964,1373,1841,2265,1842,1374) (966,1375,1362,1765,1305,1376)(967,1183,1626,2080,1846,1377)(971,1381, 1850,2272,1852,1382)(976,1388,1389)(983,1394,1862,2281,1864,1395)(990, 1405,1875,2288,1876,1406)(1006,1422,1893,1633,1191,1423)(1007,1424,1894, 2301,1896,1425)(1023,1436,1715,2160,1909,1437)(1024,1438,1910,2306,1911, 1439)(1027,1441,1914,2103,1656,1442)(1032,1447,1140,1577,1921,1448)(1038, 1455,1407,1877,1491,1456)(1042,1461,1935,2034,1936,1462)(1043,1328,1791, 1944,1471,1052)(1045,1465,1939,2321,1940,1466)(1053,1472,1945,2284,1869, 1399)(1054,1473,1947,2327,1948,1474)(1058,1479,1950,2328,1951,1480)(1064, 1486,1463,1738,1906,1487)(1065,1488,1957,2335,1958,1489)(1071,1494,1468, 1942,1961,1495)(1073,1497,1886,1415,1885,1498)(1074,1499,1964,2138,1965, 1500)(1075,1501,1966,1710,1255,1502)(1079,1506,1973,1763,1302,1507)(1083, 1511,1165,1606,1475,1512)(1084,1513,1229,1650,1979,1514)(1086,1517,1982, 2352,1983,1518)(1090,1400,1870,2285,1987,1522)(1095,1526,1160,1600,1992, 1527)(1100,1530,1994,2361,1996,1531)(1104,1535,1536)(1108,1540,1450,1924, 2004,1541)(1110,1543,2007,2146,1703,1544)(1116,1550,1696,1242,1695,1414) (1118,1552,2013,1750,1837,1553)(1121,1557,1594,2050,1827,1558)(1125,1559, 1420,1891,2018,1560)(1127,1562,2020,2097,1648,1563)(1132,1567,2022,2040, 1587,1568)(1134,1570,1651,1203,1564,1571)(1137,1573,1323,1785,2028,1574) (1139,1575,2029,2043,2031,1576)(1142,1233,1687,2133,2032,1579)(1144,1581, 1397,1867,2035,1582)(1152,1590,1303,1764,1920,1445)(1157,1596,2052,2207, 2054,1597)(1164,1484,1720,1263,1719,1605)(1168,1607,2060,2302,1895,1608) (1174,1253,1708,1902,2068,1615)(1177,1293,1665,1211,1664,1618)(1179,1621, 2073,1833,1364,1622)(1192,1634,2087,2033,1580,1635)(1193,1636,1583,2036, 2089,1637)(1195,1639,1561,2019,1845,1640)(1204,1652,2098,2200,1768,1653) (1207,1658,2105,2277,1857,1659)(1210,1662,1291,1751,1766,1663)(1216,1670, 1289,1749,2117,1671)(1221,1674,2121,2130,1685,1675)(1223,1677,1686,2131, 2124,1678)(1227,1681,2126,2452,2128,1682)(1234,1688,2134,1770,1309,1689) (1249,1701,2144,1941,1467,1702)(1258,1712,2157,2473,2158,1713)(1259,1317, 1778,2208,2159,1714)(1264,1721,2163,2419,2086,1631)(1267,1725,1986,2225, 1793,1726)(1268,1727,1976,1508,1975,1728)(1275,1733,2174,2398,2053,1734) (1276,1614,2067,2026,1808,1342)(1283,1739,2178,1863,2180,1740)(1285,1742, 2182,2488,2183,1743)(1298,1387,1856,1952,1481,1757)(1315,1776,1898,1426, 1897,1777)(1318,1779,2209,2511,2211,1780)(1320,1781,2212,2513,2214,1782) (1324,1786,2219,1988,1523,1787)(1326,1789,1515,1980,2223,1790)(1332,1797, 1384,1717,2161,1798)(1333,1366,1836,1847,1378,1799)(1334,1800,1379,1848, 1693,1801)(1335,1802,2230,2524,2232,1803)(1339,1804,2062,1609,2061,1805) (1341,1806,2235,2529,2237,1807)(1347,1813,1747,2112,2245,1814)(1349,1817, 2246,1937,2248,1818)(1353,1820,1692,2137,2210,1821)(1357,1825,1666,2113, 1892,1826)(1359,1828,2256,2283,1868,1829)(1361,1831,1871,2286,2012,1551) (1383,1853,1617,2071,2275,1854)(1393,1624,1602,2056,2280,1860)(1409,1878, 2290,2162,2292,1879)(1416,1887,1874,2063,2297,1888)(1418,1889,1679,2125, 2299,1890)(1428,1900,2303,2466,2279,1901)(1431,1904,2132,2454,2305,1905) (1440,1912,2308,2405,2066,1913)(1443,1916,1619,1792,2224,1917)(1449,1922, 1758,2195,2311,1923)(1452,1926,1641,2092,1880,1927)(1457,1930,1931)(1460, 1934,2319,2510,2205,1773)(1469,1943,2324,2445,2116,1669)(1493,1861,1956, 2334,2336,1960)(1496,1962,2337,2316,2129,1683)(1504,1970,1697,2139,1938, 1971)(1519,1984,2000,2364,2055,1601)(1525,1989,2355,2608,2356,1990)(1528, 1993,2359,2467,2150,1706)(1534,1997,1981,2148,2041,1998)(1542,2005,2370, 2621,2372,2006)(1545,1822,2250,2542,2373,2008)(1546,1915,1589,2042,2295, 1884)(1555,1691,2136,2456,2377,2015)(1569,2023,2051,2228,1795,2024)(1585, 1815,1704,2147,2388,2037)(1591,2044,2393,2639,2394,2045)(1592,2046,2395, 2257,1882,2047)(1611,1744,2184,2490,2404,2065)(1616,2069,1690,2135,2408, 2070)(1623,2075,1672,2118,2376,2076)(1625,2077,2412,2164,1722,2078)(1627, 2081,2030,2119,1673,2082)(1643,1824,2252,2544,2426,2093)(1645,1752,2189, 2495,2428,2094)(1654,2099,2432,2498,2194,2100)(1660,2107,2439,2177,2440, 2108)(1661,2109,1745,2185,2291,2110)(1698,2140,2460,2677,2453,2141)(1699, 1759,2142)(1709,2152,2218,1784,2217,2153)(1711,2154,2470,2694,2471,2155) (1729,2169,2478,2244,2354,2170)(1731,1865,2282,2422,2192,1755)(1732,2171, 2479,2698,2480,2172)(1735,2175,2483,2704,2484,2176)(1753,2190,2496,2585, 2318,1932)(1761,2198,2351,2603,2502,2199)(1771,2202,1858,2278,2506,2203) (1772,1928,2106,2437,2508,2204)(1783,2215,2515,2726,2516,2216)(1809,2238, 2531,2734,2533,2239)(1811,2241,2535,2263,1838,2242)(1819,2249,2476,2167, 2442,2111)(1832,2258,1843,2267,1963,2259)(1834,2260,2520,2268,1844,2261) (1849,2269,2528,2234,2527,2270)(1851,1995,2151,2468,2559,2273)(1855,2276, 2562,2504,2201,1908)(1883,2293,2566,2593,2567,2294)(1925,2312,2581,2762, 2582,2313)(1929,2314,2287,2193,2127,2315)(1946,2325,2590,2526,2233,2014) (1953,2330,2307,2577,2387,2331)(1955,2333,2323,2587,2543,2251)(1967,2338, 2402,2320,2399,2339)(1968,2340,2597,2416,2083,2341)(1972,2343,2385,2027, 2384,2344)(1974,2345,2600,2769,2601,2346)(1978,2349,2450,2658,2430,2350) (1991,2357,2059,2095,2429,2358)(1999,2363,2614,2652,2417,2084)(2001,2365, 2615,2638,2584,2317)(2003,2367,2618,2779,2619,2368)(2011,2374,2624,2662, 2435,2375)(2017,2378,2229,2494,2188,2379)(2021,2380,2457,2444,2115,2220) (2025,2382,2348,2602,2630,2383)(2038,2389,2166,2181,2487,2390)(2048,2247, 2539,2477,2168,2264)(2058,2400,2401)(2072,2409,2418,2653,2514,2213)(2074, 2122,2443,2651,2415,2221)(2079,2414,2503,2571,2298,2123)(2088,2420,2595, 2332,2594,2421)(2090,2423,2650,2664,2438,2424)(2091,2425,2655,2740,2545, 2253)(2101,2433,2434)(2104,2406,2407,2645,2663,2436)(2120,2447,2222,2518, 2672,2448)(2143,2461,2685,2781,2625,2462)(2145,2463,2687,2802,2688,2464) (2156,2472,2616,2366,2549,2262)(2165,2474,2604,2692,2469,2475)(2173,2403, 2623,2727,2701,2481)(2179,2486,2707,2574,2304,2310)(2187,2492,2706,2575, 2617,2493)(2196,2499,2626,2782,2716,2500)(2226,2521,2592,2326,2591,2347) (2231,2240,2534,2289,2565,2525)(2236,2530,2629,2693,2705,2485)(2243,2537, 2517,2728,2676,2538)(2254,2546,2555,2749,2669,2547)(2255,2548,2743,2576, 2724,2512)(2266,2552,2747,2586,2322,2553)(2271,2556,2750,2633,2505,2329) (2274,2560,2561)(2296,2569,2760,2738,2540,2570)(2300,2572,2573)(2309, 2578,2557,2751,2598,2579)(2342,2599,2768,2777,2613,2362)(2353,2605,2708, 2489,2683,2606)(2360,2610,2773,2686,2758,2611)(2369,2550,2642,2396,2641, 2411)(2371,2589,2765,2761,2580,2622)(2381,2627,2755,2563,2741,2628)(2386, 2631,2667,2441,2666,2632)(2391,2634,2784,2817,2754,2635)(2392,2636,2568, 2759,2710,2637)(2397,2643,2680,2799,2786,2644)(2410,2646,2696,2804,2737, 2647)(2413,2648,2766,2735,2532,2649)(2427,2541,2656)(2431,2659,2772,2609, 2771,2660)(2446,2620,2491,2519,2730,2670)(2449,2522,2731,2554,2748,2673) (2451,2674,2717,2523,2732,2675)(2455,2678,2507,2719,2798,2679)(2458,2583, 2744,2785,2800,2681)(2459,2501,2665,2794,2801,2682)(2465,2689,2711,2807, 2718,2690)(2482,2702,2805,2736,2536,2703)(2497,2712,2588,2764,2691,2713) (2509,2721,2640,2714,2808,2722)(2551,2745,2792,2809,2720,2746)(2558,2752, 2815,2763,2816,2753)(2564,2756,2661,2793,2818,2757)(2596,2767,2700,2795, 2668,2684)(2607,2770,2699)(2612,2775,2803,2695,2788,2776)(2654,2789,2742, 2814,2791,2790)(2657,2778,2822,2823,2780,2739)(2671,2796,2828,2831,2830, 2797)(2697,2774,2733,2806,2709,2715)(2723,2810,2787,2725,2783,2811)(2729, 2812,2820,2819,2821,2813)(2824,2833,2835,2834,2827,2825)(2826,2832,2829);