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