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