/*
Group G = 5^{1+4}:6"A6.
Automorphism group is 5^4:2"A6.4, and has order \phi(|G|).
Should work in Magma 2.8 and above.
|G|     = 6750000 = 2^4 * 3^3 * 5^6.
|Aut G| = 1800000 = 2^6 * 3^2 * 5^5.
Smallest known perfect group for which |Aut G| = \phi(|G|).
[As of 22nd June 2004.]
*/


x1:=\[1,3,5,7,9,11,13,15,2,18,20,22,24,26,28,30,32,34,36,38,40,42,44,4,47,49,
51,53,55,57,59,61,63,65,67,69,71,6,74,76,78,80,82,84,85,87,89,91,93,95,97,99,8,
102,104,106,108,110,112,114,116,118,120,122,10,125,127,128,130,132,134,136,138,
140,142,144,115,147,149,12,151,153,155,157,158,160,75,162,164,166,167,169,14,
172,174,176,178,180,182,184,186,188,190,192,194,196,198,16,50,201,203,205,207,
209,211,17,212,214,216,218,181,221,223,225,227,229,231,233,235,19,238,240,242,
244,246,248,250,202,253,255,257,46,260,21,129,264,266,268,270,272,274,276,278,
280,281,283,23,286,288,290,292,294,296,25,299,301,303,305,307,309,311,312,314,
109,317,319,321,27,324,326,328,330,332,334,336,338,340,341,343,345,234,29,349,
351,353,355,357,359,361,363,365,367,369,175,31,372,374,376,378,380,382,384,386,
388,390,392,394,33,397,399,401,403,405,407,409,411,413,415,417,419,35,422,423,
425,427,429,431,433,435,437,439,441,443,37,446,448,450,451,452,454,456,458,460,
462,39,465,467,469,471,473,475,335,478,480,482,41,485,487,489,491,493,495,497,
499,501,256,504,43,507,509,350,511,513,514,516,45,519,521,523,525,310,528,530,
532,534,536,538,539,541,543,545,547,48,210,551,552,421,555,540,558,560,562,564,
566,533,569,375,571,573,575,577,579,581,583,585,587,589,591,593,52,596,598,600,
602,604,605,606,608,610,488,54,614,616,617,618,620,622,624,626,83,629,556,631,
633,56,636,638,640,642,644,646,648,650,652,58,654,73,656,658,660,662,664,666,
667,204,669,185,60,672,674,676,77,679,681,261,683,684,62,687,370,690,691,693,
695,697,699,701,703,705,707,64,393,711,713,715,717,284,719,720,722,724,726,66,
729,731,733,734,736,738,740,92,743,68,746,748,750,145,753,755,757,461,760,762,
764,766,767,70,769,771,773,775,777,778,780,782,285,783,785,787,789,72,792,793,
795,797,799,800,718,802,804,806,808,810,812,152,815,817,819,821,346,823,825,
827,828,829,831,833,835,836,838,840,842,844,846,848,850,677,853,855,857,79,860,
861,863,864,866,868,870,81,873,875,877,879,881,883,884,886,888,584,856,892,894,
895,224,897,245,900,197,903,904,657,907,909,910,86,371,912,914,916,918,920,88,
922,924,921,749,927,928,929,931,933,935,937,939,90,941,943,945,940,947,949,951,
953,954,956,958,959,961,463,854,965,94,968,970,267,973,974,688,976,977,979,981,
96,851,985,987,989,991,567,994,996,998,1000,154,1003,1005,98,621,1009,1010,121,
1013,1014,1015,809,1018,1020,1022,1024,1025,1027,100,1029,1031,377,1033,1035,
101,1037,1039,318,1042,962,1045,1043,1048,1050,103,1053,1054,1055,1057,1059,
1060,651,1062,1064,1066,105,1069,1071,1072,1074,1076,1078,1079,1081,518,1083,
1085,865,107,1089,1091,510,1094,698,1097,1099,1100,1102,813,1105,1107,1109,592,
159,111,500,215,1114,1115,1116,1118,869,765,113,1121,1123,1125,1127,1129,1131,
304,1134,779,148,647,1138,1140,117,1143,1145,1147,505,1150,1112,1152,457,1155,
119,1158,1160,1161,1162,1164,1166,1168,1092,1170,1172,1174,1176,1178,1180,1182,
1184,1186,788,1189,1148,1192,1194,455,123,1198,1200,1202,1203,124,1206,430,
1208,1210,1212,1213,1215,925,1218,1220,1222,601,1225,126,1228,1229,1231,1232,
1234,1236,1237,1239,1240,1242,1244,1245,1247,191,163,1250,1252,1254,1256,1257,
1258,282,410,1262,995,1265,492,131,1268,790,1087,1272,1274,1276,1278,1173,1281,
1282,839,1284,133,1287,515,1289,1290,1011,1293,816,682,1296,135,1299,880,1300,
1302,1084,1304,1305,1307,1309,137,1311,1313,830,1316,1318,1320,1322,1324,139,
1327,237,1330,1332,563,1335,1336,496,986,742,1339,1340,141,1343,1344,1346,1348,
1317,1351,1325,1354,1088,143,1191,385,1360,1362,1364,1366,1368,1370,483,1373,
146,1376,1378,1380,1382,1384,479,347,1156,1389,565,1363,1392,1393,1395,187,171,
1399,1401,1051,1402,1403,1405,1407,1408,948,150,1410,464,665,1413,1414,1416,
395,1419,1421,1374,1424,1426,1428,685,1430,1432,1433,1435,878,1438,1440,1442,
1444,1446,1448,1450,1451,756,574,1454,156,1456,442,1459,735,1233,1462,1464,
1466,1468,568,1470,1472,1474,1476,1478,1480,1481,1483,161,1484,1486,1488,1490,
1492,1494,1496,1498,1500,1501,1503,1505,1506,1315,1508,1510,170,1512,165,506,
999,737,1518,588,615,1522,763,1080,1526,607,1529,316,1531,1533,168,1535,1536,
1538,1539,1541,1543,1545,1547,1259,1550,1551,291,1552,832,1554,1556,1558,1559,
595,1334,1561,1563,1565,173,322,1569,946,1504,1573,611,1575,1577,1429,1579,
1581,1482,364,1584,1586,177,1415,923,1226,1591,1111,1593,1595,1597,661,1341,
179,859,1601,1602,1603,1605,1606,843,1608,1609,1610,1110,1613,368,1616,1328,
1618,1620,1622,1624,1626,1627,183,1629,972,1631,1633,1635,1263,1638,1639,262,
1641,1643,1645,1646,1647,1329,1650,1652,1654,1656,1658,544,1661,1663,1665,1667,
189,1669,1670,1672,1673,1674,470,938,1678,845,1680,1682,1095,1683,193,1685,
1687,1689,1691,1693,1695,1697,1698,195,1701,1702,1704,1706,1708,1044,1711,1713,
1714,1715,751,1716,434,1719,1721,373,1724,686,1727,1729,1731,791,199,348,1068,
1736,1738,1739,200,1742,1668,1744,936,1746,1747,1748,1750,1752,444,1754,1756,
1292,582,526,1759,459,206,1761,1623,1763,1765,208,557,1769,1771,876,1773,1775,
1777,1779,1780,1781,1782,1784,1786,1787,1640,1788,1790,1792,1793,447,1795,213,
1797,1776,222,1799,643,1800,905,1157,1753,1473,1804,1805,1458,1807,402,1809,
217,1811,1357,1814,871,1816,678,1818,1820,474,219,1823,1824,1826,1677,623,1830,
1831,220,1834,1061,1248,1838,1840,1842,1843,1844,1845,1846,1171,1849,702,1852,
1854,1856,1857,1859,1860,1861,1863,252,1722,1866,1868,1870,700,1872,1235,226,
1875,1876,1877,1879,1881,1882,1884,1385,1887,1889,1372,228,1767,1891,1892,1894,
1032,1567,1439,1897,1104,230,1477,1900,1901,1903,1905,1851,1582,232,1909,1019,
1912,1049,1915,1917,1919,1921,1923,1924,1925,1927,1929,1931,1933,1913,1936,236,
352,1937,1939,1941,1942,1943,1944,1001,1945,546,1947,1762,1514,239,1950,1952,
1954,1956,1958,1959,1960,1962,241,1965,453,1926,1967,1969,1971,1973,243,381,
1976,1108,1978,1980,1982,1984,1985,1986,1149,1653,1990,247,1993,1516,249,1703,
1283,1995,1420,727,1619,730,714,2000,297,251,2003,689,2005,1948,2007,1117,1524,
2010,1949,2011,969,2013,2015,2017,2018,254,2021,805,559,2025,2026,2028,2029,
445,542,2032,1350,2035,553,2037,2038,258,896,1391,259,2043,2044,2046,1983,673,
2050,1590,2052,2053,2055,1549,1568,1487,2058,1630,2060,2062,2064,263,2067,2068,
2054,2071,2073,440,2076,1632,2079,2081,2083,265,2085,2086,414,1406,2036,2089,
1400,1230,818,1493,893,2092,1396,2094,1388,1636,269,2097,645,2048,1266,2101,
761,2103,271,2104,2105,2107,862,2110,273,867,2113,2115,1555,2040,2117,2118,659,
1671,613,275,2122,671,1710,1778,2126,2127,2129,449,277,2132,2134,1681,1600,934,
418,2093,520,279,2137,1418,2140,2041,2142,2143,2144,1333,2146,2147,663,2150,
2152,2154,1086,2157,2158,2160,2161,1047,1463,2164,824,287,2166,1441,2168,2169,
2171,2172,391,2175,649,289,517,2178,2179,1808,2181,320,2183,2184,2186,2187,963,
2022,2190,293,2192,1604,486,2194,2196,2198,2180,315,957,578,295,2202,2030,1755,
2204,2206,2208,298,2210,1819,2056,2212,2213,1246,1796,1093,2215,300,1690,2219,
2221,2222,1457,2224,1588,302,1994,2229,1997,2232,2234,2236,494,2238,1906,306,
2241,1996,1345,1135,2244,2246,2248,2250,308,759,2253,1740,476,1124,1469,1423,
1153,2257,2259,2260,2261,2263,2265,2266,313,1825,1306,1221,599,2270,899,2272,
1764,2273,2274,2275,1431,2277,2278,627,2016,1847,2282,2256,2285,814,2287,2288,
2289,2291,597,2072,2295,2296,2145,2298,1546,2300,323,2042,2303,837,2305,2307,
1119,325,1572,2311,1991,2312,1867,1832,327,1835,2318,1445,2321,2322,2324,329,
2252,1251,2327,1021,2329,331,1571,744,2082,1587,1017,2335,2337,477,333,481,
2008,2225,732,1331,1720,2342,2344,383,2346,2348,337,1471,2351,944,1377,1836,
2352,2353,2354,339,709,1090,2358,1275,1485,2360,2362,2364,2365,1046,342,2368,
2369,2371,901,625,745,344,1760,490,1201,2376,2378,2380,398,2170,1802,2323,1527,
1177,706,1253,2385,2386,1576,2389,2390,2197,2392,2394,2148,1285,2397,1871,1992,
2400,2401,2402,2404,2406,971,354,2409,2410,2411,2412,2414,2415,2417,2214,356,
2418,2419,2421,2423,2425,358,2427,1523,408,1696,2429,2430,1723,1040,2431,360,
2433,396,2434,1359,2435,2437,362,1974,1732,1475,2304,2439,2216,807,2442,2444,
2223,2445,366,2446,1113,2448,2450,2451,580,570,389,2156,2454,1453,1902,1002,
1865,2458,2271,1828,2031,2462,2269,2464,716,2466,2014,1614,2468,379,387,2469,
502,1356,2242,2472,2474,1966,1953,2279,1785,2477,1938,1725,2363,952,2479,1365,
2482,2218,2483,1297,1679,786,1264,2486,2487,2488,484,1553,2449,2491,1999,2493,
2494,2207,2495,2496,2498,1810,1443,2501,1607,2503,1207,1542,1515,2506,1193,
2098,2509,2510,2139,2512,2513,1745,2515,2517,1880,590,2520,1520,400,2523,2399,
2525,2526,2528,2420,2334,2530,1812,2532,2533,2534,2123,404,1216,2538,1858,1768,
2024,1381,1770,2116,406,2542,1052,1326,2544,1850,1169,2546,2087,2548,1726,2550,
2313,2553,2554,2556,412,1280,2558,2552,1310,2155,2561,2562,2563,2565,1530,2567,
1312,1733,2569,416,2570,2571,1294,882,2128,2574,1425,2575,2276,1422,420,2577,
2527,2432,1963,2579,1560,2581,2583,2585,428,2059,424,2586,1271,2587,2589,1899,
2591,2593,2594,426,1016,2595,1082,2597,2149,2598,2600,2602,2286,2603,2584,2290,
2605,2607,1314,1916,2608,2610,1151,432,2336,1397,1898,2195,1465,2306,2560,436,
1540,1041,841,2615,2541,2616,438,2618,776,2620,2621,2622,2624,1977,2625,1023,
2039,2628,1961,1012,1664,2629,2633,2634,2636,2001,2638,2640,1886,1532,2641,
2643,1146,2645,2375,2646,2211,2590,586,630,2648,1436,2649,1791,548,2407,911,
1261,781,1133,2654,2540,2379,1417,2136,2657,1337,2319,2659,1599,594,1649,609,
572,1743,1398,2665,2667,890,2668,2662,2670,2671,2658,1988,2459,466,728,2673,
2471,2074,1056,468,2677,2651,2679,2091,887,508,2683,2642,2685,1409,472,1030,
2635,2687,696,1935,1890,798,1598,2690,1570,1758,1142,2185,2693,2205,2696,1067,
2697,1596,1502,2699,1564,1813,2702,2330,2704,2443,1666,2706,1036,2096,2708,
2652,2710,1955,2713,1855,2716,2718,1007,2519,2720,1946,2314,1286,2177,2724,852,
2726,2728,847,2730,2566,2545,2733,1159,2734,1411,2163,2735,641,2737,2220,1675,
2738,2639,2739,2153,498,2663,2741,794,2119,2698,2557,1920,2745,1460,2747,2370,
503,1390,978,1815,2061,2749,2751,1896,2753,2755,1167,2422,1122,2758,2320,2199,
2761,2109,2345,2650,2762,2063,1684,512,2315,2765,2767,1349,1853,2770,692,2744,
2771,2772,2773,1144,2045,2310,2775,1566,2777,960,2778,2034,2780,522,997,2781,
2701,2191,2508,524,2393,2785,527,1766,2254,2788,2789,2791,529,2792,2793,2774,
2794,2796,2797,531,801,2800,2228,535,2516,1361,2551,2804,2805,2485,2783,537,
2807,2461,2808,2809,2537,2258,2299,1730,2813,2814,2518,2162,2692,1449,1806,549,
653,2817,2367,2819,1617,1519,2108,2267,1205,1219,2821,550,2601,1295,1615,2825,
2049,1277,1893,2799,2826,554,2669,2802,2326,2828,2413,2830,1461,2832,1499,913,
2834,2835,2837,932,2006,561,1918,2841,2842,1497,2281,1241,2845,1594,1196,1467,
975,849,1511,1120,1004,1209,1751,2849,1136,1249,967,2853,2339,2854,2644,2855,
2531,576,2080,754,2373,2859,2860,2511,2084,2861,2803,2529,2863,2476,2133,2748,
2173,2555,2866,2666,2867,1888,1491,902,919,2870,2871,2112,2872,1319,2873,2875,
803,2876,1972,1128,2878,2879,2880,1930,796,2882,2877,874,2868,2884,2262,710,
2719,2475,1968,2888,2293,2889,1717,603,2135,2047,993,1227,2894,1728,2806,2895,
2896,1772,2815,2695,2898,1075,1676,1839,1455,612,2308,2328,680,1718,1077,2847,
2902,1288,1662,982,2033,2709,988,2904,2120,619,2906,1412,2316,2460,1371,1686,
2349,2908,2909,2911,2912,2438,2913,2915,2661,628,2917,2467,2918,2833,1096,2829,
2672,2920,2743,2388,2453,632,2848,2874,2372,2922,2924,2356,1833,634,2926,1922,
2927,2928,635,942,637,2930,639,2931,2933,2727,1660,2858,2470,2396,826,2936,
1642,950,1712,1098,2939,2892,2125,1700,2188,2331,1223,2919,2907,1179,2942,2492,
1141,1574,1521,655,2750,2943,2944,2945,1592,2947,1981,668,2938,2357,2768,2441,
2760,670,2949,2951,2905,2952,2953,1637,2954,2002,2955,675,1267,2268,2957,2095,
2447,2623,1190,2121,1822,2766,926,1848,1798,2578,1534,2703,2102,2674,694,2130,
1578,2754,2962,2714,2964,2864,2088,2827,930,2114,2966,770,2869,1394,2934,2968,
2167,2490,704,2151,1008,1447,1707,2456,2717,2763,2972,2543,1655,2689,2325,708,
741,2756,2455,2481,2975,1801,712,1204,2317,2193,2923,2974,2405,2614,2981,2798,
2983,1270,2844,2231,1211,721,2436,723,2984,1181,2986,2547,1548,725,1794,2988,
2138,2235,2521,2990,2991,2992,2457,2989,2361,2226,2885,1537,992,2997,2998,1269,
739,2999,3000,3001,3002,2019,2484,3003,2857,2725,3006,2740,1557,3008,747,3009,
1183,2099,1709,2280,774,1737,2967,2247,2921,752,1951,3015,2023,3017,2985,2836,
1139,758,2779,1028,2239,3020,3021,2795,768,2240,2946,2664,3023,1878,2801,3005,
2707,772,1694,3026,3027,3028,2596,2576,1911,2245,2682,2637,858,1783,1291,3013,
2090,1895,2752,3032,784,984,2786,2843,3033,3034,3036,891,820,2729,2478,822,
2572,2233,1026,2009,1864,2165,3038,1934,1199,1279,3039,1273,3040,917,2700,1197,
811,1185,2182,1749,3042,2100,2891,2971,3043,1705,3044,3045,2065,3046,3016,2925,
2611,2886,2935,2200,3050,1837,2846,2106,3022,834,3052,1987,2381,2632,908,2302,
1829,1525,2816,3004,3053,3025,1998,1585,1928,1611,3054,1165,1509,1589,1869,
3055,3056,1817,3057,3058,2428,885,2051,2653,2426,2973,1379,1562,1874,1495,2965,
1386,3011,2606,1528,3061,990,1940,872,2189,3062,898,1238,3064,1735,2070,3066,
1154,2812,1355,2995,2069,1321,1187,2243,1612,2617,2203,889,3068,1648,3070,2359,
1910,2504,1507,2688,2818,2746,2124,2251,2959,2776,2660,2294,906,3069,1644,2982,
2176,2131,2769,2264,1298,2822,915,1914,3063,1657,1741,3074,2782,2004,2309,3076,
3077,1132,2732,1907,1821,2408,2066,2463,2840,1163,2627,2715,2790,3080,2301,
2932,1101,1038,2502,1323,1757,3081,1688,2865,2347,2823,2539,2489,3083,2705,955,
2387,2852,1827,2227,2723,2956,2977,3085,964,1873,2338,2383,3041,966,2027,2676,
2958,1367,2377,2824,980,1979,3030,1544,983,3088,1255,2524,2631,2424,3086,2283,
1358,2681,1513,2588,2656,2012,1437,3060,3092,1006,2838,2514,3094,1073,2712,
2970,3087,1058,2237,1841,3090,1659,2916,3018,1224,2784,2839,2887,2686,2684,
1387,3012,2403,2787,3082,1034,3029,3099,3097,2655,2507,1634,3101,2937,1692,
2366,1375,3098,1063,1957,2382,2398,2820,2416,1065,3091,1479,3089,1103,1070,
2899,2297,1989,2680,2340,3103,1427,2994,2969,1188,2559,1517,2341,1175,2856,
1789,3051,1338,3014,1970,3078,1106,2897,2893,2057,2980,2217,3108,2811,3100,
1126,3084,1130,1342,3067,2993,1137,2230,1489,3071,2350,3072,2883,2721,1404,
2612,2711,2831,3109,2141,2881,1883,2077,1195,1583,2111,1580,3104,2201,2759,
2910,3095,3106,2979,1260,2731,2810,1214,2592,1217,3112,3113,2255,2914,2343,
2626,2900,2903,3115,3116,1803,3117,2978,3118,3102,1243,2395,2500,1301,2355,
2694,2549,2850,1734,3047,1353,2941,3048,2609,2505,2764,1651,3114,2722,3119,
3120,2209,2940,2452,3096,2391,1352,2691,1303,2851,1308,3024,3031,2580,3121,
2333,3122,1347,3123,1975,3110,1932,2332,2564,2647,2374,1369,2480,1625,1383,
1628,2499,3037,2497,2440,2976,1699,2987,2159,2473,1434,3065,1452,3019,2613,
3107,3059,2960,2742,2284,2536,1862,2604,2384,2465,2568,2961,2757,1774,2736,
3125,1621,3075,3007,2678,2963,2901,2675,2535,2174,3035,2599,3079,3010,2948,
2573,1964,2249,2582,3105,2522,3073,2950,3124,2890,2619,1885,3049,3111,2630,
1904,1908,2075,2078,2996,2020,3093,2862,2929,2292];

y1:=\[2,4,6,8,10,12,14,16,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,46,48,
50,52,54,56,58,60,62,64,66,68,70,72,73,75,77,79,81,83,3,86,88,90,92,94,96,98,
100,101,103,105,107,109,111,113,115,117,119,121,123,124,126,80,129,131,133,135,
137,139,141,143,145,146,148,91,150,152,154,156,84,159,116,161,163,165,167,168,
170,171,173,175,177,179,181,183,185,187,189,191,193,195,197,199,108,200,202,
204,206,208,210,1,44,213,215,217,219,220,222,224,226,228,230,232,234,236,237,
239,241,243,245,247,249,251,252,254,256,258,259,261,262,263,265,267,269,271,
273,275,277,279,140,282,284,285,287,289,291,293,295,297,298,300,302,304,306,
308,310,244,313,315,316,318,320,322,323,325,327,329,331,333,335,337,339,85,342,
344,346,347,348,350,352,354,356,358,360,362,364,366,368,370,57,371,373,375,377,
379,381,383,385,387,389,391,393,395,396,398,400,402,404,406,408,410,412,414,
416,418,420,421,212,424,426,428,430,432,434,436,438,440,442,444,445,447,449,
433,53,453,455,457,459,461,463,464,466,468,470,472,474,476,477,479,481,483,484,
486,488,490,492,494,496,498,500,502,503,505,506,508,510,93,512,328,515,517,518,
520,522,524,526,527,529,531,533,535,537,169,540,542,544,546,548,549,550,76,553,
554,556,557,559,561,563,565,567,568,570,9,572,574,576,578,580,582,584,586,588,
590,592,594,595,597,599,601,603,164,223,607,609,611,612,613,615,184,221,619,
621,623,625,627,628,630,397,632,634,635,637,639,641,643,645,647,649,651,30,653,
655,136,657,659,661,663,665,336,668,469,670,158,671,673,675,677,678,680,172,
682,467,685,686,688,689,157,692,694,696,698,700,702,704,706,708,709,710,712,
714,716,314,718,317,721,723,725,727,728,730,732,711,735,737,739,741,742,744,
745,747,749,751,752,754,756,758,759,761,763,765,34,746,768,770,772,774,776,229,
779,781,216,534,784,786,788,790,791,340,794,796,798,180,5,801,803,805,807,809,
811,813,814,816,818,820,669,822,824,826,579,764,830,832,834,452,837,839,841,
843,845,847,849,851,852,854,856,858,859,652,862,831,865,867,869,871,872,874,
876,878,880,882,201,885,887,889,890,891,893,324,896,151,898,899,901,902,810,
905,906,908,808,248,127,911,913,915,917,919,921,691,923,925,926,802,203,231,
930,932,934,936,938,940,240,942,944,929,946,948,950,952,11,955,957,24,960,962,
963,964,966,967,969,971,972,288,112,975,697,978,980,982,983,984,986,988,990,
992,993,995,997,999,1001,1002,1004,1006,1007,1008,155,1011,1012,378,525,1016,
1017,1019,1021,1023,280,1026,1028,250,1030,253,1032,1034,7,1036,1038,1040,1041,
1043,1044,1046,1047,1049,1051,1052,1050,650,1056,1058,1054,1061,596,1063,1065,
1067,1068,1070,462,1073,1075,1077,539,1080,1082,602,1084,1086,1087,1088,1090,
1092,1093,1095,1096,1098,1029,1101,1103,1104,1106,1108,42,1110,1111,985,1112,
1113,555,636,1117,676,1119,1120,419,1122,1124,1126,1128,1130,1132,1133,1135,
1136,334,1137,1139,1141,1142,1144,1146,1148,1149,1055,1151,1153,1154,1156,1157,
1159,558,281,1163,1165,1167,974,1169,1171,1173,1175,1177,1179,1181,1183,1185,
1187,1188,1190,1191,1193,1195,1196,1197,1199,1201,551,1204,1205,1207,762,1209,
1211,614,1214,1216,1217,1219,1221,1223,1224,1226,1227,61,1230,1225,1233,1235,
528,1238,209,1241,1243,904,1246,1248,1249,122,1251,1253,1255,598,547,1259,1260,
1261,1263,1264,415,1266,1267,1269,1270,1271,1273,1275,1277,1279,1280,1072,264,
1283,1285,1286,1288,543,425,1291,1292,1294,1009,1295,1297,1298,884,924,1301,
307,1303,1284,1306,1308,405,1310,1312,1314,1315,1317,1319,1321,1323,1325,1326,
1328,1329,1331,1333,1334,701,489,51,1337,1338,495,1341,1342,246,1345,1347,1349,
1350,1352,1353,1355,1356,1357,1358,1359,1361,1363,1365,1367,1369,1371,1372,
1374,1375,1377,1379,1381,1383,1385,1386,1387,1388,1390,1391,299,1252,1394,1396,
1397,1398,1400,38,1066,624,1404,1406,1150,1409,1408,1178,1411,1412,1107,954,
1415,1417,1418,1420,1422,1423,1425,1427,928,1429,1431,881,1434,1436,1437,1439,
1441,1443,1445,1447,1449,1085,1014,1452,1453,40,1455,1457,1458,1460,683,1461,
1463,1465,1467,1469,59,1471,1473,1475,1477,1479,519,1482,303,274,1485,1487,
1489,1491,1493,1495,1497,1499,1158,1502,1504,1506,622,1507,1509,1511,283,1513,
1514,1515,1516,1517,1519,1520,1521,1523,1524,1525,1527,1528,1530,1330,1532,829,
1534,1166,1537,825,1540,1542,1544,1546,1548,1549,290,877,981,1553,13,1555,1557,
703,610,1069,1560,1562,1564,1566,1567,1568,1570,1571,1572,499,1574,1576,1551,
1578,1580,1582,1583,1343,1585,1587,1588,1045,1589,1590,1592,642,1594,1596,1501,
1598,1599,1600,935,1324,789,1604,1559,1607,726,198,1393,1611,1612,1614,1615,
1459,1617,1619,1621,1623,1625,1522,427,1628,1630,1362,1632,1634,1636,1637,15,
1640,429,1642,1644,460,1344,1648,1649,1651,1653,1655,1657,1659,1660,1662,1664,
1666,560,1668,1186,1671,1652,1672,1675,1676,1677,1426,1679,1681,1531,372,1684,
1376,1686,1688,1690,1692,1694,1696,176,1699,1700,1378,1703,1705,1707,1709,1710,
1712,260,1468,863,973,1717,1718,1720,1722,1723,1725,1726,1728,1730,1732,1733,
110,1734,1735,1737,1368,1740,1741,1743,1309,1745,695,672,1665,1749,1751,1753,
1554,1755,654,1757,1758,989,431,451,1760,1631,1762,1764,1766,1767,1768,1770,
1772,74,1774,1776,1778,875,538,196,1783,1785,658,566,1382,1789,1791,646,1794,
1713,593,1796,1798,162,666,417,1498,1801,736,1802,1803,458,478,214,1806,1721,
1808,1810,1627,1812,1813,819,1815,1817,870,1819,1821,1822,583,959,1825,1827,
1828,1829,1348,1832,1833,1835,1836,1837,1839,1841,363,1210,575,166,1847,1848,
1850,1851,1853,1855,778,1858,357,367,1862,1864,766,1865,1867,1869,1170,1871,
1873,1105,1874,633,1488,1878,1880,1843,1883,1885,1886,1888,1890,1866,1399,1838,
1811,1893,1895,276,1005,1896,473,1898,1899,1719,996,1902,1904,1906,435,1907,
1908,1910,1911,1913,1914,1916,1918,1920,1922,1870,233,1926,1928,1930,1932,1934,
1935,1584,1503,638,1938,1940,511,18,1937,1742,581,1946,516,979,1948,1421,1949,
1951,1953,1955,1957,1887,662,1961,1963,1964,65,1456,1966,1968,1970,1972,1905,
1974,1975,626,1977,1979,1981,1983,89,1168,1987,1988,1989,1991,1992,376,1115,
1845,1994,309,977,1996,1997,1998,1999,949,2001,755,2002,1172,2004,2006,1793,
2008,411,2009,589,1486,2012,330,2014,2016,160,2019,2020,2022,2023,2024,286,
2027,1876,1433,2030,2031,2033,2034,2036,585,757,2039,2040,664,2041,2042,292,
2045,2047,2048,2049,909,2051,47,2054,2056,1985,1759,2057,20,2059,2061,2063,
2065,2066,1533,2069,2070,2072,2074,2075,2077,2078,2080,2082,2084,99,1995,2087,
1293,2088,894,144,399,1824,1777,2090,2091,2093,793,1380,2095,600,2096,2098,
2099,2100,1939,2102,792,1213,132,1220,2106,2108,2109,2111,1750,2112,2114,1780,
134,2116,1232,2119,2120,1569,1754,2121,2123,2124,2125,1320,2015,2128,2130,1131,
2131,2133,1081,2135,2136,120,1448,1960,733,242,2138,2139,2141,1816,1682,866,
2145,1558,1879,2148,2149,2151,2153,2155,2156,2005,2159,22,2162,2163,118,2165,
715,1228,2157,2167,857,2170,927,2173,2174,2176,382,2177,1414,188,2180,2178,
2182,2183,454,2185,1881,2188,879,2189,2191,587,2193,1354,2097,2195,2197,2199,
2200,2201,738,1366,130,2203,1678,1472,2205,2207,2209,1954,2211,1143,1048,268,
343,1784,2204,2214,2216,2217,2218,2220,1622,2223,2137,2225,2226,2227,2228,2230,
2231,2233,2235,2237,2028,2239,1192,2240,403,1464,2242,2243,2245,2247,2249,2198,
2251,2252,2254,296,178,1765,2255,2256,1059,2258,1478,2146,2262,2264,2208,564,
2104,2267,2268,2143,2269,2271,674,32,1752,2260,1547,2276,916,71,2279,2280,388,
2281,2283,2284,278,2286,821,920,2290,2292,2293,2294,2046,2297,769,2113,2299,26,
2301,2302,2068,2304,2306,2308,2309,2310,2044,394,1714,2313,2314,2315,2316,2317,
2319,2320,1062,2323,2166,1305,2325,2326,812,2328,2330,2331,2332,2333,2334,1116,
1716,2336,2338,1927,2339,2340,2337,1512,1706,2341,1138,2343,2345,114,2347,2349,
2350,1639,1121,914,186,724,1125,1037,2355,2356,782,2357,2250,1654,2359,2361,
2363,690,2366,2367,319,1494,2370,1724,2372,2373,2374,1410,895,2375,912,2377,
2379,28,2172,795,2381,2382,1756,2383,2384,78,125,2387,2388,1074,2391,437,2393,
2335,2395,2396,2398,2399,1240,1539,2037,2403,2405,2407,1620,2408,2402,1010,608,
2413,892,2416,2025,1616,1302,1900,2420,2422,2424,2426,2154,2428,605,2071,2085,
2000,2126,1603,2322,380,2432,507,2291,705,326,2436,1057,648,1561,2438,475,684,
2440,2441,513,2443,2253,1820,2360,374,681,2447,2449,2236,2452,1917,2453,521,
976,1545,1962,2455,2456,2457,1123,2459,2460,2461,2463,2348,1647,2465,1480,2467,
257,931,1698,2265,2470,225,1147,2471,2473,2475,1206,2476,359,491,2067,656,2478,
573,1281,2480,2481,272,855,2194,2484,2485,2161,1667,2158,532,2489,1635,1805,
2490,2492,941,1959,1430,2278,1980,2497,2499,2064,2500,2502,1799,1834,2504,2430,
2505,604,2507,2508,1773,2511,1161,1595,2346,2514,2516,838,2518,2519,1669,2521,
2522,937,2524,1697,2527,2529,2495,1818,2531,102,2029,577,2535,2536,2537,1508,
1145,2539,2540,409,1336,2541,667,401,2483,1200,2543,541,1444,2545,2118,2547,
1958,2549,2551,2552,63,2555,2557,679,1944,2559,1602,2560,2181,1282,2486,2564,
2566,349,815,266,2568,660,1300,1442,2572,1581,1748,2573,2110,2073,2576,2474,
2021,1258,2578,1440,1079,2164,2580,1830,2582,2584,1407,2553,2392,1100,1786,
1646,2588,422,2590,2592,1316,1218,835,2466,1208,2596,1969,2410,2599,2601,1027,
1626,182,2604,106,2606,1236,1788,2365,2609,991,2611,2612,1535,783,2464,1237,
1395,2613,2614,1670,1892,2598,1064,1790,2567,2617,1024,2619,1763,2003,2394,
2623,1687,205,2626,1912,2627,2629,2630,2631,2632,2055,2385,2635,2637,443,2639,
270,36,238,2642,1304,2644,2196,743,1809,2647,1274,386,1129,2548,2303,2650,2651,
2556,2652,1215,1322,2653,1250,149,1176,2655,301,2656,2658,2510,965,2660,2661,
2662,1683,2663,2664,2657,2369,2666,777,2583,2186,2669,2079,2672,2620,1565,2643,
1685,1424,82,2674,2675,1861,2676,2678,2501,2680,2681,2682,1127,1629,2684,2246,
1868,1035,1643,2686,1470,1392,2688,2060,2689,1731,2691,1335,2692,2503,2628,
2694,2695,471,1708,2698,846,1859,1454,2700,2701,2140,2703,305,2705,2371,2581,
2707,2602,2709,1739,2711,2712,2714,2715,2717,1936,2719,1689,1360,2721,2722,
2723,194,2168,2725,2727,1015,2729,2731,2732,2344,2677,2215,456,1624,900,2488,
2736,943,729,2450,448,1875,1152,1428,2740,67,2742,2743,174,2273,2744,530,1364,
2746,2748,1715,95,1318,2129,1496,2418,2750,734,2752,2754,569,1296,2756,2757,
2759,2738,2760,312,1990,2431,509,2043,1929,2763,2683,2764,2766,2768,2587,2769,
620,873,956,332,2603,1078,2774,2624,797,2776,2597,1505,2765,2779,142,1941,1541,
2710,2782,2593,2775,2783,2784,2780,907,1020,2786,2787,1276,2790,2771,255,2638,
1781,1736,2795,2685,1244,2798,2799,2801,1563,2802,1573,2803,2605,2448,2241,
2806,1278,1695,1779,2544,1307,1638,2810,2811,2812,799,1245,2646,2616,970,840,
2307,2815,2277,2816,1160,2818,800,1446,2589,128,2820,1782,1993,987,2822,2823,
903,2824,2425,998,1174,1265,2115,2618,2827,1577,2053,1901,1109,2829,1674,2831,
2833,616,1891,2213,2836,2838,2839,2840,49,1556,842,2843,1202,1510,2844,1184,
2575,2187,2846,2640,2847,1982,922,2848,1272,1691,2850,2851,2852,2127,2788,2737,
1943,207,2376,2856,2248,961,2857,2858,1872,968,1608,1140,2122,2862,2767,1882,
2864,311,2865,2353,2668,1846,958,1332,2868,2404,1490,2869,1222,2035,2761,1984,
719,2874,2368,1761,2103,2877,886,2679,918,2849,1373,2881,2498,1641,2883,2704,
2885,2270,2423,423,2886,2887,2853,2739,2890,2891,2892,2893,1476,2305,1231,836,
2285,392,1680,2362,338,2897,1518,2702,2171,2389,2899,1769,1042,2900,2517,2901,
2352,1416,1162,2785,2903,1877,1792,2622,2735,355,2665,2772,2905,562,2451,2608,
868,2907,2870,2491,606,2910,571,1978,1538,2914,2916,1543,2909,947,2770,1919,
2919,2794,939,1083,2561,1419,767,2641,1182,1857,2921,487,2923,2295,2925,644,
2859,2190,1053,1661,55,2929,897,1746,2792,1102,2932,192,2889,2706,2934,2935,
2261,2569,2937,2574,2938,1039,2437,2898,211,771,2940,341,780,787,2941,2634,
2610,2863,2625,773,2931,2749,2724,2908,1164,1094,1618,2946,1804,1099,2730,2948,
1118,1229,2011,1591,1466,2950,1921,450,493,2821,775,1346,2920,1579,2884,2956,
2202,2958,2713,2282,2636,497,2807,2957,2595,2570,2959,910,2960,1797,2961,2751,
864,2224,536,2026,294,2288,2963,2800,1575,2965,883,1155,2342,2781,1673,2967,
1976,2439,2936,2092,2777,2808,1854,2969,1438,2232,2970,2411,2971,2880,2973,
2667,2871,2974,1863,1609,2942,1483,1405,2976,2977,2728,218,2978,2979,1656,1840,
2980,2819,2259,2982,2860,1947,1842,523,2479,2972,1701,1925,2007,2985,1693,2987,
827,1903,2257,2989,1289,2926,2659,1586,2275,2993,2994,1290,1738,2995,2132,1268,
2996,2414,2888,153,1257,2266,1060,1031,2696,2755,2621,3004,1860,3005,1022,3007,
2274,69,1952,850,2895,1729,2951,3010,390,2081,3011,3012,2229,3013,3014,2918,
3016,2805,3018,1933,2924,3019,3000,640,1956,2083,1552,1450,3022,2648,2975,2272,
2992,2955,3024,3025,3002,2670,482,1986,1247,2311,848,2615,1967,2469,2427,3029,
3030,365,1915,138,2446,384,3031,722,2933,1299,2520,485,2144,3035,2546,2010,
1711,2966,2968,2477,1339,2981,3037,2058,817,2896,2525,804,514,2842,1601,1823,
1013,1313,2943,853,446,2421,1597,3041,3009,2866,1242,1942,2962,2988,1826,3017,
1254,3047,2390,2964,3048,3049,2708,2693,2797,1432,2565,2210,1658,3051,2454,407,
2825,2482,3052,2364,2804,2206,3036,2105,2718,1089,3046,2671,1484,753,2018,1702,
860,2147,439,2515,2828,2758,1884,2086,2433,1909,2633,2983,1462,2089,3044,1727,
3039,1973,3059,3060,2855,2654,1212,3045,2577,2813,760,2506,2062,3063,1831,3065,
351,2160,369,3067,2902,2944,2915,2298,707,2458,227,699,2697,806,97,1965,3069,
2600,147,3042,3071,345,1413,545,2649,2175,2953,2238,1950,2762,2076,2954,3072,
2419,2534,2487,2594,3003,2509,2429,2117,2791,3073,2219,720,994,1550,3075,823,
2523,1451,2745,1849,2287,1287,1003,87,2444,2472,3078,3079,321,1924,1189,1234,
2861,2837,888,1114,1593,2817,2493,1844,235,2984,3082,693,2222,2244,631,1018,
3006,2927,1650,2949,480,687,3034,3084,1474,1775,2930,1403,2773,3027,2945,2894,
3086,2351,1097,3087,1610,2312,2741,1526,2532,2607,3089,1633,3090,3091,844,2101,
3021,2289,2513,3070,2906,3085,2591,1795,2876,2558,1492,3093,933,1071,3095,2904,
3096,2879,2533,2378,3097,591,1025,3038,2380,2699,2841,1800,3098,629,3054,2150,
2179,3081,2107,2997,1971,2530,2834,1645,3100,2875,2814,3102,1747,1663,1704,361,
2442,2324,1923,1814,748,2528,3050,1000,1744,731,2928,104,2571,2538,1787,3033,
2952,1076,3099,1384,2832,1194,465,2872,2415,2809,3104,2032,3105,3106,2550,2234,
3107,2321,3058,2826,3083,2142,2793,1311,3061,2221,2830,618,1351,1370,2645,1856,
2687,3074,2263,2878,3032,2496,2327,353,2991,2747,2038,1889,1239,3088,2720,2733,
2845,3026,2013,3110,1033,2386,3111,951,2999,2562,717,713,1401,3028,1613,3108,
2947,1500,3094,552,441,3114,2789,1435,1256,1606,413,2726,617,1262,2409,2017,
785,2412,2050,828,3043,2400,1402,2796,2417,2922,3119,2318,501,1807,3055,1894,
2563,2542,2462,861,2986,1180,3118,3112,750,2192,1536,2835,2468,3109,3053,2734,
3121,1771,1327,3040,2867,2094,2169,2854,2296,1091,2434,2579,3101,3056,1852,
2716,2329,2554,3103,3023,2586,2152,3008,3116,2354,2358,1931,3080,2673,190,1340,
1481,2406,3001,3123,504,3077,3076,3115,3062,3124,3057,1203,3064,3066,2052,2445,
1897,2873,2212,3122,3120,2512,2913,3125,945,2990,3068,3015,3020,2753,1389,2134,
740,833,1529,3092,3117,1198,2494,1134,2184,2435,2300,2912,3113,2585,1945,2998,
2526,2778,2882,2917,2397,953,2401,1605,2939,2690,2911];



x2:=\[3126,3131,3128,3136,3130,3127,3134,3138,3132,3139,3129,3141,3133,3135,
3140,3137,3142,3143];

y2:=\[3127,3132,3133,3126,3134,3135,3129,3131,3138,3128,3140,3130,3137,3142,
3136,3143,3139,3141];


// G<x,y>:=PermutationGroup<{3126..3143}|x2,y2>;
// G<x,y>:=PermutationGroup<3125|x1,y1>;
G<x,y>:=PermutationGroup<3143|x1 cat x2,y1 cat y2>;


AU:=AutomorphismGroup(G);
#G;
#AU,"\t",EulerPhi(#G);