PermutationGroup<5040|
\[2,5,8,6,1,12,16,11,22,20,3,4,31,34,28,17,7,42,45,26,
50,25,56,54,9,10,64,37,68,71,33,75,13,35,14,83,15,88,91,
94,97,43,18,104,48,109,107,19,79,51,21,120,123,60,128,59,
134,132,23,24,142,145,148,66,153,27,158,70,162,29,72,30,168,
171,77,176,32,181,116,86,187,190,84,36,196,186,200,89,38,
207,92,39,212,96,216,40,98,41,224,227,230,233,236,105,44,
242,113,141,112,251,249,46,47,260,263,49,147,269,272,121,52,
278,126,284,282,53,157,129,55,296,299,137,304,136,308,57,58,
315,318,321,246,144,326,61,146,62,267,150,335,63,339,259,155,
345,65,350,291,159,67,357,360,164,364,69,369,372,375,169,73,
381,173,386,74,391,394,178,398,76,402,405,183,103,78,413,416,
80,188,81,423,191,82,430,433,436,439,197,85,446,448,201,87,
452,222,456,459,461,208,90,205,468,471,213,93,478,481,218,
486,95,490,355,494,455,498,225,99,505,229,199,100,231,101,
515,235,520,102,182,526,529,532,535,538,245,544,542,106,108,
553,556,255,561,254,563,565,110,111,574,577,580,342,262,586,
114,264,115,592,595,117,599,270,118,606,273,119,612,615,618,
621,279,122,628,630,288,314,287,639,637,124,125,648,651,127,
407,657,660,662,297,130,667,302,673,671,131,330,305,133,685,
688,310,693,135,698,701,704,634,317,709,138,319,139,567,323,
720,140,724,647,328,731,143,736,680,654,741,744,747,337,751,
149,755,341,760,151,152,763,766,347,771,154,775,778,352,783,
156,788,791,412,794,358,160,800,362,803,161,807,366,812,163,
816,819,371,206,165,373,166,826,376,167,831,428,835,838,382,
170,845,847,368,388,853,172,858,421,393,862,174,395,175,868,
871,399,177,878,881,404,886,179,406,180,564,894,426,897,899,
220,414,184,906,418,910,185,915,918,821,922,424,189,929,824,
740,834,935,431,192,942,435,460,193,437,194,953,440,195,960,
962,965,968,971,447,198,228,980,983,986,453,202,993,203,457,
204,999,209,947,370,1007,410,1011,1014,1016,619,469,210,1024,
472,211,1031,1034,1036,579,865,479,214,1045,483,1047,215,1052,
914,488,1058,217,1062,492,1066,219,921,495,221,1076,1079,499,
223,1086,1089,1091,1094,1097,506,226,1104,1106,1109,902,465,
1053,1115,1117,516,232,1123,948,340,522,1131,234,1135,997,1140,
527,237,1146,531,1149,238,533,239,1157,537,1162,240,539,241,
1170,1173,548,573,547,1182,1180,243,244,1191,1194,294,266,554,
247,1203,559,1209,1207,248,590,562,250,568,292,569,1222,717,
252,253,1227,1230,1233,1177,576,1239,256,578,257,1039,582,1248,
258,1252,1255,1190,588,638,261,1265,1215,331,593,265,707,552,
1174,1201,1278,600,268,1285,597,1288,1051,1291,607,271,1298,
904,1300,1303,613,274,1309,616,275,1315,620,1020,276,622,277,
913,1326,1329,1331,1334,629,280,633,1342,1340,281,283,1351,
1354,643,1263,642,1363,1361,285,286,1371,1374,1377,727,650,
1383,289,652,290,1390,591,1394,718,658,293,714,551,1404,663,
295,1409,1411,1414,668,298,1418,1420,677,697,676,1429,1427,300,
301,1438,1441,303,780,1447,790,1451,686,306,1456,691,1460,1168,
307,713,694,309,1472,1475,1424,700,1480,311,702,312,1486,706,
1490,313,1272,1437,711,1498,316,1503,1467,1402,1218,1509,320,
1397,1513,722,1518,322,1147,726,1525,324,325,1196,1532,1534,
733,1538,327,1542,1544,738,474,329,1550,932,742,332,1556,745,
333,1562,748,334,1567,787,752,336,1574,1577,757,1580,338,1583,
754,519,1585,1588,765,1590,343,767,344,1236,1597,1600,772,346,
1606,988,777,1613,348,779,349,1445,1619,1566,785,1607,351,1627,
1570,789,353,1349,792,354,1634,795,356,1639,1029,1642,1645,801,
359,1651,805,1656,361,1660,809,1663,363,1666,890,813,365,1674,
1677,818,1681,367,385,1686,390,1689,784,409,1693,827,374,1057,
1197,1703,832,377,1710,378,836,379,1716,839,380,1721,958,1725,
1728,1730,846,383,849,1739,384,1744,1747,1750,855,946,387,1757,
1760,859,389,1636,815,864,1769,392,1040,1773,1692,870,1777,396,
872,397,1785,1787,1790,1793,1796,880,1801,400,882,401,1809,
1812,1665,888,1818,403,1823,1669,493,1828,1831,896,1836,408,
463,1843,901,1847,411,1003,1852,1199,1210,907,415,1861,1863,
912,1867,417,1324,1055,917,1872,419,919,420,1877,891,923,422,
1884,1886,1729,1889,1890,930,425,1893,427,1897,1899,936,429,
1904,1907,1908,1911,1914,943,432,1134,1922,1755,434,1127,843,
1928,1931,1933,954,438,1940,1714,808,1724,1945,961,441,964,
1952,442,966,443,1961,970,1966,444,972,445,1971,1973,1976,1979,
1982,1984,1070,982,1989,449,984,450,1995,987,451,1609,1084,
2003,2005,2006,994,454,2013,1985,1139,2018,1000,458,2024,1712,
510,1443,513,2031,1008,462,1027,1095,1012,464,2036,511,2041,
1017,466,2045,2048,467,768,2051,528,1025,470,2058,1633,1459,
1522,2063,1032,473,2070,737,1015,1037,475,2078,476,477,2083,
2086,2089,1804,1046,480,1049,2098,482,2101,1274,1054,1113,484,
485,2108,1699,1059,487,1103,928,1064,2119,489,2122,1068,2126,
491,2130,1987,2132,991,2136,1145,2139,1077,496,2146,1081,2150,
497,1993,770,2002,1612,1087,500,2160,1090,501,1092,502,2168,
1096,2033,503,1098,504,2176,2179,2180,1183,2117,1105,507,1108,
2191,508,1111,2195,509,1586,512,2201,1005,2205,1118,514,2210,
2212,2215,1968,1124,517,2222,2224,518,2228,2231,666,1133,1529,
521,1921,1137,2237,523,2053,524,1141,525,1320,822,2247,1998,
1023,1246,2250,1151,1004,530,2254,2242,696,2256,2257,1158,534,
2263,1548,1842,1164,2271,536,2275,2034,2280,1464,2282,1171,540,
2289,1176,1276,2291,541,543,758,2299,1186,2304,1185,2184,2307,
545,546,2315,2318,2320,1258,1193,2262,549,1195,550,1531,1701,
2332,609,2335,602,2133,1204,555,2343,2345,1213,1226,1212,1855,
1792,557,558,2354,560,2359,2361,1508,1880,2366,1243,1223,566,
2372,2375,2349,1229,2379,570,1231,571,2384,1235,2167,572,1021,
2391,2353,1241,2397,575,2401,2367,2357,1564,723,2408,1250,1358,
581,2415,1253,583,1489,1257,2423,584,585,938,1630,2431,2434,
587,2437,1267,2442,589,1339,2449,2452,2454,594,2458,604,2460,
596,2465,1279,598,1069,1322,2472,2474,2476,1286,601,945,1289,
603,2238,1292,605,2488,2047,2493,2496,2499,1299,608,1301,610,
2135,1304,611,2512,2515,2518,2520,1310,614,2527,1283,2529,2531,
1316,617,2538,2540,934,1560,2545,2471,2548,623,2552,1328,1698,
624,1330,625,1333,2558,626,1335,627,2563,716,2567,2447,1346,
1370,1345,2575,2573,631,632,2582,2585,683,2358,1352,635,2594,
1357,2599,2597,636,1387,1477,2608,1366,2613,1365,2615,640,641,
825,2620,2623,2570,1373,2628,644,1375,645,2636,1379,2638,646,
2641,2644,2581,1385,1381,649,1632,1249,1697,2323,1391,653,2655,
2657,1395,655,2662,656,2107,1220,2666,2668,659,2672,1406,2676,
661,2680,2682,1410,664,1412,665,2198,1130,1192,2693,2695,1419,
669,1423,2704,2702,670,672,2710,2245,1433,2715,1432,2720,2718,
674,675,2723,2726,2729,1495,1440,2732,678,1442,679,1150,2738,
681,1811,1448,682,2746,2748,1452,684,2752,2755,2757,1457,687,
2760,2060,1463,2764,2248,689,690,2773,2775,692,1546,955,2780,
2782,1473,695,2786,1154,2790,2606,2793,2772,1482,2799,699,2163,
2777,2803,1487,703,2808,2420,1492,2813,705,2816,2819,708,2587,
2102,1500,2827,710,1297,2830,1505,2834,712,1718,2839,715,1337,
2844,2382,2321,1515,2851,719,1376,1549,1519,721,2860,2861,797,
2863,1521,1527,2868,725,2577,2233,927,728,1533,729,1535,730,
2881,2884,1539,732,2889,2892,1543,734,1545,735,1937,2854,2267,
2855,1551,739,2904,1708,2096,2910,1557,743,2914,2916,1142,1439,
1563,746,2406,2923,1622,1569,2926,749,750,2930,1616,2934,1576,
2938,753,759,2942,762,1581,756,2948,1178,2890,1587,2199,761,
1579,2957,1592,2961,764,2634,2000,2966,2969,1599,2972,769,1083,
2975,2977,2009,2978,1476,1608,823,773,774,2984,2987,2156,1615,
2770,776,1999,2929,2999,1621,2524,781,782,3008,3010,2016,3015,
1628,786,1775,2430,3024,2649,1009,1635,793,1766,2281,3033,1640,
796,3037,1643,798,3041,1646,799,3046,2081,3049,3051,1653,3055,
802,2502,1764,1657,804,3063,3066,1661,806,1026,957,3070,1814,
1668,3072,810,811,3076,1805,3079,3081,1676,3084,814,861,3088,
2526,866,1683,3093,817,3097,867,1688,3102,820,1143,3109,3112,
1685,1367,3116,1883,969,2329,2105,828,3120,829,2155,1704,830,
3126,1902,3128,2907,3130,1711,833,2028,3137,1942,3140,1717,837,
2838,951,1602,1722,840,1912,841,1726,842,3153,949,1888,1731,
844,1144,1093,3160,3163,3165,3167,1659,1741,2612,848,3173,3174,
1745,850,1765,1749,3181,851,1751,852,1678,3189,3190,854,3192,
1759,3197,856,1761,857,3202,3057,3060,3178,860,1821,1647,1770,
863,3213,3039,1680,3218,3021,1673,1779,2030,869,2253,3223,1080,
3225,3227,1786,873,1789,3230,874,1791,875,2351,1795,3238,876,
1797,877,2128,3245,2829,1803,2576,879,2092,3078,3074,3187,3095,
1810,883,2742,1813,884,885,3175,1892,3264,1820,1167,887,3207,
3270,1825,3274,889,1107,3280,1829,892,3069,1832,893,2276,3290,
1006,1838,3293,895,3297,3299,3301,2204,1844,898,3307,3106,1849,
3313,900,2216,2955,1853,903,2049,905,3327,1172,3329,3332,2326,
1862,908,1865,3338,909,2470,1868,911,3209,3346,3349,1874,3352,
916,3355,3357,1878,920,2313,2364,2981,3364,3118,1885,924,1887,
925,926,1530,1061,3291,3263,1894,931,3300,1762,1898,933,1319,
1758,3122,2330,2609,1905,937,2390,1259,1909,939,1436,1913,3149,
940,1915,941,2898,3406,3409,3412,3415,944,1287,3064,3420,3422,
1392,3424,1929,950,1496,1719,3428,1934,952,2635,3433,1468,3437,
2865,1469,2537,956,3443,3444,1946,959,3446,3447,2100,3452,2363,
1954,2042,963,3458,3442,1735,3462,2023,1641,1962,967,3470,3371,
3151,1696,2143,2218,3475,2939,1972,973,1975,3479,974,1977,975,
3486,1981,3491,976,1983,977,1986,2015,978,979,3497,1990,981,
2012,3503,2032,1430,1996,985,2554,1074,1572,2937,3513,989,2004,
990,1072,2007,992,3521,2174,3524,2309,3463,2014,995,996,3014,
3221,2019,998,2208,3537,3539,3157,2025,1001,3212,3302,1002,3547,
3027,1835,1082,1010,2279,2346,2037,1013,3553,2862,1153,1035,
2797,1155,3561,2046,1018,2492,2050,3324,1019,2052,1022,2241,
1344,3179,2894,3251,1662,1771,1028,3158,3579,2064,1030,3584,
2857,1958,3587,3589,2071,1033,3593,2559,1649,3597,3599,3170,
2079,1038,3365,3048,2503,2084,1041,3610,2088,3613,1042,2091,
2203,1043,1044,3620,1100,2864,2908,3625,2099,1048,3450,2103,
2824,1050,3013,1327,2022,2665,2110,3138,1056,3348,3640,3642,
3645,3647,3650,1060,3652,2120,1063,3658,2124,3662,1065,1325,
2127,1067,3243,3670,1280,3673,2134,2338,1071,2508,2137,1073,
3680,2140,1075,2479,3685,3474,2963,3691,2147,1078,3696,3698,
1782,2544,3375,1116,3706,3123,1085,3710,3712,3714,2161,1088,
3717,2802,2011,3720,2311,2389,1733,1152,3516,2990,3726,3518,
1603,3728,2177,1099,3732,2094,2181,1101,3738,3740,1102,3744,
2758,3748,3750,3753,3730,1826,3229,3634,3758,2196,1110,3763,
2690,1112,3769,2202,1114,2579,1161,2153,3532,3776,3536,3778,
2211,1119,2213,1120,3782,2217,3319,1121,1122,3788,3464,3791,
2223,1125,2226,3152,1126,3798,2229,1128,3574,2232,1129,1132,
1713,3809,2069,2239,2485,1136,3429,1138,2040,1784,2487,2714,
3540,1732,2768,2170,2251,1148,1753,3222,2169,3825,2043,2258,
1156,1470,3830,3831,1415,2264,1159,2021,3459,1160,3198,3456,
3768,2273,3842,1163,3845,2277,3289,1165,3770,1166,1819,2993,
2283,1169,3853,3855,3856,2734,2686,1857,2525,2294,2314,2510,
1175,1504,3870,1217,3873,2302,1455,3875,1179,2327,2305,1181,
2378,2310,3362,2164,1184,3519,3888,3361,3864,2317,3894,1187,
2319,1188,2322,2849,1189,2651,3868,3903,2815,3881,1244,1388,
1706,3908,2333,1198,3912,2336,1200,3760,1202,3920,3922,3924,
1670,2344,1205,2348,3552,3928,1206,1208,2483,1211,2869,2394,
2355,1214,3937,2328,2589,2360,1216,2297,3861,3455,1219,3945,
1399,1221,2439,3947,3950,3952,2373,1224,2792,2377,3494,1225,
3668,2381,3694,1228,2847,3883,2385,1232,3964,3965,3211,1234,
3392,2393,2189,1237,1238,2402,3393,2399,3978,1240,3981,2403,
3974,1242,3986,3987,1245,3990,2410,3991,1247,1400,2446,3997,
3998,2417,4000,1251,2876,2826,1254,4006,2414,2425,4008,1256,
1431,4012,4013,4016,1260,2432,1261,1520,2435,1262,4022,2438,
1264,2754,4023,3994,2444,4027,1266,1963,3996,1268,3595,2451,
2456,1269,2453,1270,2455,1271,4033,2260,2459,1273,2461,1275,
2172,4040,4041,2466,1277,4047,4049,4052,3343,1281,2473,1282,
1312,4057,2477,1284,2562,3684,4062,1859,4065,3292,4068,1290,
4070,3322,2489,1293,3656,2475,1294,2494,1295,4078,2498,3806,
1296,1501,3535,1781,3059,3607,4084,2463,3550,4087,1302,3073,
3866,4092,2513,1305,4097,2517,3333,1306,2519,1307,2521,1308,
3890,4104,3005,3746,3089,2528,1311,2530,1313,2532,1314,3515,
3485,2973,2386,3441,2539,1317,2542,3466,1318,4089,3703,2546,
1321,3799,2549,1323,4129,3666,2125,3961,3508,4136,3603,2713,
2560,3596,1332,4055,4060,2565,4144,1336,3743,2569,4149,1338,
1341,4152,1523,2054,3819,2578,3249,2873,1343,2090,3569,2645,
2584,1454,1347,2586,1348,1930,4163,1350,1396,2842,1672,3719,
2595,1353,4169,2603,2619,2602,3396,4171,1355,1356,3976,4180,
1359,4184,2611,3386,4187,1360,2632,2614,1362,2617,1882,1364,
4195,4170,2621,1368,4199,2625,4203,1369,4205,4177,2630,1667,
1372,3053,1740,2413,2880,3432,1516,1541,2640,2448,1378,2642,
1380,4217,1384,1382,2874,3568,3204,1386,4224,1389,2875,3972,
3501,1926,4230,2659,4233,1393,2843,4236,2590,3943,2261,1398,
2411,2436,2669,1401,1939,4242,2674,4005,1403,4245,2677,1405,
4247,4165,2681,1407,2683,1408,4253,4255,3859,3563,2663,3631,
1413,1742,2207,2694,1416,2696,1417,4064,4265,3833,3862,4269,
2708,2722,2707,2745,2440,1421,1422,4276,2711,1425,2287,3228,
1426,2716,1428,4278,2426,4280,1994,4282,3623,2725,4287,1434,
2727,1435,4074,1910,1471,3844,1561,4110,2712,1484,3808,2109,
2739,1444,4299,4301,1446,2810,4303,4275,2747,1449,2749,1450,
2902,3308,2753,1453,2368,2583,4309,2300,3747,4311,2761,1458,
3036,4314,2767,3326,3741,1461,1462,3176,2994,4319,2796,2774,
1465,2776,1466,2735,3275,2986,2259,3460,2730,2533,1598,3405,
2787,1474,4327,2960,1605,3734,3954,2795,4331,1478,1479,1953,
3820,2801,1992,1481,1483,2804,1485,2214,3812,4340,2809,1488,
2992,4036,2837,2814,1491,1860,2818,4346,1493,2821,1944,1494,
4145,3723,1497,4284,4004,2828,1499,3248,2831,1502,3863,2421,
2295,2268,2523,4345,1506,2841,2660,1507,4031,2840,2845,1510,
4363,1511,3982,1512,1947,2853,4368,1514,2899,1517,4372,2895,
4374,4376,2433,1524,3556,2572,3624,2670,3002,4157,2870,3932,
1526,4385,4388,1528,3426,3394,4003,2859,3029,4393,1593,2883,
2919,1536,2885,1537,4397,3146,4400,2891,2951,1540,2637,2325,
3575,2066,4370,3026,2931,1547,3430,3183,3067,4409,2905,1552,
4349,1553,1554,3654,2911,1555,2370,3918,2915,1558,2917,1559,
2162,4112,4117,3957,2887,2924,1565,3689,2927,1568,4151,2956,
2932,1916,1571,3017,2935,1573,4427,1594,2940,3477,1575,1596,
2944,4045,1578,4436,3020,4439,2949,1582,2029,1584,2159,2407,
2062,3320,1617,2959,3785,1589,4329,2962,1591,3690,4306,3438,
2967,1595,4447,2941,4448,4450,2784,4115,2087,2976,1601,1720,
2979,1604,4425,3363,3655,4455,2985,1610,4322,2989,4457,1611,
3725,4460,2743,1637,1614,4464,2173,4158,4467,3000,1618,4470,
4381,2947,4472,1620,2852,3682,3009,1623,3011,1624,3548,3633,
1625,3016,1626,3674,4435,3030,4438,1629,3841,2650,3025,1631,
3145,1778,3286,4377,4479,1943,1969,3034,1638,4485,4313,1960,
4488,3216,4192,3042,1644,4260,2076,3206,1768,2980,1648,2074,
3533,3052,1650,4211,4500,3056,1652,3203,4504,1654,1655,3200,
4510,3065,3419,1658,1738,2750,1743,3285,3071,1664,2629,3551,
3217,2506,2342,4175,1671,2592,4248,1776,1869,4523,3085,1675,
1783,4508,1752,1679,4503,3119,3278,3094,1682,3254,4533,3099,
2600,1684,4535,4537,3104,4538,1687,4318,3310,3898,1840,3111,
4542,1690,3113,1691,1876,4138,3117,1694,1695,4386,3121,1700,
3384,1702,1895,4189,3127,1705,3129,1707,3131,1709,3404,4109,
4563,4565,2643,2234,2737,4566,3141,1715,2571,3431,4569,2897,
2922,3417,3354,1723,4575,3427,3796,3154,1727,4582,1956,1959,
3578,3210,3161,1734,4587,1957,4588,3166,1736,3169,2514,1737,
3601,2274,4238,2691,3068,3261,4317,3558,1746,3572,3062,3182,
1748,3821,4305,3186,4600,3253,3101,2252,3191,1754,3193,1756,
3377,2480,4506,1900,2835,3678,4509,4507,1896,1763,4222,4335,
4492,1767,4610,3082,4585,3482,3544,2059,2484,3323,1772,1806,
3219,1774,3695,3510,1780,2501,4621,3086,4623,2243,2557,3756,
3231,1788,4626,1856,4628,3852,2553,3925,3240,2044,1794,4517,
4494,1798,3882,3247,4498,1799,1800,1802,4113,3576,4641,1807,
1808,4605,4609,1834,3096,3004,4647,1815,4649,1816,3265,1817,
3215,3255,4294,4643,3271,1822,2404,4077,3276,4291,1824,4656,
4459,4257,3282,4452,1827,3854,2269,1830,4482,4661,2347,1833,
3257,3376,2350,3294,1837,4343,4430,3298,1839,3108,3124,3303,
3545,1841,4669,2744,4090,3309,4307,1845,1846,4672,4674,3315,
4558,1848,4332,4357,4681,1850,1851,2998,2244,3266,1854,4029,
4021,3233,3761,3330,1858,3805,2481,4098,2209,4690,3467,2129,
3340,4694,1864,4391,3366,1866,3244,3939,3347,1870,3639,3350,
1871,3632,3353,1873,4572,3356,1875,3114,2982,4702,3413,1879,
3886,1881,2616,3604,3672,2909,3502,4491,2551,3471,4010,4708,
4549,3704,1891,4531,3702,4298,4713,3469,4715,1932,1901,4216,
1903,2564,4719,4721,4723,3144,1906,3472,2652,3134,3098,4727,
4728,1955,3907,4729,4556,4116,4560,4325,3408,4733,1917,3410,
1918,2823,3414,4703,1919,3416,1920,3975,4740,1923,3421,1924,
3423,1925,3425,1927,2646,1965,3383,3815,4407,4568,1935,3435,
3164,1936,4133,3439,4446,1938,4403,1941,3156,3031,2820,4250,
2850,3449,4570,1948,1949,4481,3453,1950,4134,1951,3284,4758,
3399,3837,4259,4648,2067,1991,3790,3517,3591,4072,4316,4361,
2445,1964,2396,4744,1967,3032,3773,1970,2771,3481,4765,1974,
2388,2219,4768,4114,3487,1978,4328,4748,3722,3492,1980,4586,
3956,4711,3771,3498,1988,3971,3651,4227,4707,2800,4777,3683,
4422,3495,1997,3915,2017,4780,4782,3514,2001,2783,2249,4762,
2996,2166,3923,3522,2008,4785,3525,2010,4788,4789,3638,2116,
4790,3795,3775,3571,2200,3832,2020,2265,4750,2106,3818,3490,
3787,4798,2026,2027,4800,2950,4477,4567,3075,2509,2035,3554,
2038,4576,2039,4484,4573,3848,4793,3239,4659,4141,2341,4664,
4807,4809,4221,4160,4289,3050,2055,4811,3803,2056,2057,4320,
2061,2954,4589,3001,2596,4817,3585,2065,2675,3588,2068,2236,
3567,2541,2165,3594,2072,2639,2073,3598,2075,3044,4822,2077,
4700,4139,2080,2284,2759,2082,4414,4825,3611,2085,4302,2974,
2791,4406,4615,4496,4545,4828,3621,2093,4824,2703,2095,3626,
2097,3816,3369,3933,4493,3829,4699,2104,3757,4118,4262,4833,
4094,2111,3641,2112,3643,2113,4123,3646,2114,3648,2115,4188,
3529,4776,3653,2118,3367,3358,4075,2424,3660,4841,2121,4579,
3664,4845,2123,4847,3370,4522,2306,2362,3337,3644,3342,3675,
2933,2131,4483,4851,4606,3506,3681,2138,4440,4206,2141,3687,
3527,2142,4756,4421,2144,3692,2145,4692,3959,4618,3697,2148,
3700,4081,2149,2848,4712,2151,2152,2400,3707,2154,4051,4581,
3711,2157,3713,2158,2952,3295,4404,2918,4865,4166,3592,3985,
3541,3411,3035,2171,2462,4869,3729,2175,3754,3359,3733,2178,
3614,3531,4528,4808,3739,2182,3742,4315,2183,4146,3745,2185,
2290,2186,3749,2187,3752,4873,2188,2392,2190,2365,2192,2193,
3759,2194,3917,4687,3992,3765,4874,2197,4876,2285,3840,3534,
3850,4773,4367,4764,3100,2206,2692,3789,3334,4797,4032,3543,
2805,3107,4794,4443,2886,4037,3483,4877,2220,3792,2221,3339,
4883,3735,2225,4884,3800,4095,2227,4683,4886,2230,4555,4688,
3865,2896,4162,3810,2235,4578,4339,4839,4604,2240,4831,4812,
2246,4155,4336,2901,2968,3546,3306,3826,2255,4111,3105,2689,
2457,2664,2500,3899,4893,3636,2340,2266,4894,4896,2270,4480,
3843,2272,4292,3171,3927,3235,4805,4787,2278,4592,3847,3605,
3941,3767,3857,2286,3262,2288,4900,3669,4267,4046,2292,2497,
2293,2817,3901,4726,3871,2296,4905,3874,2298,3878,3887,2741,
2301,3813,4351,2303,3344,3962,2721,3896,2308,4907,3889,2312,
4103,4639,4611,4354,3895,2316,4909,3526,3783,2699,4350,2324,
2678,2893,4657,3667,3372,4451,3909,2331,4913,4924,3913,2334,
4925,4779,3630,2337,4416,4384,3921,2339,3836,4091,3564,4631,
4927,4324,3288,3931,4908,4355,2352,4176,4714,4932,3969,3938,
2356,4076,2679,3283,4574,2688,4532,3755,4020,3948,2369,4655,
2912,2618,3953,2371,2374,4135,2376,4108,4571,2380,4514,3236,
2383,3708,2536,3967,3489,2387,4745,4749,3968,4775,4226,4186,
2395,3147,4179,4379,3979,2398,4792,3705,3701,3135,4321,4583,
3272,3989,3226,2405,2953,3993,4840,2409,4024,3451,2412,2633,
2422,2427,4001,2416,3155,2418,2419,4244,2833,2719,3657,4942,
3906,4286,3999,4014,2428,4943,4017,2429,2671,4944,4935,2765,
2667,2706,2441,4486,3277,4028,2443,4684,4629,2591,4795,2450,
4142,4743,4344,3542,3577,4741,2505,4042,2464,4911,4101,4434,
2832,4048,2467,4050,2468,3963,4053,2469,4872,4143,3860,2491,
2555,4130,2478,3250,3195,4015,4264,4066,2482,4420,3214,4428,
4071,2486,3336,2788,4290,2490,3345,4654,4079,2495,4099,4408,
3260,4392,4085,2504,4710,4088,2507,4122,3824,3520,4093,2511,
3528,2547,4891,3168,2516,4885,4832,4348,3566,2522,2836,4810,
4383,4718,2921,4561,4295,4419,2882,4061,2534,2535,4442,4326,
4405,3814,4760,4922,2543,3671,4859,4965,4940,3911,4949,4131,
4553,2550,3473,4705,4249,4853,4058,4966,4193,2556,4011,2687,
4689,2561,3387,4220,2566,4767,4962,4150,2568,4371,3142,4148,
2763,2574,4197,4382,4466,2971,2580,4614,2736,4164,2588,3940,
2593,4868,3318,3582,2598,4173,3677,2601,4972,4516,3629,4208,
4974,2604,4181,2605,3538,3565,4185,2607,4921,4190,4194,4552,
2610,3512,4490,3115,3649,3951,3919,4596,3468,4200,2622,4863,
4463,4204,2624,4207,3505,2626,2627,4418,4980,2631,2709,4981,
4223,4513,4225,3136,3797,3562,2822,2647,2648,4640,3023,3385,
2653,2654,3457,4902,4231,2656,4025,4234,2658,4985,4237,2661,
4593,4251,4901,3139,4018,3784,2673,3586,3341,3902,4519,3454,
4358,4757,4273,4254,2684,4256,2685,4630,4988,2781,4359,4899,
3835,3335,2697,4266,2698,2700,4559,4272,4992,4663,2701,4987,
2903,2705,4212,4174,4279,2717,4007,3162,3884,4698,4352,3314,
4140,4288,2724,4624,2728,2778,2731,3398,4550,2733,3766,4668,
4540,4300,2740,3877,4394,3305,3851,4511,4360,2751,4919,4310,
2756,3606,4167,2762,4154,2766,4198,2769,3828,3478,4038,4577,
2779,4635,3846,2785,2920,4073,4770,2789,4338,4333,4679,2794,
5000,4608,2798,3232,4880,2806,4341,2807,4914,3715,2811,2812,
3867,3557,4044,4412,4920,4704,2825,3688,4917,3929,3418,4680,
3445,3043,2964,3381,3817,4364,2846,3269,4432,4390,3006,4598,
3807,2928,4373,2856,4375,2858,2877,2878,2879,4395,4941,2866,
2867,4959,4196,4387,3091,2871,4389,2872,3772,4246,4952,4378,
3612,3977,3484,3786,4671,4963,4401,2888,4201,4751,4864,3635,
4444,2900,3699,4274,4240,3196,2906,3150,4613,4475,2913,3038,
4979,3827,4796,2925,3679,4938,5002,3047,3618,4429,4468,2936,
4665,3312,4995,3736,2943,4478,4437,2945,2946,3003,3007,5012,
3403,2958,3615,4030,2965,3822,4449,2970,4159,3400,4658,3110,
4126,4456,2983,4458,2988,3092,4462,3560,2991,4978,4465,2995,
2997,3321,4069,3904,3581,4954,3259,4838,5007,4977,3504,3012,
3018,3019,3022,3995,3028,4850,4347,3724,4232,3811,4417,3910,
3040,3628,3045,3916,4633,4213,4755,3616,4637,5018,4502,3914,
3054,4529,4505,3058,4411,4594,4526,3061,3180,3184,3727,4956,
4619,4849,3077,4620,4054,3080,3234,3609,3905,4525,3619,3083,
3087,4644,4433,3090,3208,3194,4934,3258,4380,3774,5010,3188,
4539,3103,3379,5022,4453,4998,4398,4426,5023,4564,3602,4701,
3268,4602,3125,4059,4717,4888,4731,3397,4285,4724,3132,3133,
4297,3395,5024,3983,4241,4801,3143,3391,4754,4937,3148,3177,
4933,4413,4803,3984,4487,4685,4120,4860,4002,3721,4739,3159,
4772,4281,3434,4814,3461,4802,4304,3172,3201,5028,4156,4946,
4645,4986,3185,3256,4607,3380,4119,3267,3199,4551,3205,4601,
4530,4916,3663,3608,4666,4497,3573,4989,3220,3960,3241,4622,
3224,3988,3570,5016,4337,3480,4520,4445,3279,3237,4261,3242,
3930,4686,4961,3246,4958,4915,4214,4642,3252,4365,4982,4369,
4871,4082,4590,3858,5031,4308,4991,5001,3273,4936,4026,4469,
3281,4219,4105,4662,3287,4990,4183,3296,4161,3801,4562,4670,
3304,4544,4673,3311,4431,4996,4283,3980,4769,3316,3317,4168,
4819,4667,3325,3661,4323,3328,3331,4034,4263,5026,4854,4732,
3793,4270,4235,4993,4676,3351,4548,3374,3731,3360,3880,3436,
3794,3368,4709,3373,4857,3507,3378,4603,4931,4716,3382,4834,
4861,4720,3388,4722,3389,4725,4268,3390,4903,4557,4293,4730,
3401,3402,5032,4735,3764,3407,5020,5004,4753,4926,4356,4947,
4399,4763,4132,3970,4423,4752,3966,3936,4182,3440,5013,4997,
3448,3617,4353,4239,4228,4210,4580,5019,3465,4035,3476,4627,
3751,4820,4396,4994,3488,4774,3493,3496,4955,3499,3500,4476,
4697,3509,4781,3511,4191,4334,4546,4786,3523,4889,3897,3686,
4791,3530,4677,4461,4243,3780,4067,4878,3781,4096,3823,3549,
4882,3555,5036,3559,3737,4102,4806,3590,4660,4616,4362,4650,
3580,3600,4471,4818,3583,4821,4147,4682,4815,4499,4830,4521,
4019,3872,4524,4636,3622,3627,4856,4835,4554,3637,4804,5011,
5015,3879,3762,4842,3659,4737,4652,4612,4124,4848,3665,4906,
3676,4172,4948,3955,3693,4967,4100,4086,4953,4846,3709,4107,
4342,4402,3716,4866,3718,4258,4312,4512,4898,4960,4518,4766,
4734,4009,4296,3777,3779,4599,4330,3834,4591,4706,4218,4080,
4887,3802,3804,3849,4675,4799,4128,4881,4895,3838,4897,3839,
5035,4632,4056,4410,4984,3869,3935,4827,4515,3876,4634,3885,
5006,4923,5039,4489,4862,3891,3892,3893,4736,4651,3900,3973,
4964,4043,4127,4501,4584,4928,3926,4137,4951,3934,4904,3942,
3944,3946,3949,3958,4746,4543,4454,4534,4875,4063,4826,4761,
4957,4039,5025,4892,4125,5033,4083,5038,4816,4771,4215,4597,
4976,4106,4646,4829,4153,4742,4121,4950,4929,5014,4474,5027,
4973,4617,4277,5040,4975,4178,4638,4415,4202,4209,4759,4495,
4527,4837,4229,4696,4879,4252,4867,4971,4271,4844,4695,4778,
4678,4366,4890,4738,4939,4541,4783,5030,5009,4912,4843,4441,
5008,4968,4910,4424,5021,4983,5005,4747,4855,4473,5017,4625,
4823,4945,4918,4536,4999,4784,4547,4852,5034,5037,5029,4595,
4653,4813,4693,4930,4691,4870,4836,4969,4858,5003,4970],
\[3,1,9,10,13,4,2,19,23,24,27,29,32,5,6,26,40,7,46,47,
8,53,57,58,61,63,65,11,69,12,74,76,78,80,68,14,86,15,16,
95,17,100,102,18,106,110,111,114,20,70,94,21,124,125,22,131,
44,135,138,140,143,25,149,151,154,156,28,161,163,165,96,31,
30,172,174,177,179,182,33,185,34,35,193,152,36,199,37,203,
205,38,209,175,39,215,217,219,220,222,41,228,42,234,43,238,
240,243,244,45,248,252,253,256,258,261,48,186,49,50,51,141,
276,52,281,285,286,289,54,150,294,55,300,301,56,307,90,311,
313,316,59,322,60,324,327,329,331,107,62,334,336,338,340,64,
343,346,348,351,66,235,355,67,361,363,365,367,370,71,72,378,
264,73,384,387,389,392,75,396,198,400,403,77,408,410,411,79,
417,419,263,421,81,426,428,82,434,83,84,442,444,85,449,395,
227,87,218,88,460,89,463,465,467,91,92,474,476,93,482,484,
487,489,491,493,97,497,98,501,503,99,508,509,481,511,513,101,
518,521,523,524,103,530,104,536,105,541,545,546,549,551,108,
557,558,109,564,280,567,570,572,575,112,581,113,584,587,589,
591,148,115,116,597,117,602,604,118,609,145,119,120,619,121,
624,626,122,631,632,123,636,640,641,644,646,649,126,654,127,
128,661,129,368,666,130,670,674,675,678,132,323,683,133,689,
690,134,696,699,136,705,137,707,710,712,714,282,139,719,721,
723,725,142,729,732,734,737,144,740,146,147,510,749,480,753,
756,758,455,761,660,764,153,769,359,773,776,155,781,784,786,
157,158,162,159,797,768,160,802,804,806,808,810,383,814,817,
164,820,529,822,342,824,166,390,433,167,522,168,169,841,843,
170,848,171,851,854,856,779,173,860,863,865,371,867,869,176,
874,876,879,178,884,887,889,891,360,180,895,181,898,900,183,
620,904,184,909,911,913,916,187,921,188,925,927,189,362,190,
934,191,938,940,192,945,946,948,949,951,194,956,958,195,963,
196,969,197,974,976,978,981,200,201,989,991,202,915,537,997,
204,1002,1004,1005,206,1010,207,1015,208,1019,1021,1023,210,
1027,1029,211,1035,212,750,213,1042,1043,214,840,1048,1050,
1053,216,1056,507,1060,1063,1065,1067,1069,1071,1072,1074,221,
1080,1082,1084,223,767,224,1095,225,1100,1102,226,1107,1110,
229,1112,230,1116,231,1119,1121,232,1126,233,1129,1132,1134,
1136,1138,236,1143,1144,237,1148,1150,1152,1154,1155,239,1160,
1163,1165,1166,1168,241,1174,1175,242,1179,1183,1184,1187,1189,
1192,245,1197,246,1199,1201,247,1206,1210,1211,532,249,582,
1217,250,1220,297,251,601,314,1225,1228,254,1234,255,1237,1240,
1242,1244,542,257,1247,1249,1251,259,1256,260,1260,1262,701,
1266,262,1269,435,409,265,1274,266,1135,267,1281,1283,268,1287,
269,416,270,1294,1296,271,1108,272,273,1306,1307,274,1312,873,
275,1127,1318,1319,1320,1322,277,1327,278,1332,279,1336,1338,
469,1343,1344,1347,1349,283,1355,1356,284,1360,669,1364,1367,
1369,1372,287,1378,288,1381,1384,1386,659,321,290,1393,291,292,
1399,979,293,1403,1405,1055,405,295,296,1020,568,1416,298,1421,
1422,299,1426,1430,1431,1434,1436,1439,302,1402,303,304,1450,
305,754,625,306,1459,1461,1462,1465,308,706,1470,309,1476,310,
1478,1481,1483,1484,671,312,1489,1491,1493,1494,315,514,1499,
1501,1504,317,1507,318,319,560,320,1514,1516,1317,1520,1522,
1523,1526,1528,790,325,730,326,1536,746,1540,1188,328,1009,
1548,1236,330,1553,1051,618,332,1333,1560,333,1564,1565,1568,
335,1571,1573,1575,337,1578,918,1582,933,339,394,1586,341,1589,
1591,1593,757,1596,344,1598,345,1602,1604,1607,347,1611,1614,
1456,1617,747,349,1620,350,1623,1530,1625,478,352,1130,485,353,
1039,1633,354,1146,1034,356,1164,357,358,1648,1649,1652,1654,
944,1658,759,1662,1664,1645,1667,364,1670,1672,1675,366,1679,
1682,1684,1685,1687,369,1690,372,1692,373,1695,1697,374,375,
376,1706,1708,377,1712,970,1714,379,1719,962,380,1723,381,1729,
382,1733,1735,1737,1740,1742,385,1748,386,1753,833,1131,1758,
388,1762,1329,1765,391,1124,1033,838,1772,393,1774,1775,1778,
1780,818,1783,397,1788,398,1794,399,1799,1802,1804,1806,807,
401,1270,402,1816,1819,1821,1824,404,1827,406,407,1834,1837,
1839,1841,908,1845,1848,1850,412,413,490,414,1857,1859,415,
1864,1208,931,1869,1871,418,441,1873,1875,1388,1876,420,1880,
1881,1883,422,926,423,1622,424,980,1064,425,1895,427,1900,1901,
1902,429,762,430,1912,431,1917,1919,432,1923,1924,1925,1926,
1927,436,1932,437,1936,1938,438,866,439,1944,440,1948,1769,
1951,1953,1955,1957,1959,443,1964,1062,1967,1968,1093,445,1974,
446,1980,447,1985,448,1988,995,1991,1096,1993,450,1998,1089,
451,1570,452,1149,453,2009,2011,454,456,2017,457,2020,2022,458,
2027,459,1547,2030,461,901,1971,462,1133,700,2034,464,2039,
2042,2043,688,466,2049,2006,627,468,2053,2054,2056,470,857,471,
2062,472,2066,2068,473,2072,2073,2074,2076,475,1284,2081,477,
2087,2090,479,1945,2095,2096,1311,1694,2102,483,2104,2106,2107,
1106,2109,486,2112,2114,2116,488,2118,2026,2121,2123,1231,1700,
2128,2131,492,2133,2135,494,1760,495,2142,2144,496,2149,2151,
2152,2153,498,2155,499,763,752,500,1897,577,2164,2166,502,2169,
2171,2172,2173,2174,504,1608,505,2183,506,2186,2188,2190,2192,
2193,2194,1125,2197,2198,2200,512,526,2132,2206,2208,1605,515,
2216,516,2220,2221,517,2225,2227,519,935,520,1437,1147,2234,
2235,2236,2238,1097,2240,1007,973,1686,525,2246,2248,527,1659,
528,608,2252,1929,2231,2224,531,2170,1836,533,2260,1792,534,
2266,535,2269,2272,2274,2276,2278,538,2281,539,2285,2287,540,
2290,2293,612,2295,2297,543,2300,2301,544,1603,1205,2309,2311,
2313,2316,547,2321,548,1498,2325,2326,2328,580,550,1913,552,
917,553,2028,554,2340,2341,555,2346,2347,556,1671,2350,1291,
1822,1011,559,2357,561,2362,562,563,1137,565,1235,2370,566,
2376,569,1866,2380,2100,2339,1207,571,2387,2388,2390,573,2392,
574,2004,2398,2070,2402,576,2405,578,579,2409,2411,2413,1424,
2416,834,821,583,2245,2424,2426,2361,585,2429,586,1273,1379,
588,2440,2443,2445,590,2450,592,593,728,594,1081,595,2463,596,
1786,1326,598,1061,599,2475,600,2478,2479,2480,2481,2483,603,
2487,1172,605,2491,606,2497,607,2501,2503,2505,2506,610,1784,
2510,611,2516,928,613,2523,2525,614,664,615,616,2534,2536,617,
2541,2543,2544,621,2146,622,2550,623,2554,982,2097,2141,2555,
2556,2559,1396,2561,2562,2564,628,2568,629,792,630,2572,2576,
2577,2579,2580,2583,633,2588,634,2591,1285,635,2527,2600,2601,
2604,637,638,2609,2610,639,1552,1398,1113,923,1886,642,2624,
643,2626,2629,2631,2633,1340,645,2448,2639,2052,647,1216,648,
2627,2648,1022,2582,650,651,652,2652,782,653,2658,1987,819,655,
2663,656,947,657,658,2671,2673,2675,1313,2678,662,663,2685,715,
2688,1227,665,1922,667,1407,668,2698,2699,2701,2705,2706,1963,
2259,672,1328,2713,673,2717,1458,2139,1976,2721,2724,676,2531,
677,2730,2733,1707,2735,704,679,680,1282,681,2473,1896,682,
2177,2750,778,684,685,686,1678,2684,687,2762,2763,2765,2766,
2769,2771,1203,691,2777,692,693,2781,694,1521,1716,695,2789,
2791,697,2794,698,1597,2800,1046,2005,2035,702,2805,1358,703,
2811,998,2692,2815,2817,2820,2780,708,709,2826,1512,2308,2829,
711,2832,2835,2836,713,2840,2842,2679,716,717,718,2850,2852,
2578,1517,720,2856,2858,2314,722,2862,2864,724,2866,2869,2871,
2872,726,727,2875,1370,1934,1246,2879,2882,731,1469,2887,2890,
733,2751,2412,2896,1513,735,736,2616,738,1330,2902,739,2906,
741,742,2913,2686,743,744,811,745,2919,2921,1702,2275,748,2925,
2085,2928,2929,2931,751,919,2936,2939,1811,2941,2943,755,2945,
2202,800,2476,760,2267,2715,2954,2956,2958,2318,1647,2432,2964,
765,766,2970,2971,2973,2548,1576,770,2024,771,2726,772,2201,
2981,2982,1567,774,2988,775,2991,2993,2995,777,2998,780,3002,
3004,3006,2969,2822,783,3013,785,2979,3019,787,788,789,791,
3027,1345,3029,793,794,795,2885,3036,796,2091,3039,798,3044,
2086,799,3047,3050,801,3054,2614,1167,3058,803,2990,1443,3064,
805,3067,2472,3069,2025,1641,809,2966,2241,3073,3074,3077,812,
3080,813,3083,2997,3051,3086,815,2418,816,3091,2691,3095,3098,
3100,3101,3103,3105,3107,3110,823,2382,3114,825,1696,826,1588,
827,1111,828,3122,829,3124,1907,830,1566,831,1952,832,3132,
3134,3136,835,3139,836,3143,3144,837,1665,839,3147,3070,2273,
3150,1981,2218,842,1950,1109,3157,1973,844,3159,845,3164,846,
3168,847,2797,3170,3171,1016,849,914,2366,850,1861,2207,3183,
1661,3186,852,2937,853,2917,855,3195,3198,3199,3201,1651,2674,
858,859,3204,3205,861,862,3210,3211,864,3215,3217,2910,1335,
868,1738,2533,3221,1843,870,871,3226,872,1006,3229,2075,2528,
1557,1676,3234,875,3236,3239,1509,3241,1666,877,3246,878,1916,
1600,1323,3251,880,3252,881,882,3256,1655,883,2466,3259,3225,
885,3262,886,2682,1833,1739,3269,888,3272,3275,3277,890,3281,
1070,1414,892,2694,2375,893,3291,894,2372,2707,3295,2798,896,
3302,897,2261,3305,3308,899,3311,3314,3316,3318,902,2498,3322,
903,2047,905,2560,906,3333,907,1800,3206,3336,3339,3341,910,
3061,1452,3345,912,2976,2335,2467,924,2837,1773,3358,3008,920,
2377,3203,922,3366,2611,3368,3370,3371,1054,1258,1984,929,930,
3378,3346,1763,932,3381,1404,2460,3382,3383,3385,936,3388,3390,
937,3394,3395,3397,939,3399,2632,3401,3402,3404,941,3407,942,
3413,943,2530,1300,3418,1941,1703,1815,1736,3391,2265,950,3108,
3429,2212,3431,952,3434,953,3438,954,3025,955,1846,957,3445,
1123,3417,959,3448,960,961,3454,2613,2709,3456,3459,964,3461,
965,3464,966,3466,3468,967,1722,968,1986,977,2264,971,972,1460,
3478,990,3480,3482,2592,3484,975,3489,3138,2653,3493,3076,3496,
2217,1418,1079,2587,3499,3501,2758,983,3066,984,3505,3506,985,
3510,986,987,988,1177,2184,3518,3303,3519,2179,992,2935,993,
3527,994,3529,3531,3532,996,3218,3534,2210,1482,999,3540,1000,
3542,3543,1001,2067,3546,1003,3549,1732,1008,3422,3102,1012,
1502,1209,1013,3555,1014,3558,3326,3560,1017,3235,1428,1018,
3565,2059,3566,2878,3569,3570,3571,1024,3574,1025,3577,1026,
2756,1028,3580,3581,1537,1030,3548,1031,2980,1032,3591,1726,
3389,3595,2853,1036,3600,1037,2728,3602,1038,3606,1040,3608,
1663,1041,3612,3614,3615,1947,3618,1527,2977,1044,1045,3623,
3564,1047,3627,3629,1049,2488,2818,3631,3607,1052,3635,3636,
3410,2581,3637,1057,1303,1058,3373,1059,2741,3152,2243,3654,
3656,3659,3661,3663,3665,1066,1754,2739,3669,1068,3671,3674,
3676,2148,3677,3678,3679,2760,1073,2743,3683,1075,3686,1076,
3689,1077,3694,3695,1078,3699,3701,2162,3508,3705,1083,3709,
1569,1085,1086,1087,3320,3716,1088,1090,3719,1091,2987,1092,
2399,3723,1094,3724,3727,2374,2799,1098,3731,2048,1099,3734,
3735,3462,1101,3741,3743,1103,2806,1104,3751,1105,2697,3755,
3515,2147,3550,3760,3761,3764,3766,3767,3770,2747,3771,1114,
1115,3774,3188,1117,3777,1118,3779,2793,3781,2038,1120,3783,
3785,3786,3787,1122,3776,3196,3071,3449,3795,1639,3747,3799,
3801,2406,1128,3804,3805,3807,2213,3146,3811,3812,3031,3813,
2422,2918,1139,1140,1141,1142,3817,2774,3819,1145,2695,3821,
3585,1151,3823,1153,3828,3288,2830,1156,1492,1157,1158,3833,
3835,1159,3836,3838,1161,1339,1162,2776,1292,3844,2644,2734,
3846,3847,3849,3298,2716,3588,2690,3852,1169,3078,1170,1427,
1171,3860,3862,3863,1173,3865,3867,3869,1176,3872,1178,3324,
1809,3877,3879,1180,2322,2182,1181,2094,1182,1558,2996,2940,
1185,3891,1186,3892,2898,1691,3897,2291,2813,3899,2499,1190,
1191,3904,3273,1193,1797,1194,1195,1196,3075,2515,1198,2288,
3915,1200,3918,1202,3923,2662,1204,3598,3926,3927,2348,2257,
1412,2912,2365,3096,1212,1213,3921,1233,1214,3939,1215,1286,
3940,1776,2496,1218,3943,1219,1899,3920,1221,1222,3951,1223,
2414,2740,1224,2125,3955,3354,1226,3165,3958,3960,1229,1230,
1868,2303,1232,3966,2900,3037,3969,2512,3971,3972,3950,1238,
1239,3977,1534,3980,1241,3983,2296,1705,1243,3988,1334,1245,
3228,3992,1432,3995,1248,2421,1250,2704,2646,4002,1252,1253,
1389,1254,1255,3643,4009,4010,3160,1257,1259,2379,4018,2417,
4020,1261,4021,2731,1263,2371,2408,1264,3330,1265,4025,2586,
2677,4029,1267,4031,1268,4032,3362,2903,2651,3688,4035,4036,
1271,1272,3893,2816,2519,3227,1275,1698,1276,4044,4046,1277,
1278,1279,1280,3351,2569,4055,4056,3845,4058,2563,4059,4061,
4063,4064,1288,3703,1289,4069,1290,2848,4073,1805,1293,1362,
3603,3045,4077,1295,4080,1755,4081,4082,1297,1674,1298,2058,
1299,4086,3982,1301,4089,1302,4091,1304,4095,4096,1305,3729,
3189,4099,3626,4100,2834,4101,1308,4105,1309,4107,1310,2453,
3832,4108,4110,4111,4112,1314,4113,1315,2933,1316,1506,3441,
1640,2553,4120,4121,4007,4123,4125,1321,4128,3673,4130,1324,
4133,1325,4135,4137,4138,1331,3284,1385,2612,4142,3374,3906,
4145,3651,1337,4148,3245,1994,2435,1341,3030,3446,1342,4053,
2596,4158,4159,3009,3000,1346,2484,1891,4161,3997,1377,1348,
2681,4165,1350,2659,1351,1352,2178,3238,1353,4047,1354,4026,
2161,3274,4174,4176,4178,1357,4182,1359,4186,2495,4189,4191,
1361,2625,4192,1449,1363,2015,1365,1366,2077,2597,1368,4202,
1779,3621,4206,1371,3848,2205,3021,1801,1373,4212,1374,1375,
3141,1376,4181,4215,1632,4216,1579,1380,4219,2434,1382,1383,
2656,3575,1387,4225,2565,1390,1391,4228,1392,4232,1559,4235,
1394,1395,4239,2660,1397,3903,2749,1400,4017,4163,1401,3522,
4243,3896,2745,3874,3421,2158,2427,1406,2589,4249,4250,4251,
1408,2176,1409,1410,4258,1411,4259,1413,1415,4260,4261,2036,
4262,1417,4195,2867,1419,4270,4271,1420,2494,4273,4274,2456,
3155,1423,2430,2214,1425,2471,2474,1910,1485,2635,4153,1429,
3685,4283,1433,4285,3400,2385,2711,2702,1435,4291,1544,1438,
3485,4294,1440,4296,1441,1442,3202,1577,1444,1445,4238,1446,
1447,1448,4304,4305,3797,3335,3469,1451,3191,1807,1453,3172,
1454,3639,1455,1457,2792,2938,4312,2584,2833,2788,3843,1466,
3941,2447,1463,1556,1464,4209,3230,2279,1475,4321,1467,1468,
4324,2393,2668,1471,1472,1473,2159,4326,1474,4328,2930,2137,
1477,2926,4332,2880,2256,1479,1480,4337,2810,2968,2032,2666,
3538,3435,1486,1487,4343,2368,1488,3455,1490,2454,3885,1781,
3746,4347,4348,4349,4256,3458,1495,1496,4351,1497,4353,2018,
1500,1668,4354,2420,3528,1503,4356,4357,2337,1505,2669,2282,
4358,4359,4361,1508,3523,4248,1510,2693,1511,2037,2978,4366,
4355,4369,1515,4370,4114,1518,2955,1519,4298,4378,4193,1720,
4345,1524,4380,1525,3472,2457,4384,4386,3340,2549,1529,4143,
1531,1532,1533,4394,1535,4295,4279,2386,2433,2230,1538,4399,
1539,4402,2924,4404,3012,1541,1542,1543,4406,1545,1546,4393,
1549,1550,1701,1551,4252,4411,2514,4413,3696,1554,3509,3922,
1555,3728,4417,4418,3964,4419,1561,4150,1562,1601,1563,3556,
3594,4420,3864,3996,4423,4424,4388,4117,4052,1572,3014,4426,
4428,1574,4430,2060,4431,4065,4432,4433,2870,2736,1580,1581,
3624,3576,1583,4090,1584,1585,3834,1587,4043,2228,4340,3011,
1590,3861,3989,1592,4016,1594,2477,3123,1595,2522,1970,4451,
1709,2922,1599,2947,4363,3447,2824,3287,1606,1814,4454,1609,
4201,1851,1610,3443,3344,4459,1612,4461,1613,3001,1731,4405,
1615,1616,4468,4254,2111,1618,3986,1619,4473,2209,4475,1621,
2157,3973,2949,4476,1624,3248,2905,3680,2942,1626,1627,4320,
1628,1898,1629,1630,4481,2839,1631,2719,1634,4477,1635,1636,
1637,4310,2857,1638,3613,4487,1642,4489,1643,4284,4491,1644,
3214,1646,4493,2801,4495,2863,3655,4479,1946,1650,4501,2271,
3596,1653,2827,4303,4507,1656,1657,4122,4484,4512,3185,2451,
1660,4513,3479,2397,1761,2250,4515,1669,3038,4048,4517,4518,
2283,4520,1673,4524,2972,2469,4471,1677,4527,4528,1680,3702,
1681,4236,3055,4532,1683,3948,2782,4534,4536,3348,2439,4023,
4293,4330,1688,4540,1689,4541,4442,4543,4545,4436,3174,1693,
4190,3648,3452,1699,3858,3670,3068,2657,4241,1704,4554,4555,
3414,4556,4557,3406,4559,1710,4564,1711,3090,3439,1713,4567,
3537,3433,1715,3492,4570,1717,1718,2965,1721,4573,4576,1724,
1725,4578,4580,1727,1728,3554,1730,4584,1795,4586,1734,2189,
1930,4396,1787,4589,4590,4591,3179,2605,1741,2712,4594,1743,
1744,1745,3853,1746,1747,3886,4599,3184,1749,1750,4601,1751,
1752,2407,3065,4604,3567,2502,1756,3962,1757,3208,2061,3744,
1759,1764,4581,4600,4087,4292,1766,4609,1767,1768,4611,2888,
1770,4613,1771,1943,4614,2786,4616,4617,1777,3282,2462,4620,
1782,2986,3644,3945,1785,4624,4173,3773,1789,1790,4629,1791,
4630,1793,2843,3855,4632,1935,1796,2084,1798,3841,4636,4626,
4628,4638,1803,4640,3016,4643,4644,1808,4280,1810,1812,4646,
1813,4566,2191,3691,3099,4650,1817,1818,1820,2134,4653,2526,
4633,1823,3514,3024,3128,4582,1825,1826,4657,2759,2877,1828,
1829,4659,1830,1831,1832,3984,4253,2129,1835,2444,4663,2532,
1838,3477,4465,1972,1840,3800,3750,4668,1842,3693,1844,2292,
4526,2962,2247,4549,1847,4676,2985,3017,4392,1849,4682,3020,
4683,1852,3756,1853,4458,1854,1855,4686,1856,2082,3260,1858,
4229,1921,1860,1862,4691,1863,4693,2490,4695,4696,1865,3405,
1867,2244,3436,2122,1870,4698,2384,1872,3476,3976,1874,3327,
4661,3299,3765,1877,1878,4106,1879,3310,3647,1882,4705,1884,
2108,1885,4325,4615,1887,1888,1889,1890,4711,1892,3563,1893,
1894,4547,3393,3023,3106,2567,4717,1903,4486,1904,4724,1905,
3416,1906,3684,4684,1908,2493,1909,2078,1911,3914,4033,1914,
4652,1915,4732,4734,4612,2916,3713,1918,4737,4739,4071,4455,
3420,1920,3985,3255,1940,4742,4725,4078,1995,3220,1928,1931,
2783,3242,1933,3913,4746,2513,4714,4748,1937,4749,4485,3127,
1939,4753,1942,3630,2358,4572,2057,3135,2156,3936,4497,1949,
4755,2101,3450,4757,4222,1954,4759,3697,1956,2641,4760,1958,
4761,1960,4519,1961,4155,1962,4703,3355,1965,1966,4514,2773,
1969,2768,4175,4383,2136,3895,4766,1975,4309,1977,4149,2140,
1978,2014,1979,4771,3937,2895,1982,1983,4492,4561,4774,2332,
1989,3473,1990,3690,1992,3742,2957,1996,4619,1997,3970,1999,
2000,2951,4342,2001,2002,2003,4427,2809,2007,4784,2237,2008,
3752,3796,2010,2764,2012,4183,2013,4792,4793,2016,3257,2019,
2960,3792,2021,3309,4796,2023,2828,4511,3975,3650,3963,3306,
2029,2438,2031,2033,3830,2893,4266,4416,4210,2040,2359,2041,
4806,3289,2044,2045,2046,2754,4808,2050,2051,3323,2718,4437,
2647,2055,4812,2636,4335,4276,4319,3517,3126,4815,2063,2064,
4819,2844,2065,4444,4820,4316,2069,3733,2071,2165,4802,3605,
4177,3369,4482,4675,4787,4352,4823,2079,4803,2080,2808,3916,
4824,2083,4076,4827,3954,2934,3022,4331,2088,2089,2195,2092,
4829,3084,2093,2804,2689,3356,4496,3158,2098,3721,2099,4577,
2103,4654,2105,3026,3649,4834,2110,3692,3794,4836,3463,4127,
2113,3457,2642,4092,3497,2115,4839,2117,4040,2517,4499,2119,
2703,2120,4410,4126,3745,4843,4844,3328,4846,3902,2124,2126,
2127,3292,2785,4144,2130,4287,4169,3668,2825,3933,4852,3488,
3822,4637,2138,3788,4278,3490,2598,2343,2143,3547,4333,3166,
4853,2145,4855,2509,4710,3625,3520,2664,4098,3280,2150,2650,
4857,3965,4858,3015,2154,3360,4478,3990,4862,4863,4817,2160,
2607,2778,2163,3961,3481,2167,2168,2356,2594,2298,4062,4861,
2542,4546,2175,4627,4085,2507,3237,3802,2180,2181,4870,4871,
4317,2459,2621,4872,3498,3911,2185,4807,2654,2187,4395,3487,
4441,4791,3806,4535,2436,4856,2518,3866,3622,2727,2196,4267,
4875,4094,3772,4533,2199,4318,2520,3223,2203,2204,2637,3297,
2814,2344,2849,2915,2211,4692,4569,3611,2215,4448,2670,4879,
3163,2219,4004,4592,4697,2222,2223,4401,4198,2226,3839,3930,
4706,2251,2229,2946,4859,4275,2232,4167,2233,2838,4738,4054,
2373,4889,2239,2752,2242,4625,3010,4160,2249,4778,2253,4891,
2254,3317,3718,2255,4674,2258,3880,4265,2262,2859,2263,4850,
4885,3859,4204,2268,3593,2270,3271,4323,2708,2640,4382,3270,
2277,4898,3908,2280,4327,4899,2284,4635,4057,2590,2286,4139,
3042,2289,3633,4901,3739,3725,4902,3949,2294,2404,4788,2320,
4906,4667,2923,2485,2299,3088,4102,4042,2302,3526,2304,2305,
2306,2307,4910,2310,4912,3875,2312,2784,4045,2315,4466,4450,
2317,4918,2319,4919,2323,3738,2324,4367,3910,2327,2329,2330,
4344,4756,2331,2333,3708,4883,2334,4832,2336,3116,4408,2338,
4188,3573,4264,3589,4900,2342,4211,4452,4876,2345,2349,2351,
3928,2352,2353,2354,2355,4551,2441,3332,2449,2360,2363,3365,
2364,3968,2367,2753,4825,2369,4483,4187,4494,2437,3398,4751,
4618,2378,2883,4030,3840,2381,3209,2383,3403,3912,3640,4648,
2389,3868,2391,4799,4529,2394,4602,2395,2396,2539,3140,4938,
4939,3442,2400,3809,2401,2403,4300,3882,4892,2787,3824,4776,
4940,4701,2410,3494,3952,3842,3946,2415,4245,4234,4070,4743,
2819,2419,4704,2423,3758,4015,3363,2425,3953,3384,2907,2428,
3148,3224,2504,2431,3609,3258,3782,4005,4935,3007,2442,2854,
3137,4301,2446,2672,3775,4945,2452,3342,4729,2455,2458,2461,
4699,4346,4104,2464,4946,2465,4948,4003,3778,4131,4949,2468,
4950,3349,2470,4951,3364,3177,4952,3808,3642,4523,4780,4072,
3181,4457,3264,2482,3092,4642,2757,4664,2486,4954,2489,4662,
2492,3089,4409,4794,4217,4504,3097,2500,3182,3831,4141,3197,
4869,3706,2508,3359,4896,4051,2511,3511,4957,3491,3423,3411,
3856,4687,2521,4920,4075,4608,2524,4162,4558,2529,4689,3194,
3161,4961,4962,4963,2535,2537,2538,2540,4315,4685,4634,3762,
2545,3377,2546,2547,4929,3500,4921,3657,2551,3131,2552,4769,
4669,3919,4707,4894,2557,2558,3736,3825,4904,2899,3732,2566,
4967,3085,4968,2570,4360,2571,2573,2894,2574,2575,2846,3664,
4890,4338,2585,3561,3604,4860,4785,2593,2595,4199,3040,4941,
2599,4011,3993,2602,4973,2603,4308,3931,3601,2623,4568,2606,
4538,3715,4024,4932,2608,3331,3711,3873,3286,2615,2617,3502,
2618,2619,2620,3283,4154,2622,3687,3768,2967,2761,2914,2963,
4490,2628,2630,4474,2729,2634,2638,4218,4060,3942,2643,3043,
2645,4180,4690,2649,4750,4136,4708,4574,3444,2655,3545,2823,
2953,3810,2983,3994,4134,4255,2661,3521,2665,2667,4230,3769,
4986,4435,2676,4607,2680,4621,3343,4088,2683,3167,3056,4947,
4231,2687,4814,3392,3115,4722,4989,2696,2744,4851,4811,2746,
2700,4991,4049,4124,4735,3173,3851,4993,2710,2714,4994,4937,
3884,2720,4116,4014,2722,2920,2723,3338,4848,2725,2812,2861,
2803,2732,3062,3304,4376,2737,2738,4509,3087,3376,2742,4506,
4237,3590,2748,3120,2755,4996,4913,4429,3740,4981,4377,2772,
2767,3562,2770,4928,2775,3967,4115,2779,2892,2984,4997,4522,
4998,4371,2790,4999,3268,3162,2795,2796,4797,3079,2802,4539,
3293,4728,2807,3129,4575,4917,4716,4398,2909,4893,2821,5003,
3233,3666,3878,2831,4196,4118,4257,3837,2841,5004,2845,4596,
3033,2847,4656,2851,4583,3263,4311,2855,3827,3957,3583,4914,
3803,2860,4213,2865,4990,4972,3533,2868,4971,3193,3495,3207,
4013,4579,2873,2874,2876,4147,2989,2881,2884,4375,2886,3408,
2897,4372,3034,2889,4911,2891,4151,4306,2901,4854,2904,4119,
3592,3041,2908,2911,4984,3572,3620,4083,4184,4438,2927,3451,
2994,2932,4942,3213,3667,3265,3850,4397,3947,5011,3535,2944,
3512,3935,3681,4777,2948,2950,2952,3321,2959,2961,3018,3559,
4880,4460,3467,3300,2974,2975,3883,4864,4818,4849,4816,5001,
3290,4350,3104,2992,3109,3319,4953,3278,4623,2999,4666,3003,
3524,3748,3005,4172,4828,4681,3504,4221,3551,3279,4214,3028,
3032,5016,3035,4786,4548,3737,4074,4830,4414,5018,3046,4770,
3048,3049,3052,3053,4721,4226,4881,3057,4909,5019,3059,4982,
3060,4809,3814,3063,3638,4741,3072,4129,3816,4944,4622,4867,
3142,3081,3082,4447,5007,4631,4934,4289,5020,3428,3093,3094,
3219,4813,3470,4651,4302,4593,4001,4269,3253,3372,4288,4034,
3111,3660,3112,3113,3117,3118,3119,3121,4719,3125,3586,4733,
3329,4244,3130,4842,3793,4456,3133,5026,4765,3712,3717,4521,
3753,3974,3584,3145,3617,4956,3149,4895,4779,3151,3240,3153,
4314,3154,5024,3156,3503,4915,4470,3250,4835,3415,4744,4037,
3169,4500,4365,3175,3176,3178,3180,4983,3944,4022,3187,3190,
4702,3192,4874,3200,4006,3815,4510,4368,3212,3353,4464,3216,
4290,4179,4805,3222,5014,3857,3730,3350,3991,3231,4772,3232,
4678,3379,3698,4768,4762,4905,3243,3244,4598,3247,4467,3249,
4208,4958,4364,4745,4801,3254,3938,5030,3261,3704,4865,3266,
3267,3475,5031,3276,4272,4068,4767,4988,3285,3460,3552,5032,
3294,4537,3296,3301,3934,4544,4783,3307,3387,4008,3818,3312,
4246,3313,3315,5033,3898,4156,4516,3726,4339,3325,4641,3829,
3780,3334,4505,3430,3337,4740,4597,4964,3871,3347,3662,3616,
3352,3357,4916,3894,3361,3714,3367,4924,3474,3672,3375,3959,
3757,4508,3380,4970,4977,4028,3386,3426,4247,4565,4446,4845,
5025,4992,3396,4795,3513,4882,3465,3784,4530,4718,3653,4240,
3409,4873,3412,4498,4975,3419,4563,3424,3425,3427,4164,3432,
3749,4713,3437,4373,3440,4560,4440,3599,3453,4884,4730,4463,
4170,5035,4585,3471,4866,3619,4679,3483,3587,3486,4673,4888,
4313,4647,4720,4897,4093,4480,3507,3632,4976,4439,3682,3516,
4926,4263,4039,3525,5029,3854,3646,3530,4281,4041,3536,3539,
5002,3541,4987,3544,4804,4299,3553,3924,3557,3579,4595,4907,
5015,5023,3568,3628,4200,3578,4754,3876,3582,4197,5017,4979,
4789,3597,3900,5037,4207,3987,3610,4322,4525,4434,5013,5000,
3634,4688,4985,4723,4610,3641,3645,3888,3652,3658,3759,3978,
4715,4660,4943,4027,4233,3675,4700,4764,4782,4019,4712,4587,
3700,3754,4341,3707,5034,3710,5009,4821,4449,4329,4878,3720,
3722,4841,4132,4833,3956,4542,3763,4050,5010,4166,4146,5028,
3789,3790,3791,4810,4297,3798,4067,4168,4694,4837,3820,3917,
3826,4798,4969,4205,4936,4605,4503,4097,4980,4773,4562,4140,
3870,3905,4965,5008,3881,5039,4886,3887,3979,3889,3890,4389,
4387,5006,4955,4822,4763,3901,3907,3909,5036,4588,3925,4752,
4203,3929,3932,3999,4012,4412,3981,3998,4277,4374,4242,4966,
4922,4000,4908,4847,4307,4736,4038,4606,4220,4550,4930,4415,
4472,4066,5038,4079,4084,4223,4103,4645,4109,4381,4403,4731,
4391,4670,5040,4672,4995,4152,4157,4171,4282,4469,4658,4390,
4185,4194,4422,5027,4747,4421,4224,4227,4800,4603,4960,4502,
4925,4831,4268,4726,4781,4649,5022,4286,4462,4727,4531,4840,
4877,4334,4336,4400,4887,4362,4379,4385,4407,4665,4425,4790,
4443,4445,4453,4775,4927,4488,4978,4838,4931,4868,4553,4959,
4639,4552,4677,4571,4933,4709,4680,4671,4655,4974,5005,4758,
4903,4826,4923,5012,5021]
/*order=39916800=2^8*3^4*5^2*7*11*/>
