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