{ 1, 2, 4, 5, 10, 11, 15, 18, 19, 27, 32, 38, 44, 48, 55, 61, 65, 82, 103, 104, 106, 122, 153, 170, 209, 231, 234, 250, 251, 253, 254, 255, 256, 257, 259, 301, 303, 307, 320, 332, 333, 342, 348, 376, 378, 382, 386, 393, 427, 432, 443, 444, 448, 463, 464, 465, 466, 467, 470, 479, 481, 492, 493, 498, 499, 523, 524, 527, 528, 533, 534, 542, 554, 573, 576, 595, 615, 627, 646, 652, 656, 666, 679, 681, 694, 714, 723, 744, 764, 782, 783, 803, 821, 828, 849, 866, 867, 892, 893, 903, 926, 927, 929, 955, 1042, 1043, 1044, 1057, 1058, 1119, 1120, 1121, 1122, 1130, 1131, 1195, 1214, 1232, 1293, 1369, 1434, 1435, 1526, 1627, 1628, 1649, 1757, 1773, 1776, 1777, 1922, 1946, 1947, 2085, 2258, 2290, 2300, 2313, 2448, 2716, 2787 }
{ 6, 7, 8, 9, 12, 13, 14, 16, 17, 20, 21, 22, 23, 24, 25, 28, 29, 30, 33, 34, 35, 36, 37, 39, 40, 41, 42, 45, 46, 53, 66, 72, 73, 75, 86, 128, 158, 171, 179, 206, 215, 216, 217, 230, 279, 298, 306, 310, 356, 357, 385, 398, 412, 415, 428, 429, 477, 478, 491, 532, 543, 555, 559, 603, 642, 701, 734, 754, 755, 839, 842, 1123, 1196, 1278, 1605, 1758, 1870, 2433 }
{ 26, 31, 43, 47, 49, 54, 56, 57, 59, 60, 62, 69, 70, 71, 74, 79, 80, 83, 84, 85, 87, 88, 93, 94, 95, 96, 100, 101, 102, 105, 107, 108, 109, 110, 114, 115, 120, 152, 172, 207, 214, 229, 233, 252, 269, 274, 281, 282, 285, 286, 287, 291, 292, 305, 308, 309, 315, 316, 319, 324, 325, 326, 329, 331, 334, 336, 337, 346, 347, 353, 372, 375, 383, 384, 387, 394, 399, 403, 411, 414, 426, 440, 441, 442, 449, 450, 453, 476, 482, 483, 484, 485, 486, 487, 488, 489, 490, 494, 495, 496, 500, 505, 537, 541, 549, 550, 551, 552, 577, 578, 579, 583, 594, 604, 613, 614, 621, 622, 634, 643, 644, 651, 654, 655, 676, 686, 691, 698, 700, 703, 704, 711, 712, 713, 717, 731, 737, 740, 784, 785, 798, 799, 813, 814, 848, 853, 869, 901, 917, 918, 919, 922, 925, 930, 933, 967, 968, 974, 979, 980, 983, 986, 990, 991, 992, 994, 998, 1004, 1011, 1014, 1016, 1019, 1027, 1029, 1032, 1033, 1036, 1065, 1072, 1084, 1085, 1086, 1107, 1126, 1140, 1141, 1142, 1157, 1161, 1166, 1167, 1175, 1177, 1178, 1179, 1181, 1189, 1190, 1203, 1204, 1205, 1206, 1207, 1208, 1211, 1219, 1223, 1224, 1226, 1227, 1228, 1229, 1233, 1242, 1245, 1246, 1247, 1261, 1262, 1263, 1265, 1267, 1269, 1270, 1273, 1274, 1275, 1276, 1279, 1280, 1282, 1284, 1289, 1294, 1295, 1296, 1314, 1326, 1327, 1341, 1342, 1343, 1349, 1352, 1360, 1373, 1374, 1380, 1403, 1407, 1408, 1409, 1415, 1437, 1438, 1439, 1461, 1462, 1470, 1471, 1473, 1482, 1484, 1485, 1486, 1487, 1488, 1489, 1490, 1503, 1512, 1514, 1518, 1548, 1549, 1578, 1579, 1580, 1585, 1586, 1589, 1594, 1597, 1604, 1612, 1629, 1645, 1653, 1661, 1662, 1663, 1664, 1665, 1695, 1704, 1705, 1707, 1708, 1732, 1733, 1734, 1735, 1744, 1762, 1775, 1805, 1808, 1809, 1823, 1840, 1857, 1858, 1860, 1861, 1863, 1864, 1935, 1941, 1954, 1956, 1964, 1972, 2008, 2028, 2029, 2030, 2032, 2034, 2037, 2070, 2073, 2074, 2076, 2077, 2103, 2105, 2106, 2109, 2111, 2112, 2180, 2199, 2200, 2226, 2235, 2236, 2239, 2241, 2320, 2333, 2446, 2447, 2529, 2595, 2691, 2770, 2841, 2873 }
{ 3, 50, 51, 52, 58, 67, 68, 76, 77, 78, 81, 89, 90, 91, 92, 97, 98, 99, 111, 112, 116, 117, 118, 119, 121, 123, 124, 125, 126, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 204, 205, 208, 210, 211, 212, 213, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 232, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 258, 260, 261, 262, 263, 264, 265, 266, 267, 268, 270, 271, 272, 273, 275, 276, 277, 278, 280, 288, 289, 290, 294, 295, 296, 297, 299, 300, 302, 304, 311, 312, 313, 314, 317, 318, 321, 322, 323, 327, 328, 330, 335, 339, 340, 341, 343, 344, 345, 349, 350, 352, 354, 355, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 373, 374, 377, 379, 380, 381, 388, 389, 390, 391, 392, 395, 396, 397, 400, 401, 404, 405, 406, 407, 408, 409, 410, 416, 417, 418, 419, 420, 421, 422, 423, 424, 430, 431, 433, 434, 435, 436, 437, 438, 445, 446, 451, 452, 454, 455, 456, 457, 458, 459, 460, 461, 462, 468, 469, 473, 474, 475, 480, 497, 502, 503, 504, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 520, 521, 522, 525, 526, 529, 530, 539, 540, 544, 545, 546, 553, 556, 557, 558, 562, 564, 565, 568, 571, 574, 575, 580, 585, 588, 589, 590, 591, 592, 593, 596, 597, 605, 606, 607, 608, 609, 610, 612, 616, 617, 618, 620, 623, 630, 631, 632, 633, 635, 636, 637, 638, 645, 648, 650, 653, 657, 658, 659, 662, 663, 664, 665, 667, 668, 669, 670, 671, 672, 673, 674, 677, 678, 680, 682, 683, 687, 688, 689, 690, 692, 693, 697, 702, 705, 706, 707, 708, 709, 721, 722, 725, 726, 727, 729, 732, 733, 738, 743, 745, 746, 747, 748, 749, 750, 751, 752, 758, 759, 760, 762, 777, 780, 789, 791, 792, 795, 796, 797, 806, 807, 812, 818, 822, 823, 824, 825, 826, 831, 832, 833, 837, 838, 840, 841, 843, 844, 845, 846, 847, 850, 851, 852, 854, 855, 858, 859, 862, 868, 873, 877, 878, 879, 880, 881, 884, 885, 887, 888, 889, 890, 891, 898, 899, 900, 902, 904, 908, 909, 913, 914, 920, 921, 928, 931, 932, 940, 941, 942, 943, 947, 948, 949, 953, 956, 957, 958, 959, 965, 966, 973, 975, 982, 987, 989, 993, 996, 999, 1001, 1008, 1010, 1012, 1017, 1022, 1025, 1026, 1028, 1030, 1047, 1048, 1049, 1050, 1051, 1054, 1055, 1056, 1059, 1060, 1066, 1077, 1078, 1079, 1080, 1081, 1083, 1089, 1091, 1094, 1095, 1096, 1097, 1102, 1103, 1109, 1113, 1114, 1115, 1116, 1124, 1127, 1128, 1132, 1133, 1134, 1135, 1136, 1138, 1139, 1143, 1144, 1145, 1152, 1154, 1155, 1156, 1158, 1162, 1163, 1176, 1184, 1185, 1187, 1192, 1193, 1194, 1199, 1200, 1202, 1210, 1212, 1213, 1217, 1218, 1220, 1221, 1225, 1239, 1240, 1241, 1243, 1244, 1249, 1250, 1252, 1253, 1254, 1257, 1258, 1259, 1260, 1264, 1281, 1285, 1286, 1287, 1291, 1297, 1299, 1302, 1303, 1304, 1305, 1306, 1315, 1317, 1320, 1324, 1325, 1328, 1331, 1332, 1333, 1334, 1335, 1340, 1346, 1347, 1348, 1350, 1351, 1353, 1354, 1355, 1356, 1358, 1359, 1361, 1362, 1368, 1370, 1371, 1372, 1379, 1387, 1388, 1389, 1391, 1399, 1404, 1405, 1406, 1410, 1411, 1412, 1416, 1417, 1418, 1420, 1421, 1424, 1425, 1426, 1427, 1431, 1436, 1440, 1443, 1455, 1458, 1459, 1460, 1463, 1469, 1472, 1476, 1477, 1478, 1479, 1491, 1492, 1495, 1497, 1498, 1499, 1500, 1501, 1502, 1510, 1511, 1515, 1519, 1520, 1522, 1523, 1525, 1527, 1528, 1529, 1531, 1538, 1545, 1550, 1555, 1556, 1557, 1558, 1559, 1560, 1561, 1570, 1571, 1575, 1577, 1581, 1584, 1590, 1600, 1602, 1603, 1606, 1607, 1608, 1609, 1610, 1611, 1615, 1616, 1617, 1618, 1624, 1625, 1626, 1630, 1631, 1632, 1634, 1635, 1636, 1637, 1640, 1642, 1643, 1648, 1650, 1651, 1652, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1676, 1679, 1681, 1684, 1687, 1688, 1689, 1696, 1697, 1698, 1700, 1701, 1702, 1703, 1706, 1710, 1714, 1719, 1720, 1721, 1722, 1729, 1730, 1731, 1736, 1738, 1739, 1740, 1743, 1745, 1746, 1747, 1750, 1753, 1754, 1755, 1756, 1759, 1767, 1768, 1769, 1771, 1774, 1784, 1788, 1789, 1790, 1791, 1792, 1796, 1797, 1798, 1799, 1800, 1801, 1802, 1806, 1807, 1810, 1811, 1814, 1815, 1816, 1817, 1818, 1819, 1821, 1822, 1824, 1825, 1826, 1827, 1828, 1832, 1833, 1834, 1837, 1838, 1839, 1841, 1842, 1845, 1846, 1847, 1848, 1849, 1853, 1854, 1855, 1856, 1867, 1869, 1871, 1873, 1874, 1875, 1876, 1879, 1881, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1897, 1898, 1899, 1900, 1901, 1902, 1904, 1905, 1906, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1921, 1925, 1928, 1930, 1931, 1932, 1933, 1934, 1937, 1938, 1939, 1940, 1942, 1943, 1944, 1945, 1952, 1953, 1955, 1957, 1960, 1963, 1965, 1966, 1970, 1971, 1973, 1974, 1976, 1977, 1978, 1979, 1980, 1981, 1986, 1993, 1994, 1995, 1998, 1999, 2000, 2001, 2002, 2004, 2006, 2007, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2017, 2018, 2019, 2022, 2023, 2024, 2025, 2035, 2036, 2038, 2039, 2040, 2041, 2045, 2046, 2049, 2050, 2054, 2058, 2059, 2061, 2062, 2063, 2065, 2066, 2067, 2068, 2069, 2071, 2072, 2082, 2083, 2084, 2086, 2089, 2090, 2091, 2093, 2094, 2095, 2096, 2098, 2099, 2100, 2101, 2102, 2113, 2114, 2115, 2116, 2117, 2119, 2123, 2124, 2125, 2126, 2130, 2131, 2132, 2134, 2137, 2140, 2146, 2147, 2151, 2154, 2155, 2159, 2165, 2166, 2167, 2168, 2171, 2173, 2175, 2176, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2204, 2208, 2209, 2210, 2212, 2215, 2216, 2221, 2224, 2227, 2228, 2233, 2237, 2240, 2242, 2243, 2245, 2246, 2247, 2248, 2249, 2251, 2252, 2253, 2254, 2255, 2259, 2261, 2265, 2266, 2267, 2268, 2269, 2272, 2273, 2278, 2280, 2281, 2282, 2285, 2286, 2287, 2291, 2293, 2294, 2295, 2298, 2299, 2301, 2302, 2305, 2308, 2309, 2312, 2314, 2315, 2316, 2317, 2318, 2324, 2325, 2326, 2328, 2334, 2337, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2349, 2351, 2352, 2355, 2356, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2370, 2373, 2374, 2375, 2376, 2378, 2382, 2383, 2389, 2392, 2393, 2396, 2397, 2398, 2399, 2400, 2401, 2403, 2405, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 2421, 2423, 2428, 2431, 2432, 2437, 2438, 2439, 2440, 2445, 2449, 2455, 2457, 2462, 2463, 2466, 2488, 2491, 2492, 2493, 2494, 2497, 2501, 2502, 2504, 2506, 2509, 2510, 2513, 2514, 2516, 2517, 2518, 2527, 2533, 2538, 2539, 2540, 2546, 2547, 2548, 2549, 2550, 2556, 2557, 2562, 2569, 2570, 2571, 2572, 2574, 2576, 2577, 2578, 2579, 2586, 2589, 2590, 2593, 2594, 2596, 2601, 2602, 2607, 2610, 2611, 2622, 2623, 2626, 2627, 2629, 2634, 2635, 2637, 2638, 2639, 2648, 2653, 2654, 2655, 2656, 2660, 2663, 2666, 2667, 2668, 2669, 2670, 2677, 2679, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2692, 2693, 2694, 2696, 2698, 2699, 2701, 2714, 2715, 2717, 2718, 2721, 2733, 2736, 2737, 2738, 2741, 2742, 2743, 2744, 2745, 2747, 2750, 2751, 2755, 2757, 2762, 2763, 2764, 2765, 2767, 2768, 2771, 2772, 2775, 2776, 2777, 2780, 2782, 2786, 2789, 2792, 2794, 2797, 2800, 2804, 2805, 2806, 2807, 2808, 2811, 2814, 2815, 2816, 2817, 2821, 2822, 2824, 2828, 2829, 2832, 2833, 2835, 2838, 2839, 2845, 2847, 2850, 2852, 2855, 2859, 2862, 2863, 2865, 2866, 2874, 2875, 2882, 2883, 2885, 2887, 2888, 2889, 2894, 2895, 2896, 2897, 2899, 2900, 2907, 2909, 2912, 2914, 2915, 2916, 2917, 2918, 2919, 2921, 2927, 2935, 2942, 2943, 2946, 2947, 2948, 2950, 2953, 2959, 2960, 2961, 2966, 2970, 2980, 2981, 2982, 2983, 2985, 2987, 2988, 2994, 2997, 2998, 3011, 3012, 3013, 3014, 3016, 3019, 3021, 3025, 3026, 3027, 3029, 3030, 3033, 3034, 3036, 3037, 3038, 3039, 3045, 3046, 3049, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3065, 3066, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3083, 3084, 3087, 3088, 3089, 3090, 3091, 3092, 3095, 3096, 3099, 3100, 3102, 3108, 3109, 3115, 3116, 3117, 3118, 3120, 3121, 3123, 3124, 3126, 3127, 3129, 3131, 3132, 3133, 3134, 3135, 3136, 3139, 3140, 3141, 3142, 3143, 3145, 3147, 3150, 3154 }
{ 63, 64, 113, 145, 203, 283, 284, 293, 338, 351, 368, 369, 370, 371, 402, 413, 425, 439, 447, 471, 472, 501, 518, 519, 531, 535, 536, 538, 547, 548, 560, 561, 563, 566, 567, 569, 570, 572, 581, 582, 584, 586, 587, 598, 599, 600, 601, 602, 611, 619, 625, 626, 628, 629, 639, 640, 641, 647, 649, 660, 661, 675, 684, 699, 710, 724, 728, 730, 735, 736, 739, 742, 753, 756, 757, 761, 763, 773, 775, 776, 778, 779, 781, 786, 787, 788, 790, 800, 808, 809, 819, 820, 827, 829, 830, 834, 874, 886, 907, 910, 915, 916, 923, 924, 934, 939, 950, 954, 960, 961, 962, 963, 964, 971, 976, 981, 984, 988, 995, 997, 1000, 1002, 1003, 1005, 1006, 1007, 1009, 1013, 1015, 1018, 1031, 1034, 1035, 1045, 1046, 1052, 1053, 1061, 1064, 1067, 1068, 1071, 1073, 1076, 1082, 1090, 1104, 1110, 1111, 1112, 1125, 1129, 1137, 1151, 1153, 1159, 1160, 1168, 1169, 1170, 1171, 1172, 1173, 1180, 1182, 1183, 1186, 1188, 1191, 1201, 1215, 1216, 1222, 1230, 1231, 1234, 1235, 1236, 1237, 1238, 1248, 1251, 1255, 1256, 1266, 1268, 1277, 1283, 1288, 1290, 1292, 1298, 1300, 1301, 1307, 1308, 1311, 1316, 1318, 1319, 1321, 1322, 1323, 1329, 1330, 1336, 1344, 1345, 1357, 1363, 1375, 1376, 1384, 1390, 1392, 1393, 1394, 1397, 1398, 1402, 1419, 1428, 1429, 1432, 1433, 1441, 1442, 1444, 1449, 1450, 1464, 1465, 1466, 1474, 1475, 1483, 1493, 1494, 1496, 1504, 1513, 1516, 1517, 1530, 1532, 1533, 1541, 1544, 1551, 1552, 1568, 1569, 1572, 1576, 1587, 1588, 1591, 1592, 1593, 1598, 1599, 1601, 1621, 1633, 1638, 1639, 1641, 1644, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1680, 1682, 1683, 1685, 1694, 1709, 1715, 1716, 1725, 1726, 1737, 1760, 1761, 1763, 1764, 1770, 1772, 1785, 1786, 1787, 1813, 1820, 1835, 1836, 1843, 1844, 1850, 1859, 1862, 1865, 1866, 1877, 1878, 1880, 1882, 1883, 1884, 1885, 1895, 1909, 1919, 1920, 1929, 1936, 1958, 1961, 1962, 1967, 1968, 1969, 1982, 1983, 1996, 1997, 2003, 2005, 2016, 2026, 2027, 2031, 2033, 2042, 2043, 2044, 2053, 2064, 2075, 2078, 2087, 2088, 2092, 2097, 2104, 2107, 2110, 2118, 2122, 2127, 2133, 2141, 2142, 2143, 2144, 2145, 2150, 2156, 2162, 2172, 2174, 2177, 2178, 2179, 2203, 2205, 2206, 2207, 2211, 2217, 2222, 2225, 2234, 2238, 2250, 2256, 2257, 2260, 2270, 2271, 2279, 2283, 2284, 2292, 2296, 2319, 2323, 2327, 2329, 2330, 2335, 2336, 2347, 2348, 2350, 2357, 2367, 2381, 2386, 2387, 2388, 2390, 2391, 2402, 2404, 2406, 2407, 2408, 2420, 2429, 2430, 2434, 2441, 2442, 2443, 2444, 2454, 2456, 2467, 2468, 2469, 2470, 2471, 2472, 2473, 2474, 2475, 2481, 2489, 2490, 2495, 2496, 2498, 2505, 2515, 2520, 2521, 2528, 2532, 2534, 2535, 2541, 2542, 2545, 2551, 2553, 2558, 2559, 2560, 2561, 2563, 2564, 2565, 2566, 2573, 2575, 2580, 2581, 2582, 2583, 2587, 2588, 2591, 2592, 2597, 2598, 2599, 2600, 2605, 2606, 2608, 2609, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 2621, 2628, 2630, 2631, 2632, 2636, 2640, 2641, 2642, 2649, 2650, 2657, 2661, 2662, 2671, 2675, 2676, 2678, 2689, 2690, 2695, 2697, 2700, 2704, 2705, 2708, 2709, 2710, 2711, 2719, 2720, 2722, 2723, 2724, 2725, 2728, 2731, 2732, 2748, 2749, 2756, 2758, 2759, 2760, 2761, 2766, 2769, 2773, 2774, 2783, 2784, 2785, 2788, 2790, 2791, 2793, 2795, 2796, 2803, 2809, 2810, 2812, 2813, 2820, 2834, 2836, 2837, 2840, 2842, 2843, 2844, 2846, 2848, 2849, 2851, 2853, 2854, 2856, 2864, 2867, 2868, 2869, 2870, 2871, 2872, 2879, 2880, 2881, 2886, 2890, 2893, 2898, 2908, 2928, 2934, 2938, 2949, 2952, 2964, 2965, 2967, 2968, 2969, 2976, 2977, 2978, 2979, 2984, 3005, 3008, 3015, 3020, 3022, 3028, 3032, 3035, 3040, 3043, 3044, 3047, 3055, 3067, 3068, 3080, 3085, 3086, 3093, 3094, 3101, 3106, 3107, 3110, 3111, 3112, 3113, 3114, 3119, 3122, 3125, 3130, 3137, 3138, 3148, 3149, 3151, 3152, 3153 }
{ }