[ [ 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 23, 30, 32, 33, 35, 41, 42, 43, 44, 46, 49, 50, 
      51, 52, 53, 54, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 74, 75, 78, 79, 80, 81, 83, 84, 88, 89, 
      90, 91, 93, 94, 96, 97, 99, 101, 102, 105, 106, 108, 112, 115, 118, 119, 120, 125, 126, 127, 129, 
      130, 131, 135, 138, 139, 140, 141, 142, 143, 145, 148, 149, 153, 154, 160, 161, 162, 164, 167, 
      168, 171, 173, 175, 176, 177, 178, 179, 180, 182, 183, 186, 187, 188, 190, 191, 192, 194, 195, 
      197, 198, 200, 203, 206, 208, 209, 210, 212, 216, 218, 219, 221, 222, 227, 229, 230, 231, 233, 
      234, 236, 238, 240, 241, 242, 243, 244, 246, 248, 252, 254, 255, 256, 260, 262, 264, 267, 268, 
      270, 271, 272, 273, 279, 283, 286, 289, 290, 292, 295, 299, 302, 305, 306, 311, 312, 314, 315, 
      316, 321, 322, 325, 327, 330, 332, 333, 335, 336, 337, 344, 347, 348, 350, 351, 352, 353, 355, 
      356, 358, 359, 361, 363, 365, 368, 369, 371, 372, 373, 375, 377, 378, 379, 386, 387, 389, 390, 
      393, 394, 396, 397, 399, 402, 403, 404, 408, 409, 411, 419, 420, 421, 422, 423, 425, 426, 428, 
      429, 430, 431, 432, 433, 434, 435, 438, 439, 440, 443, 444, 445, 447, 449, 452, 453, 454, 455, 
      456, 458, 459, 464, 465, 466, 468, 470, 471, 472, 474, 475, 477, 479, 480, 481, 482, 486, 487, 
      488, 492, 493, 498, 499, 503, 504, 507, 508, 511, 513, 515, 520, 524, 525, 529, 530, 532, 534, 
      535, 536, 537, 538, 540, 542, 543, 545, 549, 550, 552, 554, 555, 556, 558, 559, 560, 563, 570, 
      573, 577, 586, 587, 588, 589, 591, 594, 595, 596, 598, 599, 600, 602, 603, 605, 606, 608, 610, 
      611, 612, 615, 617, 620, 621, 622, 625, 626, 627, 629, 632, 633, 634, 636, 637, 638, 639, 640, 
      646, 650, 652, 653, 654, 659, 660, 661, 663, 665, 666, 668, 669, 670, 671, 672, 675, 677, 680, 
      681, 682, 685, 686, 689, 690, 691, 692, 696, 697, 699, 700, 701, 702, 703, 704, 708, 710, 711, 
      713, 714, 715, 718, 719, 720, 722, 723, 725, 726, 727, 728, 729, 730, 731, 732, 734, 736, 738, 
      741, 745, 748, 749, 750, 754, 755, 756, 761, 763, 765, 766, 767, 768, 770, 777, 778, 780, 783, 
      784, 785, 786, 787, 788, 789, 790, 793, 794, 796, 797, 799, 803, 804, 805, 808, 812, 815, 816, 
      818, 820, 821, 822, 829, 831, 833, 834, 839, 840, 842, 844, 845, 847, 848, 853, 854, 855, 856, 
      858, 860, 861, 865, 866, 867, 868, 869, 870, 872, 874, 879, 882, 884, 885, 886, 888, 889, 891, 
      892, 893, 896, 898, 899, 900, 902, 905, 907, 908, 909, 911, 914, 915, 918, 919, 920, 923, 925, 
      927, 929, 931, 934, 938, 939, 943, 944, 949, 951, 953, 956, 957, 959, 961, 962, 964, 966, 967, 
      969, 972, 974, 977, 981, 983, 984, 985, 987, 989, 991, 992, 994, 996, 998, 999, 1001, 1004, 1005, 
      1006, 1010, 1011, 1012, 1013, 1015, 1020, 1021, 1023, 1024, 1025, 1026, 1028, 1029, 1030, 1032, 
      1034, 1039, 1040, 1041, 1042, 1046, 1048, 1052, 1053, 1054, 1055, 1056, 1061, 1062, 1065, 1067, 
      1068, 1069, 1070, 1078, 1079, 1080, 1081, 1086, 1089, 1092, 1097, 1098, 1099, 1102, 1105, 1108, 
      1111, 1112, 1115, 1116, 1117, 1121, 1123, 1124, 1126, 1128, 1129, 1130, 1131, 1134, 1136, 1137, 
      1138, 1142, 1144, 1145, 1146, 1148, 1150, 1151, 1153, 1154, 1155, 1159, 1160, 1161, 1162, 1163, 
      1164, 1169, 1170, 1171, 1172, 1178, 1179, 1181, 1184, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 
      1200, 1201, 1203, 1205, 1210, 1211, 1214, 1215, 1219, 1220, 1224, 1226, 1227, 1230, 1231, 1232, 
      1233, 1234, 1235, 1237, 1240, 1246, 1247, 1251, 1253, 1257, 1260, 1265, 1267, 1268, 1271, 1272, 
      1275, 1278, 1279, 1280, 1283, 1284, 1287, 1288, 1291, 1292, 1293, 1296, 1297, 1298, 1300, 1302, 
      1303, 1308, 1310, 1314, 1316, 1317, 1318, 1322, 1323, 1324, 1325, 1327, 1332, 1334, 1338, 1340, 
      1342, 1343, 1345, 1346, 1347, 1348, 1349, 1358, 1359, 1360, 1361, 1362, 1364, 1366, 1367, 1371, 
      1373, 1377, 1378, 1379, 1382, 1384, 1385, 1386, 1389, 1390, 1391, 1392, 1394, 1396, 1398, 1400, 
      1401, 1403, 1406, 1409, 1411, 1413, 1415, 1417, 1418, 1419, 1421, 1422, 1424, 1425, 1426, 1429, 
      1430, 1431, 1432, 1434, 1442, 1445, 1446, 1447, 1448, 1452, 1453, 1454, 1455, 1456, 1459, 1460, 
      1462, 1464, 1465, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1479, 1484, 1485, 1486, 
      1490, 1492, 1499, 1500, 1501, 1502, 1506, 1511, 1512, 1514, 1515, 1516, 1518, 1519, 1521, 1522, 
      1523, 1528, 1529, 1530, 1531, 1534, 1535, 1537, 1538, 1539, 1545, 1547, 1551, 1553, 1556, 1561, 
      1563, 1564, 1565, 1573, 1574, 1575, 1576, 1577, 1581, 1582, 1584, 1590, 1592, 1597, 1598, 1600, 
      1601, 1602, 1603, 1604, 1605, 1610, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 1621, 1623, 
      1624, 1625, 1626, 1627, 1629, 1630, 1635, 1639, 1645, 1646, 1649, 1650, 1654, 1656, 1658, 1659, 
      1664, 1665, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1677, 1680, 1686, 1689, 1690, 1691, 1693, 
      1694, 1695, 1696, 1697, 1698, 1701, 1703, 1705, 1706, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 
      1717, 1718, 1720, 1721, 1722, 1726, 1727, 1730, 1731, 1732, 1733, 1734, 1735, 1737, 1738, 1739, 
      1740, 1741, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 1754, 1755, 1758, 1760, 1761, 1762, 1765, 
      1766, 1768, 1769, 1770, 1771, 1772, 1774, 1775, 1778, 1783, 1784, 1785, 1787, 1789, 1791, 1792, 
      1799, 1801, 1802, 1803, 1804, 1805, 1806, 1808, 1809, 1811, 1812, 1813, 1814, 1815, 1818, 1820, 
      1821, 1823, 1825, 1828, 1829, 1831, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1842, 1844, 1848, 
      1851, 1852, 1853, 1857, 1858, 1859, 1860, 1862, 1863, 1864, 1865, 1868, 1869, 1872, 1873, 1874, 
      1879, 1882, 1887, 1891, 1892, 1894, 1897, 1899, 1901, 1902, 1904, 1908, 1909, 1910, 1914, 1916, 
      1918, 1920, 1921, 1924, 1925, 1928, 1935, 1937, 1938, 1942, 1945, 1946, 1948, 1949, 1951, 1952, 
      1956, 1957, 1958, 1960, 1961, 1963, 1966, 1969, 1970, 1972, 1975, 1976, 1977, 1978, 1979, 1981, 
      1982, 1983, 1989, 1991, 1994, 1996, 1999, 2002, 2004, 2007, 2010, 2011, 2015, 2019, 2021, 2023, 
      2028, 2033, 2037, 2039, 2040, 2042, 2043, 2044, 2048, 2055, 2059, 2060, 2062, 2064, 2065, 2069, 
      2071, 2072, 2074, 2076, 2078, 2081, 2082, 2086, 2087, 2088, 2092, 2095, 2096, 2099, 2103, 2105, 
      2107, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2120, 2121, 2122, 2124, 2128, 2129, 2130, 
      2131, 2132, 2134, 2135, 2136, 2137, 2138, 2139, 2141, 2142, 2143, 2145, 2146, 2147, 2151, 2152, 
      2156, 2157, 2158, 2159, 2161, 2164, 2165, 2169, 2170, 2172, 2174, 2176, 2177, 2178, 2180, 2182, 
      2187, 2188, 2191, 2192, 2194, 2197, 2198, 2200, 2201, 2202, 2205, 2206, 2207, 2211, 2212, 2213, 
      2215, 2217, 2220, 2224, 2226, 2228, 2229, 2230, 2232, 2236, 2237, 2238, 2239, 2240, 2241, 2242, 
      2243, 2244, 2247, 2248, 2249, 2250, 2254, 2255, 2258, 2259, 2260, 2261, 2264, 2270, 2272, 2273, 
      2274, 2275, 2278, 2279, 2281, 2284, 2286, 2288, 2290, 2291, 2292, 2294, 2295, 2297, 2298, 2302, 
      2303, 2306, 2308, 2309, 2311, 2313, 2314, 2318, 2320, 2327, 2328, 2330, 2334, 2336, 2337, 2342, 
      2343, 2345, 2346, 2347, 2349, 2350, 2351, 2353, 2355, 2357, 2363, 2364, 2365, 2368, 2369, 2370, 
      2371, 2372, 2373, 2374, 2375, 2378, 2383, 2385, 2386, 2387, 2388, 2390, 2391, 2395, 2396, 2397, 
      2398, 2400, 2403, 2407, 2409, 2410, 2412, 2413, 2414, 2415, 2416, 2418, 2421, 2422, 2423, 2425, 
      2427, 2428, 2431, 2434, 2437, 2439, 2444, 2445, 2447, 2448, 2450, 2452, 2459, 2460, 2462, 2463, 
      2464, 2469, 2470, 2472, 2473, 2475, 2476, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2487, 2488, 
      2489, 2491, 2498, 2499, 2500, 2502, 2506, 2508, 2512, 2514, 2519, 2520, 2522, 2523, 2524, 2527, 
      2528, 2529, 2530, 2533, 2535, 2536, 2537, 2538, 2539, 2542, 2543, 2544, 2547, 2551, 2557, 2562, 
      2564, 2565, 2573, 2576, 2579, 2580, 2582, 2583, 2584, 2587, 2589, 2590, 2591, 2592, 2593, 2594, 
      2595, 2596, 2597, 2599, 2600, 2601, 2602, 2605, 2608, 2609, 2610, 2613, 2614, 2618, 2619, 2620, 
      2623, 2626, 2627, 2628, 2629, 2631, 2633, 2634, 2635, 2638, 2639, 2641, 2642, 2643, 2647, 2650, 
      2651, 2653, 2655, 2657, 2658, 2660, 2662, 2666, 2667, 2670, 2672, 2673, 2674, 2675, 2676, 2677, 
      2678, 2680, 2683, 2685, 2686, 2688, 2689, 2690, 2692, 2696, 2697, 2701, 2702, 2703, 2704, 2705, 
      2706, 2709, 2710, 2714, 2715, 2718, 2720, 2721, 2722, 2727, 2732, 2733, 2735, 2736, 2737, 2738, 
      2739, 2741, 2744, 2746, 2748, 2749, 2750, 2751, 2753, 2755, 2759, 2762, 2764, 2766, 2767, 2769, 
      2771, 2773, 2774, 2776, 2777, 2781, 2782, 2783, 2785, 2786, 2787, 2788, 2789, 2790, 2792, 2796, 
      2799, 2802, 2807, 2809, 2810, 2811, 2815, 2816, 2817, 2818, 2820, 2821, 2824, 2825, 2826, 2827, 
      2829, 2831, 2832, 2833, 2836, 2839, 2844, 2845, 2847, 2849, 2850, 2852, 2853, 2856, 2857, 2859, 
      2864, 2866, 2867, 2868, 2870, 2871, 2872, 2873, 2874, 2876, 2877, 2878, 2880, 2881, 2882, 2883, 
      2885, 2890, 2892, 2893, 2894, 2896, 2897, 2898, 2899, 2900, 2901, 2902, 2904, 2907, 2908, 2909, 
      2911, 2912, 2915, 2916, 2917, 2918, 2920, 2921, 2922, 2923, 2926, 2929, 2930, 2931, 2932, 2933, 
      2934, 2937, 2938, 2940, 2941, 2947, 2948, 2949, 2950, 2951, 2953, 2957, 2958, 2959, 2961, 2962, 
      2964, 2971, 2972, 2973, 2974, 2978, 2979, 2981, 2982, 2983, 2986, 2989, 2991, 2992, 2993, 2994, 
      2995, 3000, 3001, 3002, 3003, 3004, 3005, 3008, 3011, 3016, 3021, 3023, 3025, 3026, 3027, 3031, 
      3036, 3037, 3039, 3041, 3042, 3043, 3047, 3048, 3050, 3053, 3055, 3057, 3061, 3062, 3069, 3070, 
      3071, 3072, 3075, 3076, 3079, 3080, 3089, 3091, 3095, 3097, 3098, 3101, 3103, 3110, 3111, 3114, 
      3119, 3122, 3126, 3127, 3130, 3131, 3133, 3135, 3136, 3137, 3144, 3145, 3147, 3155, 3157, 3158, 
      3160, 3161, 3162, 3167, 3169, 3171, 3172, 3175, 3177, 3178, 3180, 3181, 3183, 3185, 3189, 3191, 
      3192, 3193, 3196, 3197, 3198, 3199, 3201, 3205, 3206, 3208, 3209, 3210, 3217, 3220, 3221, 3224, 
      3228, 3230, 3231, 3238, 3239, 3243, 3246, 3248, 3250, 3252, 3253, 3254, 3255, 3256, 3257, 3261, 
      3262, 3263, 3264, 3265, 3266, 3267, 3270, 3271, 3272, 3273, 3276, 3279, 3280, 3284, 3286, 3288, 
      3289, 3290, 3291, 3292, 3293, 3294, 3295, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3305, 3307, 
      3309, 3310, 3311, 3314, 3316, 3318, 3319, 3322, 3323, 3325, 3328, 3329, 3330, 3331, 3333, 3334, 
      3336, 3337, 3338, 3340, 3341, 3342, 3345, 3346, 3349, 3350, 3351, 3352, 3355, 3358, 3361, 3363, 
      3365, 3367, 3370, 3371, 3372, 3374, 3375, 3376, 3378, 3380, 3382, 3384, 3386, 3388, 3391, 3393, 
      3395, 3396, 3397, 3399, 3401, 3403, 3404, 3406, 3407, 3409, 3410, 3411, 3412, 3413, 3416, 3418, 
      3419, 3421, 3422, 3423, 3427, 3428, 3432, 3433, 3436, 3437, 3439, 3444, 3445, 3448, 3450, 3451, 
      3452, 3454, 3456, 3458, 3459, 3461, 3462, 3463, 3464, 3466, 3469, 3470, 3471, 3472, 3474, 3476, 
      3479, 3482, 3485, 3487, 3490, 3492, 3493, 3495, 3496, 3497, 3498, 3500, 3503, 3507, 3508, 3509, 
      3510, 3511, 3513, 3514, 3516, 3517, 3518, 3519, 3521, 3522, 3524, 3526, 3527, 3528, 3529, 3532, 
      3533, 3534, 3536, 3538, 3542, 3545, 3546, 3547, 3551, 3554, 3555, 3556, 3557, 3559, 3562, 3563, 
      3565, 3566, 3572, 3573, 3574, 3575, 3578, 3579, 3581, 3582, 3585, 3587, 3588, 3589, 3594, 3598, 
      3599, 3600, 3601, 3604, 3605, 3607, 3608, 3609, 3612, 3613, 3614, 3615, 3616, 3619, 3621, 3623, 
      3624, 3626, 3629, 3630, 3631, 3634, 3636, 3637, 3638, 3640, 3642, 3644, 3645, 3646, 3647, 3650, 
      3653, 3654, 3655, 3656, 3660, 3663, 3664, 3666, 3668, 3671, 3672, 3673, 3675, 3676, 3682, 3683, 
      3687, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3697, 3698, 3699, 3700, 3703, 3707, 3710, 3712, 
      3713, 3715, 3719, 3720, 3722, 3723, 3724, 3727, 3728, 3731, 3734, 3735, 3736, 3737, 3742, 3743, 
      3746, 3747, 3748, 3749, 3752, 3755, 3756, 3757, 3760, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 
      3770, 3771, 3773, 3774, 3779, 3783, 3787, 3788, 3792, 3794, 3796, 3797, 3798, 3801, 3802, 3805, 
      3806, 3812, 3813, 3814, 3815, 3817, 3818, 3819, 3821, 3824, 3825, 3826, 3827, 3828, 3829, 3832, 
      3833, 3834, 3835, 3840, 3841, 3842, 3844, 3845, 3846, 3847, 3848, 3849, 3850, 3851, 3854, 3856, 
      3858, 3859, 3861, 3862, 3864, 3865, 3867, 3869, 3870, 3876, 3878, 3880, 3881, 3884, 3887, 3890, 
      3892, 3893, 3894, 3898, 3900, 3901, 3909, 3913, 3914, 3922, 3925, 3928, 3929, 3930, 3932, 3934, 
      3935, 3937, 3938, 3941, 3944, 3945, 3946, 3947, 3948, 3950, 3951, 3952, 3953, 3955, 3956, 3957, 
      3960, 3963, 3964, 3966, 3967, 3968, 3969, 3970, 3971, 3973, 3974, 3983, 3984, 3985, 3988, 3989, 
      3990, 3993, 3994, 3996, 3999, 4000, 4001, 4002, 4005, 4009, 4010, 4013, 4015, 4016, 4018, 4022, 
      4023, 4024, 4026, 4027, 4034, 4037, 4038, 4043, 4044, 4053, 4055, 4056, 4057, 4058, 4061, 4063, 
      4065, 4067, 4068, 4069, 4070, 4072, 4074, 4075, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 
      4088, 4089, 4091, 4094, 4095, 4096, 4100, 4102, 4103, 4104, 4108, 4109, 4111, 4113, 4114, 4117, 
      4118, 4119, 4121, 4123, 4126, 4127, 4128, 4129, 4130, 4131, 4134, 4138, 4139, 4148, 4151, 4154, 
      4155, 4156, 4157, 4160, 4162, 4163, 4164, 4166, 4170, 4173, 4175, 4178, 4181, 4182, 4183, 4186, 
      4187, 4189, 4190, 4194, 4195, 4198, 4200, 4204, 4207, 4208, 4211, 4212, 4213, 4216, 4218, 4220, 
      4221, 4223, 4224, 4225, 4227, 4230, 4231, 4232, 4233, 4239, 4244, 4245, 4249, 4251, 4255, 4262, 
      4263, 4264, 4265, 4266, 4268, 4269, 4270, 4271, 4272, 4273, 4275, 4276, 4277, 4278, 4280, 4283, 
      4286, 4287, 4292, 4293, 4294, 4296, 4300, 4301, 4302, 4303, 4305, 4309, 4312, 4313, 4314, 4317, 
      4319, 4321, 4323, 4326, 4328, 4329, 4330, 4331, 4332, 4333, 4335, 4336, 4339, 4340, 4342, 4343, 
      4346, 4347, 4348, 4349, 4351, 4356, 4358, 4361, 4366, 4372, 4375, 4376, 4378, 4379, 4380, 4384, 
      4385, 4386, 4387, 4388, 4389, 4390, 4391, 4392, 4394, 4396, 4397, 4399, 4401, 4402, 4405, 4408, 
      4410, 4411, 4414, 4415, 4416, 4417, 4418, 4419, 4421, 4424, 4427, 4428, 4429, 4432, 4434, 4435, 
      4436, 4439, 4441, 4442, 4443, 4446, 4447, 4448, 4450, 4453, 4456, 4458, 4460, 4462, 4463, 4464, 
      4465, 4467, 4468, 4469, 4470, 4471, 4472, 4474, 4475, 4476, 4478, 4479, 4480, 4481, 4484, 4486, 
      4490, 4494, 4495, 4496, 4500, 4502, 4503, 4504, 4506, 4507, 4508, 4510, 4511, 4516, 4517, 4520, 
      4521, 4522, 4523, 4527, 4528, 4530, 4531, 4534, 4535, 4536, 4538, 4543, 4544, 4545, 4547, 4548, 
      4549, 4550, 4553, 4554, 4557, 4558, 4561, 4563, 4565, 4567, 4568, 4569, 4570, 4571, 4572, 4574, 
      4577, 4580, 4581, 4585, 4588, 4589, 4593, 4594, 4596, 4600, 4603, 4604, 4605, 4609, 4610, 4611, 
      4613, 4614, 4615, 4617, 4618, 4619, 4622, 4623, 4624, 4625, 4626, 4627, 4632, 4634, 4635, 4639, 
      4641, 4644, 4645, 4646, 4648, 4649, 4650, 4651, 4655, 4658, 4659, 4660, 4662, 4663, 4664, 4667, 
      4671, 4675, 4677, 4682, 4684, 4685, 4686, 4687, 4689, 4693, 4695, 4696, 4697, 4698, 4701, 4702, 
      4704, 4705, 4706, 4707, 4708, 4711, 4712, 4713, 4714, 4715, 4718, 4724, 4726, 4728, 4731, 4732, 
      4735, 4736, 4737, 4738, 4741, 4744, 4745, 4749, 4750, 4754, 4755, 4756, 4757, 4758, 4759, 4762, 
      4768, 4769, 4770, 4772, 4773, 4774, 4775, 4778, 4784, 4785, 4788, 4789, 4790, 4791, 4794, 4798, 
      4799, 4800, 4807, 4808, 4809, 4810, 4811, 4813, 4817, 4818, 4821, 4822, 4823, 4824, 4828, 4829, 
      4834, 4836, 4838, 4840, 4842, 4845, 4846, 4847, 4848, 4849, 4850, 4851, 4852, 4854, 4857, 4861, 
      4862, 4863, 4864, 4866, 4867, 4870, 4874, 4875, 4876, 4878, 4880, 4882, 4883, 4884, 4885, 4889, 
      4890, 4892, 4897, 4898, 4900, 4903, 4906, 4908, 4910, 4915, 4916, 4921, 4924, 4930, 4931, 4937, 
      4942, 4943, 4946, 4947, 4948, 4949, 4950, 4953, 4954, 4955, 4956, 4957, 4959, 4962, 4963, 4966, 
      4967, 4969, 4971, 4972, 4975, 4977, 4978, 4979, 4981, 4982, 4983, 4985, 4987, 4988, 4989, 4991, 
      4992, 4995, 4996, 4997, 4998, 4999, 5001, 5003, 5004, 5006, 5008, 5011, 5012, 5015, 5021, 5022, 
      5023, 5025, 5027, 5028, 5033, 5039, 5040, 5041, 5043, 5045, 5047, 5049, 5051, 5054, 5056, 5057, 
      5059, 5063, 5065, 5068, 5070, 5072, 5073, 5075, 5076, 5077, 5079, 5083, 5085, 5086, 5088, 5089, 
      5090, 5093, 5095, 5096, 5098, 5102, 5103, 5104, 5105, 5109, 5110, 5111, 5115, 5120, 5126, 5127, 
      5128, 5131, 5132, 5133, 5136, 5137, 5138, 5139, 5142, 5143, 5144, 5145, 5146, 5147, 5149, 5150, 
      5151, 5155, 5156, 5157, 5158, 5159, 5163, 5164, 5165, 5168, 5170, 5175, 5179, 5180, 5181, 5183, 
      5184, 5186, 5188, 5189, 5191, 5193, 5195, 5196, 5197, 5198, 5200, 5201, 5204, 5206, 5207, 5208, 
      5210, 5211, 5216, 5217, 5219, 5222, 5224, 5225, 5229, 5230, 5233, 5235, 5237, 5239, 5242, 5243, 
      5247, 5248, 5249, 5250, 5251, 5253, 5254, 5258, 5260, 5262, 5263, 5264, 5265, 5266, 5267, 5269, 
      5270, 5275, 5277, 5278, 5279, 5281, 5282, 5283, 5289, 5290, 5292, 5293, 5296, 5297, 5299, 5301, 
      5302, 5303, 5305, 5306, 5308, 5309, 5310, 5311, 5314, 5316, 5317, 5318, 5319, 5320, 5323, 5326, 
      5329, 5330, 5332, 5336, 5338, 5339, 5340, 5341, 5344, 5346, 5347, 5348, 5350, 5351, 5352, 5353, 
      5354, 5355, 5358, 5360, 5362, 5363, 5365, 5367, 5370, 5373, 5374, 5377, 5378, 5379, 5380, 5381, 
      5382, 5383, 5384, 5387, 5389, 5390, 5391, 5394, 5395, 5398, 5400, 5402, 5403, 5405, 5407, 5408, 
      5409, 5410, 5411, 5412, 5413, 5415, 5417, 5418, 5424, 5425, 5426, 5428, 5429, 5432, 5433, 5434, 
      5435, 5440, 5444, 5447, 5449, 5450, 5451, 5452, 5453, 5454, 5455, 5456, 5458, 5461, 5462, 5471, 
      5475, 5477, 5478, 5482, 5484, 5485, 5486, 5487, 5488, 5492, 5493, 5494, 5496, 5499, 5501, 5502, 
      5503, 5506, 5515, 5516, 5519, 5520, 5521, 5523, 5524, 5526, 5529, 5530, 5531, 5533, 5534, 5538, 
      5539, 5542, 5544, 5545, 5547, 5548, 5549, 5550, 5553, 5554, 5557, 5559, 5560, 5561, 5563, 5565, 
      5568, 5569, 5570, 5572, 5575, 5576, 5577, 5579, 5580, 5581, 5582, 5583, 5585, 5587, 5588, 5589, 
      5592, 5594, 5595, 5596, 5597, 5601, 5602, 5604, 5606, 5608, 5611, 5612, 5615, 5616, 5619, 5620, 
      5625, 5626, 5627, 5628, 5629, 5630, 5631, 5632, 5633, 5636, 5637, 5638, 5640, 5643, 5646, 5647, 
      5648, 5650, 5652, 5653, 5654, 5655, 5656, 5658, 5659, 5662, 5663, 5664, 5665, 5667, 5668, 5669, 
      5670, 5671, 5672, 5674, 5676, 5677, 5678, 5682, 5683, 5686, 5688, 5692, 5693, 5694, 5695, 5697, 
      5698, 5700, 5702, 5704, 5707, 5708, 5709, 5710, 5719, 5720, 5723, 5724, 5725, 5727, 5729, 5730, 
      5731, 5732, 5733, 5734, 5735, 5737, 5738, 5739, 5740, 5746, 5748, 5750, 5753, 5754, 5756, 5757, 
      5759, 5765, 5766, 5767, 5776, 5777, 5778, 5779, 5780, 5783, 5787, 5790, 5791, 5793, 5795, 5797, 
      5800, 5801, 5802, 5803, 5805, 5806, 5807, 5808, 5809, 5810, 5811, 5812, 5813, 5815, 5816, 5818, 
      5821, 5822, 5823, 5825, 5828, 5829, 5830, 5833, 5835, 5836, 5837, 5841, 5842, 5847, 5848, 5849, 
      5853, 5854, 5856, 5862, 5863, 5865, 5866, 5874, 5875, 5876, 5878, 5880, 5882, 5885, 5887, 5889, 
      5890, 5891, 5892, 5895, 5896, 5899, 5900, 5902, 5903, 5909, 5911, 5912, 5913, 5914, 5915, 5918, 
      5919, 5920, 5922, 5923, 5924, 5928, 5934, 5936, 5939, 5940, 5943, 5946, 5948, 5949, 5951, 5952, 
      5953, 5954, 5955, 5956, 5957, 5958, 5960, 5963, 5966, 5967, 5969, 5971, 5972, 5977, 5978, 5980, 
      5981, 5982, 5983, 5985, 5990, 5991, 5994, 5995, 5996, 5997, 5998, 6000, 6001, 6004, 6011, 6013, 
      6014, 6017, 6020, 6021, 6024, 6025, 6030, 6031, 6032, 6033, 6036, 6037, 6042, 6043, 6045, 6046, 
      6049, 6052, 6053, 6054, 6055, 6056, 6058, 6060, 6062, 6064, 6065, 6066, 6068, 6070, 6074, 6077, 
      6080, 6081, 6082, 6083, 6085, 6089, 6091, 6092, 6096, 6098, 6100, 6102, 6104, 6106, 6107, 6110, 
      6112, 6113, 6116, 6119, 6121, 6123, 6126, 6128, 6129, 6130, 6131, 6134, 6135, 6139, 6140, 6142, 
      6144, 6145, 6146, 6147, 6149, 6152, 6154, 6155, 6156, 6160, 6162, 6165, 6166, 6167, 6169, 6173, 
      6175, 6176, 6180, 6183, 6186, 6187, 6189, 6190, 6191, 6194, 6196, 6199, 6200, 6202, 6203, 6204, 
      6205, 6206, 6207, 6208, 6209, 6211, 6212, 6213, 6215, 6216, 6219, 6221, 6227, 6229, 6231, 6232, 
      6233, 6234, 6236, 6237, 6238, 6241, 6243, 6245, 6246, 6248, 6249, 6250, 6253, 6255, 6256, 6257, 
      6258, 6259, 6260, 6261, 6263, 6265, 6268, 6270, 6271, 6273, 6274, 6275, 6276, 6279, 6280, 6284, 
      6288, 6289, 6290, 6294, 6295, 6296, 6297, 6298, 6299, 6301, 6303, 6305, 6306, 6307, 6308, 6310, 
      6311, 6312, 6314, 6315, 6316, 6317, 6320, 6322, 6323, 6324, 6326, 6327, 6332, 6335, 6336, 6338, 
      6341, 6342, 6346, 6347, 6349, 6351, 6352, 6354, 6356, 6357, 6358, 6361, 6366, 6367, 6369, 6372, 
      6373, 6375, 6377, 6381, 6382, 6383, 6385, 6386, 6391, 6394, 6397, 6398, 6399, 6400, 6401, 6402, 
      6403, 6404, 6406, 6407, 6409, 6410, 6412, 6414, 6415, 6416, 6421, 6424, 6428, 6429, 6430, 6431, 
      6432, 6435, 6436, 6437, 6438, 6440, 6442, 6443, 6444, 6446, 6447, 6448, 6449, 6454, 6456, 6457, 
      6459, 6460, 6461, 6462, 6463, 6464, 6467, 6469, 6472, 6476, 6477, 6480, 6481, 6482, 6484, 6486, 
      6488, 6490, 6491, 6492, 6494, 6495, 6496, 6497, 6499, 6501, 6505, 6506, 6508, 6509, 6510, 6511, 
      6514, 6515, 6517, 6519, 6521, 6523, 6525, 6526, 6529, 6530, 6531, 6533, 6537, 6538, 6539, 6542, 
      6546, 6548, 6549, 6550, 6553, 6554, 6556, 6558, 6559, 6561, 6566, 6569, 6572, 6576, 6578, 6579, 
      6581, 6583, 6585, 6587, 6589, 6592, 6593, 6594, 6595, 6596, 6598, 6599, 6600, 6602, 6604, 6606, 
      6615, 6617, 6618, 6619, 6621, 6623, 6624, 6628, 6629, 6630, 6631, 6632, 6633, 6636, 6638, 6639, 
      6640, 6644, 6645, 6646, 6647, 6648, 6649, 6652, 6655, 6657, 6658, 6660, 6661, 6663, 6665, 6668, 
      6669, 6672, 6674, 6675, 6678, 6679, 6680, 6681, 6684, 6688, 6690, 6691, 6692, 6693, 6697, 6698, 
      6701, 6704, 6707, 6709, 6710, 6713, 6714, 6718, 6719, 6724, 6725, 6726, 6730, 6731, 6732, 6735, 
      6737, 6738, 6739, 6741, 6743, 6744, 6745, 6749, 6752, 6755, 6756, 6757, 6758, 6759, 6764, 6765, 
      6769, 6771, 6772, 6773, 6774, 6775, 6782, 6786, 6792, 6794, 6797, 6799, 6803, 6804, 6810, 6811, 
      6814, 6815, 6821, 6822, 6824, 6825, 6827, 6828, 6829, 6833, 6836, 6837, 6838, 6839, 6842, 6843, 
      6847, 6848, 6850, 6853, 6855, 6856, 6862, 6866, 6867, 6868, 6869, 6871, 6872, 6873, 6874, 6875, 
      6876, 6877, 6878, 6881, 6883, 6884, 6887, 6889, 6890, 6891, 6894, 6895, 6898, 6901, 6904, 6907, 
      6908, 6909, 6910, 6911, 6915, 6916, 6917, 6921, 6923, 6928, 6929, 6930, 6931, 6932, 6933, 6936, 
      6937, 6938, 6940, 6942, 6944, 6951, 6952, 6953, 6956, 6957, 6959, 6961, 6962, 6963, 6964, 6965, 
      6966, 6967, 6969, 6970, 6971, 6972, 6974, 6975, 6977, 6978, 6981, 6982, 6984, 6986, 6987, 6991, 
      6992, 6993, 6994, 6995, 6996, 7000, 7003, 7004, 7005, 7010, 7011, 7012, 7013, 7014, 7015, 7017, 
      7018, 7019, 7020, 7021, 7022, 7027, 7028, 7030, 7032, 7035, 7036, 7039, 7041, 7042, 7044, 7048, 
      7049, 7050, 7051, 7052, 7053, 7054, 7056, 7062, 7066, 7067, 7070, 7071, 7075, 7076, 7077, 7079, 
      7081, 7082, 7083, 7085, 7087, 7090, 7092, 7094, 7095, 7096, 7097, 7099, 7102, 7104, 7105, 7109, 
      7111, 7117, 7118, 7119, 7120, 7121, 7124, 7126, 7127, 7129, 7132, 7134, 7138, 7139, 7142, 7143, 
      7145, 7146, 7148, 7150, 7154, 7156, 7157, 7160, 7163, 7165, 7166, 7167, 7168, 7170, 7171, 7172, 
      7174, 7175, 7179, 7180, 7182, 7183, 7185, 7186, 7190, 7191, 7193, 7194, 7197, 7198, 7201, 7204, 
      7205, 7207, 7209, 7210, 7214, 7222, 7223, 7225, 7226, 7227, 7228, 7229, 7231, 7234, 7235, 7236, 
      7237, 7239, 7240, 7242, 7243, 7245, 7246, 7247, 7250, 7253, 7258, 7261, 7262, 7266, 7267, 7269, 
      7270, 7271, 7273, 7275, 7280, 7281, 7282, 7283, 7284, 7287, 7294, 7295, 7297, 7298, 7299, 7301, 
      7306, 7307, 7308, 7309, 7312, 7317, 7318, 7319, 7320, 7321, 7322, 7328, 7330, 7331, 7334, 7338, 
      7342, 7343, 7345, 7347, 7350, 7353, 7355, 7356, 7358, 7362, 7363, 7364, 7367, 7369, 7370 ], 
  [ 3, 3, 7, 38, 58, 79, 82, 84, 88, 104, 106, 117, 129, 133, 135, 144, 148, 159, 162, 179, 183, 184, 
      185, 186, 187, 187, 189, 218, 219, 223, 229, 238, 239, 256, 258, 269, 276, 279, 287, 298, 309, 
      320, 321, 323, 324, 327, 328, 333, 352, 358, 359, 361, 365, 367, 375, 384, 394, 413, 420, 421, 
      438, 447, 447, 456, 477, 478, 480, 481, 483, 485, 486, 488, 497, 508, 511, 513, 515, 519, 525, 
      527, 535, 536, 537, 539, 540, 542, 545, 558, 584, 588, 596, 597, 607, 611, 615, 617, 637, 646, 
      650, 653, 654, 658, 664, 674, 680, 686, 692, 695, 698, 707, 711, 721, 722, 724, 728, 742, 748, 
      750, 752, 756, 802, 816, 817, 821, 833, 838, 845, 859, 864, 865, 875, 876, 882, 904, 916, 917, 
      920, 920, 941, 947, 951, 957, 958, 964, 965, 974, 989, 997, 1001, 1005, 1007, 1015, 1017, 1023, 
      1029, 1033, 1035, 1041, 1042, 1045, 1047, 1060, 1062, 1066, 1067, 1076, 1080, 1083, 1084, 1093, 
      1103, 1110, 1113, 1116, 1120, 1150, 1152, 1158, 1167, 1169, 1174, 1175, 1176, 1178, 1179, 1182, 
      1193, 1194, 1223, 1228, 1229, 1237, 1242, 1243, 1253, 1258, 1261, 1266, 1270, 1274, 1276, 1285, 
      1287, 1295, 1298, 1309, 1312, 1318, 1323, 1344, 1382, 1390, 1394, 1397, 1401, 1404, 1406, 1407, 
      1414, 1415, 1419, 1426, 1462, 1467, 1490, 1491, 1510, 1521, 1522, 1523, 1557, 1558, 1559, 1560, 
      1579, 1583, 1584, 1598, 1599, 1600, 1603, 1603, 1617, 1618, 1620, 1625, 1627, 1632, 1635, 1645, 
      1661, 1663, 1672, 1673, 1675, 1676, 1683, 1690, 1701, 1731, 1734, 1741, 1743, 1744, 1755, 1757, 
      1769, 1770, 1774, 1778, 1779, 1785, 1797, 1847, 1850, 1854, 1869, 1871, 1895, 1897, 1899, 1907, 
      1909, 1912, 1916, 1923, 1926, 1929, 1931, 1939, 1942, 1978, 2006, 2010, 2037, 2041, 2049, 2051, 
      2060, 2064, 2069, 2079, 2081, 2086, 2089, 2093, 2099, 2104, 2108, 2111, 2114, 2126, 2135, 2136, 
      2139, 2160, 2162, 2171, 2176, 2189, 2195, 2198, 2202, 2203, 2208, 2212, 2223, 2235, 2236, 2242, 
      2248, 2254, 2273, 2289, 2290, 2300, 2301, 2303, 2317, 2320, 2324, 2339, 2344, 2363, 2366, 2371, 
      2387, 2392, 2399, 2402, 2403, 2408, 2423, 2428, 2429, 2436, 2465, 2466, 2468, 2486, 2491, 2496, 
      2526, 2542, 2549, 2555, 2557, 2561, 2566, 2580, 2583, 2620, 2624, 2625, 2627, 2632, 2635, 2650, 
      2656, 2659, 2673, 2676, 2679, 2685, 2693, 2694, 2716, 2732, 2735, 2740, 2741, 2759, 2760, 2763, 
      2772, 2773, 2780, 2794, 2795, 2800, 2801, 2804, 2806, 2810, 2811, 2814, 2817, 2818, 2831, 2843, 
      2851, 2853, 2856, 2859, 2864, 2870, 2889, 2894, 2905, 2906, 2921, 2929, 2937, 2964, 2984, 2993, 
      3003, 3005, 3022, 3041, 3048, 3051, 3055, 3059, 3066, 3079, 3081, 3082, 3084, 3087, 3089, 3091, 
      3095, 3104, 3105, 3110, 3111, 3126, 3132, 3133, 3137, 3156, 3161, 3169, 3170, 3184, 3185, 3192, 
      3194, 3198, 3199, 3210, 3211, 3211, 3216, 3226, 3227, 3230, 3247, 3255, 3260, 3263, 3268, 3281, 
      3285, 3288, 3292, 3298, 3303, 3306, 3314, 3323, 3330, 3333, 3348, 3350, 3357, 3363, 3364, 3383, 
      3391, 3392, 3397, 3399, 3415, 3420, 3423, 3424, 3427, 3433, 3441, 3451, 3470, 3471, 3525, 3526, 
      3534, 3534, 3546, 3553, 3555, 3561, 3562, 3570, 3576, 3579, 3582, 3590, 3593, 3596, 3603, 3612, 
      3617, 3621, 3644, 3648, 3650, 3682, 3683, 3685, 3688, 3689, 3690, 3693, 3694, 3727, 3731, 3737, 
      3740, 3744, 3747, 3778, 3781, 3801, 3808, 3808, 3821, 3823, 3854, 3864, 3866, 3871, 3879, 3926, 
      3927, 3934, 3936, 3942, 3945, 3959, 3961, 3965, 3967, 3987, 3995, 3996, 4004, 4007, 4011, 4026, 
      4034, 4035, 4037, 4040, 4047, 4057, 4063, 4064, 4073, 4078, 4082, 4083, 4086, 4099, 4124, 4134, 
      4140, 4145, 4191, 4194, 4196, 4212, 4231, 4250, 4265, 4268, 4269, 4274, 4292, 4296, 4308, 4310, 
      4312, 4315, 4316, 4324, 4336, 4339, 4341, 4363, 4372, 4376, 4382, 4397, 4404, 4406, 4411, 4434, 
      4435, 4443, 4450, 4455, 4460, 4469, 4470, 4472, 4475, 4479, 4481, 4485, 4488, 4498, 4509, 4511, 
      4513, 4522, 4528, 4533, 4533, 4562, 4565, 4573, 4575, 4580, 4582, 4585, 4595, 4596, 4597, 4628, 
      4643, 4647, 4666, 4671, 4681, 4684, 4691, 4695, 4704, 4705, 4707, 4721, 4723, 4724, 4740, 4744, 
      4744, 4753, 4765, 4775, 4784, 4786, 4833, 4837, 4854, 4860, 4862, 4863, 4870, 4881, 4889, 4895, 
      4899, 4909, 4936, 4937, 4938, 4946, 4955, 4964, 4979, 4981, 4984, 4995, 4999, 5010, 5015, 5018, 
      5033, 5048, 5057, 5071, 5079, 5086, 5120, 5121, 5139, 5154, 5157, 5162, 5164, 5175, 5176, 5184, 
      5190, 5192, 5197, 5204, 5210, 5211, 5213, 5217, 5219, 5222, 5226, 5229, 5230, 5235, 5251, 5266, 
      5273, 5275, 5276, 5317, 5320, 5323, 5336, 5343, 5368, 5370, 5376, 5384, 5391, 5394, 5397, 5399, 
      5402, 5419, 5421, 5422, 5432, 5438, 5439, 5440, 5444, 5449, 5450, 5454, 5455, 5457, 5460, 5461, 
      5485, 5500, 5516, 5518, 5526, 5540, 5544, 5545, 5547, 5550, 5554, 5561, 5564, 5570, 5576, 5577, 
      5580, 5583, 5586, 5591, 5613, 5615, 5620, 5622, 5629, 5647, 5653, 5689, 5694, 5701, 5706, 5710, 
      5712, 5713, 5723, 5724, 5728, 5730, 5736, 5739, 5747, 5749, 5772, 5773, 5774, 5775, 5800, 5807, 
      5807, 5812, 5813, 5817, 5818, 5822, 5825, 5830, 5832, 5835, 5855, 5859, 5860, 5865, 5866, 5867, 
      5871, 5873, 5875, 5879, 5886, 5889, 5903, 5906, 5915, 5922, 5923, 5926, 5927, 5939, 5949, 5976, 
      5978, 5979, 5990, 5992, 5997, 6001, 6008, 6011, 6021, 6026, 6029, 6035, 6040, 6048, 6049, 6051, 
      6053, 6062, 6070, 6071, 6073, 6078, 6083, 6086, 6121, 6122, 6131, 6139, 6140, 6148, 6158, 6161, 
      6166, 6167, 6171, 6172, 6174, 6177, 6198, 6202, 6206, 6211, 6214, 6233, 6250, 6259, 6264, 6269, 
      6272, 6294, 6296, 6303, 6320, 6325, 6347, 6356, 6358, 6360, 6361, 6364, 6374, 6380, 6385, 6387, 
      6393, 6402, 6429, 6437, 6441, 6443, 6452, 6456, 6481, 6483, 6492, 6508, 6519, 6520, 6524, 6537, 
      6541, 6544, 6546, 6551, 6565, 6575, 6576, 6577, 6580, 6588, 6592, 6593, 6607, 6615, 6617, 6628, 
      6630, 6633, 6639, 6644, 6656, 6656, 6664, 6666, 6677, 6694, 6711, 6712, 6715, 6724, 6736, 6743, 
      6752, 6753, 6754, 6756, 6761, 6771, 6773, 6777, 6794, 6801, 6804, 6812, 6823, 6828, 6835, 6840, 
      6841, 6845, 6853, 6856, 6863, 6864, 6866, 6869, 6877, 6881, 6892, 6897, 6911, 6915, 6918, 6926, 
      6932, 6933, 6949, 6968, 6969, 6978, 6989, 6994, 6998, 7001, 7005, 7009, 7011, 7012, 7025, 7027, 
      7028, 7033, 7036, 7041, 7042, 7046, 7049, 7052, 7055, 7057, 7060, 7063, 7067, 7079, 7086, 7092, 
      7095, 7113, 7115, 7119, 7135, 7146, 7151, 7169, 7180, 7181, 7195, 7205, 7226, 7228, 7245, 7246, 
      7258, 7259, 7266, 7274, 7277, 7286, 7295, 7296, 7298, 7300, 7301, 7303, 7315, 7318, 7324, 7328, 
      7335, 7351, 7365 ] ]