[ [ 1, 3, 5, 11, 12, 13, 15, 19, 22, 23, 26, 30, 33, 39, 40, 41, 44, 45, 48, 49, 53, 55, 59, 60, 64, 
      69, 71, 74, 75, 76, 77, 78, 81, 83, 85, 86, 87, 88, 90, 92, 96, 97, 98, 101, 104, 107, 108, 110, 
      112, 116, 117, 118, 119, 120, 123, 127, 128, 129, 132, 135, 136, 137, 139, 140, 141, 144, 147, 
      148, 149, 150, 151, 153, 155, 157, 158, 160, 162, 164, 167, 168, 169, 174, 175, 181, 183, 186, 
      188, 191, 192, 196, 198, 199, 200, 201, 203, 205, 206, 207, 208, 210, 212, 213, 215, 217, 218, 
      222, 224, 225, 226, 230, 233, 235, 236, 240, 242, 243, 249, 251, 252, 254, 255, 256, 257, 258, 
      260, 264, 265, 266, 269, 271, 272, 275, 276, 277, 278, 281, 283, 284, 285, 288, 290, 291, 293, 
      297, 300, 301, 302, 304, 305, 306, 307, 308, 310, 313, 314, 315, 316, 317, 318, 319, 320, 322, 
      323, 325, 326, 327, 329, 330, 335, 337, 338, 339, 340, 341, 342, 343, 344, 349, 350, 352, 353, 
      355, 357, 359, 360, 364, 367, 369, 370, 371, 372, 378, 380, 382, 383, 384, 385, 386, 387, 388, 
      389, 390, 393, 394, 395, 399, 401, 403, 405, 406, 407, 409, 411, 415, 417, 419, 421, 423, 426, 
      427, 428, 430, 432, 434, 437, 438, 442, 445, 446, 447, 449, 452, 460, 461, 462, 464, 467, 469, 
      470, 471, 473, 476, 477, 478, 479, 482, 483, 484, 488, 491, 492, 495, 497, 499, 502, 504, 505, 
      506, 507, 508, 509, 510, 511, 514, 515, 518, 519, 520, 522, 523, 525, 527, 528, 531, 532, 533, 
      534, 535, 536, 537, 540, 541, 542, 547, 548, 549, 552, 554, 556, 558, 560, 561, 562, 563, 565, 
      567, 568, 569, 571, 575, 577, 578, 580, 581, 582, 584, 585, 586, 587, 591, 592, 593, 595, 596, 
      597, 599, 600, 601, 603, 604, 611, 612, 613, 614, 615, 616, 617, 619, 620, 624, 625, 626, 630, 
      631, 634, 638, 639, 640, 641, 642, 643, 644, 645, 647, 649, 650, 653, 654, 655, 656, 657, 659, 
      661, 664, 672, 674, 675, 677, 680, 681, 683, 684, 686, 688, 691, 694, 695, 697, 699, 701, 702, 
      705, 706, 709, 710, 711, 713, 714, 719, 722, 724, 725, 727, 730, 732, 734, 736, 737, 739, 740, 
      742, 744, 746, 748, 749, 750, 751, 755, 756, 757, 761, 762, 763, 764, 771, 772, 773, 774, 775, 
      776, 777, 782, 784, 789, 790, 791, 792, 793, 796, 797, 804, 806, 807, 809, 812, 813, 814, 818, 
      819, 820, 822, 823, 824, 828, 829, 831, 832, 833, 837, 840, 843, 845, 847, 851, 852, 855, 857, 
      861, 862, 863, 865, 867, 870, 871, 872, 876, 880, 886, 887, 890, 892, 896, 904, 905, 906, 909, 
      912, 915, 916, 918, 922, 924, 925, 926, 927, 931, 932, 935, 937, 940, 941, 942, 948, 949, 954, 
      955, 957, 959, 963, 965, 966, 969, 972, 974, 975, 978, 979, 980, 981, 983, 984, 986, 987, 988, 
      989, 993, 996, 999, 1000, 1002, 1003, 1006, 1009, 1011, 1012, 1013, 1015, 1016, 1018, 1021, 1022, 
      1025, 1027, 1029, 1030, 1033, 1035, 1036, 1037, 1039, 1040, 1041, 1044, 1046, 1048, 1052, 1053, 
      1057, 1060, 1065, 1066, 1068, 1072, 1073, 1074, 1076, 1077, 1079, 1080, 1081, 1082, 1083, 1086, 
      1087, 1089, 1090, 1091, 1092, 1093, 1095, 1097, 1098, 1099, 1101, 1102, 1104, 1106, 1108, 1114, 
      1119, 1120, 1122, 1123, 1124, 1125, 1126, 1127, 1131, 1133, 1135, 1137, 1138, 1139, 1140, 1141, 
      1144, 1145, 1148, 1149, 1150, 1151, 1152, 1153, 1157, 1160, 1162, 1164, 1165, 1171, 1172, 1174, 
      1175, 1176, 1178, 1184, 1186, 1188, 1191, 1192, 1193, 1194, 1196, 1197, 1201, 1202, 1204, 1205, 
      1207, 1214, 1216, 1217, 1218, 1222, 1223, 1226, 1227, 1228, 1229, 1230, 1231, 1233, 1234, 1236, 
      1237, 1238, 1240, 1241, 1242, 1243, 1244, 1249, 1250, 1253, 1255, 1256, 1258, 1259, 1264, 1267, 
      1269, 1270, 1273, 1274, 1275, 1276, 1279, 1281, 1283, 1286, 1288, 1290, 1292, 1293, 1294, 1295, 
      1297, 1301, 1302, 1303, 1306, 1308, 1310, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 
      1322, 1323, 1324, 1332, 1333, 1335, 1336, 1339, 1341, 1343, 1344, 1345, 1348, 1349, 1350, 1352, 
      1354, 1355, 1359, 1360, 1361, 1364, 1366, 1368, 1369, 1370, 1371, 1372, 1373, 1374, 1377, 1379, 
      1381, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 1393, 1396, 1399, 1400, 1403, 1405, 1406, 1407, 
      1411, 1420, 1421, 1424, 1428, 1429, 1430, 1433, 1434, 1436, 1438, 1440, 1442, 1445, 1446, 1451, 
      1452, 1453, 1456, 1459, 1460, 1463, 1464, 1467, 1469, 1471, 1472, 1475, 1478, 1479, 1480, 1481, 
      1483, 1485, 1486, 1487, 1490, 1494, 1495, 1498, 1499, 1500, 1502, 1503, 1505, 1506, 1511, 1512, 
      1513, 1516, 1518, 1520, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 1530, 1532, 1534, 1538, 
      1539, 1543, 1544, 1545, 1550, 1553, 1554, 1555, 1557, 1558, 1559, 1560, 1561, 1562, 1564, 1565, 
      1568, 1569, 1571, 1572, 1573, 1574, 1577, 1579, 1580, 1581, 1583, 1584, 1585, 1586, 1587, 1588, 
      1589, 1595, 1596, 1598, 1603, 1604, 1605, 1606, 1608, 1609, 1610, 1612, 1616, 1617, 1618, 1619, 
      1620, 1621, 1623, 1624, 1625, 1626, 1627, 1628, 1630, 1631, 1632, 1633, 1635, 1637, 1638, 1639, 
      1640, 1641, 1642, 1644, 1649, 1650, 1651, 1655, 1656, 1657, 1659, 1660, 1662, 1663, 1664, 1665, 
      1666, 1674, 1676, 1677, 1678, 1679, 1681, 1682, 1683, 1684, 1685, 1687, 1690, 1695, 1696, 1697, 
      1700, 1701, 1702, 1703, 1704, 1707, 1708, 1709, 1712, 1714, 1716, 1717, 1718, 1720, 1723, 1725, 
      1726, 1727, 1728, 1729, 1730, 1733, 1736, 1737, 1738, 1739, 1741, 1742, 1747, 1748, 1750, 1753, 
      1760, 1765, 1766, 1768, 1769, 1771, 1772, 1773, 1775, 1776, 1777, 1778, 1780, 1782, 1783, 1786, 
      1787, 1789, 1790, 1794, 1795, 1798, 1799, 1801, 1803, 1804, 1808, 1811, 1812, 1813, 1814, 1817, 
      1822, 1825, 1826, 1827, 1829, 1830, 1831, 1833, 1834, 1838, 1839, 1842, 1844, 1845, 1850, 1854, 
      1855, 1859, 1860, 1861, 1862, 1863, 1865, 1868, 1869, 1870, 1873, 1875, 1876, 1880, 1883, 1884, 
      1886, 1887, 1889, 1891, 1892, 1893, 1896, 1897, 1898, 1902, 1903, 1904, 1905, 1907, 1908, 1909, 
      1912, 1913, 1915, 1917, 1918, 1920, 1921, 1923, 1925, 1928, 1930, 1931, 1932, 1934, 1937, 1938, 
      1939, 1941, 1943, 1949, 1951, 1952, 1955, 1956, 1958, 1959, 1960, 1961, 1962, 1966, 1969, 1971, 
      1973, 1974, 1975, 1976, 1977, 1979, 1982, 1983, 1984, 1989, 1991, 1992, 1995, 1996, 1997, 1998, 
      1999, 2000, 2002, 2003, 2004, 2005, 2007, 2011, 2015, 2016, 2017, 2018, 2021, 2022, 2023, 2024, 
      2026, 2027, 2028, 2029, 2030, 2031, 2032, 2035, 2036, 2038, 2040, 2043, 2044, 2047, 2049, 2052, 
      2053, 2055, 2059, 2060, 2061, 2062, 2063, 2067, 2069, 2070, 2072, 2073, 2074, 2075, 2077, 2078, 
      2079, 2080, 2082, 2085, 2086, 2092, 2095, 2096, 2097, 2099, 2102, 2106, 2108, 2109, 2111, 2113, 
      2115, 2116, 2120, 2123, 2124, 2125, 2127, 2129, 2134, 2135, 2136, 2138, 2139, 2140, 2141, 2143, 
      2145, 2146, 2148, 2152, 2153, 2155, 2157, 2160, 2162, 2165, 2168, 2171, 2172, 2173, 2174, 2176, 
      2177, 2179, 2180, 2181, 2183, 2184, 2185, 2187, 2188, 2189, 2190, 2191, 2192, 2194, 2197, 2198, 
      2201, 2203, 2206, 2213, 2215, 2216, 2218, 2219, 2222, 2223, 2225, 2226, 2227, 2228, 2229, 2230, 
      2232, 2233, 2235, 2236, 2237, 2238, 2240, 2243, 2244, 2245, 2249, 2250, 2253, 2254, 2256, 2259, 
      2260, 2261, 2262, 2263, 2264, 2267, 2269, 2270, 2271, 2275, 2276, 2278, 2280, 2283, 2284, 2286, 
      2290, 2292, 2295, 2296, 2297, 2300, 2302, 2305, 2306, 2309, 2310, 2313, 2314, 2315, 2317, 2318, 
      2320, 2321, 2322, 2325, 2328, 2332, 2333, 2334, 2335, 2336, 2346, 2347, 2349, 2351, 2353, 2354, 
      2356, 2357, 2358, 2359, 2360, 2361, 2364, 2365, 2366, 2367, 2368, 2369, 2372, 2375, 2376, 2377, 
      2383, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393, 2395, 2396, 2399, 2401, 2402, 2403, 
      2404, 2405, 2406, 2408, 2410, 2411, 2414, 2416, 2418, 2419, 2421, 2422, 2425, 2432, 2433, 2434, 
      2436, 2438, 2439, 2440, 2441, 2442, 2443, 2447, 2449, 2451, 2452, 2453, 2454, 2455, 2458, 2459, 
      2460, 2461, 2465, 2468, 2471, 2472, 2474, 2477, 2478, 2479, 2480, 2482, 2483, 2486, 2487, 2488, 
      2490, 2493, 2497, 2499, 2500, 2501, 2504, 2507, 2509, 2511, 2512, 2514, 2515, 2516, 2519, 2520, 
      2521, 2523, 2525, 2526, 2527, 2529, 2530, 2532, 2533, 2534, 2540, 2543, 2544, 2546, 2549, 2550, 
      2552, 2554, 2556, 2557, 2560, 2561, 2562, 2563, 2564, 2566, 2567, 2570, 2571, 2575, 2576, 2577, 
      2578, 2579, 2582, 2583, 2585, 2589, 2591, 2592, 2593, 2595, 2596, 2597, 2598, 2599, 2601, 2602, 
      2603, 2610, 2611, 2612, 2614, 2616, 2620, 2624, 2625, 2628, 2629, 2632, 2636, 2638, 2639, 2640, 
      2641, 2642, 2644, 2646, 2649, 2650, 2652, 2655, 2656, 2657, 2658, 2660, 2661, 2662, 2664, 2668, 
      2671, 2673, 2675, 2677, 2679, 2681, 2683, 2684, 2685, 2687, 2689, 2691, 2695, 2696, 2701, 2707, 
      2708, 2709, 2713, 2715, 2718, 2719, 2725, 2727, 2728, 2732, 2733, 2734, 2735, 2736, 2737, 2742, 
      2746, 2748, 2751, 2752, 2754, 2755, 2757, 2761, 2763, 2764, 2765, 2767, 2768, 2769, 2771, 2772, 
      2773, 2774, 2775, 2776, 2780, 2781, 2784, 2786, 2787, 2788, 2792, 2793, 2797, 2800, 2802, 2804, 
      2805, 2807, 2808, 2812, 2813, 2814, 2815, 2817, 2818, 2821, 2822, 2824, 2827, 2829, 2830, 2833, 
      2835, 2838, 2840, 2842, 2843, 2844, 2846, 2847, 2849, 2851, 2854, 2855, 2856, 2859, 2860, 2862, 
      2865, 2866, 2869, 2870, 2871, 2872, 2876, 2878, 2879, 2880, 2884, 2885, 2887, 2888, 2890, 2892, 
      2894, 2896, 2897, 2900, 2902, 2905, 2906, 2910, 2911, 2912, 2914, 2916, 2920, 2924, 2926, 2931, 
      2932, 2938, 2940, 2942, 2944, 2946, 2947, 2951, 2955, 2957, 2958, 2959, 2960, 2962, 2963, 2964, 
      2966, 2970, 2971, 2973, 2975, 2976, 2980, 2981, 2983, 2984, 2986, 2987, 2989, 2991, 2993, 2995, 
      2996, 2997, 3000, 3001, 3002, 3003, 3004, 3011, 3012, 3015, 3017, 3019, 3022, 3023, 3028, 3030, 
      3034, 3036, 3040, 3041, 3043, 3044, 3045, 3047, 3050, 3052, 3055, 3056, 3058, 3059, 3060, 3061, 
      3062, 3064, 3067, 3068, 3069, 3070, 3071, 3074, 3076, 3079, 3080, 3081, 3082, 3085, 3087, 3090, 
      3091, 3093, 3096, 3098, 3099, 3101, 3102, 3103, 3106, 3108, 3109, 3110, 3111, 3112, 3113, 3118, 
      3119, 3123, 3125, 3130, 3131, 3132, 3140, 3142, 3143, 3144, 3145, 3146, 3147, 3149, 3150, 3152, 
      3154, 3160, 3162, 3163, 3167, 3170, 3173, 3174, 3175, 3177, 3178, 3179, 3180, 3181, 3182, 3183, 
      3184, 3185, 3186, 3188, 3189, 3191, 3194, 3195, 3196, 3197, 3198, 3202, 3203, 3204, 3206, 3209, 
      3210, 3212, 3214, 3215, 3216, 3218, 3219, 3220, 3223, 3224, 3225, 3227, 3228, 3230, 3231, 3233, 
      3234, 3235, 3238, 3239, 3240, 3241, 3242, 3244, 3248, 3253, 3256, 3257, 3258, 3259, 3260, 3261, 
      3262, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3275, 3278, 3279, 3280, 3282, 3284, 3287, 3288, 
      3289, 3290, 3294, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3306, 3307, 3311, 3316, 3318, 
      3322, 3324, 3325, 3327, 3328, 3329, 3330, 3332, 3333, 3334, 3337, 3338, 3340, 3344, 3345, 3347, 
      3349, 3351, 3353, 3357, 3358, 3363, 3364, 3365, 3367, 3368, 3371, 3374, 3375, 3376, 3377, 3379, 
      3380, 3381, 3385, 3386, 3388, 3389, 3396, 3398, 3402, 3405, 3407, 3409, 3415, 3418, 3419, 3422, 
      3427, 3430, 3431, 3432, 3434, 3435, 3437, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 
      3449, 3451, 3452, 3453, 3455, 3456, 3457, 3462, 3464, 3465, 3466, 3473, 3474, 3475, 3476, 3477, 
      3480, 3482, 3483, 3484, 3485, 3490, 3491, 3493, 3494, 3495, 3496, 3499, 3500, 3501, 3502, 3504, 
      3505, 3508, 3509, 3510, 3513, 3515, 3516, 3517, 3524, 3525, 3528, 3530, 3531, 3533, 3534, 3535, 
      3536, 3541, 3543, 3546, 3549, 3550, 3551, 3553, 3554, 3556, 3558, 3562, 3564, 3566, 3568, 3569, 
      3571, 3572, 3573, 3577, 3578, 3580, 3583, 3586, 3587, 3590, 3591, 3592, 3594, 3597, 3598, 3599, 
      3601, 3602, 3605, 3611, 3614, 3615, 3619, 3621, 3622, 3623, 3625, 3626, 3627, 3628, 3632, 3633, 
      3634, 3635, 3636, 3638, 3641, 3642, 3647, 3648, 3649, 3652, 3654, 3655, 3658, 3659, 3660, 3664, 
      3668, 3676, 3677, 3679, 3680, 3681, 3683, 3686, 3689, 3693, 3695, 3696, 3699, 3701, 3703, 3704, 
      3711, 3714, 3715, 3718, 3724, 3726, 3730, 3731, 3735, 3738, 3739, 3741, 3742, 3743, 3746, 3747, 
      3750, 3751, 3754, 3757, 3759, 3762, 3763, 3765, 3766, 3767, 3770, 3771, 3773, 3774, 3776, 3777, 
      3778, 3780, 3790, 3791, 3792, 3794, 3795, 3796, 3797, 3799, 3800, 3802, 3803, 3804, 3807, 3808, 
      3810, 3811, 3814, 3815, 3818, 3819, 3822, 3825, 3826, 3828, 3830, 3832, 3833, 3834, 3835, 3841, 
      3844, 3847, 3848, 3852, 3856, 3857, 3858, 3860, 3861, 3864, 3865, 3870, 3871, 3872, 3873, 3877, 
      3880, 3881, 3884, 3887, 3888, 3891, 3894, 3896, 3897, 3903, 3904, 3905, 3909, 3910, 3914, 3915, 
      3918, 3922, 3923, 3925, 3926, 3927, 3928, 3935, 3937, 3938, 3939, 3942, 3945, 3947, 3949, 3952, 
      3954, 3955, 3956, 3957, 3959, 3960, 3961, 3962, 3963, 3965, 3971, 3974, 3975, 3976, 3978, 3982, 
      3983, 3985, 3986, 3987, 3989, 3992, 3996, 3997, 4007, 4008, 4009, 4012, 4014, 4015, 4016, 4017, 
      4019, 4022, 4028, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 4042, 4044, 4045, 
      4046, 4047, 4049, 4052, 4054, 4060, 4061, 4063, 4064, 4066, 4067, 4068, 4069, 4071, 4073, 4075, 
      4078, 4081, 4084, 4086, 4088, 4089, 4091, 4092, 4094, 4095, 4097, 4098, 4100, 4101, 4102, 4104, 
      4105, 4106, 4109, 4110, 4111, 4113, 4115, 4117, 4118, 4123, 4126, 4129, 4133, 4135, 4138, 4140, 
      4141, 4142, 4143, 4144, 4149, 4150, 4153, 4154, 4155, 4156, 4161, 4166, 4169, 4175, 4176, 4178, 
      4179, 4182, 4183, 4184, 4187, 4188, 4190, 4191, 4195, 4199, 4201, 4202, 4203, 4204, 4205, 4208, 
      4211, 4212, 4215, 4216, 4217, 4218, 4219, 4221, 4222, 4224, 4226, 4228, 4229, 4230, 4232, 4233, 
      4234, 4235, 4236, 4237, 4240, 4241, 4244, 4246, 4247, 4249, 4251, 4252, 4255, 4258, 4260, 4261, 
      4266, 4267, 4268, 4271, 4272, 4273, 4275, 4276, 4283, 4284, 4286, 4288, 4289, 4290, 4292, 4293, 
      4295, 4297, 4298, 4299, 4300, 4302, 4303, 4307, 4308, 4311, 4313, 4314, 4315, 4318, 4324, 4325, 
      4328, 4330, 4332, 4334, 4335, 4336, 4337, 4339, 4340, 4342, 4343, 4344, 4346, 4348, 4350, 4351, 
      4352, 4355, 4357, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4373, 4378, 4380, 4382, 
      4388, 4389, 4390, 4391, 4392, 4396, 4399, 4403, 4405, 4406, 4407, 4408, 4409, 4411, 4412, 4415, 
      4416, 4417, 4420, 4421, 4423, 4426, 4427, 4428, 4429, 4431, 4434, 4436, 4441, 4444, 4447, 4448, 
      4451, 4452, 4453, 4457, 4460, 4461, 4463, 4464, 4467, 4471, 4474, 4476, 4477, 4478, 4480, 4481, 
      4482, 4485, 4487, 4488, 4491, 4493, 4494, 4495, 4496, 4497, 4498, 4501, 4502, 4504, 4507, 4508, 
      4510, 4512, 4513, 4516, 4517, 4520, 4521, 4522, 4523, 4527, 4528, 4529, 4533, 4536, 4538, 4540, 
      4542, 4543, 4544, 4545, 4547, 4548, 4549, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4559, 4560, 
      4562, 4563, 4566, 4567, 4569, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4580, 4581, 4587, 4588, 
      4589, 4590, 4591, 4593, 4594, 4595, 4596, 4597, 4598, 4600, 4603, 4606, 4607, 4608, 4610, 4611, 
      4613, 4614, 4617, 4619, 4620, 4621, 4622, 4623, 4626, 4632, 4635, 4637, 4638, 4640, 4643, 4644, 
      4648, 4649, 4650, 4652, 4656, 4658, 4659, 4660, 4662, 4664, 4666, 4667, 4668, 4669, 4671, 4673, 
      4677, 4683, 4685, 4687, 4689, 4690, 4692, 4693, 4694, 4696, 4699, 4700, 4704, 4705, 4707, 4710, 
      4715, 4716, 4718, 4720, 4723, 4725, 4726, 4729, 4733, 4734, 4735, 4736, 4737, 4738, 4740, 4746, 
      4749, 4750, 4752, 4755, 4756, 4757, 4758, 4759, 4761, 4765, 4766, 4769, 4770, 4771, 4773, 4774, 
      4780, 4781, 4783, 4786, 4787, 4790, 4791, 4793, 4795, 4796, 4797, 4799, 4801, 4802, 4804, 4807, 
      4810, 4812, 4813, 4816, 4820, 4821, 4822, 4824, 4827, 4829, 4831, 4833, 4835, 4838, 4840, 4841, 
      4842, 4843, 4845, 4848, 4849, 4852, 4853, 4854, 4856, 4863, 4864, 4867, 4868, 4869, 4870, 4871, 
      4874, 4875, 4877, 4879, 4885, 4886, 4887, 4889, 4891, 4892, 4893, 4894, 4896, 4897, 4898, 4899, 
      4902, 4906, 4907, 4908, 4913, 4914, 4915, 4916, 4917, 4919, 4920, 4924, 4927, 4928, 4929, 4930, 
      4936, 4937, 4939, 4944, 4947, 4948, 4949, 4950, 4951, 4953, 4955, 4958, 4959, 4960, 4961, 4962, 
      4963, 4968, 4969, 4971, 4974, 4975, 4977, 4979, 4980, 4981, 4982, 4983, 4984, 4992, 4993, 4994, 
      4995, 4996, 5000, 5001, 5002, 5003, 5004, 5006, 5009, 5010, 5012, 5014, 5015, 5017, 5018, 5019, 
      5020, 5021, 5022, 5023, 5029, 5032, 5035, 5037, 5038, 5039, 5041, 5042, 5043, 5046, 5047, 5048, 
      5049, 5051, 5052, 5054, 5055, 5057, 5058, 5059, 5061, 5062, 5063, 5065, 5067, 5069, 5070, 5072, 
      5074, 5076, 5077, 5078, 5080, 5082, 5083, 5084, 5085, 5086, 5088, 5089, 5090, 5092, 5093, 5094, 
      5095, 5096, 5097, 5098, 5099, 5100, 5102, 5103, 5106, 5108, 5109, 5110, 5111, 5112, 5115, 5116, 
      5117, 5118, 5119, 5120, 5122, 5129, 5130, 5136, 5137, 5142, 5144, 5150, 5155, 5159, 5161, 5162, 
      5166, 5168, 5169, 5174, 5175, 5176, 5177, 5179, 5181, 5182, 5185, 5186, 5189, 5192, 5194, 5196, 
      5198, 5205, 5207, 5208, 5209, 5211, 5212, 5213, 5214, 5219, 5221, 5222, 5224, 5226, 5227, 5228, 
      5239, 5240, 5242, 5243, 5247, 5248, 5251, 5252, 5253, 5255, 5256, 5259, 5261, 5266, 5268, 5269, 
      5270, 5273, 5274, 5275, 5277, 5280, 5281, 5282, 5285, 5286, 5289, 5291, 5292, 5294, 5296, 5297, 
      5301, 5304, 5307, 5308, 5311, 5314, 5315, 5317, 5319, 5321, 5324, 5325, 5328, 5330, 5332, 5334, 
      5335, 5336, 5337, 5340, 5342, 5346, 5348, 5350, 5352, 5353, 5354, 5360, 5364, 5366, 5368, 5369, 
      5371, 5378, 5380, 5383, 5384, 5385, 5387, 5388, 5390, 5394, 5395, 5401, 5402, 5403, 5405, 5406, 
      5409, 5414, 5416, 5418, 5419, 5420, 5421, 5422, 5423, 5425, 5427, 5429, 5432, 5436, 5439, 5440, 
      5443, 5444, 5445, 5448, 5449, 5451, 5452, 5453, 5456, 5457, 5462, 5464, 5465, 5468, 5472, 5473, 
      5476, 5477, 5479, 5480, 5481, 5482, 5486, 5493, 5495, 5496, 5501, 5502, 5503, 5504, 5506, 5507, 
      5509, 5510, 5512, 5514, 5515, 5517, 5518, 5519, 5520, 5521, 5523, 5526, 5528, 5532, 5533, 5536, 
      5537, 5539, 5540, 5542, 5543, 5545, 5546, 5547, 5550, 5551, 5552, 5554, 5555, 5558, 5562, 5565, 
      5567, 5570, 5573, 5574, 5578, 5579, 5582, 5588, 5591, 5592, 5594, 5595, 5596, 5597, 5599, 5600, 
      5601, 5602, 5605, 5614, 5616, 5617, 5618, 5620, 5621, 5623, 5625, 5629, 5636, 5637, 5638, 5640, 
      5645, 5646, 5648, 5651, 5652, 5654, 5655, 5659, 5660, 5662, 5663, 5664, 5668, 5671, 5675, 5676, 
      5680, 5684, 5685, 5688, 5689, 5691, 5692, 5696, 5703, 5705, 5706, 5707, 5710, 5716, 5717, 5718, 
      5720, 5722, 5723, 5724, 5725, 5729, 5730, 5731, 5732, 5733, 5736, 5741, 5743, 5744, 5745, 5746, 
      5747, 5752, 5754, 5755, 5757, 5759, 5760, 5761, 5762, 5763, 5764, 5766, 5767, 5768, 5769, 5770, 
      5771, 5773, 5779, 5780, 5782, 5783, 5789, 5791, 5794, 5795, 5797, 5798, 5799, 5800, 5801, 5804, 
      5805, 5807, 5808, 5810, 5811, 5814, 5815, 5816, 5819, 5823, 5824, 5825, 5826, 5827, 5830, 5835, 
      5838, 5840, 5842, 5845, 5846, 5847, 5849, 5850, 5854, 5856, 5857, 5858, 5860, 5864, 5865, 5866, 
      5868, 5870, 5871, 5872, 5875, 5876, 5877, 5878, 5879, 5880, 5885, 5886, 5887, 5888, 5889, 5890, 
      5892, 5895, 5901, 5904, 5907, 5908, 5909, 5910, 5914, 5915, 5917, 5918, 5919, 5920, 5921, 5922, 
      5925, 5930, 5931, 5935, 5936, 5937, 5938, 5939, 5940, 5947, 5949, 5951, 5954, 5955, 5956, 5958, 
      5959, 5961, 5962, 5965, 5967, 5968, 5971, 5972, 5973, 5974, 5976, 5979, 5980, 5981, 5982, 5983, 
      5984, 5992, 5998, 6004, 6006, 6007, 6010, 6011, 6013, 6014, 6016, 6017, 6021, 6022, 6023, 6025, 
      6029, 6030, 6031, 6032, 6033, 6035, 6036, 6037, 6040, 6041, 6042, 6045, 6046, 6048, 6051, 6052, 
      6054, 6055, 6057, 6060, 6061, 6062, 6063, 6064, 6065, 6068, 6069, 6071, 6073, 6076, 6078, 6082, 
      6083, 6085, 6086, 6087, 6088, 6091, 6094, 6095, 6099, 6102, 6104, 6107, 6109, 6111, 6112, 6114, 
      6115, 6120, 6124, 6125, 6126, 6128, 6129, 6130, 6132, 6133, 6135, 6136, 6138, 6140, 6144, 6145, 
      6147, 6148, 6151, 6153, 6154, 6156, 6158, 6159, 6160, 6163, 6169, 6172, 6173, 6175, 6176, 6179, 
      6181, 6182, 6187, 6188, 6192, 6194, 6198, 6199, 6202, 6203, 6205, 6206, 6207, 6210, 6211, 6214, 
      6215, 6216, 6218, 6221, 6223, 6226, 6227, 6228, 6229, 6231, 6232, 6233, 6235, 6240, 6241, 6242, 
      6243, 6247, 6248, 6251, 6253, 6254, 6256, 6258, 6259, 6261, 6265, 6266, 6268, 6270, 6271, 6272, 
      6277, 6284, 6287, 6288, 6291, 6292, 6293, 6295, 6296, 6298, 6299, 6300, 6303, 6305, 6307, 6309, 
      6316, 6317, 6318, 6319, 6320, 6324, 6325, 6326, 6330, 6334, 6338, 6339, 6344, 6350, 6351, 6352, 
      6353, 6354, 6358, 6359, 6361, 6362, 6363, 6375, 6377, 6378, 6379, 6380, 6381, 6382, 6384, 6387, 
      6388, 6389, 6391, 6393, 6394, 6395, 6396, 6397, 6398, 6399, 6401, 6402, 6407, 6409, 6410, 6412, 
      6414, 6415, 6417, 6418, 6419, 6420, 6425, 6426, 6427, 6431, 6432, 6433, 6435, 6436, 6438, 6439, 
      6440, 6441, 6444, 6445, 6446, 6447, 6449, 6452, 6453, 6454, 6459, 6461, 6462, 6463, 6464, 6466, 
      6468, 6473, 6475, 6476, 6477, 6481, 6491, 6493, 6494, 6495, 6497, 6498, 6500, 6501, 6503, 6508, 
      6509, 6511, 6513, 6516, 6518, 6520, 6522, 6524, 6527, 6528, 6529, 6532, 6534, 6535, 6536, 6537, 
      6539, 6540, 6541, 6543, 6548, 6549, 6551, 6554, 6555, 6557, 6558, 6563, 6564, 6565, 6566, 6568, 
      6575, 6576, 6578, 6579, 6580, 6583, 6586, 6590, 6594, 6595, 6598, 6600, 6601, 6602, 6603, 6604, 
      6608, 6610, 6612, 6613, 6614, 6615, 6616, 6617, 6618, 6620, 6621, 6622, 6623, 6624, 6625, 6629, 
      6630, 6633, 6637, 6638, 6640, 6648, 6649, 6652, 6653, 6655, 6656, 6657, 6659, 6662, 6663, 6664, 
      6665, 6667, 6668, 6672, 6673, 6675, 6677, 6678, 6681, 6688, 6690, 6694, 6696, 6698, 6700, 6703, 
      6709, 6711, 6712, 6714, 6717, 6721, 6724, 6725, 6726, 6727, 6728, 6729, 6730, 6731, 6732, 6733, 
      6734, 6735, 6736, 6737, 6740, 6741, 6744, 6747, 6748, 6751, 6752, 6756, 6757, 6759, 6761, 6764, 
      6765, 6767, 6769, 6773, 6775, 6777, 6779, 6781, 6788, 6793, 6797, 6800, 6801, 6804, 6805, 6806, 
      6807, 6808, 6810, 6812, 6813, 6815, 6818, 6820, 6821, 6822, 6824, 6829, 6831, 6832, 6833, 6834, 
      6835, 6839, 6841, 6845, 6847, 6848, 6849, 6850, 6851, 6853, 6855, 6857, 6858, 6860, 6861, 6866, 
      6867, 6868, 6869, 6873, 6874, 6877, 6878, 6879, 6880, 6881, 6882, 6883, 6887, 6888, 6889, 6891, 
      6893, 6895, 6896, 6899, 6900, 6901, 6904, 6906, 6908, 6909, 6910, 6911, 6914, 6915, 6917, 6919, 
      6920, 6921, 6922, 6925, 6926, 6928, 6929, 6930, 6931, 6933, 6935, 6936, 6938, 6939, 6940, 6941, 
      6944, 6946, 6948, 6949, 6955, 6956, 6958, 6960, 6962, 6964, 6966, 6967, 6969, 6974, 6975, 6977, 
      6979, 6980, 6981, 6985, 6986, 6989, 6992, 6995, 6997, 6999, 7000, 7001, 7002, 7005, 7006, 7008, 
      7012, 7013, 7014, 7015, 7018, 7019, 7020, 7021, 7022, 7023, 7025, 7027, 7028, 7030, 7032, 7033, 
      7036, 7037, 7038, 7041, 7043, 7044, 7046, 7049, 7051, 7052, 7054, 7056, 7060, 7066, 7068, 7069, 
      7070, 7071, 7076, 7077, 7078, 7079, 7082, 7084, 7086, 7088, 7089, 7090, 7094, 7096, 7097, 7101, 
      7102, 7104, 7105, 7106, 7107, 7108, 7110, 7112, 7113, 7115, 7116, 7117, 7119, 7122, 7123, 7124, 
      7126, 7127, 7131, 7132, 7134, 7136, 7137, 7140, 7142, 7144, 7145, 7146, 7147, 7149, 7150, 7151, 
      7154, 7156, 7157, 7158, 7159, 7160, 7162, 7165, 7169, 7170, 7171, 7172, 7173, 7174, 7175, 7176, 
      7178, 7181, 7182, 7183, 7184, 7186, 7187, 7188, 7189, 7190, 7191, 7192, 7193, 7195, 7196, 7197, 
      7198, 7199, 7202, 7203, 7206, 7208, 7209, 7210, 7211, 7212, 7213, 7214, 7215, 7216, 7219, 7223, 
      7224, 7225, 7226, 7227, 7229, 7231, 7232, 7235, 7236, 7239, 7241, 7244, 7248, 7252, 7253, 7255, 
      7257, 7258, 7259, 7262, 7263, 7264, 7267, 7268, 7271, 7272, 7274, 7277, 7278, 7281, 7282, 7284, 
      7285, 7286, 7293, 7294, 7295, 7297, 7298, 7299, 7301, 7302, 7303, 7304, 7305, 7307, 7308, 7309, 
      7310, 7311, 7312, 7316, 7319, 7322, 7323, 7325, 7329, 7330, 7331, 7332, 7334, 7336, 7337, 7338, 
      7339, 7340, 7341, 7343, 7346, 7349, 7350, 7351, 7352, 7355, 7356, 7357, 7358, 7359, 7360, 7361, 
      7362, 7363, 7365, 7369, 7371 ], [ 3, 11, 16, 23, 34, 35, 36, 43, 56, 68, 81, 82, 93, 95, 96, 99, 
      102, 113, 128, 132, 142, 143, 154, 161, 179, 186, 189, 206, 219, 220, 221, 234, 242, 247, 248, 
      249, 251, 280, 284, 286, 292, 297, 318, 320, 324, 332, 343, 347, 348, 376, 377, 381, 385, 386, 
      386, 390, 391, 410, 414, 426, 429, 430, 431, 432, 433, 434, 439, 439, 444, 449, 454, 456, 461, 
      484, 485, 491, 508, 509, 524, 528, 529, 545, 553, 556, 577, 580, 582, 583, 585, 590, 598, 609, 
      619, 625, 647, 651, 669, 670, 677, 700, 703, 711, 715, 720, 750, 756, 763, 770, 778, 783, 794, 
      795, 798, 799, 800, 802, 803, 804, 807, 811, 820, 821, 823, 831, 833, 836, 841, 849, 860, 870, 
      878, 898, 909, 910, 913, 940, 951, 952, 953, 978, 997, 999, 1000, 1017, 1052, 1064, 1067, 1068, 
      1076, 1080, 1085, 1090, 1107, 1112, 1116, 1132, 1143, 1144, 1148, 1158, 1163, 1171, 1172, 1184, 
      1215, 1223, 1241, 1249, 1250, 1259, 1261, 1265, 1266, 1267, 1273, 1284, 1286, 1306, 1308, 1313, 
      1316, 1320, 1321, 1324, 1347, 1364, 1368, 1403, 1406, 1412, 1414, 1415, 1417, 1423, 1426, 1429, 
      1437, 1452, 1461, 1471, 1479, 1485, 1487, 1493, 1513, 1515, 1519, 1524, 1544, 1550, 1554, 1563, 
      1567, 1573, 1577, 1578, 1588, 1602, 1615, 1616, 1623, 1630, 1640, 1645, 1646, 1647, 1652, 1674, 
      1685, 1695, 1699, 1703, 1704, 1727, 1728, 1730, 1731, 1749, 1751, 1753, 1771, 1773, 1787, 1789, 
      1790, 1791, 1796, 1800, 1813, 1835, 1836, 1866, 1871, 1872, 1883, 1886, 1890, 1893, 1900, 1914, 
      1930, 1933, 1938, 1941, 1949, 1952, 1953, 1963, 1964, 1966, 1978, 1983, 1985, 2005, 2006, 2009, 
      2014, 2021, 2039, 2042, 2051, 2054, 2060, 2067, 2070, 2077, 2078, 2078, 2079, 2084, 2089, 2096, 
      2104, 2111, 2112, 2115, 2116, 2128, 2137, 2141, 2142, 2149, 2150, 2153, 2156, 2165, 2166, 2171, 
      2176, 2185, 2187, 2191, 2202, 2205, 2206, 2208, 2212, 2217, 2220, 2223, 2226, 2228, 2229, 2232, 
      2242, 2244, 2245, 2246, 2256, 2259, 2266, 2270, 2272, 2278, 2280, 2285, 2287, 2292, 2314, 2316, 
      2367, 2378, 2390, 2395, 2397, 2403, 2406, 2407, 2410, 2418, 2419, 2424, 2425, 2433, 2435, 2455, 
      2456, 2459, 2461, 2461, 2474, 2474, 2490, 2492, 2509, 2511, 2514, 2523, 2535, 2552, 2557, 2558, 
      2564, 2573, 2582, 2588, 2591, 2609, 2616, 2620, 2621, 2626, 2628, 2630, 2632, 2633, 2634, 2656, 
      2672, 2673, 2674, 2681, 2702, 2710, 2714, 2715, 2738, 2746, 2760, 2773, 2776, 2791, 2792, 2794, 
      2807, 2814, 2826, 2833, 2836, 2844, 2862, 2879, 2885, 2888, 2889, 2890, 2892, 2896, 2905, 2917, 
      2919, 2922, 2923, 2931, 2938, 2942, 2942, 2950, 2956, 2961, 2965, 2968, 2974, 2977, 2978, 2980, 
      2993, 2994, 3004, 3005, 3008, 3009, 3024, 3034, 3036, 3042, 3043, 3058, 3065, 3067, 3073, 3078, 
      3081, 3083, 3097, 3098, 3109, 3110, 3118, 3137, 3140, 3144, 3146, 3153, 3157, 3165, 3180, 3186, 
      3189, 3194, 3195, 3199, 3203, 3209, 3213, 3216, 3231, 3244, 3248, 3252, 3261, 3265, 3266, 3267, 
      3272, 3276, 3279, 3288, 3290, 3314, 3319, 3331, 3341, 3343, 3347, 3353, 3382, 3385, 3390, 3391, 
      3396, 3402, 3414, 3423, 3431, 3443, 3449, 3452, 3466, 3472, 3477, 3489, 3500, 3510, 3528, 3535, 
      3536, 3537, 3543, 3546, 3550, 3553, 3554, 3560, 3567, 3586, 3608, 3609, 3610, 3611, 3620, 3623, 
      3624, 3625, 3628, 3646, 3655, 3657, 3661, 3665, 3666, 3672, 3678, 3688, 3690, 3692, 3694, 3695, 
      3697, 3698, 3709, 3719, 3724, 3728, 3736, 3740, 3742, 3757, 3760, 3762, 3763, 3775, 3776, 3796, 
      3811, 3833, 3839, 3845, 3845, 3848, 3859, 3867, 3868, 3878, 3882, 3892, 3893, 3913, 3928, 3930, 
      3941, 3959, 3971, 3984, 3986, 3992, 3998, 4006, 4020, 4022, 4026, 4032, 4039, 4050, 4057, 4062, 
      4065, 4069, 4090, 4092, 4093, 4106, 4113, 4117, 4118, 4119, 4126, 4131, 4132, 4137, 4140, 4144, 
      4148, 4155, 4159, 4168, 4179, 4182, 4184, 4203, 4207, 4209, 4218, 4230, 4236, 4259, 4261, 4276, 
      4287, 4288, 4294, 4295, 4297, 4315, 4321, 4323, 4327, 4329, 4332, 4354, 4355, 4359, 4362, 4363, 
      4369, 4375, 4378, 4382, 4387, 4391, 4407, 4408, 4409, 4419, 4426, 4433, 4439, 4440, 4448, 4450, 
      4452, 4457, 4458, 4463, 4465, 4478, 4480, 4484, 4490, 4495, 4496, 4502, 4503, 4509, 4519, 4528, 
      4538, 4546, 4549, 4551, 4563, 4588, 4593, 4602, 4605, 4610, 4617, 4619, 4621, 4631, 4642, 4644, 
      4645, 4659, 4666, 4670, 4678, 4684, 4686, 4695, 4702, 4718, 4722, 4723, 4728, 4737, 4743, 4749, 
      4753, 4756, 4765, 4766, 4767, 4768, 4781, 4796, 4798, 4804, 4832, 4836, 4876, 4877, 4885, 4885, 
      4887, 4890, 4892, 4893, 4915, 4922, 4936, 4939, 4942, 4944, 4948, 4956, 4958, 4965, 4970, 4971, 
      4980, 4993, 4999, 5040, 5049, 5065, 5068, 5073, 5077, 5085, 5095, 5100, 5100, 5107, 5113, 5115, 
      5137, 5138, 5145, 5151, 5161, 5167, 5169, 5180, 5182, 5183, 5185, 5188, 5199, 5199, 5209, 5218, 
      5219, 5227, 5228, 5241, 5247, 5250, 5251, 5255, 5266, 5267, 5289, 5291, 5306, 5307, 5313, 5324, 
      5329, 5330, 5341, 5344, 5353, 5357, 5366, 5385, 5398, 5411, 5414, 5426, 5429, 5449, 5456, 5473, 
      5476, 5504, 5516, 5526, 5531, 5536, 5537, 5539, 5545, 5557, 5569, 5574, 5582, 5591, 5601, 5609, 
      5615, 5622, 5625, 5630, 5660, 5664, 5673, 5680, 5699, 5701, 5705, 5719, 5720, 5722, 5738, 5750, 
      5755, 5760, 5769, 5789, 5823, 5827, 5837, 5838, 5843, 5852, 5857, 5862, 5864, 5868, 5882, 5891, 
      5895, 5901, 5902, 5906, 5912, 5918, 5925, 5937, 5950, 5954, 5963, 5967, 5974, 5982, 5992, 5994, 
      6006, 6007, 6010, 6022, 6030, 6035, 6036, 6041, 6056, 6059, 6072, 6082, 6084, 6092, 6094, 6096, 
      6109, 6112, 6122, 6138, 6149, 6160, 6169, 6176, 6180, 6187, 6190, 6196, 6201, 6204, 6211, 6218, 
      6237, 6259, 6259, 6260, 6264, 6268, 6271, 6277, 6280, 6286, 6304, 6308, 6328, 6334, 6345, 6368, 
      6370, 6372, 6375, 6380, 6400, 6405, 6421, 6444, 6445, 6450, 6455, 6458, 6460, 6470, 6482, 6484, 
      6485, 6497, 6503, 6505, 6515, 6520, 6542, 6548, 6555, 6556, 6562, 6564, 6570, 6580, 6582, 6593, 
      6612, 6627, 6640, 6657, 6658, 6661, 6668, 6669, 6696, 6699, 6711, 6719, 6734, 6737, 6741, 6748, 
      6749, 6752, 6769, 6783, 6784, 6785, 6787, 6796, 6800, 6825, 6827, 6837, 6838, 6839, 6841, 6844, 
      6845, 6862, 6867, 6872, 6881, 6885, 6892, 6902, 6907, 6907, 6910, 6913, 6916, 6925, 6930, 6950, 
      6968, 6970, 6976, 6977, 6994, 7008, 7038, 7041, 7043, 7044, 7058, 7068, 7094, 7109, 7117, 7143, 
      7145, 7149, 7162, 7166, 7169, 7172, 7175, 7176, 7179, 7180, 7189, 7195, 7196, 7199, 7201, 7209, 
      7222, 7225, 7235, 7239, 7241, 7245, 7256, 7257, 7258, 7266, 7267, 7274, 7278, 7285, 7289, 7291, 
      7332, 7340, 7342, 7344, 7345, 7350, 7353, 7354, 7360 ] ]