euckrfreq.py

######################## BEGIN LICENSE BLOCK ########################
# The Original Code is Mozilla Communicator client code.
#
# The Initial Developer of the Original Code is
# Netscape Communications Corporation.
# Portions created by the Initial Developer are Copyright (C) 1998
# the Initial Developer. All Rights Reserved.
#
# Contributor(s):
#   Mark Pilgrim - port to Python
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License as published by the Free Software Foundation; either
# version 2.1 of the License, or (at your option) any later version.
# 
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
# 
# You should have received a copy of the GNU Lesser General Public
# License along with this library; if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
# 02110-1301  USA
######################### END LICENSE BLOCK #########################

# Sampling from about 20M text materials include literature and computer technology

# 128  --> 0.79
# 256  --> 0.92
# 512  --> 0.986
# 1024 --> 0.99944
# 2048 --> 0.99999
#
# Idea Distribution Ratio = 0.98653 / (1-0.98653) = 73.24
# Random Distribution Ration = 512 / (2350-512) = 0.279.
# 
# Typical Distribution Ratio  

EUCKR_TYPICAL_DISTRIBUTION_RATIO = 6.0

EUCKR_TABLE_SIZE = 2352

# Char to FreqOrder table , 
EUCKRCharToFreqOrder = ( \
  13, 130, 120,1396, 481,1719,1720, 328, 609, 212,1721, 707, 400, 299,1722,  87,
1397,1723, 104, 536,1117,1203,1724,1267, 685,1268, 508,1725,1726,1727,1728,1398,
1399,1729,1730,1731, 141, 621, 326,1057, 368,1732, 267, 488,  20,1733,1269,1734,
 945,1400,1735,  47, 904,1270,1736,1737, 773, 248,1738, 409, 313, 786, 429,1739,
 116, 987, 813,1401, 683,  75,1204, 145,1740,1741,1742,1743,  16, 847, 667, 622,
 708,1744,1745,1746, 966, 787, 304, 129,1747,  60, 820, 123, 676,1748,1749,1750,
1751, 617,1752, 626,1753,1754,1755,1756, 653,1757,1758,1759,1760,1761,1762, 856,
 344,1763,1764,1765,1766,  89, 401, 418, 806, 905, 848,1767,1768,1769, 946,1205,
 709,1770,1118,1771, 241,1772,1773,1774,1271,1775, 569,1776, 999,1777,1778,1779,
1780, 337, 751,1058,  28, 628, 254,1781, 177, 906, 270, 349, 891,1079,1782,  19,
1783, 379,1784, 315,1785, 629, 754,1402, 559,1786, 636, 203,1206,1787, 710, 567,
1788, 935, 814,1789,1790,1207, 766, 528,1791,1792,1208,1793,1794,1795,1796,1797,
1403,1798,1799, 533,1059,1404,1405,1156,1406, 936, 884,1080,1800, 351,1801,1802,
1803,1804,1805, 801,1806,1807,1808,1119,1809,1157, 714, 474,1407,1810, 298, 899,
 885,1811,1120, 802,1158,1812, 892,1813,1814,1408, 659,1815,1816,1121,1817,1818,
1819,1820,1821,1822, 319,1823, 594, 545,1824, 815, 937,1209,1825,1826, 573,1409,
1022,1827,1210,1828,1829,1830,1831,1832,1833, 556, 722, 807,1122,1060,1834, 697,
1835, 900, 557, 715,1836,1410, 540,1411, 752,1159, 294, 597,1211, 976, 803, 770,
1412,1837,1838,  39, 794,1413, 358,1839, 371, 925,1840, 453, 661, 788, 531, 723,
 544,1023,1081, 869,  91,1841, 392, 430, 790, 602,1414, 677,1082, 457,1415,1416,
1842,1843, 475, 327,1024,1417, 795, 121,1844, 733, 403,1418,1845,1846,1847, 300,
 119, 711,1212, 627,1848,1272, 207,1849,1850, 796,1213, 382,1851, 519,1852,1083,
 893,1853,1854,1855, 367, 809, 487, 671,1856, 663,1857,1858, 956, 471, 306, 857,
1859,1860,1160,1084,1861,1862,1863,1864,1865,1061,1866,1867,1868,1869,1870,1871,
 282,  96, 574,1872, 502,1085,1873,1214,1874, 907,1875,1876, 827, 977,1419,1420,
1421, 268,1877,1422,1878,1879,1880, 308,1881,   2, 537,1882,1883,1215,1884,1885,
 127, 791,1886,1273,1423,1887,  34, 336, 404, 643,1888, 571, 654, 894, 840,1889,
   0, 886,1274, 122, 575, 260, 908, 938,1890,1275, 410, 316,1891,1892, 100,1893,
1894,1123,  48,1161,1124,1025,1895, 633, 901,1276,1896,1897, 115, 816,1898, 317,
1899, 694,1900, 909, 734,1424, 572, 866,1425, 691,  85, 524,1010, 543, 394, 841,
1901,1902,1903,1026,1904,1905,1906,1907,1908,1909,  30, 451, 651, 988, 310,1910,
1911,1426, 810,1216,  93,1912,1913,1277,1217,1914, 858, 759,  45,  58, 181, 610,
 269,1915,1916, 131,1062, 551, 443,1000, 821,1427, 957, 895,1086,1917,1918, 375,
1919, 359,1920, 687,1921, 822,1922, 293,1923,1924,  40, 662, 118, 692,  29, 939,
 887, 640, 482, 174,1925,  69,1162, 728,1428, 910,1926,1278,1218,1279, 386, 870,
 217, 854,1163, 823,1927,1928,1929,1930, 834,1931,  78,1932, 859,1933,1063,1934,
1935,1936,1937, 438,1164, 208, 595,1938,1939,1940,1941,1219,1125,1942, 280, 888,
1429,1430,1220,1431,1943,1944,1945,1946,1947,1280, 150, 510,1432,1948,1949,1950,
1951,1952,1953,1954,1011,1087,1955,1433,1043,1956, 881,1957, 614, 958,1064,1065,
1221,1958, 638,1001, 860, 967, 896,1434, 989, 492, 553,1281,1165,1959,1282,1002,
1283,1222,1960,1961,1962,1963,  36, 383, 228, 753, 247, 454,1964, 876, 678,1965,
1966,1284, 126, 464, 490, 835, 136, 672, 529, 940,1088,1435, 473,1967,1968, 467,
  50, 390, 227, 587, 279, 378, 598, 792, 968, 240, 151, 160, 849, 882,1126,1285,
 639,1044, 133, 140, 288, 360, 811, 563,1027, 561, 142, 523,1969,1970,1971,   7,
 103, 296, 439, 407, 506, 634, 990,1972,1973,1974,1975, 645,1976,1977,1978,1979,
1980,1981, 236,1982,1436,1983,1984,1089, 192, 828, 618, 518,1166, 333,1127,1985,
 818,1223,1986,1987,1988,1989,1990,1991,1992,1993, 342,1128,1286, 746, 842,1994,
1995, 560, 223,1287,  98,   8, 189, 650, 978,1288,1996,1437,1997,  17, 345, 250,
 423, 277, 234, 512, 226,  97, 289,  42, 167,1998, 201,1999,2000, 843, 836, 824,
 532, 338, 783,1090, 182, 576, 436,1438,1439, 527, 500,2001, 947, 889,2002,2003,
2004,2005, 262, 600, 314, 447,2006, 547,2007, 693, 738,1129,2008,  71,1440, 745,
 619, 688,2009, 829,2010,2011, 147,2012,  33, 948,2013,2014,  74, 224,2015,  61,
 191, 918, 399, 637,2016,1028,1130, 257, 902,2017,2018,2019,2020,2021,2022,2023,
2024,2025,2026, 837,2027,2028,2029,2030, 179, 874, 591,  52, 724, 246,2031,2032,
2033,2034,1167, 969,2035,1289, 630, 605, 911,1091,1168,2036,2037,2038,1441, 912,
2039, 623,2040,2041, 253,1169,1290,2042,1442, 146, 620, 611, 577, 433,2043,1224,
 719,1170, 959, 440, 437, 534,  84, 388, 480,1131, 159, 220, 198, 679,2044,1012,
 819,1066,1443, 113,1225, 194, 318,1003,1029,2045,2046,2047,2048,1067,2049,2050,
2051,2052,2053,  59, 913, 112,2054, 632,2055, 455, 144, 739,1291,2056, 273, 681,
 499,2057, 448,2058,2059, 760,2060,2061, 970, 384, 169, 245,1132,2062,2063, 414,
1444,2064,2065,  41, 235,2066, 157, 252, 877, 568, 919, 789, 580,2067, 725,2068,
2069,1292,2070,2071,1445,2072,1446,2073,2074,  55, 588,  66,1447, 271,1092,2075,
1226,2076, 960,1013, 372,2077,2078,2079,2080,2081,1293,2082,2083,2084,2085, 850,
2086,2087,2088,2089,2090, 186,2091,1068, 180,2092,2093,2094, 109,1227, 522, 606,
2095, 867,1448,1093, 991,1171, 926, 353,1133,2096, 581,2097,2098,2099,1294,1449,
1450,2100, 596,1172,1014,1228,2101,1451,1295,1173,1229,2102,2103,1296,1134,1452,
 949,1135,2104,2105,1094,1453,1454,1455,2106,1095,2107,2108,2109,2110,2111,2112,
2113,2114,2115,2116,2117, 804,2118,2119,1230,1231, 805,1456, 405,1136,2120,2121,
2122,2123,2124, 720, 701,1297, 992,1457, 927,1004,2125,2126,2127,2128,2129,2130,
  22, 417,2131, 303,2132, 385,2133, 971, 520, 513,2134,1174,  73,1096, 231, 274,
 962,1458, 673,2135,1459,2136, 152,1137,2137,2138,2139,2140,1005,1138,1460,1139,
2141,2142,2143,2144,  11, 374, 844,2145, 154,1232,  46,1461,2146, 838, 830, 721,
1233, 106,2147,  90, 428, 462, 578, 566,1175, 352,2148,2149, 538,1234, 124,1298,
2150,1462, 761, 565,2151, 686,2152, 649,2153,  72, 173,2154, 460, 415,2155,1463,
2156,1235, 305,2157,2158,2159,2160,2161,2162, 579,2163,2164,2165,2166,2167, 747,
2168,2169,2170,2171,1464, 669,2172,2173,2174,2175,2176,1465,2177,  23, 530, 285,
2178, 335, 729,2179, 397,2180,2181,2182,1030,2183,2184, 698,2185,2186, 325,2187,
2188, 369,2189, 799,1097,1015, 348,2190,1069, 680,2191, 851,1466,2192,2193,  10,
2194, 613, 424,2195, 979, 108, 449, 589,  27, 172,  81,1031,  80, 774, 281, 350,
1032, 525, 301, 582,1176,2196, 674,1045,2197,2198,1467, 730, 762,2199,2200,2201,
2202,1468,2203, 993,2204,2205, 266,1070, 963,1140,2206,2207,2208, 664,1098, 972,
2209,2210,2211,1177,1469,1470, 871,2212,2213,2214,2215,2216,1471,2217,2218,2219,
2220,2221,2222,2223,2224,2225,2226,2227,1472,1236,2228,2229,2230,2231,2232,2233,
2234,2235,1299,2236,2237, 200,2238, 477, 373,2239,2240, 731, 825, 777,2241,2242,
2243, 521, 486, 548,2244,2245,2246,1473,1300,  53, 549, 137, 875,  76, 158,2247,
1301,1474, 469, 396,1016, 278, 712,2248, 321, 442, 503, 767, 744, 941,1237,1178,
1475,2249,  82, 178,1141,1179, 973,2250,1302,2251, 297,2252,2253, 570,2254,2255,
2256,  18, 450, 206,2257, 290, 292,1142,2258, 511, 162,  99, 346, 164, 735,2259,
1476,1477,   4, 554, 343, 798,1099,2260,1100,2261,  43, 171,1303, 139, 215,2262,
2263, 717, 775,2264,1033, 322, 216,2265, 831,2266, 149,2267,1304,2268,2269, 702,
1238, 135, 845, 347, 309,2270, 484,2271, 878, 655, 238,1006,1478,2272,  67,2273,
 295,2274,2275, 461,2276, 478, 942, 412,2277,1034,2278,2279,2280, 265,2281, 541,
2282,2283,2284,2285,2286,  70, 852,1071,2287,2288,2289,2290,  21,  56, 509, 117,
 432,2291,2292, 331, 980, 552,1101, 148, 284, 105, 393,1180,1239, 755,2293, 187,
2294,1046,1479,2295, 340,2296,  63,1047, 230,2297,2298,1305, 763,1306, 101, 800,
 808, 494,2299,2300,2301, 903,2302,  37,1072,  14,   5,2303,  79, 675,2304, 312,
2305,2306,2307,2308,2309,1480,   6,1307,2310,2311,2312,   1, 470,  35,  24, 229,
2313, 695, 210,  86, 778,  15, 784, 592, 779,  32,  77, 855, 964,2314, 259,2315,
 501, 380,2316,2317,  83, 981, 153, 689,1308,1481,1482,1483,2318,2319, 716,1484,
2320,2321,2322,2323,2324,2325,1485,2326,2327, 128,  57,  68, 261,1048, 211, 170,
1240,  31,2328,  51, 435, 742,2329,2330,2331, 635,2332, 264, 456,2333,2334,2335,
 425,2336,1486, 143, 507, 263, 943,2337, 363, 920,1487, 256,1488,1102, 243, 601,
1489,2338,2339,2340,2341,2342,2343,2344, 861,2345,2346,2347,2348,2349,2350, 395,
2351,1490,1491,  62, 535, 166, 225,2352,2353, 668, 419,1241, 138, 604, 928,2354,
1181,2355,1492,1493,2356,2357,2358,1143,2359, 696,2360, 387, 307,1309, 682, 476,
2361,2362, 332,  12, 222, 156,2363, 232,2364, 641, 276, 656, 517,1494,1495,1035,
 416, 736,1496,2365,1017, 586,2366,2367,2368,1497,2369, 242,2370,2371,2372,1498,
2373, 965, 713,2374,2375,2376,2377, 740, 982,1499, 944,1500,1007,2378,2379,1310,
1501,2380,2381,2382, 785, 329,2383,2384,1502,2385,2386,2387, 932,2388,1503,2389,
2390,2391,2392,1242,2393,2394,2395,2396,2397, 994, 950,2398,2399,2400,2401,1504,
1311,2402,2403,2404,2405,1049, 749,2406,2407, 853, 718,1144,1312,2408,1182,1505,
2409,2410, 255, 516, 479, 564, 550, 214,1506,1507,1313, 413, 239, 444, 339,1145,
1036,1508,1509,1314,1037,1510,1315,2411,1511,2412,2413,2414, 176, 703, 497, 624,
 593, 921, 302,2415, 341, 165,1103,1512,2416,1513,2417,2418,2419, 376,2420, 700,
2421,2422,2423, 258, 768,1316,2424,1183,2425, 995, 608,2426,2427,2428,2429, 221,
2430,2431,2432,2433,2434,2435,2436,2437, 195, 323, 726, 188, 897, 983,1317, 377,
 644,1050, 879,2438, 452,2439,2440,2441,2442,2443,2444, 914,2445,2446,2447,2448,
 915, 489,2449,1514,1184,2450,2451, 515,  64, 427, 495,2452, 583,2453, 483, 485,
1038, 562, 213,1515, 748, 666,2454,2455,2456,2457, 334,2458, 780, 996,1008, 705,
1243,2459,2460,2461,2462,2463, 114,2464, 493,1146, 366, 163,1516, 961,1104,2465,
 291,2466,1318,1105,2467,1517, 365,2468, 355, 951,1244,2469,1319,2470, 631,2471,
2472, 218,1320, 364, 320, 756,1518,1519,1321,1520,1322,2473,2474,2475,2476, 997,
2477,2478,2479,2480, 665,1185,2481, 916,1521,2482,2483,2484, 584, 684,2485,2486,
 797,2487,1051,1186,2488,2489,2490,1522,2491,2492, 370,2493,1039,1187,  65,2494,
 434, 205, 463,1188,2495, 125, 812, 391, 402, 826, 699, 286, 398, 155, 781, 771,
 585,2496, 590, 505,1073,2497, 599, 244, 219, 917,1018, 952, 646,1523,2498,1323,
2499,2500,  49, 984, 354, 741,2501, 625,2502,1324,2503,1019, 190, 357, 757, 491,
  95, 782, 868,2504,2505,2506,2507,2508,2509, 134,1524,1074, 422,1525, 898,2510,
 161,2511,2512,2513,2514, 769,2515,1526,2516,2517, 411,1325,2518, 472,1527,2519,
2520,2521,2522,2523,2524, 985,2525,2526,2527,2528,2529,2530, 764,2531,1245,2532,
2533,  25, 204, 311,2534, 496,2535,1052,2536,2537,2538,2539,2540,2541,2542, 199,
 704, 504, 468, 758, 657,1528, 196,  44, 839,1246, 272, 750,2543, 765, 862,2544,
2545,1326,2546, 132, 615, 933,2547, 732,2548,2549,2550,1189,1529,2551, 283,1247,
1053, 607, 929,2552,2553,2554, 930, 183, 872, 616,1040,1147,2555,1148,1020, 441,
 249,1075,2556,2557,2558, 466, 743,2559,2560,2561,  92, 514, 426, 420, 526,2562,
2563,2564,2565,2566,2567,2568, 185,2569,2570,2571,2572, 776,1530, 658,2573, 362,
2574, 361, 922,1076, 793,2575,2576,2577,2578,2579,2580,1531, 251,2581,2582,2583,
2584,1532,  54, 612, 237,1327,2585,2586, 275, 408, 647, 111,2587,1533,1106, 465,
   3, 458,   9,  38,2588, 107, 110, 890, 209,  26, 737, 498,2589,1534,2590, 431,
 202,  88,1535, 356, 287,1107, 660,1149,2591, 381,1536, 986,1150, 445,1248,1151,
 974,2592,2593, 846,2594, 446, 953, 184,1249,1250, 727,2595, 923, 193, 883,2596,
2597,2598, 102, 324, 539, 817,2599, 421,1041,2600, 832,2601,  94, 175, 197, 406,
2602, 459,2603,2604,2605,2606,2607, 330, 555,2608,2609,2610, 706,1108, 389,2611,
2612,2613,2614, 233,2615, 833, 558, 931, 954,1251,2616,2617,1537, 546,2618,2619,
1009,2620,2621,2622,1538, 690,1328,2623, 955,2624,1539,2625,2626, 772,2627,2628,
2629,2630,2631, 924, 648, 863, 603,2632,2633, 934,1540, 864, 865,2634, 642,1042,
 670,1190,2635,2636,2637,2638, 168,2639, 652, 873, 542,1054,1541,2640,2641,2642,  # 512, 256
#Everything below is of no interest for detection purpose
2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,
2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,
2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,
2691,2692,2693,2694,2695,2696,2697,2698,2699,1542, 880,2700,2701,2702,2703,2704,
2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,
2721,2722,2723,2724,2725,1543,2726,2727,2728,2729,2730,2731,2732,1544,2733,2734,
2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,
2751,2752,2753,2754,1545,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,
2766,1546,2767,1547,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,
2780,2781,2782,2783,2784,2785,2786,1548,2787,2788,2789,1109,2790,2791,2792,2793,
2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,
2810,2811,2812,1329,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,
2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,
2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,
1549,2857,2858,2859,2860,1550,2861,2862,1551,2863,2864,2865,2866,2867,2868,2869,
2870,2871,2872,2873,2874,1110,1330,2875,2876,2877,2878,2879,2880,2881,2882,2883,
2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,
2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,
2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,1331,
2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,1552,2944,2945,
2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,
2962,2963,2964,1252,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,
2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,
2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,
3009,3010,3011,3012,1553,3013,3014,3015,3016,3017,1554,3018,1332,3019,3020,3021,
3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,
3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,1555,3051,3052,
3053,1556,1557,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,
3067,1558,3068,3069,3070,3071,3072,3073,3074,3075,3076,1559,3077,3078,3079,3080,
3081,3082,3083,1253,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,
3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,1152,3109,3110,
3111,3112,3113,1560,3114,3115,3116,3117,1111,3118,3119,3120,3121,3122,3123,3124,
3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,
3141,3142,3143,3144,3145,3146,3147,3148,3149,3150,3151,3152,3153,3154,3155,3156,
3157,3158,3159,3160,3161,3162,3163,3164,3165,3166,3167,3168,3169,3170,3171,3172,
3173,3174,3175,3176,1333,3177,3178,3179,3180,3181,3182,3183,3184,3185,3186,3187,
3188,3189,1561,3190,3191,1334,3192,3193,3194,3195,3196,3197,3198,3199,3200,3201,
3202,3203,3204,3205,3206,3207,3208,3209,3210,3211,3212,3213,3214,3215,3216,3217,
3218,3219,3220,3221,3222,3223,3224,3225,3226,3227,3228,3229,3230,3231,3232,3233,
3234,1562,3235,3236,3237,3238,3239,3240,3241,3242,3243,3244,3245,3246,3247,3248,
3249,3250,3251,3252,3253,3254,3255,3256,3257,3258,3259,3260,3261,3262,3263,3264,
3265,3266,3267,3268,3269,3270,3271,3272,3273,3274,3275,3276,3277,1563,3278,3279,
3280,3281,3282,3283,3284,3285,3286,3287,3288,3289,3290,3291,3292,3293,3294,3295,
3296,3297,3298,3299,3300,3301,3302,3303,3304,3305,3306,3307,3308,3309,3310,3311,
3312,3313,3314,3315,3316,3317,3318,3319,3320,3321,3322,3323,3324,3325,3326,3327,
3328,3329,3330,3331,3332,3333,3334,3335,3336,3337,3338,3339,3340,3341,3342,3343,
3344,3345,3346,3347,3348,3349,3350,3351,3352,3353,3354,3355,3356,3357,3358,3359,
3360,3361,3362,3363,3364,1335,3365,3366,3367,3368,3369,3370,3371,3372,3373,3374,
3375,3376,3377,3378,3379,3380,3381,3382,3383,3384,3385,3386,3387,1336,3388,3389,
3390,3391,3392,3393,3394,3395,3396,3397,3398,3399,3400,3401,3402,3403,3404,3405,
3406,3407,3408,3409,3410,3411,3412,3413,3414,1337,3415,3416,3417,3418,3419,1338,
3420,3421,3422,1564,1565,3423,3424,3425,3426,3427,3428,3429,3430,3431,1254,3432,
3433,3434,1339,3435,3436,3437,3438,3439,1566,3440,3441,3442,3443,3444,3445,3446,
3447,3448,3449,3450,3451,3452,3453,3454,1255,3455,3456,3457,3458,3459,1567,1191,
3460,1568,1569,3461,3462,3463,1570,3464,3465,3466,3467,3468,1571,3469,3470,3471,
3472,3473,1572,3474,3475,3476,3477,3478,3479,3480,3481,3482,3483,3484,3485,3486,
1340,3487,3488,3489,3490,3491,3492,1021,3493,3494,3495,3496,3497,3498,1573,3499,
1341,3500,3501,3502,3503,3504,3505,3506,3507,3508,3509,3510,3511,1342,3512,3513,
3514,3515,3516,1574,1343,3517,3518,3519,1575,3520,1576,3521,3522,3523,3524,3525,
3526,3527,3528,3529,3530,3531,3532,3533,3534,3535,3536,3537,3538,3539,3540,3541,
3542,3543,3544,3545,3546,3547,3548,3549,3550,3551,3552,3553,3554,3555,3556,3557,
3558,3559,3560,3561,3562,3563,3564,3565,3566,3567,3568,3569,3570,3571,3572,3573,
3574,3575,3576,3577,3578,3579,3580,1577,3581,3582,1578,3583,3584,3585,3586,3587,
3588,3589,3590,3591,3592,3593,3594,3595,3596,3597,3598,3599,3600,3601,3602,3603,
3604,1579,3605,3606,3607,3608,3609,3610,3611,3612,3613,3614,3615,3616,3617,3618,
3619,3620,3621,3622,3623,3624,3625,3626,3627,3628,3629,1580,3630,3631,1581,3632,
3633,3634,3635,3636,3637,3638,3639,3640,3641,3642,3643,3644,3645,3646,3647,3648,
3649,3650,3651,3652,3653,3654,3655,3656,1582,3657,3658,3659,3660,3661,3662,3663,
3664,3665,3666,3667,3668,3669,3670,3671,3672,3673,3674,3675,3676,3677,3678,3679,
3680,3681,3682,3683,3684,3685,3686,3687,3688,3689,3690,3691,3692,3693,3694,3695,
3696,3697,3698,3699,3700,1192,3701,3702,3703,3704,1256,3705,3706,3707,3708,1583,
1257,3709,3710,3711,3712,3713,3714,3715,3716,1584,3717,3718,3719,3720,3721,3722,
3723,3724,3725,3726,3727,3728,3729,3730,3731,3732,3733,3734,3735,3736,3737,3738,
3739,3740,3741,3742,3743,3744,3745,1344,3746,3747,3748,3749,3750,3751,3752,3753,
3754,3755,3756,1585,3757,3758,3759,3760,3761,3762,3763,3764,3765,3766,1586,3767,
3768,3769,3770,3771,3772,3773,3774,3775,3776,3777,3778,1345,3779,3780,3781,3782,
3783,3784,3785,3786,3787,3788,3789,3790,3791,3792,3793,3794,3795,1346,1587,3796,
3797,1588,3798,3799,3800,3801,3802,3803,3804,3805,3806,1347,3807,3808,3809,3810,
3811,1589,3812,3813,3814,3815,3816,3817,3818,3819,3820,3821,1590,3822,3823,1591,
1348,3824,3825,3826,3827,3828,3829,3830,1592,3831,3832,1593,3833,3834,3835,3836,
3837,3838,3839,3840,3841,3842,3843,3844,1349,3845,3846,3847,3848,3849,3850,3851,
3852,3853,3854,3855,3856,3857,3858,1594,3859,3860,3861,3862,3863,3864,3865,3866,
3867,3868,3869,1595,3870,3871,3872,3873,1596,3874,3875,3876,3877,3878,3879,3880,
3881,3882,3883,3884,3885,3886,1597,3887,3888,3889,3890,3891,3892,3893,3894,3895,
1598,3896,3897,3898,1599,1600,3899,1350,3900,1351,3901,3902,1352,3903,3904,3905,
3906,3907,3908,3909,3910,3911,3912,3913,3914,3915,3916,3917,3918,3919,3920,3921,
3922,3923,3924,1258,3925,3926,3927,3928,3929,3930,3931,1193,3932,1601,3933,3934,
3935,3936,3937,3938,3939,3940,3941,3942,3943,1602,3944,3945,3946,3947,3948,1603,
3949,3950,3951,3952,3953,3954,3955,3956,3957,3958,3959,3960,3961,3962,3963,3964,
3965,1604,3966,3967,3968,3969,3970,3971,3972,3973,3974,3975,3976,3977,1353,3978,
3979,3980,3981,3982,3983,3984,3985,3986,3987,3988,3989,3990,3991,1354,3992,3993,
3994,3995,3996,3997,3998,3999,4000,4001,4002,4003,4004,4005,4006,4007,4008,4009,
4010,4011,4012,4013,4014,4015,4016,4017,4018,4019,4020,4021,4022,4023,1355,4024,
4025,4026,4027,4028,4029,4030,4031,4032,4033,4034,4035,4036,4037,4038,4039,4040,
1605,4041,4042,4043,4044,4045,4046,4047,4048,4049,4050,4051,4052,4053,4054,4055,
4056,4057,4058,4059,4060,1606,4061,4062,4063,4064,1607,4065,4066,4067,4068,4069,
4070,4071,4072,4073,4074,4075,4076,1194,4077,4078,1608,4079,4080,4081,4082,4083,
4084,4085,4086,4087,1609,4088,4089,4090,4091,4092,4093,4094,4095,4096,4097,4098,
4099,4100,4101,4102,4103,4104,4105,4106,4107,4108,1259,4109,4110,4111,4112,4113,
4114,4115,4116,4117,4118,4119,4120,4121,4122,4123,4124,1195,4125,4126,4127,1610,
4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,1356,4138,4139,4140,4141,4142,
4143,4144,1611,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,
4158,4159,4160,4161,4162,4163,4164,4165,4166,4167,4168,4169,4170,4171,4172,4173,
4174,4175,4176,4177,4178,4179,4180,4181,4182,4183,4184,4185,4186,4187,4188,4189,
4190,4191,4192,4193,4194,4195,4196,4197,4198,4199,4200,4201,4202,4203,4204,4205,
4206,4207,4208,4209,4210,4211,4212,4213,4214,4215,4216,4217,4218,4219,1612,4220,
4221,4222,4223,4224,4225,4226,4227,1357,4228,1613,4229,4230,4231,4232,4233,4234,
4235,4236,4237,4238,4239,4240,4241,4242,4243,1614,4244,4245,4246,4247,4248,4249,
4250,4251,4252,4253,4254,4255,4256,4257,4258,4259,4260,4261,4262,4263,4264,4265,
4266,4267,4268,4269,4270,1196,1358,4271,4272,4273,4274,4275,4276,4277,4278,4279,
4280,4281,4282,4283,4284,4285,4286,4287,1615,4288,4289,4290,4291,4292,4293,4294,
4295,4296,4297,4298,4299,4300,4301,4302,4303,4304,4305,4306,4307,4308,4309,4310,
4311,4312,4313,4314,4315,4316,4317,4318,4319,4320,4321,4322,4323,4324,4325,4326,
4327,4328,4329,4330,4331,4332,4333,4334,1616,4335,4336,4337,4338,4339,4340,4341,
4342,4343,4344,4345,4346,4347,4348,4349,4350,4351,4352,4353,4354,4355,4356,4357,
4358,4359,4360,1617,4361,4362,4363,4364,4365,1618,4366,4367,4368,4369,4370,4371,
4372,4373,4374,4375,4376,4377,4378,4379,4380,4381,4382,4383,4384,4385,4386,4387,
4388,4389,4390,4391,4392,4393,4394,4395,4396,4397,4398,4399,4400,4401,4402,4403,
4404,4405,4406,4407,4408,4409,4410,4411,4412,4413,4414,4415,4416,1619,4417,4418,
4419,4420,4421,4422,4423,4424,4425,1112,4426,4427,4428,4429,4430,1620,4431,4432,
4433,4434,4435,4436,4437,4438,4439,4440,4441,4442,1260,1261,4443,4444,4445,4446,
4447,4448,4449,4450,4451,4452,4453,4454,4455,1359,4456,4457,4458,4459,4460,4461,
4462,4463,4464,4465,1621,4466,4467,4468,4469,4470,4471,4472,4473,4474,4475,4476,
4477,4478,4479,4480,4481,4482,4483,4484,4485,4486,4487,4488,4489,1055,4490,4491,
4492,4493,4494,4495,4496,4497,4498,4499,4500,4501,4502,4503,4504,4505,4506,4507,
4508,4509,4510,4511,4512,4513,4514,4515,4516,4517,4518,1622,4519,4520,4521,1623,
4522,4523,4524,4525,4526,4527,4528,4529,4530,4531,4532,4533,4534,4535,1360,4536,
4537,4538,4539,4540,4541,4542,4543, 975,4544,4545,4546,4547,4548,4549,4550,4551,
4552,4553,4554,4555,4556,4557,4558,4559,4560,4561,4562,4563,4564,4565,4566,4567,
4568,4569,4570,4571,1624,4572,4573,4574,4575,4576,1625,4577,4578,4579,4580,4581,
4582,4583,4584,1626,4585,4586,4587,4588,4589,4590,4591,4592,4593,4594,4595,1627,
4596,4597,4598,4599,4600,4601,4602,4603,4604,4605,4606,4607,4608,4609,4610,4611,
4612,4613,4614,4615,1628,4616,4617,4618,4619,4620,4621,4622,4623,4624,4625,4626,
4627,4628,4629,4630,4631,4632,4633,4634,4635,4636,4637,4638,4639,4640,4641,4642,
4643,4644,4645,4646,4647,4648,4649,1361,4650,4651,4652,4653,4654,4655,4656,4657,
4658,4659,4660,4661,1362,4662,4663,4664,4665,4666,4667,4668,4669,4670,4671,4672,
4673,4674,4675,4676,4677,4678,4679,4680,4681,4682,1629,4683,4684,4685,4686,4687,
1630,4688,4689,4690,4691,1153,4692,4693,4694,1113,4695,4696,4697,4698,4699,4700,
4701,4702,4703,4704,4705,4706,4707,4708,4709,4710,4711,1197,4712,4713,4714,4715,
4716,4717,4718,4719,4720,4721,4722,4723,4724,4725,4726,4727,4728,4729,4730,4731,
4732,4733,4734,4735,1631,4736,1632,4737,4738,4739,4740,4741,4742,4743,4744,1633,
4745,4746,4747,4748,4749,1262,4750,4751,4752,4753,4754,1363,4755,4756,4757,4758,
4759,4760,4761,4762,4763,4764,4765,4766,4767,4768,1634,4769,4770,4771,4772,4773,
4774,4775,4776,4777,4778,1635,4779,4780,4781,4782,4783,4784,4785,4786,4787,4788,
4789,1636,4790,4791,4792,4793,4794,4795,4796,4797,4798,4799,4800,4801,4802,4803,
4804,4805,4806,1637,4807,4808,4809,1638,4810,4811,4812,4813,4814,4815,4816,4817,
4818,1639,4819,4820,4821,4822,4823,4824,4825,4826,4827,4828,4829,4830,4831,4832,
4833,1077,4834,4835,4836,4837,4838,4839,4840,4841,4842,4843,4844,4845,4846,4847,
4848,4849,4850,4851,4852,4853,4854,4855,4856,4857,4858,4859,4860,4861,4862,4863,
4864,4865,4866,4867,4868,4869,4870,4871,4872,4873,4874,4875,4876,4877,4878,4879,
4880,4881,4882,4883,1640,4884,4885,1641,4886,4887,4888,4889,4890,4891,4892,4893,
4894,4895,4896,4897,4898,4899,4900,4901,4902,4903,4904,4905,4906,4907,4908,4909,
4910,4911,1642,4912,4913,4914,1364,4915,4916,4917,4918,4919,4920,4921,4922,4923,
4924,4925,4926,4927,4928,4929,4930,4931,1643,4932,4933,4934,4935,4936,4937,4938,
4939,4940,4941,4942,4943,4944,4945,4946,4947,4948,4949,4950,4951,4952,4953,4954,
4955,4956,4957,4958,4959,4960,4961,4962,4963,4964,4965,4966,4967,4968,4969,4970,
4971,4972,4973,4974,4975,4976,4977,4978,4979,4980,1644,4981,4982,4983,4984,1645,
4985,4986,1646,4987,4988,4989,4990,4991,4992,4993,4994,4995,4996,4997,4998,4999,
5000,5001,5002,5003,5004,5005,1647,5006,1648,5007,5008,5009,5010,5011,5012,1078,
5013,5014,5015,5016,5017,5018,5019,5020,5021,5022,5023,5024,5025,5026,5027,5028,
1365,5029,5030,5031,5032,5033,5034,5035,5036,5037,5038,5039,1649,5040,5041,5042,
5043,5044,5045,1366,5046,5047,5048,5049,5050,5051,5052,5053,5054,5055,1650,5056,
5057,5058,5059,5060,5061,5062,5063,5064,5065,5066,5067,5068,5069,5070,5071,5072,
5073,5074,5075,5076,5077,1651,5078,5079,5080,5081,5082,5083,5084,5085,5086,5087,
5088,5089,5090,5091,5092,5093,5094,5095,5096,5097,5098,5099,5100,5101,5102,5103,
5104,5105,5106,5107,5108,5109,5110,1652,5111,5112,5113,5114,5115,5116,5117,5118,
1367,5119,5120,5121,5122,5123,5124,5125,5126,5127,5128,5129,1653,5130,5131,5132,
5133,5134,5135,5136,5137,5138,5139,5140,5141,5142,5143,5144,5145,5146,5147,5148,
5149,1368,5150,1654,5151,1369,5152,5153,5154,5155,5156,5157,5158,5159,5160,5161,
5162,5163,5164,5165,5166,5167,5168,5169,5170,5171,5172,5173,5174,5175,5176,5177,
5178,1370,5179,5180,5181,5182,5183,5184,5185,5186,5187,5188,5189,5190,5191,5192,
5193,5194,5195,5196,5197,5198,1655,5199,5200,5201,5202,1656,5203,5204,5205,5206,
1371,5207,1372,5208,5209,5210,5211,1373,5212,5213,1374,5214,5215,5216,5217,5218,
5219,5220,5221,5222,5223,5224,5225,5226,5227,5228,5229,5230,5231,5232,5233,5234,
5235,5236,5237,5238,5239,5240,5241,5242,5243,5244,5245,5246,5247,1657,5248,5249,
5250,5251,1658,1263,5252,5253,5254,5255,5256,1375,5257,5258,5259,5260,5261,5262,
5263,5264,5265,5266,5267,5268,5269,5270,5271,5272,5273,5274,5275,5276,5277,5278,
5279,5280,5281,5282,5283,1659,5284,5285,5286,5287,5288,5289,5290,5291,5292,5293,
5294,5295,5296,5297,5298,5299,5300,1660,5301,5302,5303,5304,5305,5306,5307,5308,
5309,5310,5311,5312,5313,5314,5315,5316,5317,5318,5319,5320,5321,1376,5322,5323,
5324,5325,5326,5327,5328,5329,5330,5331,5332,5333,1198,5334,5335,5336,5337,5338,
5339,5340,5341,5342,5343,1661,5344,5345,5346,5347,5348,5349,5350,5351,5352,5353,
5354,5355,5356,5357,5358,5359,5360,5361,5362,5363,5364,5365,5366,5367,5368,5369,
5370,5371,5372,5373,5374,5375,5376,5377,5378,5379,5380,5381,5382,5383,5384,5385,
5386,5387,5388,5389,5390,5391,5392,5393,5394,5395,5396,5397,5398,1264,5399,5400,
5401,5402,5403,5404,5405,5406,5407,5408,5409,5410,5411,5412,1662,5413,5414,5415,
5416,1663,5417,5418,5419,5420,5421,5422,5423,5424,5425,5426,5427,5428,5429,5430,
5431,5432,5433,5434,5435,5436,5437,5438,1664,5439,5440,5441,5442,5443,5444,5445,
5446,5447,5448,5449,5450,5451,5452,5453,5454,5455,5456,5457,5458,5459,5460,5461,
5462,5463,5464,5465,5466,5467,5468,5469,5470,5471,5472,5473,5474,5475,5476,5477,
5478,1154,5479,5480,5481,5482,5483,5484,5485,1665,5486,5487,5488,5489,5490,5491,
5492,5493,5494,5495,5496,5497,5498,5499,5500,5501,5502,5503,5504,5505,5506,5507,
5508,5509,5510,5511,5512,5513,5514,5515,5516,5517,5518,5519,5520,5521,5522,5523,
5524,5525,5526,5527,5528,5529,5530,5531,5532,5533,5534,5535,5536,5537,5538,5539,
5540,5541,5542,5543,5544,5545,5546,5547,5548,1377,5549,5550,5551,5552,5553,5554,
5555,5556,5557,5558,5559,5560,5561,5562,5563,5564,5565,5566,5567,5568,5569,5570,
1114,5571,5572,5573,5574,5575,5576,5577,5578,5579,5580,5581,5582,5583,5584,5585,
5586,5587,5588,5589,5590,5591,5592,1378,5593,5594,5595,5596,5597,5598,5599,5600,
5601,5602,5603,5604,5605,5606,5607,5608,5609,5610,5611,5612,5613,5614,1379,5615,
5616,5617,5618,5619,5620,5621,5622,5623,5624,5625,5626,5627,5628,5629,5630,5631,
5632,5633,5634,1380,5635,5636,5637,5638,5639,5640,5641,5642,5643,5644,5645,5646,
5647,5648,5649,1381,1056,5650,5651,5652,5653,5654,5655,5656,5657,5658,5659,5660,
1666,5661,5662,5663,5664,5665,5666,5667,5668,1667,5669,1668,5670,5671,5672,5673,
5674,5675,5676,5677,5678,1155,5679,5680,5681,5682,5683,5684,5685,5686,5687,5688,
5689,5690,5691,5692,5693,5694,5695,5696,5697,5698,1669,5699,5700,5701,5702,5703,
5704,5705,1670,5706,5707,5708,5709,5710,1671,5711,5712,5713,5714,1382,5715,5716,
5717,5718,5719,5720,5721,5722,5723,5724,5725,1672,5726,5727,1673,1674,5728,5729,
5730,5731,5732,5733,5734,5735,5736,1675,5737,5738,5739,5740,5741,5742,5743,5744,
1676,5745,5746,5747,5748,5749,5750,5751,1383,5752,5753,5754,5755,5756,5757,5758,
5759,5760,5761,5762,5763,5764,5765,5766,5767,5768,1677,5769,5770,5771,5772,5773,
1678,5774,5775,5776, 998,5777,5778,5779,5780,5781,5782,5783,5784,5785,1384,5786,
5787,5788,5789,5790,5791,5792,5793,5794,5795,5796,5797,5798,5799,5800,1679,5801,
5802,5803,1115,1116,5804,5805,5806,5807,5808,5809,5810,5811,5812,5813,5814,5815,
5816,5817,5818,5819,5820,5821,5822,5823,5824,5825,5826,5827,5828,5829,5830,5831,
5832,5833,5834,5835,5836,5837,5838,5839,5840,5841,5842,5843,5844,5845,5846,5847,
5848,5849,5850,5851,5852,5853,5854,5855,1680,5856,5857,5858,5859,5860,5861,5862,
5863,5864,1681,5865,5866,5867,1682,5868,5869,5870,5871,5872,5873,5874,5875,5876,
5877,5878,5879,1683,5880,1684,5881,5882,5883,5884,1685,5885,5886,5887,5888,5889,
5890,5891,5892,5893,5894,5895,5896,5897,5898,5899,5900,5901,5902,5903,5904,5905,
5906,5907,1686,5908,5909,5910,5911,5912,5913,5914,5915,5916,5917,5918,5919,5920,
5921,5922,5923,5924,5925,5926,5927,5928,5929,5930,5931,5932,5933,5934,5935,1687,
5936,5937,5938,5939,5940,5941,5942,5943,5944,5945,5946,5947,5948,5949,5950,5951,
5952,1688,1689,5953,1199,5954,5955,5956,5957,5958,5959,5960,5961,1690,5962,5963,
5964,5965,5966,5967,5968,5969,5970,5971,5972,5973,5974,5975,5976,5977,5978,5979,
5980,5981,1385,5982,1386,5983,5984,5985,5986,5987,5988,5989,5990,5991,5992,5993,
5994,5995,5996,5997,5998,5999,6000,6001,6002,6003,6004,6005,6006,6007,6008,6009,
6010,6011,6012,6013,6014,6015,6016,6017,6018,6019,6020,6021,6022,6023,6024,6025,
6026,6027,1265,6028,6029,1691,6030,6031,6032,6033,6034,6035,6036,6037,6038,6039,
6040,6041,6042,6043,6044,6045,6046,6047,6048,6049,6050,6051,6052,6053,6054,6055,
6056,6057,6058,6059,6060,6061,6062,6063,6064,6065,6066,6067,6068,6069,6070,6071,
6072,6073,6074,6075,6076,6077,6078,6079,6080,6081,6082,6083,6084,1692,6085,6086,
6087,6088,6089,6090,6091,6092,6093,6094,6095,6096,6097,6098,6099,6100,6101,6102,
6103,6104,6105,6106,6107,6108,6109,6110,6111,6112,6113,6114,6115,6116,6117,6118,
6119,6120,6121,6122,6123,6124,6125,6126,6127,6128,6129,6130,6131,1693,6132,6133,
6134,6135,6136,1694,6137,6138,6139,6140,6141,1695,6142,6143,6144,6145,6146,6147,
6148,6149,6150,6151,6152,6153,6154,6155,6156,6157,6158,6159,6160,6161,6162,6163,
6164,6165,6166,6167,6168,6169,6170,6171,6172,6173,6174,6175,6176,6177,6178,6179,
6180,6181,6182,6183,6184,6185,1696,6186,6187,6188,6189,6190,6191,6192,6193,6194,
6195,6196,6197,6198,6199,6200,6201,6202,6203,6204,6205,6206,6207,6208,6209,6210,
6211,6212,6213,6214,6215,6216,6217,6218,6219,1697,6220,6221,6222,6223,6224,6225,
6226,6227,6228,6229,6230,6231,6232,6233,6234,6235,6236,6237,6238,6239,6240,6241,
6242,6243,6244,6245,6246,6247,6248,6249,6250,6251,6252,6253,1698,6254,6255,6256,
6257,6258,6259,6260,6261,6262,6263,1200,6264,6265,6266,6267,6268,6269,6270,6271,  #1024
6272,6273,6274,6275,6276,6277,6278,6279,6280,6281,6282,6283,6284,6285,6286,6287,
6288,6289,6290,6291,6292,6293,6294,6295,6296,6297,6298,6299,6300,6301,6302,1699,
6303,6304,1700,6305,6306,6307,6308,6309,6310,6311,6312,6313,6314,6315,6316,6317,
6318,6319,6320,6321,6322,6323,6324,6325,6326,6327,6328,6329,6330,6331,6332,6333,
6334,6335,6336,6337,6338,6339,1701,6340,6341,6342,6343,6344,1387,6345,6346,6347,
6348,6349,6350,6351,6352,6353,6354,6355,6356,6357,6358,6359,6360,6361,6362,6363,
6364,6365,6366,6367,6368,6369,6370,6371,6372,6373,6374,6375,6376,6377,6378,6379,
6380,6381,6382,6383,6384,6385,6386,6387,6388,6389,6390,6391,6392,6393,6394,6395,
6396,6397,6398,6399,6400,6401,6402,6403,6404,6405,6406,6407,6408,6409,6410,6411,
6412,6413,1702,6414,6415,6416,6417,6418,6419,6420,6421,6422,1703,6423,6424,6425,
6426,6427,6428,6429,6430,6431,6432,6433,6434,6435,6436,6437,6438,1704,6439,6440,
6441,6442,6443,6444,6445,6446,6447,6448,6449,6450,6451,6452,6453,6454,6455,6456,
6457,6458,6459,6460,6461,6462,6463,6464,6465,6466,6467,6468,6469,6470,6471,6472,
6473,6474,6475,6476,6477,6478,6479,6480,6481,6482,6483,6484,6485,6486,6487,6488,
6489,6490,6491,6492,6493,6494,6495,6496,6497,6498,6499,6500,6501,6502,6503,1266,
6504,6505,6506,6507,6508,6509,6510,6511,6512,6513,6514,6515,6516,6517,6518,6519,
6520,6521,6522,6523,6524,6525,6526,6527,6528,6529,6530,6531,6532,6533,6534,6535,
6536,6537,6538,6539,6540,6541,6542,6543,6544,6545,6546,6547,6548,6549,6550,6551,
1705,1706,6552,6553,6554,6555,6556,6557,6558,6559,6560,6561,6562,6563,6564,6565,
6566,6567,6568,6569,6570,6571,6572,6573,6574,6575,6576,6577,6578,6579,6580,6581,
6582,6583,6584,6585,6586,6587,6588,6589,6590,6591,6592,6593,6594,6595,6596,6597,
6598,6599,6600,6601,6602,6603,6604,6605,6606,6607,6608,6609,6610,6611,6612,6613,
6614,6615,6616,6617,6618,6619,6620,6621,6622,6623,6624,6625,6626,6627,6628,6629,
6630,6631,6632,6633,6634,6635,6636,6637,1388,6638,6639,6640,6641,6642,6643,6644,
1707,6645,6646,6647,6648,6649,6650,6651,6652,6653,6654,6655,6656,6657,6658,6659,
6660,6661,6662,6663,1708,6664,6665,6666,6667,6668,6669,6670,6671,6672,6673,6674,
1201,6675,6676,6677,6678,6679,6680,6681,6682,6683,6684,6685,6686,6687,6688,6689,
6690,6691,6692,6693,6694,6695,6696,6697,6698,6699,6700,6701,6702,6703,6704,6705,
6706,6707,6708,6709,6710,6711,6712,6713,6714,6715,6716,6717,6718,6719,6720,6721,
6722,6723,6724,6725,1389,6726,6727,6728,6729,6730,6731,6732,6733,6734,6735,6736,
1390,1709,6737,6738,6739,6740,6741,6742,1710,6743,6744,6745,6746,1391,6747,6748,
6749,6750,6751,6752,6753,6754,6755,6756,6757,1392,6758,6759,6760,6761,6762,6763,
6764,6765,6766,6767,6768,6769,6770,6771,6772,6773,6774,6775,6776,6777,6778,6779,
6780,1202,6781,6782,6783,6784,6785,6786,6787,6788,6789,6790,6791,6792,6793,6794,
6795,6796,6797,6798,6799,6800,6801,6802,6803,6804,6805,6806,6807,6808,6809,1711,
6810,6811,6812,6813,6814,6815,6816,6817,6818,6819,6820,6821,6822,6823,6824,6825,
6826,6827,6828,6829,6830,6831,6832,6833,6834,6835,6836,1393,6837,6838,6839,6840,
6841,6842,6843,6844,6845,6846,6847,6848,6849,6850,6851,6852,6853,6854,6855,6856,
6857,6858,6859,6860,6861,6862,6863,6864,6865,6866,6867,6868,6869,6870,6871,6872,
6873,6874,6875,6876,6877,6878,6879,6880,6881,6882,6883,6884,6885,6886,6887,6888,
6889,6890,6891,6892,6893,6894,6895,6896,6897,6898,6899,6900,6901,6902,1712,6903,
6904,6905,6906,6907,6908,6909,6910,1713,6911,6912,6913,6914,6915,6916,6917,6918,
6919,6920,6921,6922,6923,6924,6925,6926,6927,6928,6929,6930,6931,6932,6933,6934,
6935,6936,6937,6938,6939,6940,6941,6942,6943,6944,6945,6946,6947,6948,6949,6950,
6951,6952,6953,6954,6955,6956,6957,6958,6959,6960,6961,6962,6963,6964,6965,6966,
6967,6968,6969,6970,6971,6972,6973,6974,1714,6975,6976,6977,6978,6979,6980,6981,
6982,6983,6984,6985,6986,6987,6988,1394,6989,6990,6991,6992,6993,6994,6995,6996,
6997,6998,6999,7000,1715,7001,7002,7003,7004,7005,7006,7007,7008,7009,7010,7011,
7012,7013,7014,7015,7016,7017,7018,7019,7020,7021,7022,7023,7024,7025,7026,7027,
7028,1716,7029,7030,7031,7032,7033,7034,7035,7036,7037,7038,7039,7040,7041,7042,
7043,7044,7045,7046,7047,7048,7049,7050,7051,7052,7053,7054,7055,7056,7057,7058,
7059,7060,7061,7062,7063,7064,7065,7066,7067,7068,7069,7070,7071,7072,7073,7074,
7075,7076,7077,7078,7079,7080,7081,7082,7083,7084,7085,7086,7087,7088,7089,7090,
7091,7092,7093,7094,7095,7096,7097,7098,7099,7100,7101,7102,7103,7104,7105,7106,
7107,7108,7109,7110,7111,7112,7113,7114,7115,7116,7117,7118,7119,7120,7121,7122,
7123,7124,7125,7126,7127,7128,7129,7130,7131,7132,7133,7134,7135,7136,7137,7138,
7139,7140,7141,7142,7143,7144,7145,7146,7147,7148,7149,7150,7151,7152,7153,7154,
7155,7156,7157,7158,7159,7160,7161,7162,7163,7164,7165,7166,7167,7168,7169,7170,
7171,7172,7173,7174,7175,7176,7177,7178,7179,7180,7181,7182,7183,7184,7185,7186,
7187,7188,7189,7190,7191,7192,7193,7194,7195,7196,7197,7198,7199,7200,7201,7202,
7203,7204,7205,7206,7207,1395,7208,7209,7210,7211,7212,7213,1717,7214,7215,7216,
7217,7218,7219,7220,7221,7222,7223,7224,7225,7226,7227,7228,7229,7230,7231,7232,
7233,7234,7235,7236,7237,7238,7239,7240,7241,7242,7243,7244,7245,7246,7247,7248,
7249,7250,7251,7252,7253,7254,7255,7256,7257,7258,7259,7260,7261,7262,7263,7264,
7265,7266,7267,7268,7269,7270,7271,7272,7273,7274,7275,7276,7277,7278,7279,7280,
7281,7282,7283,7284,7285,7286,7287,7288,7289,7290,7291,7292,7293,7294,7295,7296,
7297,7298,7299,7300,7301,7302,7303,7304,7305,7306,7307,7308,7309,7310,7311,7312,
7313,1718,7314,7315,7316,7317,7318,7319,7320,7321,7322,7323,7324,7325,7326,7327,
7328,7329,7330,7331,7332,7333,7334,7335,7336,7337,7338,7339,7340,7341,7342,7343,
7344,7345,7346,7347,7348,7349,7350,7351,7352,7353,7354,7355,7356,7357,7358,7359,
7360,7361,7362,7363,7364,7365,7366,7367,7368,7369,7370,7371,7372,7373,7374,7375,
7376,7377,7378,7379,7380,7381,7382,7383,7384,7385,7386,7387,7388,7389,7390,7391,
7392,7393,7394,7395,7396,7397,7398,7399,7400,7401,7402,7403,7404,7405,7406,7407,
7408,7409,7410,7411,7412,7413,7414,7415,7416,7417,7418,7419,7420,7421,7422,7423,
7424,7425,7426,7427,7428,7429,7430,7431,7432,7433,7434,7435,7436,7437,7438,7439,
7440,7441,7442,7443,7444,7445,7446,7447,7448,7449,7450,7451,7452,7453,7454,7455,
7456,7457,7458,7459,7460,7461,7462,7463,7464,7465,7466,7467,7468,7469,7470,7471,
7472,7473,7474,7475,7476,7477,7478,7479,7480,7481,7482,7483,7484,7485,7486,7487,
7488,7489,7490,7491,7492,7493,7494,7495,7496,7497,7498,7499,7500,7501,7502,7503,
7504,7505,7506,7507,7508,7509,7510,7511,7512,7513,7514,7515,7516,7517,7518,7519,
7520,7521,7522,7523,7524,7525,7526,7527,7528,7529,7530,7531,7532,7533,7534,7535,
7536,7537,7538,7539,7540,7541,7542,7543,7544,7545,7546,7547,7548,7549,7550,7551,
7552,7553,7554,7555,7556,7557,7558,7559,7560,7561,7562,7563,7564,7565,7566,7567,
7568,7569,7570,7571,7572,7573,7574,7575,7576,7577,7578,7579,7580,7581,7582,7583,
7584,7585,7586,7587,7588,7589,7590,7591,7592,7593,7594,7595,7596,7597,7598,7599,
7600,7601,7602,7603,7604,7605,7606,7607,7608,7609,7610,7611,7612,7613,7614,7615,
7616,7617,7618,7619,7620,7621,7622,7623,7624,7625,7626,7627,7628,7629,7630,7631,
7632,7633,7634,7635,7636,7637,7638,7639,7640,7641,7642,7643,7644,7645,7646,7647,
7648,7649,7650,7651,7652,7653,7654,7655,7656,7657,7658,7659,7660,7661,7662,7663,
7664,7665,7666,7667,7668,7669,7670,7671,7672,7673,7674,7675,7676,7677,7678,7679,
7680,7681,7682,7683,7684,7685,7686,7687,7688,7689,7690,7691,7692,7693,7694,7695,
7696,7697,7698,7699,7700,7701,7702,7703,7704,7705,7706,7707,7708,7709,7710,7711,
7712,7713,7714,7715,7716,7717,7718,7719,7720,7721,7722,7723,7724,7725,7726,7727,
7728,7729,7730,7731,7732,7733,7734,7735,7736,7737,7738,7739,7740,7741,7742,7743,
7744,7745,7746,7747,7748,7749,7750,7751,7752,7753,7754,7755,7756,7757,7758,7759,
7760,7761,7762,7763,7764,7765,7766,7767,7768,7769,7770,7771,7772,7773,7774,7775,
7776,7777,7778,7779,7780,7781,7782,7783,7784,7785,7786,7787,7788,7789,7790,7791,
7792,7793,7794,7795,7796,7797,7798,7799,7800,7801,7802,7803,7804,7805,7806,7807,
7808,7809,7810,7811,7812,7813,7814,7815,7816,7817,7818,7819,7820,7821,7822,7823,
7824,7825,7826,7827,7828,7829,7830,7831,7832,7833,7834,7835,7836,7837,7838,7839,
7840,7841,7842,7843,7844,7845,7846,7847,7848,7849,7850,7851,7852,7853,7854,7855,
7856,7857,7858,7859,7860,7861,7862,7863,7864,7865,7866,7867,7868,7869,7870,7871,
7872,7873,7874,7875,7876,7877,7878,7879,7880,7881,7882,7883,7884,7885,7886,7887,
7888,7889,7890,7891,7892,7893,7894,7895,7896,7897,7898,7899,7900,7901,7902,7903,
7904,7905,7906,7907,7908,7909,7910,7911,7912,7913,7914,7915,7916,7917,7918,7919,
7920,7921,7922,7923,7924,7925,7926,7927,7928,7929,7930,7931,7932,7933,7934,7935,
7936,7937,7938,7939,7940,7941,7942,7943,7944,7945,7946,7947,7948,7949,7950,7951,
7952,7953,7954,7955,7956,7957,7958,7959,7960,7961,7962,7963,7964,7965,7966,7967,
7968,7969,7970,7971,7972,7973,7974,7975,7976,7977,7978,7979,7980,7981,7982,7983,
7984,7985,7986,7987,7988,7989,7990,7991,7992,7993,7994,7995,7996,7997,7998,7999,
8000,8001,8002,8003,8004,8005,8006,8007,8008,8009,8010,8011,8012,8013,8014,8015,
8016,8017,8018,8019,8020,8021,8022,8023,8024,8025,8026,8027,8028,8029,8030,8031,
8032,8033,8034,8035,8036,8037,8038,8039,8040,8041,8042,8043,8044,8045,8046,8047,
8048,8049,8050,8051,8052,8053,8054,8055,8056,8057,8058,8059,8060,8061,8062,8063,
8064,8065,8066,8067,8068,8069,8070,8071,8072,8073,8074,8075,8076,8077,8078,8079,
8080,8081,8082,8083,8084,8085,8086,8087,8088,8089,8090,8091,8092,8093,8094,8095,
8096,8097,8098,8099,8100,8101,8102,8103,8104,8105,8106,8107,8108,8109,8110,8111,
8112,8113,8114,8115,8116,8117,8118,8119,8120,8121,8122,8123,8124,8125,8126,8127,
8128,8129,8130,8131,8132,8133,8134,8135,8136,8137,8138,8139,8140,8141,8142,8143,
8144,8145,8146,8147,8148,8149,8150,8151,8152,8153,8154,8155,8156,8157,8158,8159,
8160,8161,8162,8163,8164,8165,8166,8167,8168,8169,8170,8171,8172,8173,8174,8175,
8176,8177,8178,8179,8180,8181,8182,8183,8184,8185,8186,8187,8188,8189,8190,8191,
8192,8193,8194,8195,8196,8197,8198,8199,8200,8201,8202,8203,8204,8205,8206,8207,
8208,8209,8210,8211,8212,8213,8214,8215,8216,8217,8218,8219,8220,8221,8222,8223,
8224,8225,8226,8227,8228,8229,8230,8231,8232,8233,8234,8235,8236,8237,8238,8239,
8240,8241,8242,8243,8244,8245,8246,8247,8248,8249,8250,8251,8252,8253,8254,8255,
8256,8257,8258,8259,8260,8261,8262,8263,8264,8265,8266,8267,8268,8269,8270,8271,
8272,8273,8274,8275,8276,8277,8278,8279,8280,8281,8282,8283,8284,8285,8286,8287,
8288,8289,8290,8291,8292,8293,8294,8295,8296,8297,8298,8299,8300,8301,8302,8303,
8304,8305,8306,8307,8308,8309,8310,8311,8312,8313,8314,8315,8316,8317,8318,8319,
8320,8321,8322,8323,8324,8325,8326,8327,8328,8329,8330,8331,8332,8333,8334,8335,
8336,8337,8338,8339,8340,8341,8342,8343,8344,8345,8346,8347,8348,8349,8350,8351,
8352,8353,8354,8355,8356,8357,8358,8359,8360,8361,8362,8363,8364,8365,8366,8367,
8368,8369,8370,8371,8372,8373,8374,8375,8376,8377,8378,8379,8380,8381,8382,8383,
8384,8385,8386,8387,8388,8389,8390,8391,8392,8393,8394,8395,8396,8397,8398,8399,
8400,8401,8402,8403,8404,8405,8406,8407,8408,8409,8410,8411,8412,8413,8414,8415,
8416,8417,8418,8419,8420,8421,8422,8423,8424,8425,8426,8427,8428,8429,8430,8431,
8432,8433,8434,8435,8436,8437,8438,8439,8440,8441,8442,8443,8444,8445,8446,8447,
8448,8449,8450,8451,8452,8453,8454,8455,8456,8457,8458,8459,8460,8461,8462,8463,
8464,8465,8466,8467,8468,8469,8470,8471,8472,8473,8474,8475,8476,8477,8478,8479,
8480,8481,8482,8483,8484,8485,8486,8487,8488,8489,8490,8491,8492,8493,8494,8495,
8496,8497,8498,8499,8500,8501,8502,8503,8504,8505,8506,8507,8508,8509,8510,8511,
8512,8513,8514,8515,8516,8517,8518,8519,8520,8521,8522,8523,8524,8525,8526,8527,
8528,8529,8530,8531,8532,8533,8534,8535,8536,8537,8538,8539,8540,8541,8542,8543,
8544,8545,8546,8547,8548,8549,8550,8551,8552,8553,8554,8555,8556,8557,8558,8559,
8560,8561,8562,8563,8564,8565,8566,8567,8568,8569,8570,8571,8572,8573,8574,8575,
8576,8577,8578,8579,8580,8581,8582,8583,8584,8585,8586,8587,8588,8589,8590,8591,
8592,8593,8594,8595,8596,8597,8598,8599,8600,8601,8602,8603,8604,8605,8606,8607,
8608,8609,8610,8611,8612,8613,8614,8615,8616,8617,8618,8619,8620,8621,8622,8623,
8624,8625,8626,8627,8628,8629,8630,8631,8632,8633,8634,8635,8636,8637,8638,8639,
8640,8641,8642,8643,8644,8645,8646,8647,8648,8649,8650,8651,8652,8653,8654,8655,
8656,8657,8658,8659,8660,8661,8662,8663,8664,8665,8666,8667,8668,8669,8670,8671,
8672,8673,8674,8675,8676,8677,8678,8679,8680,8681,8682,8683,8684,8685,8686,8687,
8688,8689,8690,8691,8692,8693,8694,8695,8696,8697,8698,8699,8700,8701,8702,8703,
8704,8705,8706,8707,8708,8709,8710,8711,8712,8713,8714,8715,8716,8717,8718,8719,
8720,8721,8722,8723,8724,8725,8726,8727,8728,8729,8730,8731,8732,8733,8734,8735,
8736,8737,8738,8739,8740,8741)