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Filename : gb2312freq.py
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######################## 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 #########################

# GB2312 most frequently used character table
#
# Char to FreqOrder table , from hz6763

# 512  --> 0.79  -- 0.79
# 1024 --> 0.92  -- 0.13
# 2048 --> 0.98  -- 0.06
# 6768 --> 1.00  -- 0.02
#
# Ideal Distribution Ratio = 0.79135/(1-0.79135) = 3.79
# Random Distribution Ration = 512 / (3755 - 512) = 0.157
#
# Typical Distribution Ratio about 25% of Ideal one, still much higher that RDR

GB2312_TYPICAL_DISTRIBUTION_RATIO = 0.9

GB2312_TABLE_SIZE = 3760

GB2312_CHAR_TO_FREQ_ORDER = (
1671, 749,1443,2364,3924,3807,2330,3921,1704,3463,2691,1511,1515, 572,3191,2205,
2361, 224,2558, 479,1711, 963,3162, 440,4060,1905,2966,2947,3580,2647,3961,3842,
2204, 869,4207, 970,2678,5626,2944,2956,1479,4048, 514,3595, 588,1346,2820,3409,
 249,4088,1746,1873,2047,1774, 581,1813, 358,1174,3590,1014,1561,4844,2245, 670,
1636,3112, 889,1286, 953, 556,2327,3060,1290,3141, 613, 185,3477,1367, 850,3820,
1715,2428,2642,2303,2732,3041,2562,2648,3566,3946,1349, 388,3098,2091,1360,3585,
 152,1687,1539, 738,1559,  59,1232,2925,2267,1388,1249,1741,1679,2960, 151,1566,
1125,1352,4271, 924,4296, 385,3166,4459, 310,1245,2850,  70,3285,2729,3534,3575,
2398,3298,3466,1960,2265, 217,3647, 864,1909,2084,4401,2773,1010,3269,5152, 853,
3051,3121,1244,4251,1895, 364,1499,1540,2313,1180,3655,2268, 562, 715,2417,3061,
 544, 336,3768,2380,1752,4075, 950, 280,2425,4382, 183,2759,3272, 333,4297,2155,
1688,2356,1444,1039,4540, 736,1177,3349,2443,2368,2144,2225, 565, 196,1482,3406,
 927,1335,4147, 692, 878,1311,1653,3911,3622,1378,4200,1840,2969,3149,2126,1816,
2534,1546,2393,2760, 737,2494,  13, 447, 245,2747,  38,2765,2129,2589,1079, 606,
 360, 471,3755,2890, 404, 848, 699,1785,1236, 370,2221,1023,3746,2074,2026,2023,
2388,1581,2119, 812,1141,3091,2536,1519, 804,2053, 406,1596,1090, 784, 548,4414,
1806,2264,2936,1100, 343,4114,5096, 622,3358, 743,3668,1510,1626,5020,3567,2513,
3195,4115,5627,2489,2991,  24,2065,2697,1087,2719,  48,1634, 315,  68, 985,2052,
 198,2239,1347,1107,1439, 597,2366,2172, 871,3307, 919,2487,2790,1867, 236,2570,
1413,3794, 906,3365,3381,1701,1982,1818,1524,2924,1205, 616,2586,2072,2004, 575,
 253,3099,  32,1365,1182, 197,1714,2454,1201, 554,3388,3224,2748, 756,2587, 250,
2567,1507,1517,3529,1922,2761,2337,3416,1961,1677,2452,2238,3153, 615, 911,1506,
1474,2495,1265,1906,2749,3756,3280,2161, 898,2714,1759,3450,2243,2444, 563,  26,
3286,2266,3769,3344,2707,3677, 611,1402, 531,1028,2871,4548,1375, 261,2948, 835,
1190,4134, 353, 840,2684,1900,3082,1435,2109,1207,1674, 329,1872,2781,4055,2686,
2104, 608,3318,2423,2957,2768,1108,3739,3512,3271,3985,2203,1771,3520,1418,2054,
1681,1153, 225,1627,2929, 162,2050,2511,3687,1954, 124,1859,2431,1684,3032,2894,
 585,4805,3969,2869,2704,2088,2032,2095,3656,2635,4362,2209, 256, 518,2042,2105,
3777,3657, 643,2298,1148,1779, 190, 989,3544, 414,  11,2135,2063,2979,1471, 403,
3678, 126, 770,1563, 671,2499,3216,2877, 600,1179, 307,2805,4937,1268,1297,2694,
 252,4032,1448,1494,1331,1394, 127,2256, 222,1647,1035,1481,3056,1915,1048, 873,
3651, 210,  33,1608,2516, 200,1520, 415, 102,   0,3389,1287, 817,  91,3299,2940,
 836,1814, 549,2197,1396,1669,2987,3582,2297,2848,4528,1070, 687,  20,1819, 121,
1552,1364,1461,1968,2617,3540,2824,2083, 177, 948,4938,2291, 110,4549,2066, 648,
3359,1755,2110,2114,4642,4845,1693,3937,3308,1257,1869,2123, 208,1804,3159,2992,
2531,2549,3361,2418,1350,2347,2800,2568,1291,2036,2680,  72, 842,1990, 212,1233,
1154,1586,  75,2027,3410,4900,1823,1337,2710,2676, 728,2810,1522,3026,4995, 157,
 755,1050,4022, 710, 785,1936,2194,2085,1406,2777,2400, 150,1250,4049,1206, 807,
1910, 534, 529,3309,1721,1660, 274,  39,2827, 661,2670,1578, 925,3248,3815,1094,
4278,4901,4252,  41,1150,3747,2572,2227,4501,3658,4902,3813,3357,3617,2884,2258,
 887, 538,4187,3199,1294,2439,3042,2329,2343,2497,1255, 107, 543,1527, 521,3478,
3568, 194,5062,  15, 961,3870,1241,1192,2664,  66,5215,3260,2111,1295,1127,2152,
3805,4135, 901,1164,1976, 398,1278, 530,1460, 748, 904,1054,1966,1426,  53,2909,
 509, 523,2279,1534, 536,1019, 239,1685, 460,2353, 673,1065,2401,3600,4298,2272,
1272,2363, 284,1753,3679,4064,1695,  81, 815,2677,2757,2731,1386, 859, 500,4221,
2190,2566, 757,1006,2519,2068,1166,1455, 337,2654,3203,1863,1682,1914,3025,1252,
1409,1366, 847, 714,2834,2038,3209, 964,2970,1901, 885,2553,1078,1756,3049, 301,
1572,3326, 688,2130,1996,2429,1805,1648,2930,3421,2750,3652,3088, 262,1158,1254,
 389,1641,1812, 526,1719, 923,2073,1073,1902, 468, 489,4625,1140, 857,2375,3070,
3319,2863, 380, 116,1328,2693,1161,2244, 273,1212,1884,2769,3011,1775,1142, 461,
3066,1200,2147,2212, 790, 702,2695,4222,1601,1058, 434,2338,5153,3640,  67,2360,
4099,2502, 618,3472,1329, 416,1132, 830,2782,1807,2653,3211,3510,1662, 192,2124,
 296,3979,1739,1611,3684,  23, 118, 324, 446,1239,1225, 293,2520,3814,3795,2535,
3116,  17,1074, 467,2692,2201, 387,2922,  45,1326,3055,1645,3659,2817, 958, 243,
1903,2320,1339,2825,1784,3289, 356, 576, 865,2315,2381,3377,3916,1088,3122,1713,
1655, 935, 628,4689,1034,1327, 441, 800, 720, 894,1979,2183,1528,5289,2702,1071,
4046,3572,2399,1571,3281,  79, 761,1103, 327, 134, 758,1899,1371,1615, 879, 442,
 215,2605,2579, 173,2048,2485,1057,2975,3317,1097,2253,3801,4263,1403,1650,2946,
 814,4968,3487,1548,2644,1567,1285,   2, 295,2636,  97, 946,3576, 832, 141,4257,
3273, 760,3821,3521,3156,2607, 949,1024,1733,1516,1803,1920,2125,2283,2665,3180,
1501,2064,3560,2171,1592, 803,3518,1416, 732,3897,4258,1363,1362,2458, 119,1427,
 602,1525,2608,1605,1639,3175, 694,3064,  10, 465,  76,2000,4846,4208, 444,3781,
1619,3353,2206,1273,3796, 740,2483, 320,1723,2377,3660,2619,1359,1137,1762,1724,
2345,2842,1850,1862, 912, 821,1866, 612,2625,1735,2573,3369,1093, 844,  89, 937,
 930,1424,3564,2413,2972,1004,3046,3019,2011, 711,3171,1452,4178, 428, 801,1943,
 432, 445,2811, 206,4136,1472, 730, 349,  73, 397,2802,2547, 998,1637,1167, 789,
 396,3217, 154,1218, 716,1120,1780,2819,4826,1931,3334,3762,2139,1215,2627, 552,
3664,3628,3232,1405,2383,3111,1356,2652,3577,3320,3101,1703, 640,1045,1370,1246,
4996, 371,1575,2436,1621,2210, 984,4033,1734,2638,  16,4529, 663,2755,3255,1451,
3917,2257,1253,1955,2234,1263,2951, 214,1229, 617, 485, 359,1831,1969, 473,2310,
 750,2058, 165,  80,2864,2419, 361,4344,2416,2479,1134, 796,3726,1266,2943, 860,
2715, 938, 390,2734,1313,1384, 248, 202, 877,1064,2854, 522,3907, 279,1602, 297,
2357, 395,3740, 137,2075, 944,4089,2584,1267,3802,  62,1533,2285, 178, 176, 780,
2440, 201,3707, 590, 478,1560,4354,2117,1075,  30,  74,4643,4004,1635,1441,2745,
 776,2596, 238,1077,1692,1912,2844, 605, 499,1742,3947, 241,3053, 980,1749, 936,
2640,4511,2582, 515,1543,2162,5322,2892,2993, 890,2148,1924, 665,1827,3581,1032,
 968,3163, 339,1044,1896, 270, 583,1791,1720,4367,1194,3488,3669,  43,2523,1657,
 163,2167, 290,1209,1622,3378, 550, 634,2508,2510, 695,2634,2384,2512,1476,1414,
 220,1469,2341,2138,2852,3183,2900,4939,2865,3502,1211,3680, 854,3227,1299,2976,
3172, 186,2998,1459, 443,1067,3251,1495, 321,1932,3054, 909, 753,1410,1828, 436,
2441,1119,1587,3164,2186,1258, 227, 231,1425,1890,3200,3942, 247, 959, 725,5254,
2741, 577,2158,2079, 929, 120, 174, 838,2813, 591,1115, 417,2024,  40,3240,1536,
1037, 291,4151,2354, 632,1298,2406,2500,3535,1825,1846,3451, 205,1171, 345,4238,
  18,1163, 811, 685,2208,1217, 425,1312,1508,1175,4308,2552,1033, 587,1381,3059,
2984,3482, 340,1316,4023,3972, 792,3176, 519, 777,4690, 918, 933,4130,2981,3741,
  90,3360,2911,2200,5184,4550, 609,3079,2030, 272,3379,2736, 363,3881,1130,1447,
 286, 779, 357,1169,3350,3137,1630,1220,2687,2391, 747,1277,3688,2618,2682,2601,
1156,3196,5290,4034,3102,1689,3596,3128, 874, 219,2783, 798, 508,1843,2461, 269,
1658,1776,1392,1913,2983,3287,2866,2159,2372, 829,4076,  46,4253,2873,1889,1894,
 915,1834,1631,2181,2318, 298, 664,2818,3555,2735, 954,3228,3117, 527,3511,2173,
 681,2712,3033,2247,2346,3467,1652, 155,2164,3382, 113,1994, 450, 899, 494, 994,
1237,2958,1875,2336,1926,3727, 545,1577,1550, 633,3473, 204,1305,3072,2410,1956,
2471, 707,2134, 841,2195,2196,2663,3843,1026,4940, 990,3252,4997, 368,1092, 437,
3212,3258,1933,1829, 675,2977,2893, 412, 943,3723,4644,3294,3283,2230,2373,5154,
2389,2241,2661,2323,1404,2524, 593, 787, 677,3008,1275,2059, 438,2709,2609,2240,
2269,2246,1446,  36,1568,1373,3892,1574,2301,1456,3962, 693,2276,5216,2035,1143,
2720,1919,1797,1811,2763,4137,2597,1830,1699,1488,1198,2090, 424,1694, 312,3634,
3390,4179,3335,2252,1214, 561,1059,3243,2295,2561, 975,5155,2321,2751,3772, 472,
1537,3282,3398,1047,2077,2348,2878,1323,3340,3076, 690,2906,  51, 369, 170,3541,
1060,2187,2688,3670,2541,1083,1683, 928,3918, 459, 109,4427, 599,3744,4286, 143,
2101,2730,2490,  82,1588,3036,2121, 281,1860, 477,4035,1238,2812,3020,2716,3312,
1530,2188,2055,1317, 843, 636,1808,1173,3495, 649, 181,1002, 147,3641,1159,2414,
3750,2289,2795, 813,3123,2610,1136,4368,   5,3391,4541,2174, 420, 429,1728, 754,
1228,2115,2219, 347,2223,2733, 735,1518,3003,2355,3134,1764,3948,3329,1888,2424,
1001,1234,1972,3321,3363,1672,1021,1450,1584, 226, 765, 655,2526,3404,3244,2302,
3665, 731, 594,2184, 319,1576, 621, 658,2656,4299,2099,3864,1279,2071,2598,2739,
 795,3086,3699,3908,1707,2352,2402,1382,3136,2475,1465,4847,3496,3865,1085,3004,
2591,1084, 213,2287,1963,3565,2250, 822, 793,4574,3187,1772,1789,3050, 595,1484,
1959,2770,1080,2650, 456, 422,2996, 940,3322,4328,4345,3092,2742, 965,2784, 739,
4124, 952,1358,2498,2949,2565, 332,2698,2378, 660,2260,2473,4194,3856,2919, 535,
1260,2651,1208,1428,1300,1949,1303,2942, 433,2455,2450,1251,1946, 614,1269, 641,
1306,1810,2737,3078,2912, 564,2365,1419,1415,1497,4460,2367,2185,1379,3005,1307,
3218,2175,1897,3063, 682,1157,4040,4005,1712,1160,1941,1399, 394, 402,2952,1573,
1151,2986,2404, 862, 299,2033,1489,3006, 346, 171,2886,3401,1726,2932, 168,2533,
  47,2507,1030,3735,1145,3370,1395,1318,1579,3609,4560,2857,4116,1457,2529,1965,
 504,1036,2690,2988,2405, 745,5871, 849,2397,2056,3081, 863,2359,3857,2096,  99,
1397,1769,2300,4428,1643,3455,1978,1757,3718,1440,  35,4879,3742,1296,4228,2280,
 160,5063,1599,2013, 166, 520,3479,1646,3345,3012, 490,1937,1545,1264,2182,2505,
1096,1188,1369,1436,2421,1667,2792,2460,1270,2122, 727,3167,2143, 806,1706,1012,
1800,3037, 960,2218,1882, 805, 139,2456,1139,1521, 851,1052,3093,3089, 342,2039,
 744,5097,1468,1502,1585,2087, 223, 939, 326,2140,2577, 892,2481,1623,4077, 982,
3708, 135,2131,  87,2503,3114,2326,1106, 876,1616, 547,2997,2831,2093,3441,4530,
4314,   9,3256,4229,4148, 659,1462,1986,1710,2046,2913,2231,4090,4880,5255,3392,
3274,1368,3689,4645,1477, 705,3384,3635,1068,1529,2941,1458,3782,1509, 100,1656,
2548, 718,2339, 408,1590,2780,3548,1838,4117,3719,1345,3530, 717,3442,2778,3220,
2898,1892,4590,3614,3371,2043,1998,1224,3483, 891, 635, 584,2559,3355, 733,1766,
1729,1172,3789,1891,2307, 781,2982,2271,1957,1580,5773,2633,2005,4195,3097,1535,
3213,1189,1934,5693,3262, 586,3118,1324,1598, 517,1564,2217,1868,1893,4445,3728,
2703,3139,1526,1787,1992,3882,2875,1549,1199,1056,2224,1904,2711,5098,4287, 338,
1993,3129,3489,2689,1809,2815,1997, 957,1855,3898,2550,3275,3057,1105,1319, 627,
1505,1911,1883,3526, 698,3629,3456,1833,1431, 746,  77,1261,2017,2296,1977,1885,
 125,1334,1600, 525,1798,1109,2222,1470,1945, 559,2236,1186,3443,2476,1929,1411,
2411,3135,1777,3372,2621,1841,1613,3229, 668,1430,1839,2643,2916, 195,1989,2671,
2358,1387, 629,3205,2293,5256,4439, 123,1310, 888,1879,4300,3021,3605,1003,1162,
3192,2910,2010, 140,2395,2859,  55,1082,2012,2901, 662, 419,2081,1438, 680,2774,
4654,3912,1620,1731,1625,5035,4065,2328, 512,1344, 802,5443,2163,2311,2537, 524,
3399,  98,1155,2103,1918,2606,3925,2816,1393,2465,1504,3773,2177,3963,1478,4346,
 180,1113,4655,3461,2028,1698, 833,2696,1235,1322,1594,4408,3623,3013,3225,2040,
3022, 541,2881, 607,3632,2029,1665,1219, 639,1385,1686,1099,2803,3231,1938,3188,
2858, 427, 676,2772,1168,2025, 454,3253,2486,3556, 230,1950, 580, 791,1991,1280,
1086,1974,2034, 630, 257,3338,2788,4903,1017,  86,4790, 966,2789,1995,1696,1131,
 259,3095,4188,1308, 179,1463,5257, 289,4107,1248,  42,3413,1725,2288, 896,1947,
 774,4474,4254, 604,3430,4264, 392,2514,2588, 452, 237,1408,3018, 988,4531,1970,
3034,3310, 540,2370,1562,1288,2990, 502,4765,1147,   4,1853,2708, 207, 294,2814,
4078,2902,2509, 684,  34,3105,3532,2551, 644, 709,2801,2344, 573,1727,3573,3557,
2021,1081,3100,4315,2100,3681, 199,2263,1837,2385, 146,3484,1195,2776,3949, 997,
1939,3973,1008,1091,1202,1962,1847,1149,4209,5444,1076, 493, 117,5400,2521, 972,
1490,2934,1796,4542,2374,1512,2933,2657, 413,2888,1135,2762,2314,2156,1355,2369,
 766,2007,2527,2170,3124,2491,2593,2632,4757,2437, 234,3125,3591,1898,1750,1376,
1942,3468,3138, 570,2127,2145,3276,4131, 962, 132,1445,4196,  19, 941,3624,3480,
3366,1973,1374,4461,3431,2629, 283,2415,2275, 808,2887,3620,2112,2563,1353,3610,
 955,1089,3103,1053,  96,  88,4097, 823,3808,1583, 399, 292,4091,3313, 421,1128,
 642,4006, 903,2539,1877,2082, 596,  29,4066,1790, 722,2157, 130, 995,1569, 769,
1485, 464, 513,2213, 288,1923,1101,2453,4316, 133, 486,2445,  50, 625, 487,2207,
  57, 423, 481,2962, 159,3729,1558, 491, 303, 482, 501, 240,2837, 112,3648,2392,
1783, 362,   8,3433,3422, 610,2793,3277,1390,1284,1654,  21,3823, 734, 367, 623,
 193, 287, 374,1009,1483, 816, 476, 313,2255,2340,1262,2150,2899,1146,2581, 782,
2116,1659,2018,1880, 255,3586,3314,1110,2867,2137,2564, 986,2767,5185,2006, 650,
 158, 926, 762, 881,3157,2717,2362,3587, 306,3690,3245,1542,3077,2427,1691,2478,
2118,2985,3490,2438, 539,2305, 983, 129,1754, 355,4201,2386, 827,2923, 104,1773,
2838,2771, 411,2905,3919, 376, 767, 122,1114, 828,2422,1817,3506, 266,3460,1007,
1609,4998, 945,2612,4429,2274, 726,1247,1964,2914,2199,2070,4002,4108, 657,3323,
1422, 579, 455,2764,4737,1222,2895,1670, 824,1223,1487,2525, 558, 861,3080, 598,
2659,2515,1967, 752,2583,2376,2214,4180, 977, 704,2464,4999,2622,4109,1210,2961,
 819,1541, 142,2284,  44, 418, 457,1126,3730,4347,4626,1644,1876,3671,1864, 302,
1063,5694, 624, 723,1984,3745,1314,1676,2488,1610,1449,3558,3569,2166,2098, 409,
1011,2325,3704,2306, 818,1732,1383,1824,1844,3757, 999,2705,3497,1216,1423,2683,
2426,2954,2501,2726,2229,1475,2554,5064,1971,1794,1666,2014,1343, 783, 724, 191,
2434,1354,2220,5065,1763,2752,2472,4152, 131, 175,2885,3434,  92,1466,4920,2616,
3871,3872,3866, 128,1551,1632, 669,1854,3682,4691,4125,1230, 188,2973,3290,1302,
1213, 560,3266, 917, 763,3909,3249,1760, 868,1958, 764,1782,2097, 145,2277,3774,
4462,  64,1491,3062, 971,2132,3606,2442, 221,1226,1617, 218, 323,1185,3207,3147,
 571, 619,1473,1005,1744,2281, 449,1887,2396,3685, 275, 375,3816,1743,3844,3731,
 845,1983,2350,4210,1377, 773, 967,3499,3052,3743,2725,4007,1697,1022,3943,1464,
3264,2855,2722,1952,1029,2839,2467,  84,4383,2215, 820,1391,2015,2448,3672, 377,
1948,2168, 797,2545,3536,2578,2645,  94,2874,1678, 405,1259,3071, 771, 546,1315,
 470,1243,3083, 895,2468, 981, 969,2037, 846,4181, 653,1276,2928,  14,2594, 557,
3007,2474, 156, 902,1338,1740,2574, 537,2518, 973,2282,2216,2433,1928, 138,2903,
1293,2631,1612, 646,3457, 839,2935, 111, 496,2191,2847, 589,3186, 149,3994,2060,
4031,2641,4067,3145,1870,  37,3597,2136,1025,2051,3009,3383,3549,1121,1016,3261,
1301, 251,2446,2599,2153, 872,3246, 637, 334,3705, 831, 884, 921,3065,3140,4092,
2198,1944, 246,2964, 108,2045,1152,1921,2308,1031, 203,3173,4170,1907,3890, 810,
1401,2003,1690, 506, 647,1242,2828,1761,1649,3208,2249,1589,3709,2931,5156,1708,
 498, 666,2613, 834,3817,1231, 184,2851,1124, 883,3197,2261,3710,1765,1553,2658,
1178,2639,2351,  93,1193, 942,2538,2141,4402, 235,1821, 870,1591,2192,1709,1871,
3341,1618,4126,2595,2334, 603, 651,  69, 701, 268,2662,3411,2555,1380,1606, 503,
 448, 254,2371,2646, 574,1187,2309,1770, 322,2235,1292,1801, 305, 566,1133, 229,
2067,2057, 706, 167, 483,2002,2672,3295,1820,3561,3067, 316, 378,2746,3452,1112,
 136,1981, 507,1651,2917,1117, 285,4591, 182,2580,3522,1304, 335,3303,1835,2504,
1795,1792,2248, 674,1018,2106,2449,1857,2292,2845, 976,3047,1781,2600,2727,1389,
1281,  52,3152, 153, 265,3950, 672,3485,3951,4463, 430,1183, 365, 278,2169,  27,
1407,1336,2304, 209,1340,1730,2202,1852,2403,2883, 979,1737,1062, 631,2829,2542,
3876,2592, 825,2086,2226,3048,3625, 352,1417,3724, 542, 991, 431,1351,3938,1861,
2294, 826,1361,2927,3142,3503,1738, 463,2462,2723, 582,1916,1595,2808, 400,3845,
3891,2868,3621,2254,  58,2492,1123, 910,2160,2614,1372,1603,1196,1072,3385,1700,
3267,1980, 696, 480,2430, 920, 799,1570,2920,1951,2041,4047,2540,1321,4223,2469,
3562,2228,1271,2602, 401,2833,3351,2575,5157, 907,2312,1256, 410, 263,3507,1582,
 996, 678,1849,2316,1480, 908,3545,2237, 703,2322, 667,1826,2849,1531,2604,2999,
2407,3146,2151,2630,1786,3711, 469,3542, 497,3899,2409, 858, 837,4446,3393,1274,
 786, 620,1845,2001,3311, 484, 308,3367,1204,1815,3691,2332,1532,2557,1842,2020,
2724,1927,2333,4440, 567,  22,1673,2728,4475,1987,1858,1144,1597, 101,1832,3601,
  12, 974,3783,4391, 951,1412,   1,3720, 453,4608,4041, 528,1041,1027,3230,2628,
1129, 875,1051,3291,1203,2262,1069,2860,2799,2149,2615,3278, 144,1758,3040,  31,
 475,1680, 366,2685,3184, 311,1642,4008,2466,5036,1593,1493,2809, 216,1420,1668,
 233, 304,2128,3284, 232,1429,1768,1040,2008,3407,2740,2967,2543, 242,2133, 778,
1565,2022,2620, 505,2189,2756,1098,2273, 372,1614, 708, 553,2846,2094,2278, 169,
3626,2835,4161, 228,2674,3165, 809,1454,1309, 466,1705,1095, 900,3423, 880,2667,
3751,5258,2317,3109,2571,4317,2766,1503,1342, 866,4447,1118,  63,2076, 314,1881,
1348,1061, 172, 978,3515,1747, 532, 511,3970,   6, 601, 905,2699,3300,1751, 276,
1467,3725,2668,  65,4239,2544,2779,2556,1604, 578,2451,1802, 992,2331,2624,1320,
3446, 713,1513,1013, 103,2786,2447,1661, 886,1702, 916, 654,3574,2031,1556, 751,
2178,2821,2179,1498,1538,2176, 271, 914,2251,2080,1325, 638,1953,2937,3877,2432,
2754,  95,3265,1716, 260,1227,4083, 775, 106,1357,3254, 426,1607, 555,2480, 772,
1985, 244,2546, 474, 495,1046,2611,1851,2061,  71,2089,1675,2590, 742,3758,2843,
3222,1433, 267,2180,2576,2826,2233,2092,3913,2435, 956,1745,3075, 856,2113,1116,
 451,   3,1988,2896,1398, 993,2463,1878,2049,1341,2718,2721,2870,2108, 712,2904,
4363,2753,2324, 277,2872,2349,2649, 384, 987, 435, 691,3000, 922, 164,3939, 652,
1500,1184,4153,2482,3373,2165,4848,2335,3775,3508,3154,2806,2830,1554,2102,1664,
2530,1434,2408, 893,1547,2623,3447,2832,2242,2532,3169,2856,3223,2078,  49,3770,
3469, 462, 318, 656,2259,3250,3069, 679,1629,2758, 344,1138,1104,3120,1836,1283,
3115,2154,1437,4448, 934, 759,1999, 794,2862,1038, 533,2560,1722,2342, 855,2626,
1197,1663,4476,3127,  85,4240,2528,  25,1111,1181,3673, 407,3470,4561,2679,2713,
 768,1925,2841,3986,1544,1165, 932, 373,1240,2146,1930,2673, 721,4766, 354,4333,
 391,2963, 187,  61,3364,1442,1102, 330,1940,1767, 341,3809,4118, 393,2496,2062,
2211, 105, 331, 300, 439, 913,1332, 626, 379,3304,1557, 328, 689,3952, 309,1555,
 931, 317,2517,3027, 325, 569, 686,2107,3084,  60,1042,1333,2794, 264,3177,4014,
1628, 258,3712,   7,4464,1176,1043,1778, 683, 114,1975,  78,1492, 383,1886, 510,
 386, 645,5291,2891,2069,3305,4138,3867,2939,2603,2493,1935,1066,1848,3588,1015,
1282,1289,4609, 697,1453,3044,2666,3611,1856,2412,  54, 719,1330, 568,3778,2459,
1748, 788, 492, 551,1191,1000, 488,3394,3763, 282,1799, 348,2016,1523,3155,2390,
1049, 382,2019,1788,1170, 729,2968,3523, 897,3926,2785,2938,3292, 350,2319,3238,
1718,1717,2655,3453,3143,4465, 161,2889,2980,2009,1421,  56,1908,1640,2387,2232,
1917,1874,2477,4921, 148,  83,3438, 592,4245,2882,1822,1055, 741, 115,1496,1624,
 381,1638,4592,1020, 516,3214, 458, 947,4575,1432, 211,1514,2926,1865,2142, 189,
 852,1221,1400,1486, 882,2299,4036, 351,  28,1122, 700,6479,6480,6481,6482,6483,  #last 512
)