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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 #########################

# Sampling from about 20M text materials include literature and computer technology
#
# Japanese frequency table, applied to both S-JIS and EUC-JP
# They are sorted in order.

# 128  --> 0.77094
# 256  --> 0.85710
# 512  --> 0.92635
# 1024 --> 0.97130
# 2048 --> 0.99431
#
# Ideal Distribution Ratio = 0.92635 / (1-0.92635) = 12.58
# Random Distribution Ration = 512 / (2965+62+83+86-512) = 0.191
#
# Typical Distribution Ratio, 25% of IDR

JIS_TYPICAL_DISTRIBUTION_RATIO = 3.0

# Char to FreqOrder table ,
JIS_TABLE_SIZE = 4368

# fmt: off
JIS_CHAR_TO_FREQ_ORDER = (
  40,   1,   6, 182, 152, 180, 295,2127, 285, 381,3295,4304,3068,4606,3165,3510, #   16
3511,1822,2785,4607,1193,2226,5070,4608, 171,2996,1247,  18, 179,5071, 856,1661, #   32
1262,5072, 619, 127,3431,3512,3230,1899,1700, 232, 228,1294,1298, 284, 283,2041, #   48
2042,1061,1062,  48,  49,  44,  45, 433, 434,1040,1041, 996, 787,2997,1255,4305, #   64
2108,4609,1684,1648,5073,5074,5075,5076,5077,5078,3687,5079,4610,5080,3927,3928, #   80
5081,3296,3432, 290,2285,1471,2187,5082,2580,2825,1303,2140,1739,1445,2691,3375, #   96
1691,3297,4306,4307,4611, 452,3376,1182,2713,3688,3069,4308,5083,5084,5085,5086, #  112
5087,5088,5089,5090,5091,5092,5093,5094,5095,5096,5097,5098,5099,5100,5101,5102, #  128
5103,5104,5105,5106,5107,5108,5109,5110,5111,5112,4097,5113,5114,5115,5116,5117, #  144
5118,5119,5120,5121,5122,5123,5124,5125,5126,5127,5128,5129,5130,5131,5132,5133, #  160
5134,5135,5136,5137,5138,5139,5140,5141,5142,5143,5144,5145,5146,5147,5148,5149, #  176
5150,5151,5152,4612,5153,5154,5155,5156,5157,5158,5159,5160,5161,5162,5163,5164, #  192
5165,5166,5167,5168,5169,5170,5171,5172,5173,5174,5175,1472, 598, 618, 820,1205, #  208
1309,1412,1858,1307,1692,5176,5177,5178,5179,5180,5181,5182,1142,1452,1234,1172, #  224
1875,2043,2149,1793,1382,2973, 925,2404,1067,1241, 960,1377,2935,1491, 919,1217, #  240
1865,2030,1406,1499,2749,4098,5183,5184,5185,5186,5187,5188,2561,4099,3117,1804, #  256
2049,3689,4309,3513,1663,5189,3166,3118,3298,1587,1561,3433,5190,3119,1625,2998, #  272
3299,4613,1766,3690,2786,4614,5191,5192,5193,5194,2161,  26,3377,   2,3929,  20, #  288
3691,  47,4100,  50,  17,  16,  35, 268,  27, 243,  42, 155,  24, 154,  29, 184, #  304
   4,  91,  14,  92,  53, 396,  33, 289,   9,  37,  64, 620,  21,  39, 321,   5, #  320
  12,  11,  52,  13,   3, 208, 138,   0,   7,  60, 526, 141, 151,1069, 181, 275, #  336
1591,  83, 132,1475, 126, 331, 829,  15,  69, 160,  59,  22, 157,  55,1079, 312, #  352
 109,  38,  23,  25,  10,  19,  79,5195,  61, 382,1124,   8,  30,5196,5197,5198, #  368
5199,5200,5201,5202,5203,5204,5205,5206,  89,  62,  74,  34,2416, 112, 139, 196, #  384
 271, 149,  84, 607, 131, 765,  46,  88, 153, 683,  76, 874, 101, 258,  57,  80, #  400
  32, 364, 121,1508, 169,1547,  68, 235, 145,2999,  41, 360,3027,  70,  63,  31, #  416
  43, 259, 262,1383,  99, 533, 194,  66,  93, 846, 217, 192,  56, 106,  58, 565, #  432
 280, 272, 311, 256, 146,  82, 308,  71, 100, 128, 214, 655, 110, 261, 104,1140, #  448
  54,  51,  36,  87,  67,3070, 185,2618,2936,2020,  28,1066,2390,2059,5207,5208, #  464
5209,5210,5211,5212,5213,5214,5215,5216,4615,5217,5218,5219,5220,5221,5222,5223, #  480
5224,5225,5226,5227,5228,5229,5230,5231,5232,5233,5234,5235,5236,3514,5237,5238, #  496
5239,5240,5241,5242,5243,5244,2297,2031,4616,4310,3692,5245,3071,5246,3598,5247, #  512
4617,3231,3515,5248,4101,4311,4618,3808,4312,4102,5249,4103,4104,3599,5250,5251, #  528
5252,5253,5254,5255,5256,5257,5258,5259,5260,5261,5262,5263,5264,5265,5266,5267, #  544
5268,5269,5270,5271,5272,5273,5274,5275,5276,5277,5278,5279,5280,5281,5282,5283, #  560
5284,5285,5286,5287,5288,5289,5290,5291,5292,5293,5294,5295,5296,5297,5298,5299, #  576
5300,5301,5302,5303,5304,5305,5306,5307,5308,5309,5310,5311,5312,5313,5314,5315, #  592
5316,5317,5318,5319,5320,5321,5322,5323,5324,5325,5326,5327,5328,5329,5330,5331, #  608
5332,5333,5334,5335,5336,5337,5338,5339,5340,5341,5342,5343,5344,5345,5346,5347, #  624
5348,5349,5350,5351,5352,5353,5354,5355,5356,5357,5358,5359,5360,5361,5362,5363, #  640
5364,5365,5366,5367,5368,5369,5370,5371,5372,5373,5374,5375,5376,5377,5378,5379, #  656
5380,5381, 363, 642,2787,2878,2788,2789,2316,3232,2317,3434,2011, 165,1942,3930, #  672
3931,3932,3933,5382,4619,5383,4620,5384,5385,5386,5387,5388,5389,5390,5391,5392, #  688
5393,5394,5395,5396,5397,5398,5399,5400,5401,5402,5403,5404,5405,5406,5407,5408, #  704
5409,5410,5411,5412,5413,5414,5415,5416,5417,5418,5419,5420,5421,5422,5423,5424, #  720
5425,5426,5427,5428,5429,5430,5431,5432,5433,5434,5435,5436,5437,5438,5439,5440, #  736
5441,5442,5443,5444,5445,5446,5447,5448,5449,5450,5451,5452,5453,5454,5455,5456, #  752
5457,5458,5459,5460,5461,5462,5463,5464,5465,5466,5467,5468,5469,5470,5471,5472, #  768
5473,5474,5475,5476,5477,5478,5479,5480,5481,5482,5483,5484,5485,5486,5487,5488, #  784
5489,5490,5491,5492,5493,5494,5495,5496,5497,5498,5499,5500,5501,5502,5503,5504, #  800
5505,5506,5507,5508,5509,5510,5511,5512,5513,5514,5515,5516,5517,5518,5519,5520, #  816
5521,5522,5523,5524,5525,5526,5527,5528,5529,5530,5531,5532,5533,5534,5535,5536, #  832
5537,5538,5539,5540,5541,5542,5543,5544,5545,5546,5547,5548,5549,5550,5551,5552, #  848
5553,5554,5555,5556,5557,5558,5559,5560,5561,5562,5563,5564,5565,5566,5567,5568, #  864
5569,5570,5571,5572,5573,5574,5575,5576,5577,5578,5579,5580,5581,5582,5583,5584, #  880
5585,5586,5587,5588,5589,5590,5591,5592,5593,5594,5595,5596,5597,5598,5599,5600, #  896
5601,5602,5603,5604,5605,5606,5607,5608,5609,5610,5611,5612,5613,5614,5615,5616, #  912
5617,5618,5619,5620,5621,5622,5623,5624,5625,5626,5627,5628,5629,5630,5631,5632, #  928
5633,5634,5635,5636,5637,5638,5639,5640,5641,5642,5643,5644,5645,5646,5647,5648, #  944
5649,5650,5651,5652,5653,5654,5655,5656,5657,5658,5659,5660,5661,5662,5663,5664, #  960
5665,5666,5667,5668,5669,5670,5671,5672,5673,5674,5675,5676,5677,5678,5679,5680, #  976
5681,5682,5683,5684,5685,5686,5687,5688,5689,5690,5691,5692,5693,5694,5695,5696, #  992
5697,5698,5699,5700,5701,5702,5703,5704,5705,5706,5707,5708,5709,5710,5711,5712, # 1008
5713,5714,5715,5716,5717,5718,5719,5720,5721,5722,5723,5724,5725,5726,5727,5728, # 1024
5729,5730,5731,5732,5733,5734,5735,5736,5737,5738,5739,5740,5741,5742,5743,5744, # 1040
5745,5746,5747,5748,5749,5750,5751,5752,5753,5754,5755,5756,5757,5758,5759,5760, # 1056
5761,5762,5763,5764,5765,5766,5767,5768,5769,5770,5771,5772,5773,5774,5775,5776, # 1072
5777,5778,5779,5780,5781,5782,5783,5784,5785,5786,5787,5788,5789,5790,5791,5792, # 1088
5793,5794,5795,5796,5797,5798,5799,5800,5801,5802,5803,5804,5805,5806,5807,5808, # 1104
5809,5810,5811,5812,5813,5814,5815,5816,5817,5818,5819,5820,5821,5822,5823,5824, # 1120
5825,5826,5827,5828,5829,5830,5831,5832,5833,5834,5835,5836,5837,5838,5839,5840, # 1136
5841,5842,5843,5844,5845,5846,5847,5848,5849,5850,5851,5852,5853,5854,5855,5856, # 1152
5857,5858,5859,5860,5861,5862,5863,5864,5865,5866,5867,5868,5869,5870,5871,5872, # 1168
5873,5874,5875,5876,5877,5878,5879,5880,5881,5882,5883,5884,5885,5886,5887,5888, # 1184
5889,5890,5891,5892,5893,5894,5895,5896,5897,5898,5899,5900,5901,5902,5903,5904, # 1200
5905,5906,5907,5908,5909,5910,5911,5912,5913,5914,5915,5916,5917,5918,5919,5920, # 1216
5921,5922,5923,5924,5925,5926,5927,5928,5929,5930,5931,5932,5933,5934,5935,5936, # 1232
5937,5938,5939,5940,5941,5942,5943,5944,5945,5946,5947,5948,5949,5950,5951,5952, # 1248
5953,5954,5955,5956,5957,5958,5959,5960,5961,5962,5963,5964,5965,5966,5967,5968, # 1264
5969,5970,5971,5972,5973,5974,5975,5976,5977,5978,5979,5980,5981,5982,5983,5984, # 1280
5985,5986,5987,5988,5989,5990,5991,5992,5993,5994,5995,5996,5997,5998,5999,6000, # 1296
6001,6002,6003,6004,6005,6006,6007,6008,6009,6010,6011,6012,6013,6014,6015,6016, # 1312
6017,6018,6019,6020,6021,6022,6023,6024,6025,6026,6027,6028,6029,6030,6031,6032, # 1328
6033,6034,6035,6036,6037,6038,6039,6040,6041,6042,6043,6044,6045,6046,6047,6048, # 1344
6049,6050,6051,6052,6053,6054,6055,6056,6057,6058,6059,6060,6061,6062,6063,6064, # 1360
6065,6066,6067,6068,6069,6070,6071,6072,6073,6074,6075,6076,6077,6078,6079,6080, # 1376
6081,6082,6083,6084,6085,6086,6087,6088,6089,6090,6091,6092,6093,6094,6095,6096, # 1392
6097,6098,6099,6100,6101,6102,6103,6104,6105,6106,6107,6108,6109,6110,6111,6112, # 1408
6113,6114,2044,2060,4621, 997,1235, 473,1186,4622, 920,3378,6115,6116, 379,1108, # 1424
4313,2657,2735,3934,6117,3809, 636,3233, 573,1026,3693,3435,2974,3300,2298,4105, # 1440
 854,2937,2463, 393,2581,2417, 539, 752,1280,2750,2480, 140,1161, 440, 708,1569, # 1456
 665,2497,1746,1291,1523,3000, 164,1603, 847,1331, 537,1997, 486, 508,1693,2418, # 1472
1970,2227, 878,1220, 299,1030, 969, 652,2751, 624,1137,3301,2619,  65,3302,2045, # 1488
1761,1859,3120,1930,3694,3516, 663,1767, 852, 835,3695, 269, 767,2826,2339,1305, # 1504
 896,1150, 770,1616,6118, 506,1502,2075,1012,2519, 775,2520,2975,2340,2938,4314, # 1520
3028,2086,1224,1943,2286,6119,3072,4315,2240,1273,1987,3935,1557, 175, 597, 985, # 1536
3517,2419,2521,1416,3029, 585, 938,1931,1007,1052,1932,1685,6120,3379,4316,4623, # 1552
 804, 599,3121,1333,2128,2539,1159,1554,2032,3810, 687,2033,2904, 952, 675,1467, # 1568
3436,6121,2241,1096,1786,2440,1543,1924, 980,1813,2228, 781,2692,1879, 728,1918, # 1584
3696,4624, 548,1950,4625,1809,1088,1356,3303,2522,1944, 502, 972, 373, 513,2827, # 1600
 586,2377,2391,1003,1976,1631,6122,2464,1084, 648,1776,4626,2141, 324, 962,2012, # 1616
2177,2076,1384, 742,2178,1448,1173,1810, 222, 102, 301, 445, 125,2420, 662,2498, # 1632
 277, 200,1476,1165,1068, 224,2562,1378,1446, 450,1880, 659, 791, 582,4627,2939, # 1648
3936,1516,1274, 555,2099,3697,1020,1389,1526,3380,1762,1723,1787,2229, 412,2114, # 1664
1900,2392,3518, 512,2597, 427,1925,2341,3122,1653,1686,2465,2499, 697, 330, 273, # 1680
 380,2162, 951, 832, 780, 991,1301,3073, 965,2270,3519, 668,2523,2636,1286, 535, # 1696
1407, 518, 671, 957,2658,2378, 267, 611,2197,3030,6123, 248,2299, 967,1799,2356, # 1712
 850,1418,3437,1876,1256,1480,2828,1718,6124,6125,1755,1664,2405,6126,4628,2879, # 1728
2829, 499,2179, 676,4629, 557,2329,2214,2090, 325,3234, 464, 811,3001, 992,2342, # 1744
2481,1232,1469, 303,2242, 466,1070,2163, 603,1777,2091,4630,2752,4631,2714, 322, # 1760
2659,1964,1768, 481,2188,1463,2330,2857,3600,2092,3031,2421,4632,2318,2070,1849, # 1776
2598,4633,1302,2254,1668,1701,2422,3811,2905,3032,3123,2046,4106,1763,1694,4634, # 1792
1604, 943,1724,1454, 917, 868,2215,1169,2940, 552,1145,1800,1228,1823,1955, 316, # 1808
1080,2510, 361,1807,2830,4107,2660,3381,1346,1423,1134,4108,6127, 541,1263,1229, # 1824
1148,2540, 545, 465,1833,2880,3438,1901,3074,2482, 816,3937, 713,1788,2500, 122, # 1840
1575, 195,1451,2501,1111,6128, 859, 374,1225,2243,2483,4317, 390,1033,3439,3075, # 1856
2524,1687, 266, 793,1440,2599, 946, 779, 802, 507, 897,1081, 528,2189,1292, 711, # 1872
1866,1725,1167,1640, 753, 398,2661,1053, 246, 348,4318, 137,1024,3440,1600,2077, # 1888
2129, 825,4319, 698, 238, 521, 187,2300,1157,2423,1641,1605,1464,1610,1097,2541, # 1904
1260,1436, 759,2255,1814,2150, 705,3235, 409,2563,3304, 561,3033,2005,2564, 726, # 1920
1956,2343,3698,4109, 949,3812,3813,3520,1669, 653,1379,2525, 881,2198, 632,2256, # 1936
1027, 778,1074, 733,1957, 514,1481,2466, 554,2180, 702,3938,1606,1017,1398,6129, # 1952
1380,3521, 921, 993,1313, 594, 449,1489,1617,1166, 768,1426,1360, 495,1794,3601, # 1968
1177,3602,1170,4320,2344, 476, 425,3167,4635,3168,1424, 401,2662,1171,3382,1998, # 1984
1089,4110, 477,3169, 474,6130,1909, 596,2831,1842, 494, 693,1051,1028,1207,3076, # 2000
 606,2115, 727,2790,1473,1115, 743,3522, 630, 805,1532,4321,2021, 366,1057, 838, # 2016
 684,1114,2142,4322,2050,1492,1892,1808,2271,3814,2424,1971,1447,1373,3305,1090, # 2032
1536,3939,3523,3306,1455,2199, 336, 369,2331,1035, 584,2393, 902, 718,2600,6131, # 2048
2753, 463,2151,1149,1611,2467, 715,1308,3124,1268, 343,1413,3236,1517,1347,2663, # 2064
2093,3940,2022,1131,1553,2100,2941,1427,3441,2942,1323,2484,6132,1980, 872,2368, # 2080
2441,2943, 320,2369,2116,1082, 679,1933,3941,2791,3815, 625,1143,2023, 422,2200, # 2096
3816,6133, 730,1695, 356,2257,1626,2301,2858,2637,1627,1778, 937, 883,2906,2693, # 2112
3002,1769,1086, 400,1063,1325,3307,2792,4111,3077, 456,2345,1046, 747,6134,1524, # 2128
 884,1094,3383,1474,2164,1059, 974,1688,2181,2258,1047, 345,1665,1187, 358, 875, # 2144
3170, 305, 660,3524,2190,1334,1135,3171,1540,1649,2542,1527, 927, 968,2793, 885, # 2160
1972,1850, 482, 500,2638,1218,1109,1085,2543,1654,2034, 876,  78,2287,1482,1277, # 2176
 861,1675,1083,1779, 724,2754, 454, 397,1132,1612,2332, 893, 672,1237, 257,2259, # 2192
2370, 135,3384, 337,2244, 547, 352, 340, 709,2485,1400, 788,1138,2511, 540, 772, # 2208
1682,2260,2272,2544,2013,1843,1902,4636,1999,1562,2288,4637,2201,1403,1533, 407, # 2224
 576,3308,1254,2071, 978,3385, 170, 136,1201,3125,2664,3172,2394, 213, 912, 873, # 2240
3603,1713,2202, 699,3604,3699, 813,3442, 493, 531,1054, 468,2907,1483, 304, 281, # 2256
4112,1726,1252,2094, 339,2319,2130,2639, 756,1563,2944, 748, 571,2976,1588,2425, # 2272
2715,1851,1460,2426,1528,1392,1973,3237, 288,3309, 685,3386, 296, 892,2716,2216, # 2288
1570,2245, 722,1747,2217, 905,3238,1103,6135,1893,1441,1965, 251,1805,2371,3700, # 2304
2601,1919,1078,  75,2182,1509,1592,1270,2640,4638,2152,6136,3310,3817, 524, 706, # 2320
1075, 292,3818,1756,2602, 317,  98,3173,3605,3525,1844,2218,3819,2502, 814, 567, # 2336
 385,2908,1534,6137, 534,1642,3239, 797,6138,1670,1529, 953,4323, 188,1071, 538, # 2352
 178, 729,3240,2109,1226,1374,2000,2357,2977, 731,2468,1116,2014,2051,6139,1261, # 2368
1593, 803,2859,2736,3443, 556, 682, 823,1541,6140,1369,2289,1706,2794, 845, 462, # 2384
2603,2665,1361, 387, 162,2358,1740, 739,1770,1720,1304,1401,3241,1049, 627,1571, # 2400
2427,3526,1877,3942,1852,1500, 431,1910,1503, 677, 297,2795, 286,1433,1038,1198, # 2416
2290,1133,1596,4113,4639,2469,1510,1484,3943,6141,2442, 108, 712,4640,2372, 866, # 2432
3701,2755,3242,1348, 834,1945,1408,3527,2395,3243,1811, 824, 994,1179,2110,1548, # 2448
1453, 790,3003, 690,4324,4325,2832,2909,3820,1860,3821, 225,1748, 310, 346,1780, # 2464
2470, 821,1993,2717,2796, 828, 877,3528,2860,2471,1702,2165,2910,2486,1789, 453, # 2480
 359,2291,1676,  73,1164,1461,1127,3311, 421, 604, 314,1037, 589, 116,2487, 737, # 2496
 837,1180, 111, 244, 735,6142,2261,1861,1362, 986, 523, 418, 581,2666,3822, 103, # 2512
 855, 503,1414,1867,2488,1091, 657,1597, 979, 605,1316,4641,1021,2443,2078,2001, # 2528
1209,  96, 587,2166,1032, 260,1072,2153, 173,  94, 226,3244, 819,2006,4642,4114, # 2544
2203, 231,1744, 782,  97,2667, 786,3387, 887, 391, 442,2219,4326,1425,6143,2694, # 2560
 633,1544,1202, 483,2015, 592,2052,1958,2472,1655, 419, 129,4327,3444,3312,1714, # 2576
1257,3078,4328,1518,1098, 865,1310,1019,1885,1512,1734, 469,2444, 148, 773, 436, # 2592
1815,1868,1128,1055,4329,1245,2756,3445,2154,1934,1039,4643, 579,1238, 932,2320, # 2608
 353, 205, 801, 115,2428, 944,2321,1881, 399,2565,1211, 678, 766,3944, 335,2101, # 2624
1459,1781,1402,3945,2737,2131,1010, 844, 981,1326,1013, 550,1816,1545,2620,1335, # 2640
1008, 371,2881, 936,1419,1613,3529,1456,1395,2273,1834,2604,1317,2738,2503, 416, # 2656
1643,4330, 806,1126, 229, 591,3946,1314,1981,1576,1837,1666, 347,1790, 977,3313, # 2672
 764,2861,1853, 688,2429,1920,1462,  77, 595, 415,2002,3034, 798,1192,4115,6144, # 2688
2978,4331,3035,2695,2582,2072,2566, 430,2430,1727, 842,1396,3947,3702, 613, 377, # 2704
 278, 236,1417,3388,3314,3174, 757,1869, 107,3530,6145,1194, 623,2262, 207,1253, # 2720
2167,3446,3948, 492,1117,1935, 536,1838,2757,1246,4332, 696,2095,2406,1393,1572, # 2736
3175,1782, 583, 190, 253,1390,2230, 830,3126,3389, 934,3245,1703,1749,2979,1870, # 2752
2545,1656,2204, 869,2346,4116,3176,1817, 496,1764,4644, 942,1504, 404,1903,1122, # 2768
1580,3606,2945,1022, 515, 372,1735, 955,2431,3036,6146,2797,1110,2302,2798, 617, # 2784
6147, 441, 762,1771,3447,3607,3608,1904, 840,3037,  86, 939,1385, 572,1370,2445, # 2800
1336, 114,3703, 898, 294, 203,3315, 703,1583,2274, 429, 961,4333,1854,1951,3390, # 2816
2373,3704,4334,1318,1381, 966,1911,2322,1006,1155, 309, 989, 458,2718,1795,1372, # 2832
1203, 252,1689,1363,3177, 517,1936, 168,1490, 562, 193,3823,1042,4117,1835, 551, # 2848
 470,4645, 395, 489,3448,1871,1465,2583,2641, 417,1493, 279,1295, 511,1236,1119, # 2864
  72,1231,1982,1812,3004, 871,1564, 984,3449,1667,2696,2096,4646,2347,2833,1673, # 2880
3609, 695,3246,2668, 807,1183,4647, 890, 388,2333,1801,1457,2911,1765,1477,1031, # 2896
3316,3317,1278,3391,2799,2292,2526, 163,3450,4335,2669,1404,1802,6148,2323,2407, # 2912
1584,1728,1494,1824,1269, 298, 909,3318,1034,1632, 375, 776,1683,2061, 291, 210, # 2928
1123, 809,1249,1002,2642,3038, 206,1011,2132, 144, 975, 882,1565, 342, 667, 754, # 2944
1442,2143,1299,2303,2062, 447, 626,2205,1221,2739,2912,1144,1214,2206,2584, 760, # 2960
1715, 614, 950,1281,2670,2621, 810, 577,1287,2546,4648, 242,2168, 250,2643, 691, # 2976
 123,2644, 647, 313,1029, 689,1357,2946,1650, 216, 771,1339,1306, 808,2063, 549, # 2992
 913,1371,2913,2914,6149,1466,1092,1174,1196,1311,2605,2396,1783,1796,3079, 406, # 3008
2671,2117,3949,4649, 487,1825,2220,6150,2915, 448,2348,1073,6151,2397,1707, 130, # 3024
 900,1598, 329, 176,1959,2527,1620,6152,2275,4336,3319,1983,2191,3705,3610,2155, # 3040
3706,1912,1513,1614,6153,1988, 646, 392,2304,1589,3320,3039,1826,1239,1352,1340, # 3056
2916, 505,2567,1709,1437,2408,2547, 906,6154,2672, 384,1458,1594,1100,1329, 710, # 3072
 423,3531,2064,2231,2622,1989,2673,1087,1882, 333, 841,3005,1296,2882,2379, 580, # 3088
1937,1827,1293,2585, 601, 574, 249,1772,4118,2079,1120, 645, 901,1176,1690, 795, # 3104
2207, 478,1434, 516,1190,1530, 761,2080, 930,1264, 355, 435,1552, 644,1791, 987, # 3120
 220,1364,1163,1121,1538, 306,2169,1327,1222, 546,2645, 218, 241, 610,1704,3321, # 3136
1984,1839,1966,2528, 451,6155,2586,3707,2568, 907,3178, 254,2947, 186,1845,4650, # 3152
 745, 432,1757, 428,1633, 888,2246,2221,2489,3611,2118,1258,1265, 956,3127,1784, # 3168
4337,2490, 319, 510, 119, 457,3612, 274,2035,2007,4651,1409,3128, 970,2758, 590, # 3184
2800, 661,2247,4652,2008,3950,1420,1549,3080,3322,3951,1651,1375,2111, 485,2491, # 3200
1429,1156,6156,2548,2183,1495, 831,1840,2529,2446, 501,1657, 307,1894,3247,1341, # 3216
 666, 899,2156,1539,2549,1559, 886, 349,2208,3081,2305,1736,3824,2170,2759,1014, # 3232
1913,1386, 542,1397,2948, 490, 368, 716, 362, 159, 282,2569,1129,1658,1288,1750, # 3248
2674, 276, 649,2016, 751,1496, 658,1818,1284,1862,2209,2087,2512,3451, 622,2834, # 3264
 376, 117,1060,2053,1208,1721,1101,1443, 247,1250,3179,1792,3952,2760,2398,3953, # 3280
6157,2144,3708, 446,2432,1151,2570,3452,2447,2761,2835,1210,2448,3082, 424,2222, # 3296
1251,2449,2119,2836, 504,1581,4338, 602, 817, 857,3825,2349,2306, 357,3826,1470, # 3312
1883,2883, 255, 958, 929,2917,3248, 302,4653,1050,1271,1751,2307,1952,1430,2697, # 3328
2719,2359, 354,3180, 777, 158,2036,4339,1659,4340,4654,2308,2949,2248,1146,2232, # 3344
3532,2720,1696,2623,3827,6158,3129,1550,2698,1485,1297,1428, 637, 931,2721,2145, # 3360
 914,2550,2587,  81,2450, 612, 827,2646,1242,4655,1118,2884, 472,1855,3181,3533, # 3376
3534, 569,1353,2699,1244,1758,2588,4119,2009,2762,2171,3709,1312,1531,6159,1152, # 3392
1938, 134,1830, 471,3710,2276,1112,1535,3323,3453,3535, 982,1337,2950, 488, 826, # 3408
 674,1058,1628,4120,2017, 522,2399, 211, 568,1367,3454, 350, 293,1872,1139,3249, # 3424
1399,1946,3006,1300,2360,3324, 588, 736,6160,2606, 744, 669,3536,3828,6161,1358, # 3440
 199, 723, 848, 933, 851,1939,1505,1514,1338,1618,1831,4656,1634,3613, 443,2740, # 3456
3829, 717,1947, 491,1914,6162,2551,1542,4121,1025,6163,1099,1223, 198,3040,2722, # 3472
 370, 410,1905,2589, 998,1248,3182,2380, 519,1449,4122,1710, 947, 928,1153,4341, # 3488
2277, 344,2624,1511, 615, 105, 161,1212,1076,1960,3130,2054,1926,1175,1906,2473, # 3504
 414,1873,2801,6164,2309, 315,1319,3325, 318,2018,2146,2157, 963, 631, 223,4342, # 3520
4343,2675, 479,3711,1197,2625,3712,2676,2361,6165,4344,4123,6166,2451,3183,1886, # 3536
2184,1674,1330,1711,1635,1506, 799, 219,3250,3083,3954,1677,3713,3326,2081,3614, # 3552
1652,2073,4657,1147,3041,1752, 643,1961, 147,1974,3955,6167,1716,2037, 918,3007, # 3568
1994, 120,1537, 118, 609,3184,4345, 740,3455,1219, 332,1615,3830,6168,1621,2980, # 3584
1582, 783, 212, 553,2350,3714,1349,2433,2082,4124, 889,6169,2310,1275,1410, 973, # 3600
 166,1320,3456,1797,1215,3185,2885,1846,2590,2763,4658, 629, 822,3008, 763, 940, # 3616
1990,2862, 439,2409,1566,1240,1622, 926,1282,1907,2764, 654,2210,1607, 327,1130, # 3632
3956,1678,1623,6170,2434,2192, 686, 608,3831,3715, 903,3957,3042,6171,2741,1522, # 3648
1915,1105,1555,2552,1359, 323,3251,4346,3457, 738,1354,2553,2311,2334,1828,2003, # 3664
3832,1753,2351,1227,6172,1887,4125,1478,6173,2410,1874,1712,1847, 520,1204,2607, # 3680
 264,4659, 836,2677,2102, 600,4660,3833,2278,3084,6174,4347,3615,1342, 640, 532, # 3696
 543,2608,1888,2400,2591,1009,4348,1497, 341,1737,3616,2723,1394, 529,3252,1321, # 3712
 983,4661,1515,2120, 971,2592, 924, 287,1662,3186,4349,2700,4350,1519, 908,1948, # 3728
2452, 156, 796,1629,1486,2223,2055, 694,4126,1259,1036,3392,1213,2249,2742,1889, # 3744
1230,3958,1015, 910, 408, 559,3617,4662, 746, 725, 935,4663,3959,3009,1289, 563, # 3760
 867,4664,3960,1567,2981,2038,2626, 988,2263,2381,4351, 143,2374, 704,1895,6175, # 3776
1188,3716,2088, 673,3085,2362,4352, 484,1608,1921,2765,2918, 215, 904,3618,3537, # 3792
 894, 509, 976,3043,2701,3961,4353,2837,2982, 498,6176,6177,1102,3538,1332,3393, # 3808
1487,1636,1637, 233, 245,3962, 383, 650, 995,3044, 460,1520,1206,2352, 749,3327, # 3824
 530, 700, 389,1438,1560,1773,3963,2264, 719,2951,2724,3834, 870,1832,1644,1000, # 3840
 839,2474,3717, 197,1630,3394, 365,2886,3964,1285,2133, 734, 922, 818,1106, 732, # 3856
 480,2083,1774,3458, 923,2279,1350, 221,3086,  85,2233,2234,3835,1585,3010,2147, # 3872
1387,1705,2382,1619,2475, 133, 239,2802,1991,1016,2084,2383, 411,2838,1113, 651, # 3888
1985,1160,3328, 990,1863,3087,1048,1276,2647, 265,2627,1599,3253,2056, 150, 638, # 3904
2019, 656, 853, 326,1479, 680,1439,4354,1001,1759, 413,3459,3395,2492,1431, 459, # 3920
4355,1125,3329,2265,1953,1450,2065,2863, 849, 351,2678,3131,3254,3255,1104,1577, # 3936
 227,1351,1645,2453,2193,1421,2887, 812,2121, 634,  95,2435, 201,2312,4665,1646, # 3952
1671,2743,1601,2554,2702,2648,2280,1315,1366,2089,3132,1573,3718,3965,1729,1189, # 3968
 328,2679,1077,1940,1136, 558,1283, 964,1195, 621,2074,1199,1743,3460,3619,1896, # 3984
1916,1890,3836,2952,1154,2112,1064, 862, 378,3011,2066,2113,2803,1568,2839,6178, # 4000
3088,2919,1941,1660,2004,1992,2194, 142, 707,1590,1708,1624,1922,1023,1836,1233, # 4016
1004,2313, 789, 741,3620,6179,1609,2411,1200,4127,3719,3720,4666,2057,3721, 593, # 4032
2840, 367,2920,1878,6180,3461,1521, 628,1168, 692,2211,2649, 300, 720,2067,2571, # 4048
2953,3396, 959,2504,3966,3539,3462,1977, 701,6181, 954,1043, 800, 681, 183,3722, # 4064
1803,1730,3540,4128,2103, 815,2314, 174, 467, 230,2454,1093,2134, 755,3541,3397, # 4080
1141,1162,6182,1738,2039, 270,3256,2513,1005,1647,2185,3837, 858,1679,1897,1719, # 4096
2954,2324,1806, 402, 670, 167,4129,1498,2158,2104, 750,6183, 915, 189,1680,1551, # 4112
 455,4356,1501,2455, 405,1095,2955, 338,1586,1266,1819, 570, 641,1324, 237,1556, # 4128
2650,1388,3723,6184,1368,2384,1343,1978,3089,2436, 879,3724, 792,1191, 758,3012, # 4144
1411,2135,1322,4357, 240,4667,1848,3725,1574,6185, 420,3045,1546,1391, 714,4358, # 4160
1967, 941,1864, 863, 664, 426, 560,1731,2680,1785,2864,1949,2363, 403,3330,1415, # 4176
1279,2136,1697,2335, 204, 721,2097,3838,  90,6186,2085,2505, 191,3967, 124,2148, # 4192
1376,1798,1178,1107,1898,1405, 860,4359,1243,1272,2375,2983,1558,2456,1638, 113, # 4208
3621, 578,1923,2609, 880, 386,4130, 784,2186,2266,1422,2956,2172,1722, 497, 263, # 4224
2514,1267,2412,2610, 177,2703,3542, 774,1927,1344, 616,1432,1595,1018, 172,4360, # 4240
2325, 911,4361, 438,1468,3622, 794,3968,2024,2173,1681,1829,2957, 945, 895,3090, # 4256
 575,2212,2476, 475,2401,2681, 785,2744,1745,2293,2555,1975,3133,2865, 394,4668, # 4272
3839, 635,4131, 639, 202,1507,2195,2766,1345,1435,2572,3726,1908,1184,1181,2457, # 4288
3727,3134,4362, 843,2611, 437, 916,4669, 234, 769,1884,3046,3047,3623, 833,6187, # 4304
1639,2250,2402,1355,1185,2010,2047, 999, 525,1732,1290,1488,2612, 948,1578,3728, # 4320
2413,2477,1216,2725,2159, 334,3840,1328,3624,2921,1525,4132, 564,1056, 891,4363, # 4336
1444,1698,2385,2251,3729,1365,2281,2235,1717,6188, 864,3841,2515, 444, 527,2767, # 4352
2922,3625, 544, 461,6189, 566, 209,2437,3398,2098,1065,2068,3331,3626,3257,2137, # 4368  #last 512
)
# fmt: on