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21152 lines
2.6 MiB

/*
MicroMDAEPiano
MicroMDAEPiano is a port of the MDA-EPiano sound engine
(https://sourceforge.net/projects/mda-vst/) for the Teensy-3.5/3.6 with audio shield.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef MDAEPIANODATA_H_INCLUDED
#define MDAEPIANODATA_H_INCLUDED
#ifdef USE_XFADE_DATA
#include <Arduino.h>
const int16_t epianoDataXfade[] PROGMEM = {
-7, -23, -28, -16, -30, -17, -28, -16, -31, -15, -34, -12, -35, -6, -42, 4, -58, 44, -227, -1690,
-1412, -1295, -1059, -908, -685, -518, -308, -152, 31, 182, 368, 531, 731, 948, 1195, 1439, 1694, 1950, 2228, 2487,
2742, 2988, 3225, 3428, 3624, 3790, 3969, 4108, 4253, 4382, 4495, 4591, 4647, 4689, 4737, 4794, 4846, 4920, 5003, 5077,
5189, 5290, 5405, 5517, 5635, 5779, 5921, 6049, 6197, 6345, 6541, 6759, 6986, 7224, 7484, 7727, 7983, 8235, 8497, 8760,
9049, 9319, 9617, 9871, 10137, 10372, 10601, 10817, 10998, 11123, 11227, 11284, 11322, 11335, 11339, 11340, 11310, 11255, 11174, 11066,
10940, 10791, 10631, 10462, 10285, 10073, 9889, 9673, 9472, 9265, 9048, 8819, 8590, 8315, 8063, 7788, 7531, 7295, 7078, 6880,
6699, 6510, 6328, 6170, 6015, 5838, 5663, 5478, 5293, 5090, 4885, 4673, 4433, 4181, 3908, 3602, 3281, 2952, 2637, 2349,
2108, 1917, 1763, 1641, 1547, 1504, 1459, 1426, 1399, 1388, 1347, 1302, 1263, 1207, 1139, 1077, 1019, 934, 810, 660,
508, 350, 187, 55, -46, -119, -158, -175, -184, -166, -160, -157, -146, -201, -259, -354, -446, -553, -685, -825,
-986, -1198, -1415, -1663, -1937, -2206, -2475, -2743, -2957, -3179, -3362, -3539, -3682, -3805, -3926, -4075, -4237, -4419, -4620, -4839,
-5074, -5311, -5544, -5779, -6030, -6290, -6565, -6853, -7124, -7377, -7612, -7825, -8020, -8163, -8253, -8307, -8333, -8332, -8306, -8303,
-8303, -8331, -8386, -8442, -8513, -8586, -8646, -8723, -8811, -8888, -8964, -9042, -9114, -9175, -9216, -9238, -9250, -9225, -9171, -9087,
-8978, -8869, -8772, -8705, -8677, -8675, -8707, -8769, -8852, -8965, -9081, -9196, -9322, -9446, -9554, -9656, -9751, -9845, -9923, -9993,
-10039, -10074, -10042, -10007, -9941, -9909, -9856, -9819, -9785, -9804, -9814, -9839, -9861, -9871, -9887, -9876, -9844, -9798, -9695, -9586,
-9454, -9316, -9154, -8974, -8733, -8486, -8197, -7899, -7577, -7256, -6961, -6654, -6357, -6101, -5835, -5578, -5341, -5105, -4881, -4640,
-4386, -4131, -3873, -3604, -3335, -3057, -2802, -2534, -2270, -2007, -1749, -1493, -1253, -1029, -828, -633, -451, -267, -88, 100,
281, 485, 673, 864, 1084, 1310, 1533, 1771, 2019, 2248, 2476, 2694, 2917, 3126, 3328, 3506, 3680, 3849, 4010, 4167,
4328, 4512, 4695, 4891, 5089, 5291, 5487, 5660, 5821, 5980, 6114, 6220, 6315, 6374, 6421, 6430, 6420, 6387, 6331, 6236,
6131, 6005, 5871, 5722, 5590, 5476, 5374, 5259, 5179, 5078, 4961, 4846, 4700, 4543, 4382, 4188, 3993, 3796, 3580, 3376,
3163, 2960, 2756, 2541, 2323, 2123, 1918, 1748, 1610, 1490, 1417, 1383, 1352, 1348, 1349, 1338, 1311, 1294, 1258, 1216,
1152, 1092, 1036, 982, 918, 863, 814, 762, 691, 643, 588, 551, 524, 523, 538, 572, 601, 606, 627, 610,
567, 483, 370, 232, 57, -137, -333, -536, -736, -947, -1162, -1390, -1597, -1814, -2029, -2229, -2401, -2567, -2726, -2855,
-2980, -3112, -3235, -3387, -3546, -3755, -3968, -4185, -4410, -4632, -4850, -5028, -5201, -5344, -5494, -5612, -5715, -5804, -5858, -5910,
-5934, -5931, -5911, -5865, -5787, -5712, -5638, -5566, -5498, -5472, -5463, -5443, -5438, -5437, -5430, -5397, -5373, -5333, -5293, -5245,
-5178, -5108, -5046, -4958, -4870, -4774, -4667, -4550, -4416, -4271, -4161, -4063, -3978, -3912, -3860, -3839, -3813, -3778, -3759, -3715,
-3664, -3587, -3508, -3421, -3314, -3196, -3072, -2918, -2761, -2578, -2369, -2163, -1932, -1696, -1477, -1248, -1018, -782, -538, -309,
-61, 191, 456, 733, 1030, 1331, 1649, 1948, 2258, 2578, 2895, 3209, 3530, 3854, 4173, 4464, 4755, 5030, 5300, 5555,
5806, 6045, 6284, 6498, 6701, 6890, 7079, 7240, 7395, 7518, 7620, 7715, 7771, 7829, 7902, 7970, 8032, 8104, 8160, 8222,
8266, 8308, 8350, 8402, 8452, 8503, 8563, 8616, 8668, 8725, 8781, 8827, 8851, 8857, 8857, 8846, 8824, 8815, 8823, 8845,
8869, 8896, 8932, 8946, 8963, 8971, 8999, 9002, 9012, 9015, 9020, 9030, 9040, 9035, 9024, 8995, 8936, 8847, 8736, 8613,
8480, 8332, 8201, 8071, 7922, 7775, 7650, 7500, 7338, 7170, 6994, 6819, 6642, 6452, 6292, 6121, 5972, 5809, 5641, 5461,
5251, 5019, 4789, 4540, 4294, 4044, 3801, 3585, 3387, 3180, 3008, 2841, 2680, 2527, 2372, 2225, 2091, 1955, 1846, 1755,
1665, 1585, 1487, 1378, 1265, 1136, 997, 851, 712, 569, 432, 325, 231, 148, 83, 28, -29, -87, -170, -259,
-341, -427, -514, -593, -685, -778, -880, -1014, -1156, -1310, -1489, -1679, -1866, -2063, -2264, -2447, -2620, -2776, -2934, -3089,
-3232, -3400, -3572, -3761, -3944, -4120, -4294, -4470, -4625, -4780, -4956, -5131, -5303, -5479, -5664, -5866, -6052, -6237, -6409, -6574,
-6702, -6812, -6901, -6993, -7058, -7138, -7205, -7279, -7351, -7414, -7451, -7507, -7535, -7555, -7582, -7610, -7651, -7674, -7704, -7774,
-7837, -7897, -7945, -7988, -8008, -8017, -8004, -8001, -8007, -8005, -8021, -8040, -8074, -8117, -8156, -8212, -8269, -8312, -8383, -8429,
-8504, -8587, -8685, -8777, -8899, -8995, -9092, -9169, -9228, -9288, -9324, -9351, -9388, -9403, -9432, -9461, -9486, -9510, -9535, -9547,
-9557, -9527, -9480, -9435, -9363, -9286, -9201, -9102, -8995, -8866, -8711, -8538, -8356, -8156, -7944, -7727, -7488, -7255, -6996, -6767,
-6513, -6277, -6039, -5785, -5514, -5250, -4963, -4665, -4363, -4081, -3796, -3505, -3212, -2939, -2653, -2396, -2136, -1893, -1664, -1438,
-1215, -1007, -802, -601, -412, -205, -36, 160, 370, 574, 776, 995, 1212, 1423, 1631, 1841, 2063, 2263, 2456, 2645,
2806, 2968, 3109, 3230, 3367, 3490, 3611, 3741, 3877, 4020, 4154, 4299, 4456, 4600, 4735, 4867, 5004, 5127, 5250, 5349,
5449, 5526, 5572, 5605, 5596, 5573, 5518, 5440, 5357, 5266, 5170, 5080, 5002, 4934, 4867, 4800, 4725, 4670, 4582, 4500,
4434, 4332, 4238, 4142, 4046, 3943, 3827, 3688, 3542, 3378, 3194, 3003, 2816, 2636, 2473, 2322, 2207, 2109, 2040, 1965,
1910, 1848, 1814, 1751, 1720, 1671, 1615, 1566, 1510, 1449, 1383, 1295, 1198, 1088, 954, 809, 656, 510, 387, 264,
179, 98, 49, 4, -42, -99, -157, -227, -307, -416, -506, -616, -738, -872, -1010, -1158, -1341, -1530, -1742, -1947,
-2172, -2395, -2575, -2754, -2919, -3032, -3151, -3257, -3360, -3460, -3567, -3674, -3795, -3918, -4040, -4166, -4293, -4425, -4556, -4670,
-4800, -4924, -5050, -5187, -5290, -5393, -5464, -5504, -5526, -5521, -5480, -5438, -5382, -5326, -5272, -5218, -5183, -5151, -5108, -5072,
-5043, -5003, -4967, -4933, -4895, -4872, -4834, -4805, -4761, -4707, -4650, -4563, -4454, -4328, -4191, -4036, -3884, -3738, -3609, -3476,
-3355, -3258, -3164, -3065, -2971, -2875, -2792, -2688, -2590, -2496, -2393, -2266, -2141, -1993, -1835, -1654, -1436, -1220, -992, -735,
-489, -219, 24, 263, 509, 741, 972, 1219, 1462, 1708, 1950, 2190, 2444, 2710, 2972, 3247, 3531, 3805, 4094, 4369,
4644, 4918, 5164, 5421, 5657, 5858, 6056, 6240, 6413, 6592, 6748, 6905, 7061, 7220, 7351, 7467, 7594, 7720, 7833, 7940,
8058, 8158, 8266, 8341, 8399, 8460, 8504, 8533, 8560, 8574, 8584, 8589, 8596, 8628, 8669, 8717, 8761, 8806, 8847, 8873,
8884, 8910, 8935, 8955, 8970, 8982, 8979, 8967, 8925, 8877, 8830, 8759, 8673, 8592, 8497, 8410, 8331, 8269, 8207, 8166,
8100, 8045, 7972, 7882, 7786, 7677, 7564, 7447, 7320, 7181, 7032, 6885, 6711, 6532, 6344, 6152, 5936, 5731, 5531, 5351,
5181, 5030, 4903, 4786, 4665, 4554, 4427, 4293, 4158, 4020, 3881, 3736, 3580, 3433, 3286, 3126, 2978, 2814, 2640, 2473,
2314, 2137, 1990, 1865, 1763, 1680, 1598, 1539, 1491, 1424, 1371, 1290, 1214, 1118, 1011, 894, 779, 643, 526, 399,
273, 133, -23, -169, -322, -473, -606, -722, -825, -910, -996, -1083, -1148, -1234, -1344, -1429, -1563, -1708, -1875, -2041,
-2221, -2398, -2576, -2738, -2926, -3095, -3293, -3477, -3658, -3836, -4000, -4134, -4273, -4392, -4506, -4613, -4714, -4814, -4931, -5049,
-5185, -5336, -5504, -5676, -5827, -5981, -6134, -6281, -6422, -6558, -6691, -6827, -6954, -7047, -7148, -7233, -7297, -7356, -7391, -7424,
-7450, -7461, -7497, -7544, -7597, -7686, -7766, -7858, -7946, -8028, -8108, -8199, -8256, -8335, -8395, -8458, -8502, -8553, -8579, -8612,
-8618, -8635, -8627, -8620, -8606, -8597, -8600, -8637, -8647, -8710, -8760, -8830, -8895, -8957, -9006, -9059, -9091, -9116, -9126, -9125,
-9125, -9107, -9078, -9040, -8984, -8916, -8840, -8747, -8645, -8552, -8456, -8365, -8280, -8174, -8083, -7980, -7881, -7751, -7617, -7464,
-7299, -7100, -6902, -6685, -6471, -6249, -6009, -5777, -5534, -5273, -5013, -4753, -4489, -4232, -3975, -3701, -3440, -3176, -2912, -2661,
-2388, -2142, -1881, -1615, -1371, -1124, -868, -627, -386, -157, 63, 286, 504, 699, 918, 1115, 1314, 1510, 1717, 1932,
2154, 2358, 2580, 2797, 3006, 3195, 3400, 3581, 3745, 3896, 4049, 4178, 4313, 4429, 4556, 4667, 4778, 4873, 4964, 5067,
5157, 5257, 5351, 5454, 5560, 5663, 5771, 5877, 5964, 6037, 6072, 6086, 6092, 6058, 6003, 5949, 5888, 5815, 5732, 5645,
5547, 5451, 5343, 5264, 5149, 5063, 4966, 4869, 4794, 4736, 4667, 4613, 4537, 4445, 4337, 4202, 4056, 3904, 3732, 3567,
3396, 3233, 3072, 2917, 2771, 2637, 2514, 2405, 2297, 2198, 2107, 2025, 1977, 1944, 1899, 1864, 1834, 1777, 1699, 1589,
1483, 1358, 1214, 1070, 935, 779, 638, 514, 407, 296, 201, 103, 19, -72, -153, -237, -303, -369, -428, -503,
-584, -703, -828, -991, -1178, -1378, -1577, -1806, -2036, -2232, -2446, -2625, -2808, -2954, -3107, -3249, -3394, -3523, -3650, -3764,
-3875, -3989, -4083, -4180, -4304, -4424, -4555, -4701, -4862, -5023, -5194, -5361, -5517, -5641, -5751, -5823, -5890, -5921, -5945, -5957,
-5969, -5952, -5936, -5901, -5867, -5829, -5782, -5729, -5691, -5648, -5616, -5593, -5583, -5587, -5587, -5582, -5570, -5543, -5484, -5407,
-5309, -5215, -5109, -4985, -4858, -4739, -4591, -4468, -4338, -4211, -4078, -3939, -3804, -3696, -3574, -3452, -3347, -3240, -3138, -3011,
-2872, -2712, -2525, -2325, -2112, -1874, -1642, -1374, -1109, -840, -578, -295, -26, 253, 536, 810, 1095, 1376, 1648, 1939,
2217, 2508, 2780, 3072, 3373, 3673, 3972, 4284, 4572, 4864, 5127, 5392, 5641, 5879, 6098, 6319, 6523, 6719, 6902, 7079,
7253, 7423, 7571, 7740, 7896, 8051, 8204, 8336, 8462, 8597, 8716, 8810, 8891, 8959, 9006, 9040, 9072, 9108, 9143, 9182,
9229, 9280, 9336, 9380, 9429, 9498, 9552, 9618, 9713, 9752, 9829, 9877, 9923, 9952, 9982, 9977, 9954, 9913, 9860, 9771,
9710, 9635, 9589, 9525, 9472, 9419, 9362, 9308, 9234, 9188, 9127, 9056, 8981, 8898, 8804, 8701, 8582, 8447, 8300, 8116,
7908, 7703, 7471, 7249, 7012, 6807, 6616, 6414, 6233, 6060, 5909, 5756, 5595, 5449, 5308, 5165, 5008, 4874, 4720, 4578,
4421, 4253, 4078, 3900, 3688, 3493, 3284, 3090, 2900, 2729, 2572, 2439, 2302, 2212, 2128, 2047, 1966, 1889, 1811, 1726,
1632, 1542, 1467, 1357, 1253, 1130, 994, 840, 673, 497, 328, 152, -8, -169, -315, -453, -569, -666, -771, -861,
-960, -1075, -1206, -1331, -1466, -1616, -1765, -1920, -2087, -2272, -2473, -2692, -2901, -3123, -3336, -3544, -3737, -3935, -4111, -4268,
-4395, -4524, -4641, -4734, -4845, -4969, -5106, -5239, -5363, -5513, -5647, -5795, -5945, -6097, -6274, -6440, -6594, -6750, -6906, -7047,
-7178, -7298, -7397, -7476, -7528, -7568, -7617, -7640, -7683, -7724, -7792, -7846, -7911, -7986, -8068, -8154, -8249, -8337, -8437, -8544,
-8644, -8735, -8839, -8929, -9006, -9081, -9130, -9180, -9198, -9209, -9225, -9245, -9260, -9299, -9337, -9388, -9449, -9511, -9582, -9666,
-9731, -9818, -9874, -9947, -10007, -10047, -10100, -10127, -10146, -10137, -10103, -10066, -9998, -9928, -9842, -9769, -9665, -9571, -9477, -9387,
-9305, -9204, -9105, -9013, -8892, -8766, -8622, -8465, -8300, -8120, -7922, -7715, -7496, -7257, -7011, -6756, -6497, -6226, -5954, -5692,
-5430, -5156, -4894, -4638, -4389, -4139, -3874, -3612, -3359, -3096, -2828, -2556, -2292, -2015, -1744, -1474, -1212, -949, -689, -443,
-208, 14, 240, 459, 666, 891, 1100, 1324, 1556, 1772, 2000, 2227, 2445, 2664, 2884, 3092, 3299, 3487, 3681, 3853,
4016, 4160, 4308, 4419, 4523, 4618, 4698, 4794, 4864, 4955, 5062, 5164, 5272, 5372, 5478, 5575, 5658, 5730, 5793, 5829,
5847, 5863, 5846, 5827, 5792, 5738, 5679, 5597, 5499, 5385, 5279, 5169, 5070, 4998, 4926, 4874, 4827, 4787, 4732, 4678,
4633, 4570, 4482, 4394, 4277, 4171, 4035, 3904, 3771, 3631, 3469, 3326, 3159, 2995, 2832, 2698, 2563, 2461, 2358, 2302,
2226, 2193, 2128, 2088, 2019, 1957, 1858, 1780, 1653, 1526, 1392, 1254, 1106, 966, 812, 646, 493, 330, 197, 39,
-80, -179, -271, -355, -416, -472, -530, -599, -685, -784, -901, -1050, -1192, -1358, -1531, -1713, -1884, -2061, -2241, -2420,
-2583, -2748, -2905, -3048, -3177, -3296, -3391, -3483, -3540, -3592, -3665, -3722, -3801, -3902, -4021, -4147, -4282, -4417, -4559, -4691,
-4828, -4955, -5054, -5179, -5258, -5341, -5397, -5461, -5500, -5519, -5518, -5504, -5475, -5434, -5406, -5365, -5360, -5360, -5359, -5369,
-5410, -5435, -5456, -5479, -5499, -5504, -5503, -5462, -5446, -5399, -5344, -5282, -5224, -5143, -5030, -4919, -4799, -4670, -4531, -4412,
-4302, -4207, -4111, -4017, -3936, -3850, -3766, -3655, -3542, -3416, -3277, -3107, -2929, -2744, -2540, -2325, -2104, -1875, -1625, -1358,
-1091, -836, -546, -281, -13, 254, 516, 780, 1040, 1302, 1583, 1855, 2140, 2428, 2725, 3025, 3331, 3616, 3919, 4197,
4487, 4762, 5020, 5284, 5541, 5772, 5999, 6234, 6457, 6669, 6855, 7057, 7254, 7441, 7628, 7815, 7989, 8145, 8292, 8436,
8561, 8673, 8773, 8875, 8957, 9041, 9097, 9156, 9215, 9269, 9302, 9358, 9414, 9465, 9517, 9562, 9631, 9697, 9747, 9796,
9837, 9848, 9865, 9857, 9834, 9817, 9778, 9731, 9685, 9621, 9576, 9512, 9447, 9395, 9327, 9268, 9211, 9156, 9116, 9073,
9023, 8983, 8931, 8860, 8789, 8680, 8573, 8439, 8295, 8141, 7982, 7818, 7662, 7491, 7334, 7162, 7004, 6861, 6714, 6555,
6431, 6302, 6168, 6056, 5951, 5835, 5722, 5593, 5458, 5310, 5143, 4968, 4776, 4596, 4413, 4230, 4044, 3878, 3718, 3557,
3407, 3261, 3139, 3010, 2891, 2793, 2681, 2603, 2501, 2416, 2321, 2206, 2089, 1966, 1816, 1654, 1484, 1309, 1143, 969,
794, 650, 500, 362, 216, 75, -55, -172, -293, -405, -512, -632, -735, -862, -987, -1116, -1276, -1440, -1605, -1801,
-2001, -2217, -2410, -2603, -2790, -2968, -3128, -3279, -3429, -3574, -3715, -3845, -3975, -4099, -4210, -4321, -4436, -4562, -4693, -4806,
-4949, -5107, -5254, -5420, -5600, -5765, -5935, -6078, -6211, -6342, -6455, -6546, -6636, -6725, -6801, -6874, -6934, -6996, -7063, -7115,
-7187, -7245, -7320, -7403, -7490, -7582, -7703, -7802, -7933, -8050, -8163, -8275, -8355, -8430, -8507, -8559, -8609, -8653, -8698, -8744,
-8774, -8817, -8868, -8909, -8952, -9009, -9060, -9116, -9177, -9247, -9330, -9400, -9478, -9551, -9614, -9659, -9692, -9706, -9707, -9692,
-9665, -9625, -9584, -9543, -9477, -9413, -9345, -9285, -9198, -9125, -9032, -8947, -8853, -8758, -8656, -8553, -8425, -8284, -8141, -7984,
-7802, -7616, -7408, -7204, -6973, -6749, -6514, -6288, -6056, -5809, -5560, -5331, -5093, -4841, -4592, -4350, -4108, -3855, -3608, -3350,
-3089, -2811, -2549, -2288, -2035, -1772, -1498, -1254, -1025, -779, -537, -302, -74, 140, 379, 606, 827, 1061, 1291, 1509,
1737, 1953, 2189, 2416, 2645, 2858, 3069, 3267, 3449, 3608, 3757, 3901, 4000, 4118, 4226, 4318, 4414, 4513, 4618, 4728,
4825, 4920, 5012, 5115, 5198, 5266, 5346, 5418, 5476, 5522, 5558, 5564, 5560, 5515, 5454, 5387, 5300, 5195, 5115, 5021,
4925, 4847, 4783, 4727, 4683, 4615, 4562, 4507, 4446, 4389, 4324, 4256, 4188, 4107, 4027, 3922, 3798, 3669, 3517, 3358,
3193, 3027, 2875, 2735, 2610, 2493, 2402, 2316, 2252, 2184, 2117, 2052, 1981, 1913, 1836, 1770, 1690, 1597, 1482, 1379,
1255, 1098, 940, 768, 595, 424, 263, 122, -21, -133, -237, -324, -400, -474, -565, -632, -722, -811, -915, -1029,
-1142, -1265, -1407, -1541, -1698, -1856, -2043, -2224, -2405, -2576, -2744, -2892, -2997, -3105, -3182, -3256, -3328, -3373, -3427, -3478,
-3538, -3601, -3671, -3757, -3845, -3923, -4004, -4104, -4187, -4292, -4393, -4502, -4588, -4677, -4759, -4815, -4823, -4834, -4818, -4791,
-4760, -4710, -4668, -4640, -4609, -4592, -4583, -4563, -4566, -4570, -4563, -4568, -4575, -4574, -4572, -4582, -4568, -4553, -4514, -4476,
-4408, -4321, -4207, -4093, -3975, -3850, -3711, -3584, -3481, -3365, -3260, -3146, -3059, -2960, -2846, -2724, -2611, -2476, -2349, -2203,
-2045, -1884, -1705, -1499, -1297, -1065, -814, -562, -306, -49, 211, 468, 712, 956, 1208, 1445, 1683, 1914, 2163, 2415,
2655, 2908, 3169, 3419, 3677, 3923, 4176, 4431, 4685, 4920, 5173, 5410, 5632, 5841, 6042, 6239, 6429, 6613, 6787, 6975,
7140, 7299, 7456, 7626, 7791, 7921, 8078, 8229, 8357, 8486, 8600, 8707, 8792, 8864, 8929, 8996, 9040, 9080, 9115, 9152,
9200, 9234, 9281, 9328, 9380, 9413, 9452, 9487, 9520, 9535, 9547, 9549, 9542, 9528, 9496, 9445, 9391, 9322, 9233, 9144,
9051, 8953, 8847, 8763, 8677, 8607, 8535, 8474, 8398, 8333, 8251, 8177, 8077, 7991, 7878, 7767, 7643, 7511, 7363, 7206,
7051, 6879, 6701, 6533, 6350, 6179, 6012, 5858, 5723, 5607, 5494, 5382, 5286, 5169, 5074, 4946, 4830, 4709, 4567, 4419,
4275, 4112, 3951, 3787, 3616, 3440, 3263, 3087, 2922, 2753, 2604, 2464, 2330, 2219, 2122, 2021, 1931, 1836, 1735, 1629,
1492, 1366, 1228, 1079, 919, 764, 598, 435, 262, 83, -87, -260, -430, -588, -737, -868, -998, -1120, -1213, -1314,
-1423, -1514, -1625, -1744, -1881, -2020, -2174, -2328, -2487, -2643, -2816, -2976, -3147, -3325, -3479, -3632, -3787, -3919, -4052, -4177,
-4289, -4386, -4479, -4559, -4642, -4729, -4820, -4931, -5044, -5183, -5313, -5450, -5597, -5739, -5874, -6018, -6150, -6288, -6427, -6536,
-6652, -6747, -6837, -6921, -6982, -7054, -7105, -7152, -7194, -7248, -7303, -7379, -7457, -7559, -7656, -7760, -7859, -7976, -8072, -8168,
-8250, -8347, -8428, -8500, -8558, -8623, -8670, -8704, -8735, -8762, -8760, -8772, -8774, -8793, -8815, -8838, -8885, -8911, -8989, -9022,
-9063, -9107, -9141, -9164, -9174, -9172, -9184, -9156, -9126, -9090, -9037, -8969, -8898, -8801, -8716, -8613, -8513, -8402, -8313, -8209,
-8103, -8013, -7906, -7802, -7683, -7554, -7420, -7275, -7107, -6934, -6753, -6570, -6371, -6159, -5945, -5734, -5506, -5272, -5046, -4814,
-4579, -4344, -4117, -3883, -3645, -3407, -3164, -2924, -2672, -2422, -2163, -1915, -1639, -1393, -1141, -898, -659, -416, -179, 48,
283, 510, 734, 939, 1153, 1360, 1572, 1783, 2004, 2216, 2437, 2647, 2866, 3072, 3285, 3464, 3641, 3795, 3945, 4067,
4178, 4302, 4398, 4492, 4568, 4650, 4727, 4799, 4854, 4934, 4992, 5065, 5129, 5210, 5288, 5365, 5430, 5484, 5536, 5546,
5529, 5517, 5477, 5416, 5354, 5271, 5197, 5117, 5035, 4955, 4872, 4799, 4726, 4650, 4567, 4532, 4472, 4430, 4393, 4359,
4330, 4264, 4201, 4117, 4007, 3887, 3755, 3626, 3456, 3313, 3167, 3035, 2903, 2780, 2676, 2571, 2468, 2369, 2276, 2197,
2146, 2083, 2048, 1981, 1929, 1847, 1752, 1651, 1539, 1385, 1240, 1079, 915, 754, 591, 440, 303, 166, 35, -70,
-179, -282, -391, -476, -561, -642, -724, -801, -893, -991, -1114, -1255, -1401, -1579, -1759, -1941, -2130, -2312, -2490, -2644,
-2779, -2905, -3039, -3124, -3223, -3312, -3400, -3470, -3543, -3603, -3663, -3729, -3797, -3858, -3955, -4051, -4164, -4269, -4402, -4520,
-4642, -4751, -4838, -4906, -4953, -4982, -5011, -5012, -5006, -4989, -4969, -4952, -4923, -4890, -4853, -4829, -4798, -4772, -4758, -4758,
-4765, -4775, -4784, -4805, -4793, -4787, -4754, -4708, -4656, -4572, -4473, -4371, -4241, -4120, -4001, -3866, -3744, -3615, -3476, -3345,
-3210, -3072, -2943, -2812, -2684, -2563, -2420, -2289, -2129, -1965, -1768, -1574, -1361, -1124, -886, -629, -363, -95, 166, 436,
698, 963, 1225, 1484, 1742, 2016, 2265, 2528, 2787, 3038, 3312, 3565, 3822, 4092, 4362, 4622, 4881, 5133, 5391, 5645,
5878, 6110, 6329, 6540, 6743, 6936, 7121, 7306, 7472, 7655, 7819, 7992, 8157, 8316, 8477, 8644, 8777, 8922, 9040, 9150,
9252, 9333, 9403, 9464, 9515, 9559, 9613, 9651, 9690, 9708, 9735, 9772, 9799, 9826, 9868, 9895, 9933, 9946, 9977, 9991,
10002, 9987, 9964, 9926, 9864, 9790, 9703, 9611, 9516, 9417, 9330, 9239, 9148, 9053, 8962, 8875, 8803, 8712, 8646, 8557,
8475, 8397, 8306, 8216, 8114, 7991, 7856, 7708, 7539, 7375, 7168, 6984, 6808, 6641, 6465, 6313, 6157, 6012, 5884, 5743,
5623, 5506, 5376, 5269, 5147, 5034, 4906, 4768, 4643, 4498, 4331, 4166, 3978, 3795, 3600, 3397, 3214, 3049, 2884, 2731,
2589, 2459, 2335, 2226, 2103, 2003, 1879, 1755, 1651, 1520, 1411, 1271, 1126, 980, 820, 637, 461, 268, 77, -116,
-297, -481, -640, -795, -923, -1056, -1172, -1292, -1402, -1526, -1639, -1769, -1891, -2019, -2150, -2287, -2452, -2604, -2764, -2940,
-3125, -3308, -3486, -3669, -3848, -4012, -4152, -4280, -4407, -4501, -4604, -4703, -4802, -4903, -5011, -5114, -5227, -5332, -5451, -5569,
-5708, -5850, -5991, -6135, -6286, -6440, -6580, -6711, -6858, -6987, -7098, -7172, -7273, -7332, -7400, -7458, -7521, -7593, -7670, -7742,
-7831, -7922, -8016, -8116, -8219, -8336, -8440, -8554, -8681, -8800, -8910, -9017, -9114, -9204, -9270, -9311, -9347, -9384, -9402, -9421,
-9445, -9472, -9507, -9530, -9570, -9621, -9643, -9689, -9712, -9754, -9788, -9813, -9827, -9851, -9849, -9837, -9810, -9770, -9709, -9641,
-9545, -9440, -9325, -9209, -9089, -8968, -8859, -8735, -8605, -8491, -8361, -8215, -8080, -7922, -7773, -7611, -7429, -7255, -7076, -6864,
-6663, -6439, -6199, -5961, -5706, -5451, -5216, -4950, -4702, -4445, -4195, -3940, -3691, -3439, -3180, -2905, -2639, -2368, -2097, -1825,
-1556, -1279, -1012, -737, -466, -195, 64, 326, 570, 829, 1057, 1288, 1526, 1742, 1968, 2194, 2411, 2650, 2882, 3100,
3336, 3549, 3765, 3959, 4147, 4336, 4497, 4654, 4801, 4944, 5061, 5154, 5248, 5317, 5379, 5427, 5499, 5560, 5618, 5674,
5744, 5813, 5883, 5948, 6009, 6055, 6095, 6107, 6105, 6092, 6072, 6023, 5982, 5912, 5840, 5759, 5640, 5529, 5436, 5321,
5223, 5129, 5044, 4973, 4906, 4851, 4808, 4757, 4708, 4651, 4567, 4480, 4386, 4270, 4147, 4024, 3878, 3733, 3584, 3439,
3271, 3114, 2956, 2813, 2661, 2541, 2440, 2341, 2255, 2182, 2111, 2040, 1973, 1881, 1793, 1670, 1547, 1398, 1255, 1108,
937, 774, 610, 439, 273, 97, -67, -212, -361, -495, -605, -701, -791, -872, -960, -1021, -1123, -1213, -1325, -1449,
-1591, -1747, -1906, -2070, -2227, -2395, -2559, -2713, -2867, -3020, -3170, -3296, -3394, -3516, -3591, -3662, -3711, -3768, -3820, -3862,
-3909, -3974, -4044, -4131, -4240, -4338, -4446, -4564, -4663, -4766, -4866, -4940, -5021, -5086, -5136, -5179, -5201, -5222, -5219, -5198,
-5173, -5126, -5086, -5060, -5024, -5003, -4994, -4985, -5000, -5001, -5014, -5039, -5052, -5042, -5028, -4999, -4956, -4897, -4827, -4752,
-4660, -4552, -4443, -4310, -4163, -4025, -3877, -3732, -3597, -3448, -3313, -3202, -3063, -2942, -2812, -2701, -2556, -2391, -2215, -2039,
-1830, -1622, -1389, -1172, -938, -680, -422, -172, 100, 351, 616, 871, 1137, 1391, 1657, 1891, 2140, 2383, 2636, 2883,
3124, 3384, 3644, 3885, 4148, 4411, 4664, 4921, 5145, 5398, 5621, 5845, 6047, 6272, 6458, 6662, 6836, 7016, 7202, 7376,
7541, 7722, 7889, 8054, 8195, 8327, 8471, 8602, 8710, 8828, 8906, 9000, 9072, 9137, 9194, 9237, 9270, 9301, 9322, 9342,
9374, 9389, 9420, 9456, 9478, 9510, 9549, 9568, 9571, 9563, 9533, 9510, 9457, 9402, 9346, 9265, 9189, 9097, 9003, 8904,
8814, 8708, 8599, 8509, 8411, 8324, 8249, 8180, 8117, 8050, 7987, 7901, 7820, 7708, 7588, 7467, 7333, 7181, 7027, 6869,
6708, 6549, 6393, 6241, 6085, 5933, 5788, 5659, 5532, 5419, 5315, 5215, 5115, 5033, 4928, 4823, 4712, 4585, 4438, 4294,
4128, 3953, 3790, 3622, 3456, 3297, 3126, 2975, 2828, 2678, 2541, 2419, 2299, 2184, 2066, 1966, 1869, 1782, 1672, 1571,
1442, 1316, 1161, 997, 828, 654, 470, 292, 125, -49, -207, -365, -505, -653, -788, -919, -1032, -1154, -1259, -1369,
-1474, -1585, -1692, -1808, -1939, -2086, -2239, -2415, -2593, -2764, -2939, -3111, -3274, -3434, -3580, -3726, -3861, -3990, -4103, -4218,
-4323, -4431, -4526, -4626, -4722, -4819, -4923, -5035, -5151, -5287, -5431, -5585, -5744, -5901, -6060, -6216, -6351, -6476, -6600, -6708,
-6805, -6908, -6986, -7074, -7157, -7243, -7307, -7384, -7468, -7539, -7612, -7696, -7810, -7907, -8036, -8154, -8283, -8417, -8535, -8652,
-8757, -8837, -8928, -8996, -9056, -9100, -9137, -9181, -9223, -9248, -9280, -9304, -9331, -9362, -9392, -9419, -9458, -9499, -9537, -9587,
-9629, -9685, -9707, -9718, -9721, -9699, -9659, -9614, -9554, -9488, -9416, -9319, -9232, -9145, -9040, -8929, -8815, -8707, -8597, -8473,
-8346, -8229, -8105, -7977, -7842, -7704, -7543, -7374, -7190, -6996, -6777, -6559, -6321, -6094, -5867, -5621, -5379, -5141, -4893, -4644,
-4395, -4146, -3893, -3634, -3381, -3111, -2853, -2581, -2319, -2053, -1781, -1498, -1216, -946, -675, -406, -139, 113, 356, 595,
832, 1072, 1290, 1539, 1767, 2009, 2226, 2456, 2677, 2896, 3112, 3336, 3541, 3751, 3940, 4118, 4294, 4453, 4587, 4706,
4815, 4909, 5000, 5068, 5140, 5220, 5288, 5356, 5447, 5512, 5596, 5657, 5723, 5789, 5856, 5894, 5954, 5987, 6011, 6011,
6000, 5968, 5928, 5851, 5791, 5699, 5625, 5521, 5435, 5360, 5301, 5230, 5178, 5128, 5078, 5030, 4976, 4919, 4875, 4816,
4754, 4678, 4605, 4497, 4389, 4275, 4135, 3982, 3821, 3673, 3509, 3360, 3214, 3087, 2973, 2878, 2786, 2709, 2622, 2545,
2470, 2381, 2299, 2205, 2093, 1995, 1873, 1755, 1615, 1464, 1295, 1126, 940, 770, 599, 434, 290, 152, 15, -88,
-180, -265, -357, -443, -528, -635, -727, -837, -968, -1085, -1209, -1352, -1495, -1666, -1833, -2008, -2186, -2346, -2505, -2652,
-2783, -2911, -3009, -3095, -3160, -3227, -3281, -3337, -3397, -3475, -3551, -3629, -3715, -3807, -3905, -3999, -4105, -4212, -4327, -4451,
-4548, -4658, -4740, -4807, -4872, -4912, -4940, -4945, -4924, -4911, -4890, -4861, -4850, -4842, -4842, -4842, -4850, -4859, -4879, -4887,
-4893, -4909, -4930, -4944, -4932, -4916, -4887, -4851, -4791, -4705, -4615, -4504, -4381, -4236, -4110, -3952, -3819, -3689, -3573, -3445,
-3330, -3197, -3076, -2934, -2809, -2663, -2512, -2360, -2169, -1975, -1785, -1578, -1348, -1120, -870, -618, -354, -82, 174, 441,
702, 951, 1202, 1449, 1694, 1937, 2172, 2422, 2676, 2917, 3174, 3427, 3685, 3946, 4192, 4447, 4711, 4950, 5197, 5415,
5643, 5858, 6075, 6273, 6483, 6678, 6862, 7053, 7225, 7400, 7575, 7732, 7902, 8055, 8221, 8365, 8502, 8626, 8757, 8871,
8966, 9048, 9117, 9180, 9215, 9257, 9295, 9331, 9359, 9407, 9441, 9485, 9515, 9534, 9570, 9589, 9597, 9612, 9609, 9607,
9574, 9552, 9517, 9463, 9390, 9318, 9223, 9127, 9021, 8903, 8800, 8708, 8606, 8523, 8445, 8373, 8296, 8221, 8148, 8068,
7970, 7870, 7770, 7657, 7546, 7409, 7276, 7130, 6986, 6820, 6658, 6483, 6317, 6135, 5982, 5834, 5701, 5570, 5469, 5370,
5266, 5158, 5051, 4946, 4835, 4693, 4569, 4432, 4288, 4136, 3963, 3811, 3644, 3466, 3297, 3127, 2949, 2773, 2609, 2458,
2326, 2195, 2091, 1985, 1884, 1775, 1672, 1553, 1438, 1301, 1153, 1013, 837, 673, 504, 340, 179, 1, -185, -358,
-532, -684, -856, -996, -1119, -1243, -1362, -1455, -1557, -1650, -1749, -1882, -2002, -2132, -2290, -2431, -2583, -2745, -2908, -3085,
-3230, -3388, -3552, -3714, -3850, -4011, -4125, -4273, -4381, -4471, -4576, -4657, -4734, -4818, -4916, -5022, -5124, -5257, -5387, -5529,
-5677, -5822, -5961, -6107, -6246, -6380, -6513, -6646, -6764, -6885, -6980, -7081, -7171, -7244, -7313, -7381, -7440, -7499, -7572, -7654,
-7752, -7853, -7963, -8077, -8194, -8307, -8425, -8535, -8647, -8739, -8824, -8909, -8978, -9048, -9107, -9144, -9186, -9219, -9239, -9245,
-9260, -9266, -9282, -9305, -9337, -9384, -9414, -9449, -9489, -9515, -9544, -9555, -9562, -9549, -9531, -9484, -9460, -9398, -9338, -9267,
-9188, -9090, -8986, -8872, -8767, -8643, -8524, -8407, -8301, -8180, -8070, -7942, -7820, -7687, -7535, -7376, -7206, -7024, -6830, -6639,
-6427, -6211, -5991, -5768, -5535, -5297, -5065, -4822, -4569, -4329, -4082, -3847, -3598, -3361, -3116, -2856, -2604, -2343, -2077, -1804,
-1529, -1262, -1002, -750, -481, -238, 12, 242, 475, 712, 930, 1155, 1376, 1583, 1790, 2007, 2223, 2428, 2637, 2841,
3046, 3249, 3445, 3637, 3799, 3958, 4086, 4209, 4332, 4429, 4515, 4591, 4669, 4743, 4792, 4856, 4907, 4973, 5019, 5080,
5144, 5202, 5264, 5323, 5372, 5435, 5458, 5480, 5491, 5472, 5441, 5389, 5339, 5265, 5183, 5112, 5024, 4948, 4874, 4797,
4731, 4668, 4610, 4557, 4512, 4476, 4439, 4390, 4352, 4305, 4248, 4170, 4083, 3969, 3852, 3712, 3573, 3432, 3283, 3138,
3007, 2880, 2761, 2640, 2533, 2426, 2335, 2249, 2164, 2100, 2031, 1961, 1888, 1799, 1710, 1603, 1481, 1352, 1197, 1032,
867, 696, 543, 372, 223, 100, -40, -154, -273, -379, -469, -558, -642, -715, -790, -875, -966, -1055, -1149, -1267,
-1401, -1536, -1700, -1860, -2025, -2195, -2347, -2488, -2619, -2736, -2839, -2940, -3020, -3108, -3165, -3222, -3287, -3339, -3397, -3446,
-3507, -3575, -3650, -3725, -3826, -3923, -4033, -4143, -4262, -4365, -4467, -4541, -4612, -4662, -4689, -4712, -4719, -4724, -4716, -4707,
-4686, -4682, -4654, -4640, -4621, -4618, -4630, -4615, -4619, -4639, -4656, -4661, -4662, -4670, -4647, -4603, -4553, -4489, -4410, -4300,
-4186, -4062, -3939, -3800, -3666, -3529, -3385, -3255, -3109, -2959, -2827, -2687, -2547, -2398, -2256, -2098, -1936, -1757, -1576, -1385,
-1176, -941, -711, -458, -203, 61, 326, 573, 832, 1089, 1336, 1594, 1836, 2081, 2308, 2552, 2796, 3043, 3280, 3532,
3779, 4032, 4275, 4511, 4761, 5008, 5234, 5463, 5688, 5905, 6121, 6319, 6509, 6704, 6886, 7050, 7221, 7385, 7546, 7698,
7852, 8018, 8163, 8309, 8460, 8586, 8708, 8811, 8913, 8992, 9061, 9112, 9174, 9219, 9267, 9308, 9327, 9362, 9400, 9426,
9453, 9473, 9508, 9521, 9538, 9556, 9578, 9583, 9589, 9584, 9553, 9507, 9451, 9383, 9301, 9205, 9112, 9011, 8906, 8822,
8715, 8619, 8537, 8448, 8357, 8282, 8198, 8114, 8022, 7935, 7852, 7759, 7654, 7555, 7428, 7293, 7145, 6978, 6817, 6654,
6473, 6309, 6148, 5999, 5849, 5711, 5587, 5466, 5343, 5228, 5112, 4999, 4878, 4760, 4641, 4510, 4373, 4235, 4083, 3917,
3744, 3557, 3367, 3193, 3007, 2844, 2677, 2515, 2372, 2240, 2121, 2005, 1891, 1768, 1662, 1547, 1438, 1309, 1183, 1056,
918, 766, 616, 446, 279, 99, -85, -260, -431, -611, -751, -908, -1039, -1157, -1279, -1397, -1497, -1625, -1730, -1849,
-1969, -2099, -2236, -2372, -2513, -2672, -2822, -2993, -3156, -3324, -3511, -3687, -3849, -4005, -4157, -4279, -4412, -4517, -4628, -4739,
-4829, -4935, -5045, -5139, -5261, -5378, -5508, -5645, -5774, -5908, -6057, -6203, -6350, -6500, -6642, -6789, -6921, -7036, -7151, -7243,
-7332, -7395, -7469, -7546, -7610, -7673, -7743, -7827, -7900, -7997, -8086, -8187, -8289, -8385, -8488, -8595, -8685, -8801, -8888, -8980,
-9062, -9135, -9193, -9229, -9260, -9286, -9298, -9316, -9330, -9346, -9357, -9393, -9410, -9437, -9469, -9502, -9527, -9543, -9560, -9578,
-9579, -9576, -9563, -9547, -9523, -9477, -9414, -9344, -9255, -9148, -9055, -8942, -8827, -8716, -8600, -8480, -8370, -8243, -8132, -7985,
-7849, -7709, -7551, -7383, -7210, -7020, -6822, -6620, -6416, -6201, -5966, -5720, -5488, -5222, -4978, -4719, -4469, -4221, -3975, -3722,
-3483, -3215, -2956, -2693, -2423, -2154, -1892, -1603, -1344, -1066, -787, -529, -262, 2, 243, 502, 737, 973, 1209, 1423,
1640, 1851, 2057, 2261, 2476, 2681, 2895, 3107, 3324, 3509, 3707, 3897, 4083, 4244, 4398, 4538, 4674, 4786, 4878, 4974,
5050, 5117, 5186, 5245, 5289, 5344, 5397, 5436, 5513, 5556, 5624, 5685, 5745, 5784, 5825, 5842, 5849, 5841, 5815, 5786,
5731, 5672, 5594, 5504, 5424, 5327, 5235, 5138, 5041, 4954, 4878, 4805, 4749, 4692, 4624, 4571, 4524, 4461, 4375, 4292,
4195, 4091, 3969, 3845, 3712, 3569, 3422, 3262, 3119, 2969, 2826, 2693, 2570, 2453, 2348, 2243, 2161, 2088, 2007, 1937,
1872, 1784, 1683, 1584, 1462, 1337, 1204, 1062, 912, 760, 596, 447, 291, 137, 10, -131, -255, -379, -478, -585,
-676, -759, -839, -936, -1023, -1121, -1233, -1354, -1490, -1631, -1784, -1948, -2110, -2272, -2433, -2595, -2748, -2893, -3017, -3147,
-3256, -3363, -3453, -3527, -3598, -3667, -3732, -3802, -3878, -3945, -4031, -4116, -4220, -4321, -4426, -4531, -4645, -4748, -4838, -4922,
-5000, -5065, -5104, -5138, -5167, -5173, -5168, -5156, -5140, -5110, -5095, -5062, -5047, -5021, -5010, -5004, -5007, -5007, -5010, -5012,
-5008, -5003, -4967, -4938, -4890, -4833, -4760, -4669, -4564, -4452, -4329, -4198, -4055, -3926, -3785, -3642, -3506, -3369, -3226, -3085,
-2953, -2816, -2675, -2531, -2367, -2206, -2022, -1835, -1630, -1411, -1193, -947, -693, -442, -183, 91, 348, 607, 868, 1126,
1390, 1640, 1902, 2156, 2415, 2671, 2928, 3179, 3438, 3708, 3954, 4216, 4480, 4738, 4987, 5236, 5485, 5722, 5948, 6174,
6382, 6592, 6778, 6957, 7141, 7310, 7466, 7640, 7806, 7964, 8106, 8238, 8375, 8495, 8608, 8717, 8808, 8906, 8980, 9044,
9100, 9151, 9182, 9215, 9253, 9277, 9293, 9295, 9312, 9323, 9340, 9348, 9368, 9375, 9387, 9386, 9382, 9367, 9351, 9310,
9270, 9218, 9156, 9081, 8997, 8927, 8852, 8750, 8673, 8578, 8488, 8399, 8318, 8237, 8165, 8082, 8012, 7930, 7855, 7773,
7678, 7567, 7462, 7334, 7203, 7058, 6910, 6748, 6585, 6435, 6273, 6120, 5959, 5818, 5665, 5533, 5391, 5257, 5136, 5013,
4885, 4772, 4653, 4528, 4386, 4242, 4097, 3941, 3765, 3592, 3418, 3253, 3073, 2907, 2734, 2584, 2430, 2286, 2154, 2023,
1893, 1769, 1653, 1548, 1433, 1330, 1222, 1108, 983, 845, 700, 563, 400, 243, 92, -62, -218, -366, -524, -653,
-799, -930, -1048, -1167, -1288, -1397, -1510, -1614, -1718, -1837, -1947, -2087, -2207, -2353, -2499, -2667, -2824, -2992, -3154, -3323,
-3482, -3641, -3786, -3938, -4072, -4212, -4335, -4452, -4565, -4676, -4801, -4906, -5012, -5128, -5241, -5356, -5486, -5617, -5766, -5905,
-6047, -6198, -6345, -6484, -6617, -6744, -6863, -6977, -7078, -7161, -7246, -7328, -7390, -7468, -7536, -7617, -7683, -7740, -7826, -7901,
-7986, -8080, -8176, -8287, -8380, -8475, -8584, -8674, -8760, -8834, -8902, -8958, -9012, -9048, -9081, -9118, -9148, -9172, -9208, -9238,
-9257, -9288, -9320, -9346, -9383, -9425, -9456, -9495, -9529, -9548, -9568, -9583, -9576, -9560, -9535, -9489, -9441, -9383, -9308, -9235,
-9143, -9057, -8961, -8858, -8759, -8636, -8514, -8399, -8267, -8137, -7988, -7836, -7687, -7528, -7345, -7162, -6966, -6755, -6533, -6305,
-6073, -5839, -5597, -5351, -5093, -4841, -4592, -4326, -4066, -3806, -3535, -3270, -3003, -2733, -2454, -2172, -1912, -1644, -1377, -1104,
-846, -577, -317, -64, 187, 427, 657, 893, 1116, 1339, 1565, 1781, 1994, 2211, 2427, 2646, 2853, 3064, 3271, 3466,
3654, 3833, 4002, 4166, 4321, 4450, 4582, 4689, 4795, 4878, 4958, 5041, 5114, 5186, 5257, 5332, 5401, 5462, 5534, 5596,
5659, 5707, 5762, 5799, 5827, 5838, 5832, 5817, 5782, 5743, 5680, 5616, 5541, 5458, 5374, 5288, 5197, 5110, 5032, 4959,
4899, 4831, 4763, 4710, 4653, 4583, 4523, 4444, 4363, 4271, 4154, 4045, 3919, 3789, 3645, 3506, 3353, 3212, 3069, 2932,
2810, 2688, 2577, 2485, 2387, 2308, 2219, 2145, 2067, 1986, 1890, 1806, 1698, 1588, 1460, 1321, 1176, 1031, 867, 708,
552, 396, 247, 103, -36, -159, -280, -383, -487, -589, -686, -783, -894, -988, -1098, -1219, -1350, -1474, -1627, -1781,
-1953, -2114, -2278, -2457, -2612, -2765, -2903, -3047, -3174, -3291, -3390, -3487, -3569, -3651, -3724, -3800, -3870, -3948, -4029, -4115,
-4206, -4289, -4390, -4502, -4602, -4709, -4805, -4890, -4974, -5042, -5103, -5143, -5180, -5197, -5205, -5201, -5197, -5175, -5149, -5126,
-5111, -5083, -5064, -5056, -5038, -5028, -5024, -5020, -5014, -5007, -4990, -4959, -4927, -4868, -4803, -4725, -4637, -4538, -4426, -4300,
-4172, -4037, -3905, -3771, -3633, -3488, -3370, -3225, -3096, -2963, -2817, -2681, -2532, -2379, -2209, -2029, -1828, -1631, -1409, -1180,
-943, -696, -443, -184, 73, 328, 591, 860, 1112, 1367, 1622, 1876, 2125, 2378, 2636, 2878, 3141, 3392, 3650, 3907,
4170, 4420, 4681, 4934, 5179, 5416, 5636, 5849, 6068, 6261, 6452, 6642, 6827, 7003, 7170, 7327, 7495, 7647, 7802, 7944,
8089, 8225, 8352, 8475, 8586, 8684, 8773, 8860, 8931, 8995, 9037, 9070, 9103, 9132, 9153, 9186, 9215, 9234, 9255, 9275,
9293, 9313, 9328, 9342, 9348, 9356, 9339, 9313, 9276, 9246, 9195, 9132, 9061, 8983, 8889, 8785, 8684, 8591, 8493, 8401,
8314, 8225, 8149, 8065, 7982, 7900, 7817, 7724, 7627, 7529, 7417, 7292, 7162, 7022, 6874, 6720, 6560, 6401, 6230, 6059,
5892, 5742, 5595, 5443, 5321, 5193, 5070, 4951, 4830, 4721, 4608, 4485, 4362, 4229, 4099, 3953, 3798, 3643, 3478, 3312,
3144, 2973, 2807, 2643, 2487, 2338, 2200, 2065, 1947, 1832, 1725, 1619, 1511, 1396, 1291, 1178, 1048, 919, 787, 645,
488, 330, 163, -2, -170, -331, -494, -653, -808, -949, -1084, -1217, -1334, -1447, -1570, -1676, -1785, -1910, -2032, -2154,
-2298, -2437, -2584, -2740, -2899, -3058, -3237, -3407, -3577, -3738, -3894, -4043, -4191, -4332, -4464, -4582, -4696, -4811, -4913, -5021,
-5119, -5233, -5353, -5475, -5589, -5726, -5857, -5997, -6141, -6288, -6437, -6582, -6715, -6848, -6971, -7086, -7198, -7289, -7385, -7468,
-7540, -7604, -7668, -7735, -7792, -7867, -7942, -8026, -8101, -8194, -8286, -8391, -8484, -8584, -8689, -8778, -8854, -8943, -9008, -9065,
-9118, -9165, -9196, -9229, -9248, -9257, -9273, -9280, -9289, -9308, -9330, -9354, -9378, -9403, -9433, -9464, -9490, -9509, -9519, -9527,
-9519, -9499, -9464, -9424, -9369, -9303, -9226, -9152, -9049, -8949, -8838, -8736, -8621, -8502, -8379, -8264, -8142, -8008, -7882, -7739,
-7588, -7432, -7261, -7084, -6900, -6698, -6484, -6275, -6042, -5808, -5571, -5333, -5087, -4845, -4589, -4347, -4083, -3830, -3564, -3316,
-3063, -2805, -2542, -2289, -2025, -1764, -1500, -1241, -982, -722, -466, -215, 33, 268, 510, 736, 956, 1181, 1400, 1613,
1828, 2046, 2253, 2474, 2673, 2884, 3081, 3278, 3460, 3651, 3820, 3985, 4133, 4271, 4410, 4533, 4635, 4731, 4815, 4903,
4974, 5042, 5108, 5182, 5245, 5314, 5382, 5450, 5507, 5566, 5612, 5655, 5682, 5707, 5707, 5703, 5685, 5644, 5605, 5555,
5481, 5399, 5325, 5235, 5141, 5058, 4966, 4887, 4816, 4745, 4684, 4625, 4564, 4504, 4440, 4362, 4283, 4192, 4094, 3986,
3874, 3753, 3620, 3487, 3339, 3198, 3064, 2927, 2798, 2669, 2545, 2437, 2346, 2257, 2178, 2103, 2039, 1963, 1882, 1792,
1705, 1596, 1484, 1372, 1241, 1107, 953, 806, 665, 519, 369, 234, 93, -24, -149, -264, -361, -458, -546, -629,
-712, -811, -917, -1030, -1145, -1277, -1415, -1562, -1726, -1884, -2049, -2214, -2382, -2526, -2687, -2828, -2964, -3089, -3207, -3310,
-3411, -3498, -3579, -3652, -3727, -3806, -3887, -3983, -4069, -4161, -4270, -4380, -4482, -4594, -4691, -4784, -4875, -4955, -5020, -5082,
-5122, -5154, -5168, -5178, -5176, -5155, -5132, -5112, -5082, -5048, -5022, -5005, -4990, -4972, -4963, -4965, -4949, -4940, -4915, -4892,
-4856, -4808, -4744, -4680, -4595, -4502, -4389, -4279, -4162, -4032, -3892, -3756, -3608, -3470, -3334, -3184, -3059, -2922, -2788, -2644,
-2504, -2341, -2179, -1997, -1814, -1618, -1405, -1177, -948, -700, -455, -193, 60, 319, 587, 851, 1114, 1380, 1641, 1905,
2156, 2421, 2672, 2933, 3190, 3447, 3708, 3974, 4234, 4493, 4742, 4992, 5229, 5464, 5693, 5916, 6129, 6327, 6524, 6715,
6899, 7066, 7244, 7410, 7571, 7730, 7879, 8023, 8164, 8299, 8435, 8552, 8665, 8767, 8856, 8932, 9003, 9060, 9115, 9165,
9203, 9247, 9276, 9308, 9337, 9372, 9405, 9442, 9487, 9506, 9536, 9555, 9575, 9585, 9592, 9595, 9567, 9540, 9499, 9439,
9381, 9303, 9236, 9158, 9076, 8993, 8903, 8819, 8729, 8650, 8567, 8491, 8415, 8335, 8240, 8155, 8061, 7956, 7847, 7724,
7582, 7446, 7282, 7123, 6951, 6782, 6616, 6442, 6267, 6106, 5959, 5797, 5638, 5511, 5372, 5245, 5112, 4992, 4868, 4741,
4612, 4474, 4333, 4190, 4032, 3873, 3707, 3531, 3358, 3192, 3025, 2862, 2701, 2559, 2421, 2289, 2160, 2046, 1937, 1822,
1717, 1608, 1514, 1398, 1278, 1156, 1006, 871, 720, 566, 410, 238, 70, -93, -256, -423, -578, -721, -865, -999,
-1129, -1258, -1383, -1507, -1634, -1756, -1884, -2017, -2161, -2308, -2461, -2627, -2801, -2978, -3150, -3322, -3498, -3683, -3844, -4005,
-4163, -4305, -4439, -4560, -4680, -4804, -4930, -5036, -5143, -5261, -5374, -5491, -5611, -5742, -5890, -6026, -6167, -6306, -6446, -6589,
-6729, -6864, -6991, -7103, -7208, -7301, -7392, -7470, -7541, -7617, -7687, -7755, -7819, -7891, -7964, -8042, -8128, -8220, -8313, -8412,
-8509, -8607, -8702, -8802, -8895, -8986, -9062, -9135, -9190, -9244, -9280, -9320, -9342, -9375, -9403, -9427, -9457, -9479, -9510, -9544,
-9568, -9613, -9648, -9681, -9705, -9728, -9757, -9764, -9767, -9753, -9725, -9694, -9642, -9584, -9507, -9429, -9334, -9227, -9127, -9021,
-8905, -8779, -8664, -8551, -8418, -8286, -8149, -8007, -7849, -7686, -7514, -7333, -7143, -6929, -6719, -6498, -6266, -6029, -5785, -5539,
-5292, -5040, -4784, -4538, -4290, -4029, -3786, -3528, -3269, -3014, -2752, -2492, -2229, -1963, -1694, -1427, -1160, -893, -630, -380,
-130, 110, 349, 580, 801, 1034, 1246, 1462, 1684, 1896, 2108, 2318, 2519, 2729, 2935, 3128, 3327, 3511, 3708, 3874,
4042, 4193, 4339, 4460, 4568, 4669, 4756, 4836, 4911, 4984, 5056, 5125, 5186, 5248, 5323, 5381, 5440, 5501, 5552, 5590,
5623, 5654, 5659, 5665, 5649, 5630, 5591, 5543, 5478, 5394, 5315, 5220, 5129, 5051, 4965, 4894, 4822, 4753, 4688, 4629,
4569, 4505, 4441, 4378, 4294, 4221, 4124, 4032, 3927, 3811, 3683, 3561, 3414, 3261, 3111, 2980, 2830, 2702, 2581, 2479,
2370, 2272, 2179, 2107, 2023, 1938, 1852, 1770, 1666, 1560, 1448, 1333, 1204, 1065, 929, 778, 621, 455, 304, 141,
0, -132, -257, -376, -481, -576, -675, -769, -853, -950, -1046, -1154, -1268, -1386, -1527, -1661, -1797, -1946, -2104, -2264,
-2411, -2568, -2727, -2868, -3007, -3132, -3248, -3351, -3439, -3512, -3595, -3659, -3728, -3801, -3889, -3971, -4063, -4149, -4254, -4355,
-4454, -4557, -4659, -4771, -4857, -4945, -5021, -5096, -5161, -5204, -5230, -5248, -5246, -5240, -5232, -5216, -5200, -5190, -5169, -5166,
-5163, -5160, -5157, -5161, -5162, -5150, -5151, -5127, -5116, -5077, -5038, -4991, -4941, -4866, -4770, -4669, -4556, -4431, -4295, -4165,
-4034, -3904, -3772, -3643, -3514, -3388, -3261, -3121, -2990, -2842, -2687, -2522, -2344, -2157, -1965, -1750, -1537, -1314, -1070, -815,
-556, -300, -27, 240, 501, 765, 1029, 1291, 1545, 1807, 2072, 2329, 2592, 2859, 3125, 3400, 3669, 3935, 4207, 4470,
4733, 4993, 5234, 5481, 5717, 5947, 6168, 6389, 6596, 6795, 6979, 7165, 7345, 7524, 7696, 7865, 8021, 8172, 8319, 8465,
8591, 8714, 8821, 8928, 9023, 9104, 9167, 9228, 9283, 9333, 9369, 9408, 9445, 9479, 9501, 9531, 9564, 9600, 9630, 9654,
9674, 9678, 9684, 9684, 9671, 9645, 9620, 9580, 9531, 9468, 9407, 9337, 9255, 9179, 9097, 9018, 8934, 8858, 8784, 8711,
8640, 8569, 8497, 8419, 8342, 8245, 8149, 8047, 7929, 7805, 7672, 7535, 7392, 7235, 7091, 6922, 6767, 6616, 6464, 6306,
6163, 6029, 5887, 5762, 5650, 5522, 5404, 5286, 5161, 5031, 4893, 4746, 4592, 4442, 4281, 4117, 3947, 3779, 3614, 3446,
3282, 3120, 2973, 2825, 2688, 2560, 2428, 2320, 2200, 2093, 1979, 1861, 1750, 1624, 1489, 1345, 1196, 1039, 884, 719,
549, 392, 230, 70, -98, -253, -402, -543, -681, -813, -939, -1067, -1183, -1306, -1425, -1554, -1686, -1829, -1973, -2133,
-2303, -2474, -2644, -2818, -2987, -3158, -3321, -3483, -3642, -3797, -3945, -4082, -4220, -4345, -4462, -4572, -4689, -4804, -4922, -5029,
-5157, -5285, -5415, -5551, -5709, -5852, -5998, -6142, -6282, -6415, -6548, -6664, -6781, -6893, -6995, -7091, -7177, -7256, -7334, -7404,
-7478, -7546, -7620, -7697, -7781, -7863, -7961, -8054, -8163, -8270, -8373, -8482, -8569, -8663, -8751, -8822, -8893, -8958, -9018, -9068,
-9109, -9148, -9190, -9223, -9248, -9284, -9316, -9351, -9390, -9426, -9470, -9515, -9553, -9599, -9635, -9662, -9679, -9691, -9681, -9671,
-9641, -9607, -9564, -9513, -9434, -9361, -9275, -9197, -9091, -8998, -8892, -8789, -8674, -8564, -8446, -8324, -8185, -8041, -7895, -7741,
-7562, -7385, -7188, -6989, -6773, -6554, -6332, -6108, -5870, -5628, -5378, -5135, -4890, -4641, -4390, -4144, -3893, -3639, -3393, -3127,
-2866, -2598, -2330, -2067, -1806, -1536, -1274, -1009, -767, -515, -267, -23, 209, 443, 675, 901, 1122, 1346, 1564, 1776,
1990, 2196, 2417, 2628, 2844, 3043, 3246, 3432, 3614, 3775, 3932, 4076, 4196, 4317, 4425, 4515, 4605, 4694, 4783, 4860,
4934, 5008, 5075, 5147, 5212, 5268, 5331, 5385, 5442, 5485, 5521, 5537, 5545, 5528, 5499, 5455, 5400, 5326, 5264, 5186,
5095, 5014, 4943, 4866, 4806, 4730, 4661, 4600, 4525, 4468, 4408, 4349, 4285, 4218, 4145, 4061, 3961, 3857, 3731, 3604,
3462, 3323, 3180, 3040, 2903, 2775, 2656, 2545, 2441, 2344, 2253, 2167, 2077, 1992, 1909, 1838, 1749, 1660, 1556, 1456,
1343, 1207, 1065, 916, 757, 596, 440, 293, 143, 0, -130, -244, -355, -459, -564, -660, -755, -852, -951, -1051,
-1154, -1260, -1381, -1497, -1633, -1773, -1929, -2088, -2246, -2406, -2562, -2716, -2841, -2964, -3072, -3172, -3265, -3339, -3411, -3475,
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-4608, -4543, -4454, -4363, -4262, -4146, -4021, -3896, -3780, -3647, -3525, -3396, -3280, -3153, -3023, -2883, -2750, -2608, -2467, -2315,
-2154, -1988, -1810, -1614, -1408, -1187, -953, -716, -466, -209, 47, 305, 556, 810, 1073, 1319, 1567, 1807, 2062, 2311,
2555, 2809, 3067, 3315, 3567, 3815, 4069, 4314, 4567, 4809, 5059, 5299, 5526, 5742, 5962, 6164, 6362, 6558, 6740, 6931,
7098, 7262, 7425, 7595, 7756, 7902, 8055, 8208, 8338, 8474, 8595, 8711, 8806, 8893, 8969, 9045, 9096, 9146, 9189, 9232,
9268, 9303, 9337, 9369, 9398, 9422, 9449, 9475, 9496, 9507, 9519, 9520, 9514, 9502, 9476, 9432, 9385, 9326, 9254, 9171,
9085, 8991, 8891, 8803, 8705, 8620, 8538, 8457, 8368, 8286, 8197, 8117, 8024, 7936, 7838, 7738, 7628, 7506, 7376, 7239,
7098, 6940, 6781, 6623, 6453, 6287, 6126, 5966, 5826, 5689, 5562, 5433, 5322, 5195, 5086, 4958, 4844, 4723, 4595, 4461,
4330, 4183, 4033, 3877, 3723, 3551, 3379, 3205, 3043, 2873, 2714, 2561, 2411, 2279, 2157, 2039, 1926, 1814, 1699, 1586,
1453, 1337, 1205, 1065, 922, 779, 624, 465, 299, 130, -40, -210, -378, -540, -696, -845, -987, -1123, -1240, -1355,
-1473, -1579, -1696, -1818, -1942, -2068, -2203, -2345, -2486, -2628, -2788, -2938, -3101, -3268, -3423, -3583, -3737, -3878, -4017, -4152,
-4279, -4390, -4496, -4597, -4687, -4784, -4881, -4987, -5098, -5217, -5333, -5460, -5588, -5722, -5849, -5989, -6122, -6259, -6399, -6520,
-6646, -6752, -6861, -6960, -7045, -7129, -7200, -7264, -7325, -7386, -7448, -7525, -7602, -7692, -7778, -7870, -7962, -8068, -8163, -8257,
-8348, -8447, -8533, -8615, -8691, -8764, -8822, -8874, -8916, -8950, -8963, -8982, -8998, -9013, -9034, -9052, -9087, -9101, -9154, -9177,
-9209, -9241, -9263, -9286, -9296, -9297, -9305, -9283, -9266, -9231, -9186, -9127, -9059, -8974, -8889, -8789, -8690, -8581, -8481, -8374,
-8260, -8162, -8045, -7930, -7803, -7673, -7536, -7392, -7227, -7062, -6886, -6708, -6513, -6308, -6099, -5887, -5663, -5432, -5204, -4968,
-4725, -4493, -4256, -4016, -3773, -3528, -3285, -3037, -2781, -2529, -2265, -2009, -1739, -1483, -1227, -974, -723, -471, -229, 13,
254, 493, 719, 936, 1156, 1372, 1584, 1801, 2014, 2226, 2442, 2645, 2861, 3063, 3268, 3454, 3636, 3800, 3958, 4093,
4218, 4352, 4459, 4561, 4650, 4733, 4812, 4882, 4939, 5013, 5066, 5125, 5189, 5255, 5321, 5388, 5444, 5497, 5544, 5565,
5566, 5572, 5552, 5512, 5468, 5411, 5351, 5282, 5211, 5134, 5056, 4979, 4901, 4823, 4739, 4687, 4621, 4570, 4522, 4478,
4438, 4377, 4321, 4241, 4150, 4049, 3938, 3825, 3676, 3546, 3414, 3279, 3146, 3018, 2897, 2780, 2661, 2547, 2438, 2342,
2266, 2189, 2129, 2050, 1981, 1898, 1802, 1707, 1598, 1462, 1327, 1183, 1029, 874, 717, 568, 418, 276, 133, 9,
-118, -238, -358, -459, -557, -648, -737, -821, -914, -1014, -1126, -1251, -1381, -1534, -1688, -1851, -2020, -2188, -2354, -2504,
-2644, -2777, -2916, -3019, -3127, -3231, -3324, -3405, -3483, -3550, -3610, -3677, -3744, -3805, -3889, -3972, -4067, -4162, -4273, -4378,
-4486, -4590, -4681, -4756, -4812, -4867, -4912, -4932, -4949, -4953, -4952, -4949, -4931, -4907, -4877, -4854, -4827, -4803, -4785, -4777,
-4772, -4771, -4772, -4782, -4772, -4764, -4737, -4701, -4654, -4586, -4507, -4417, -4304, -4194, -4087, -3959, -3837, -3702, -3565, -3424,
-3284, -3141, -3005, -2862, -2724, -2591, -2443, -2302, -2141, -1979, -1789, -1600, -1396, -1170, -943, -701, -447, -189, 65, 327,
585, 849, 1110, 1368, 1628, 1895, 2146, 2404, 2663, 2914, 3177, 3425, 3682, 3939, 4202, 4454, 4705, 4956, 5205, 5456,
5690, 5922, 6144, 6356, 6559, 6757, 6943, 7129, 7300, 7481, 7649, 7817, 7977, 8132, 8293, 8450, 8587, 8730, 8851, 8966,
9070, 9162, 9240, 9306, 9369, 9419, 9476, 9517, 9552, 9574, 9600, 9628, 9652, 9672, 9705, 9724, 9750, 9763, 9785, 9795,
9803, 9793, 9773, 9742, 9688, 9625, 9551, 9472, 9384, 9295, 9207, 9117, 9024, 8925, 8830, 8739, 8654, 8562, 8488, 8398,
8316, 8234, 8143, 8056, 7960, 7847, 7724, 7589, 7439, 7288, 7106, 6938, 6770, 6611, 6441, 6290, 6134, 5982, 5849, 5705,
5575, 5453, 5323, 5208, 5089, 4973, 4848, 4717, 4597, 4458, 4309, 4152, 3977, 3806, 3623, 3436, 3259, 3093, 2930, 2769,
2621, 2479, 2345, 2223, 2093, 1978, 1853, 1726, 1619, 1489, 1378, 1245, 1105, 965, 814, 645, 478, 296, 113, -70,
-244, -426, -590, -749, -885, -1030, -1156, -1287, -1408, -1533, -1653, -1781, -1902, -2025, -2153, -2285, -2436, -2580, -2733, -2898,
-3071, -3243, -3414, -3592, -3765, -3926, -4073, -4209, -4344, -4451, -4565, -4677, -4782, -4887, -4998, -5101, -5210, -5315, -5425, -5542,
-5674, -5806, -5941, -6082, -6225, -6372, -6514, -6645, -6793, -6923, -7041, -7133, -7238, -7316, -7395, -7466, -7536, -7616, -7694, -7768,
-7853, -7939, -8026, -8117, -8217, -8324, -8421, -8534, -8651, -8763, -8872, -8976, -9072, -9165, -9235, -9288, -9332, -9374, -9401, -9426,
-9453, -9481, -9510, -9532, -9563, -9601, -9619, -9651, -9674, -9704, -9728, -9750, -9762, -9779, -9778, -9767, -9744, -9709, -9653, -9592,
-9509, -9411, -9305, -9196, -9084, -8968, -8858, -8732, -8605, -8485, -8352, -8207, -8072, -7916, -7768, -7607, -7433, -7262, -7086, -6882,
-6687, -6471, -6241, -6009, -5759, -5514, -5280, -5020, -4772, -4520, -4270, -4018, -3769, -3517, -3257, -2987, -2722, -2455, -2187, -1917,
-1648, -1376, -1106, -834, -563, -296, -38, 224, 472, 727, 960, 1194, 1431, 1648, 1870, 2092, 2310, 2541, 2766, 2976,
3203, 3411, 3621, 3811, 4000, 4186, 4349, 4510, 4657, 4803, 4922, 5024, 5120, 5196, 5264, 5318, 5386, 5446, 5500, 5553,
5616, 5678, 5737, 5797, 5853, 5896, 5934, 5951, 5954, 5951, 5939, 5904, 5872, 5817, 5756, 5682, 5580, 5482, 5392, 5285,
5191, 5098, 5014, 4935, 4865, 4807, 4753, 4696, 4646, 4586, 4508, 4427, 4340, 4237, 4123, 4011, 3879, 3743, 3607, 3467,
3306, 3157, 3002, 2857, 2709, 2584, 2475, 2365, 2269, 2186, 2108, 2025, 1953, 1860, 1773, 1655, 1537, 1400, 1269, 1128,
967, 814, 657, 491, 327, 155, -5, -156, -306, -442, -562, -666, -768, -856, -948, -1020, -1122, -1210, -1318, -1434,
-1568, -1712, -1858, -2011, -2160, -2316, -2474, -2624, -2775, -2926, -3075, -3204, -3311, -3432, -3516, -3595, -3655, -3719, -3778, -3823,
-3874, -3938, -4003, -4083, -4181, -4272, -4373, -4478, -4573, -4671, -4768, -4843, -4927, -4996, -5051, -5102, -5132, -5162, -5167, -5157,
-5140, -5106, -5074, -5049, -5017, -4997, -4983, -4968, -4974, -4971, -4977, -4991, -4996, -4989, -4972, -4945, -4905, -4852, -4788, -4717,
-4629, -4530, -4425, -4297, -4156, -4021, -3875, -3731, -3590, -3440, -3300, -3179, -3034, -2907, -2769, -2649, -2499, -2333, -2157, -1980,
-1777, -1570, -1346, -1130, -900, -647, -394, -145, 121, 375, 636, 892, 1157, 1413, 1676, 1917, 2166, 2412, 2663, 2906,
3150, 3406, 3663, 3902, 4163, 4423, 4674, 4926, 5152, 5403, 5624, 5847, 6053, 6276, 6463, 6665, 6841, 7021, 7204, 7376,
7541, 7718, 7881, 8042, 8184, 8315, 8458, 8588, 8698, 8815, 8898, 8993, 9067, 9134, 9193, 9238, 9273, 9304, 9326, 9345,
9373, 9387, 9414, 9444, 9463, 9489, 9523, 9537, 9538, 9531, 9505, 9483, 9436, 9385, 9334, 9258, 9184, 9097, 9006, 8909,
8819, 8714, 8607, 8514, 8415, 8324, 8246, 8171, 8102, 8032, 7966, 7879, 7796, 7687, 7572, 7456, 7327, 7182, 7035, 6885,
6728, 6573, 6419, 6267, 6111, 5956, 5810, 5677, 5547, 5428, 5317, 5213, 5108, 5021, 4914, 4807, 4694, 4569, 4428, 4287,
4125, 3958, 3800, 3635, 3471, 3311, 3141, 2987, 2836, 2683, 2543, 2413, 2289, 2167, 2044, 1938, 1837, 1744, 1633, 1528,
1401, 1276, 1124, 966, 802, 634, 455, 279, 115, -57, -216, -375, -519, -671, -809, -945, -1063, -1189, -1298, -1412,
-1516, -1631, -1739, -1854, -1983, -2126, -2276, -2444, -2615, -2782, -2952, -3121, -3282, -3441, -3590, -3737, -3876, -4008, -4126, -4244,
-4353, -4464, -4563, -4665, -4763, -4861, -4965, -5074, -5189, -5322, -5462, -5611, -5765, -5917, -6073, -6227, -6362, -6488, -6615, -6727,
-6828, -6935, -7019, -7110, -7196, -7285, -7352, -7432, -7514, -7585, -7658, -7740, -7849, -7944, -8067, -8181, -8305, -8433, -8549, -8664,
-8767, -8848, -8940, -9010, -9072, -9120, -9160, -9206, -9247, -9274, -9305, -9329, -9355, -9382, -9409, -9434, -9466, -9504, -9535, -9581,
-9618, -9668, -9688, -9697, -9698, -9677, -9638, -9595, -9538, -9472, -9401, -9306, -9220, -9131, -9025, -8914, -8800, -8689, -8574, -8449,
-8321, -8201, -8074, -7943, -7806, -7666, -7504, -7334, -7152, -6958, -6741, -6525, -6289, -6062, -5835, -5590, -5349, -5109, -4861, -4612,
-4362, -4112, -3859, -3599, -3346, -3076, -2818, -2546, -2284, -2018, -1747, -1465, -1184, -915, -643, -374, -109, 142, 386, 626,
864, 1103, 1322, 1567, 1794, 2032, 2247, 2474, 2692, 2909, 3122, 3343, 3545, 3752, 3939, 4117, 4292, 4451, 4587, 4706,
4816, 4912, 5004, 5072, 5144, 5222, 5289, 5355, 5441, 5503, 5581, 5640, 5703, 5766, 5829, 5867, 5925, 5957, 5981, 5982,
5972, 5943, 5907, 5835, 5775, 5687, 5615, 5514, 5428, 5353, 5291, 5219, 5163, 5109, 5056, 5005, 4949, 4891, 4844, 4785,
4724, 4649, 4576, 4470, 4365, 4253, 4117, 3968, 3810, 3665, 3503, 3354, 3208, 3080, 2963, 2865, 2768, 2688, 2598, 2516,
2439, 2348, 2265, 2171, 2061, 1963, 1842, 1726, 1588, 1439, 1274, 1108, 925, 756, 587, 422, 276, 139, 0, -106,
-201, -290, -385, -473, -560, -666, -758, -868, -996, -1112, -1234, -1374, -1515, -1682, -1845, -2017, -2193, -2351, -2509, -2656,
-2788, -2916, -3017, -3105, -3172, -3242, -3298, -3356, -3417, -3495, -3569, -3647, -3731, -3820, -3916, -4007, -4112, -4217, -4329, -4451,
-4547, -4656, -4739, -4806, -4872, -4914, -4944, -4952, -4934, -4923, -4904, -4877, -4865, -4858, -4856, -4854, -4861, -4868, -4886, -4892,
-4896, -4911, -4930, -4941, -4930, -4913, -4885, -4848, -4789, -4705, -4615, -4506, -4384, -4241, -4115, -3958, -3825, -3694, -3576, -3447,
-3329, -3195, -3072, -2929, -2801, -2655, -2502, -2350, -2159, -1966, -1776, -1569, -1341, -1113, -864, -613, -349, -79, 176, 443,
703, 953, 1205, 1452, 1697, 1941, 2177, 2427, 2681, 2922, 3179, 3431, 3689, 3948, 4195, 4449, 4713, 4952, 5198, 5417,
5645, 5860, 6077, 6275, 6485, 6680, 6864, 7054, 7226, 7401, 7576, 7732, 7902, 8055, 8220, 8364, 8501, 8625, 8756, 8869,
8964, 9047, 9116, 9179, 9215, 9258, 9296, 9332, 9359, 9406, 9440, 9482, 9512, 9531, 9566, 9585, 9593, 9607, 9604, 9602,
9570, 9547, 9512, 9460, 9387, 9315, 9221, 9126, 9020, 8903, 8800, 8708, 8605, 8522, 8443, 8371, 8293, 8218, 8145, 8065,
7967, 7866, 7767, 7654, 7543, 7407, 7274, 7129, 6986, 6820, 6658, 6483, 6317, 6135, 5982, 5834, 5701, 5570, 5469, 5369,
5265, 5157, 5049, 4944, 4833, 4692, 4568, 4431, 4287, 4135, 3962, 3811, 3644, 3466, 3297, 3127, 2949, 2773, 2609, 2458,
2326, 2195, 2090, 1984, 1883, 1774, 1671, 1552, 1437, 1300, 1152, 1012, 836, 672, 503, 339, 179, -2, -149, -318,
-372, -509, -652, -848, -1055, -1281, -1474, -1656, -1775, -1854, -1864, -1834, -1751, -1644, -1499, -1340, -1158, -992, -824, -670,
-518, -380, -232, -103, 24, 132, 237, 334, 434, 535, 654, 788, 939, 1115, 1322, 1550, 1804, 2065, 2342, 2620,
2902, 3176, 3437, 3678, 3924, 4154, 4378, 4601, 4812, 5006, 5170, 5305, 5420, 5534, 5641, 5763, 5894, 6052, 6224, 6411,
6601, 6802, 6999, 7201, 7416, 7643, 7874, 8109, 8379, 8675, 8989, 9323, 9663, 9986, 10282, 10555, 10809, 11045, 11256, 11457,
11645, 11800, 11933, 12035, 12118, 12150, 12138, 12080, 11964, 11804, 11607, 11382, 11143, 10909, 10672, 10427, 10181, 9906, 9627, 9325,
9018, 8709, 8409, 8107, 7824, 7549, 7296, 7059, 6819, 6600, 6379, 6143, 5901, 5653, 5405, 5180, 4967, 4768, 4599, 4415,
4217, 4018, 3810, 3574, 3332, 3079, 2835, 2590, 2373, 2188, 2016, 1869, 1752, 1653, 1550, 1460, 1361, 1293, 1246, 1225,
1219, 1227, 1257, 1286, 1320, 1347, 1356, 1339, 1302, 1253, 1182, 1112, 1048, 1004, 979, 953, 949, 938, 915, 891,
857, 810, 762, 707, 662, 610, 557, 502, 431, 340, 235, 91, -80, -281, -488, -693, -894, -1088, -1267, -1434,
-1584, -1728, -1873, -2020, -2166, -2317, -2462, -2607, -2754, -2900, -3032, -3160, -3287, -3429, -3586, -3758, -3948, -4142, -4344, -4539,
-4715, -4867, -4989, -5085, -5165, -5227, -5289, -5337, -5383, -5435, -5498, -5556, -5605, -5650, -5684, -5719, -5748, -5775, -5833, -5898,
-5988, -6099, -6218, -6339, -6445, -6534, -6608, -6658, -6691, -6705, -6713, -6727, -6757, -6797, -6854, -6930, -7019, -7113, -7203, -7311,
-7413, -7534, -7668, -7834, -8018, -8231, -8448, -8687, -8915, -9118, -9308, -9479, -9625, -9755, -9869, -9986, -10109, -10250, -10410, -10585,
-10751, -10910, -11053, -11190, -11315, -11422, -11539, -11659, -11788, -11913, -12027, -12122, -12173, -12188, -12147, -12051, -11888, -11679, -11448, -11206,
-10953, -10703, -10444, -10191, -9909, -9607, -9282, -8923, -8537, -8145, -7734, -7320, -6890, -6450, -6006, -5546, -5077, -4590, -4089, -3577,
-3066, -2564, -2081, -1614, -1171, -753, -354, 34, 417, 797, 1168, 1540, 1902, 2265, 2624, 2968, 3316, 3661, 4014, 4364,
4700, 5025, 5334, 5625, 5893, 6134, 6359, 6578, 6790, 7004, 7216, 7432, 7636, 7849, 8041, 8224, 8392, 8534, 8672, 8796,
8909, 9012, 9106, 9179, 9222, 9233, 9193, 9119, 9005, 8850, 8674, 8480, 8287, 8100, 7917, 7745, 7591, 7428, 7265, 7096,
6919, 6719, 6504, 6292, 6091, 5886, 5691, 5496, 5295, 5076, 4854, 4610, 4358, 4096, 3840, 3602, 3385, 3201, 3043, 2930,
2858, 2799, 2753, 2705, 2643, 2578, 2497, 2420, 2343, 2269, 2207, 2159, 2099, 2043, 1977, 1896, 1802, 1708, 1608, 1511,
1428, 1373, 1342, 1329, 1329, 1339, 1345, 1336, 1304, 1255, 1183, 1092, 991, 890, 778, 661, 546, 414, 272, 101,
-80, -276, -490, -705, -919, -1117, -1295, -1453, -1595, -1723, -1855, -2002, -2150, -2313, -2498, -2702, -2907, -3110, -3308, -3512,
-3699, -3891, -4085, -4289, -4498, -4709, -4916, -5121, -5305, -5462, -5584, -5681, -5742, -5782, -5806, -5833, -5863, -5906, -5963, -6025,
-6100, -6176, -6239, -6292, -6337, -6371, -6401, -6434, -6484, -6537, -6594, -6653, -6699, -6730, -6747, -6735, -6725, -6699, -6675, -6657,
-6665, -6694, -6751, -6827, -6923, -7024, -7119, -7207, -7293, -7366, -7441, -7518, -7595, -7686, -7777, -7863, -7941, -8001, -8027, -8032,
-8010, -7966, -7902, -7828, -7757, -7685, -7617, -7545, -7453, -7351, -7210, -7043, -6833, -6598, -6320, -6015, -5681, -5322, -4938, -4516,
-4055, -3564, -3031, -2470, -1879, -1271, -659, -48, 557, 1146, 1736, 2301, 2856, 3401, 3923, 4428, 4909, 5357, 5789, 6185,
6562, 6920, 7256, 7565, 7867, 8142, 8394, 8620, 8804, 8959, 9071, 9159, 9238, 9304, 9366, 9441, 9509, 9570, 9619, 9658,
9670, 9674, 9658, 9635, 9605, 9573, 9549, 9528, 9520, 9509, 9488, 9463, 9420, 9363, 9294, 9228, 9166, 9122, 9086, 9075,
9073, 9073, 9057, 9033, 8985, 8910, 8814, 8694, 8566, 8429, 8290, 8155, 8024, 7894, 7753, 7593, 7428, 7243, 7049, 6841,
6648, 6460, 6285, 6120, 5968, 5817, 5664, 5497, 5321, 5126, 4915, 4696, 4474, 4247, 4041, 3842, 3664, 3495, 3337, 3168,
3003, 2842, 2673, 2514, 2358, 2224, 2110, 2007, 1920, 1850, 1776, 1700, 1618, 1531, 1432, 1324, 1216, 1126, 1032, 965,
901, 843, 797, 751, 688, 631, 558, 489, 417, 350, 293, 247, 204, 183, 153, 121, 69, 8, -66, -149,
-259, -360, -467, -565, -667, -768, -864, -967, -1087, -1200, -1331, -1460, -1598, -1735, -1858, -1973, -2079, -2176, -2270, -2373,
-2486, -2617, -2753, -2901, -3061, -3223, -3374, -3527, -3661, -3798, -3919, -4029, -4145, -4265, -4380, -4506, -4618, -4729, -4834, -4915,
-4983, -5046, -5092, -5145, -5207, -5275, -5357, -5449, -5539, -5634, -5725, -5799, -5866, -5917, -5962, -6000, -6042, -6083, -6138, -6197,
-6264, -6330, -6405, -6474, -6522, -6573, -6632, -6683, -6760, -6846, -6953, -7082, -7221, -7364, -7521, -7671, -7805, -7939, -8062, -8187,
-8312, -8438, -8592, -8739, -8903, -9060, -9216, -9357, -9486, -9594, -9696, -9791, -9890, -9981, -10090, -10208, -10321, -10422, -10522, -10593,
-10633, -10643, -10619, -10572, -10495, -10400, -10293, -10176, -10038, -9887, -9703, -9501, -9268, -9000, -8715, -8408, -8075, -7740, -7388, -7037,
-6675, -6304, -5913, -5508, -5081, -4646, -4197, -3742, -3292, -2844, -2398, -1971, -1550, -1138, -734, -342, 48, 423, 801, 1171,
1545, 1913, 2281, 2649, 3003, 3363, 3718, 4058, 4380, 4696, 4988, 5263, 5525, 5781, 6023, 6261, 6491, 6721, 6942, 7143,
7332, 7511, 7676, 7837, 7985, 8136, 8280, 8429, 8566, 8696, 8806, 8884, 8926, 8941, 8910, 8845, 8752, 8632, 8507, 8374,
8231, 8080, 7927, 7761, 7582, 7393, 7190, 6985, 6780, 6583, 6400, 6220, 6056, 5893, 5726, 5557, 5367, 5164, 4947, 4704,
4466, 4222, 3988, 3775, 3582, 3399, 3248, 3101, 2962, 2823, 2692, 2568, 2459, 2354, 2275, 2209, 2156, 2118, 2077, 2033,
1989, 1919, 1845, 1752, 1643, 1541, 1441, 1346, 1274, 1203, 1145, 1089, 1033, 963, 880, 792, 702, 611, 517, 430,
348, 259, 171, 73, -45, -178, -334, -509, -704, -909, -1113, -1306, -1494, -1666, -1833, -1992, -2149, -2312, -2477, -2651,
-2819, -2985, -3148, -3298, -3439, -3576, -3706, -3839, -3973, -4112, -4273, -4448, -4626, -4801, -4970, -5122, -5249, -5356, -5449, -5520,
-5577, -5629, -5677, -5730, -5777, -5817, -5858, -5893, -5909, -5928, -5938, -5954, -5977, -6009, -6061, -6134, -6212, -6295, -6373, -6443,
-6496, -6525, -6541, -6542, -6538, -6537, -6535, -6543, -6560, -6588, -6615, -6643, -6673, -6687, -6708, -6728, -6757, -6798, -6850, -6920,
-7001, -7072, -7137, -7181, -7205, -7205, -7170, -7113, -7043, -6948, -6848, -6742, -6628, -6509, -6368, -6212, -6037, -5826, -5604, -5359,
-5103, -4828, -4547, -4247, -3932, -3596, -3226, -2831, -2406, -1953, -1475, -975, -473, 44, 561, 1069, 1575, 2071, 2563, 3045,
3508, 3957, 4393, 4806, 5197, 5569, 5916, 6262, 6590, 6917, 7236, 7540, 7828, 8094, 8332, 8546, 8733, 8893, 9043, 9175,
9293, 9408, 9507, 9606, 9693, 9770, 9839, 9894, 9934, 9972, 10006, 10043, 10087, 10125, 10169, 10212, 10226, 10221, 10183, 10120,
10046, 9947, 9840, 9739, 9640, 9533, 9436, 9346, 9248, 9146, 9031, 8915, 8780, 8645, 8494, 8356, 8224, 8089, 7953, 7805,
7648, 7470, 7269, 7046, 6823, 6587, 6354, 6132, 5914, 5718, 5536, 5364, 5201, 5052, 4894, 4741, 4583, 4427, 4282, 4135,
4002, 3881, 3763, 3642, 3525, 3395, 3261, 3114, 2972, 2825, 2690, 2562, 2457, 2367, 2288, 2226, 2174, 2123, 2070, 2008,
1951, 1880, 1821, 1757, 1695, 1639, 1587, 1516, 1456, 1378, 1295, 1197, 1085, 981, 875, 759, 663, 574, 497, 428,
362, 293, 224, 137, 48, -46, -148, -247, -350, -452, -555, -665, -780, -898, -1029, -1161, -1313, -1465, -1613, -1753,
-1889, -2002, -2103, -2195, -2280, -2370, -2458, -2541, -2639, -2734, -2838, -2942, -3049, -3155, -3259, -3362, -3468, -3578, -3685, -3812,
-3936, -4068, -4199, -4309, -4420, -4512, -4583, -4649, -4704, -4763, -4820, -4886, -4954, -5037, -5120, -5215, -5314, -5416, -5510, -5604,
-5704, -5802, -5904, -6021, -6143, -6270, -6395, -6507, -6608, -6703, -6777, -6851, -6918, -6984, -7056, -7127, -7218, -7326, -7440, -7567,
-7695, -7828, -7960, -8085, -8210, -8341, -8479, -8613, -8764, -8911, -9058, -9195, -9320, -9428, -9529, -9606, -9673, -9733, -9792, -9849,
-9905, -9976, -10057, -10133, -10198, -10253, -10299, -10324, -10329, -10327, -10308, -10271, -10224, -10161, -10083, -9979, -9846, -9682, -9497, -9281,
-9030, -8769, -8491, -8195, -7891, -7580, -7260, -6930, -6584, -6225, -5851, -5461, -5052, -4623, -4182, -3737, -3279, -2818, -2351, -1892,
-1424, -968, -508, -61, 379, 811, 1239, 1651, 2058, 2462, 2856, 3241, 3613, 3975, 4329, 4660, 4977, 5286, 5574, 5850,
6122, 6373, 6612, 6832, 7034, 7205, 7355, 7481, 7586, 7675, 7758, 7839, 7925, 8017, 8107, 8192, 8272, 8346, 8395, 8429,
8439, 8432, 8415, 8375, 8327, 8271, 8201, 8128, 8024, 7910, 7778, 7627, 7468, 7304, 7145, 6998, 6864, 6738, 6630, 6526,
6422, 6325, 6214, 6086, 5946, 5793, 5628, 5462, 5290, 5129, 4968, 4811, 4643, 4478, 4311, 4141, 3975, 3817, 3669, 3544,
3434, 3341, 3272, 3213, 3162, 3112, 3064, 3002, 2926, 2833, 2734, 2634, 2539, 2437, 2349, 2257, 2166, 2070, 1972, 1874,
1772, 1672, 1577, 1488, 1409, 1341, 1280, 1237, 1193, 1138, 1077, 997, 895, 783, 644, 510, 360, 211, 55, -99,
-261, -417, -589, -759, -930, -1107, -1282, -1449, -1608, -1756, -1893, -2016, -2136, -2258, -2395, -2538, -2694, -2863, -3050, -3228,
-3415, -3596, -3775, -3946, -4106, -4261, -4413, -4563, -4702, -4834, -4969, -5088, -5187, -5268, -5337, -5395, -5438, -5480, -5533, -5593,
-5670, -5759, -5856, -5970, -6079, -6180, -6282, -6378, -6454, -6525, -6596, -6660, -6727, -6785, -6847, -6900, -6945, -6978, -7000, -7022,
-7039, -7060, -7091, -7141, -7200, -7282, -7370, -7479, -7583, -7682, -7760, -7829, -7871, -7899, -7906, -7913, -7905, -7886, -7851, -7802,
-7719, -7624, -7498, -7351, -7182, -7002, -6805, -6605, -6391, -6169, -5935, -5679, -5407, -5098, -4749, -4361, -3951, -3500, -3033, -2543,
-2045, -1529, -996, -451, 100, 662, 1221, 1776, 2318, 2846, 3360, 3850, 4314, 4769, 5202, 5623, 6031, 6421, 6800, 7160,
7491, 7807, 8092, 8346, 8578, 8784, 8967, 9137, 9289, 9426, 9548, 9651, 9739, 9809, 9877, 9935, 9991, 10054, 10119, 10184,
10251, 10308, 10349, 10380, 10395, 10384, 10367, 10329, 10272, 10211, 10147, 10085, 10018, 9942, 9867, 9777, 9691, 9587, 9482, 9381,
9289, 9191, 9109, 9018, 8929, 8817, 8702, 8569, 8416, 8238, 8052, 7849, 7629, 7423, 7208, 7000, 6802, 6609, 6413, 6224,
6028, 5843, 5654, 5485, 5320, 5169, 5020, 4883, 4750, 4618, 4477, 4332, 4178, 4020, 3843, 3679, 3506, 3346, 3197, 3055,
2930, 2822, 2708, 2610, 2517, 2430, 2344, 2265, 2199, 2130, 2076, 2016, 1969, 1914, 1855, 1780, 1701, 1612, 1506, 1394,
1284, 1176, 1074, 975, 885, 808, 727, 644, 565, 482, 400, 311, 219, 137, 49, -37, -117, -208, -299, -410,
-534, -666, -807, -958, -1101, -1247, -1386, -1514, -1636, -1750, -1858, -1968, -2068, -2168, -2266, -2366, -2468, -2566, -2651, -2743,
-2834, -2924, -3018, -3123, -3235, -3360, -3480, -3613, -3742, -3857, -3972, -4074, -4168, -4251, -4325, -4390, -4460, -4524, -4592, -4660,
-4733, -4808, -4871, -4944, -5014, -5091, -5169, -5264, -5368, -5479, -5608, -5728, -5853, -5987, -6103, -6214, -6321, -6413, -6498, -6575,
-6660, -6744, -6839, -6938, -7047, -7161, -7264, -7380, -7497, -7623, -7744, -7883, -8028, -8184, -8353, -8516, -8682, -8848, -8998, -9134,
-9260, -9368, -9468, -9558, -9640, -9729, -9817, -9904, -9987, -10070, -10153, -10226, -10289, -10352, -10409, -10456, -10503, -10543, -10580, -10600,
-10612, -10598, -10563, -10500, -10408, -10292, -10151, -9993, -9813, -9619, -9419, -9199, -8975, -8732, -8485, -8223, -7941, -7648, -7343, -7013,
-6672, -6312, -5939, -5553, -5147, -4720, -4292, -3838, -3376, -2910, -2437, -1971, -1489, -1010, -545, -71, 400, 864, 1326, 1769,
2213, 2652, 3070, 3493, 3910, 4314, 4716, 5102, 5476, 5835, 6168, 6472, 6752, 7000, 7219, 7409, 7586, 7752, 7900, 8040,
8176, 8301, 8407, 8507, 8578, 8641, 8695, 8727, 8758, 8770, 8788, 8780, 8759, 8722, 8666, 8572, 8464, 8333, 8181, 8010,
7840, 7676, 7521, 7367, 7230, 7103, 6980, 6858, 6730, 6604, 6480, 6343, 6218, 6094, 5974, 5845, 5719, 5582, 5444, 5283,
5114, 4943, 4758, 4579, 4402, 4236, 4091, 3963, 3843, 3750, 3657, 3575, 3482, 3399, 3309, 3219, 3120, 3026, 2934, 2830,
2733, 2627, 2521, 2399, 2265, 2135, 1990, 1842, 1699, 1566, 1445, 1333, 1237, 1146, 1074, 993, 915, 830, 735, 638,
534, 412, 307, 191, 75, -52, -188, -321, -470, -629, -788, -956, -1109, -1268, -1418, -1540, -1656, -1765, -1852, -1949,
-2047, -2148, -2256, -2375, -2487, -2614, -2741, -2863, -2992, -3118, -3257, -3395, -3534, -3687, -3835, -3984, -4127, -4265, -4389, -4500,
-4587, -4667, -4735, -4794, -4861, -4929, -5005, -5091, -5182, -5279, -5385, -5477, -5584, -5683, -5787, -5896, -6008, -6119, -6242, -6352,
-6464, -6563, -6660, -6738, -6798, -6841, -6881, -6911, -6942, -6983, -7036, -7109, -7186, -7265, -7360, -7450, -7530, -7603, -7675, -7754,
-7820, -7883, -7947, -8006, -8055, -8092, -8098, -8087, -8047, -7987, -7901, -7802, -7698, -7592, -7483, -7380, -7268, -7152, -7013, -6869,
-6691, -6501, -6279, -6043, -5784, -5499, -5195, -4882, -4526, -4148, -3745, -3314, -2858, -2376, -1875, -1376, -876, -376, 122, 612,
1100, 1587, 2074, 2548, 3035, 3514, 3978, 4437, 4884, 5320, 5741, 6138, 6522, 6895, 7247, 7578, 7889, 8176, 8450, 8694,
8913, 9122, 9312, 9487, 9650, 9795, 9937, 10066, 10185, 10290, 10387, 10460, 10524, 10565, 10595, 10610, 10605, 10596, 10568, 10536,
10484, 10417, 10340, 10266, 10174, 10086, 10004, 9922, 9843, 9763, 9691, 9620, 9535, 9442, 9347, 9235, 9110, 8973, 8833, 8689,
8534, 8381, 8222, 8057, 7887, 7705, 7525, 7344, 7168, 6993, 6834, 6685, 6550, 6414, 6288, 6163, 6044, 5905, 5768, 5621,
5467, 5309, 5148, 4988, 4837, 4681, 4528, 4376, 4223, 4069, 3921, 3775, 3638, 3507, 3382, 3284, 3186, 3105, 3021, 2943,
2869, 2786, 2694, 2607, 2496, 2390, 2285, 2174, 2067, 1958, 1852, 1749, 1644, 1540, 1433, 1332, 1235, 1145, 1049, 975,
901, 832, 764, 692, 619, 539, 443, 345, 241, 125, 10, -113, -234, -355, -472, -594, -711, -830, -949, -1067,
-1180, -1291, -1393, -1494, -1584, -1671, -1747, -1839, -1934, -2027, -2127, -2241, -2347, -2476, -2600, -2728, -2853, -2968, -3085, -3200,
-3310, -3414, -3523, -3624, -3726, -3825, -3912, -3998, -4068, -4139, -4208, -4273, -4349, -4429, -4511, -4612, -4717, -4823, -4938, -5053,
-5166, -5281, -5389, -5492, -5597, -5698, -5804, -5901, -6006, -6108, -6199, -6288, -6382, -6464, -6554, -6642, -6740, -6852, -6967, -7089,
-7234, -7386, -7541, -7699, -7851, -8007, -8150, -8293, -8424, -8551, -8672, -8795, -8917, -9030, -9137, -9232, -9332, -9420, -9494, -9579,
-9651, -9735, -9817, -9900, -9978, -10071, -10140, -10212, -10261, -10299, -10319, -10314, -10294, -10262, -10205, -10135, -10047, -9948, -9828, -9689,
-9528, -9367, -9179, -8982, -8777, -8555, -8331, -8081, -7829, -7557, -7272, -6958, -6633, -6282, -5919, -5541, -5138, -4726, -4302, -3863,
-3411, -2953, -2497, -2035, -1570, -1110, -649, -193, 269, 721, 1173, 1623, 2087, 2538, 2985, 3428, 3852, 4261, 4650, 5008,
5355, 5685, 5987, 6278, 6551, 6810, 7045, 7262, 7467, 7650, 7801, 7952, 8083, 8209, 8321, 8434, 8540, 8646, 8728, 8793,
8843, 8864, 8858, 8818, 8759, 8681, 8593, 8492, 8386, 8268, 8160, 8036, 7910, 7783, 7649, 7512, 7385, 7254, 7138, 7020,
6915, 6814, 6718, 6608, 6491, 6362, 6223, 6062, 5892, 5717, 5548, 5365, 5199, 5037, 4886, 4748, 4601, 4475, 4345, 4217,
4106, 3995, 3894, 3798, 3714, 3632, 3561, 3471, 3376, 3271, 3161, 3026, 2892, 2735, 2584, 2434, 2283, 2153, 2021, 1900,
1776, 1655, 1538, 1422, 1300, 1192, 1079, 975, 865, 759, 657, 545, 426, 297, 156, -5, -170, -347, -527, -695,
-870, -1019, -1171, -1307, -1447, -1575, -1700, -1816, -1936, -2051, -2156, -2264, -2361, -2461, -2555, -2646, -2749, -2864, -2981, -3110,
-3253, -3398, -3541, -3676, -3800, -3922, -4025, -4125, -4204, -4280, -4353, -4424, -4485, -4562, -4628, -4687, -4750, -4812, -4870, -4932,
-4999, -5085, -5174, -5276, -5393, -5510, -5637, -5752, -5854, -5953, -6037, -6107, -6168, -6220, -6276, -6324, -6371, -6425, -6483, -6537,
-6588, -6638, -6693, -6744, -6796, -6853, -6927, -6997, -7081, -7156, -7236, -7298, -7338, -7366, -7370, -7343, -7303, -7240, -7173, -7088,
-7002, -6904, -6807, -6685, -6565, -6415, -6258, -6090, -5905, -5716, -5520, -5311, -5085, -4850, -4595, -4318, -4020, -3686, -3326, -2947,
-2527, -2098, -1662, -1228, -784, -343, 100, 537, 984, 1426, 1869, 2306, 2736, 3168, 3591, 4001, 4406, 4799, 5189, 5564,
5934, 6298, 6644, 6975, 7291, 7586, 7863, 8122, 8357, 8572, 8774, 8961, 9133, 9291, 9436, 9570, 9694, 9803, 9904, 9994,
10076, 10149, 10204, 10252, 10269, 10283, 10271, 10246, 10197, 10138, 10070, 9994, 9905, 9811, 9722, 9632, 9542, 9444, 9346, 9251,
9145, 9037, 8933, 8819, 8705, 8591, 8470, 8340, 8200, 8043, 7880, 7713, 7525, 7341, 7161, 6984, 6806, 6639, 6482, 6336,
6193, 6060, 5932, 5801, 5675, 5551, 5428, 5305, 5192, 5068, 4955, 4833, 4707, 4569, 4428, 4285, 4137, 3986, 3847, 3705,
3576, 3452, 3341, 3242, 3146, 3057, 2973, 2887, 2790, 2710, 2620, 2530, 2441, 2343, 2252, 2153, 2047, 1938, 1819, 1698,
1570, 1443, 1316, 1198, 1083, 972, 872, 783, 700, 614, 537, 460, 369, 287, 195, 103, 12, -83, -182, -279,
-385, -493, -610, -731, -854, -970, -1093, -1203, -1308, -1406, -1497, -1573, -1647, -1714, -1792, -1862, -1937, -2013, -2095, -2185,
-2271, -2359, -2454, -2553, -2648, -2749, -2858, -2973, -3092, -3203, -3326, -3431, -3533, -3628, -3713, -3796, -3872, -3947, -4017, -4097,
-4177, -4261, -4353, -4457, -4562, -4668, -4773, -4890, -5001, -5121, -5244, -5375, -5499, -5639, -5762, -5890, -6006, -6111, -6210, -6311,
-6403, -6494, -6580, -6674, -6770, -6876, -6995, -7114, -7244, -7366, -7493, -7626, -7756, -7890, -8028, -8166, -8304, -8439, -8570, -8686,
-8801, -8894, -8985, -9060, -9134, -9196, -9251, -9310, -9375, -9442, -9512, -9575, -9645, -9708, -9766, -9812, -9857, -9890, -9913, -9930,
-9936, -9926, -9899, -9851, -9792, -9699, -9589, -9461, -9319, -9160, -8990, -8808, -8615, -8420, -8207, -7982, -7740, -7485, -7217, -6922,
-6616, -6296, -5954, -5594, -5216, -4822, -4412, -3981, -3539, -3092, -2629, -2164, -1699, -1240, -782, -323, 136, 586, 1051, 1505,
1964, 2410, 2845, 3277, 3690, 4086, 4466, 4838, 5189, 5526, 5835, 6138, 6416, 6666, 6896, 7098, 7268, 7426, 7558, 7690,
7807, 7920, 8026, 8138, 8233, 8327, 8397, 8448, 8485, 8506, 8504, 8484, 8455, 8415, 8362, 8296, 8215, 8126, 8019, 7900,
7773, 7643, 7506, 7374, 7255, 7150, 7046, 6954, 6871, 6785, 6699, 6603, 6500, 6383, 6258, 6123, 5989, 5857, 5715, 5569,
5427, 5280, 5125, 4971, 4817, 4667, 4520, 4377, 4254, 4149, 4048, 3959, 3887, 3807, 3729, 3643, 3548, 3446, 3331, 3215,
3091, 2967, 2842, 2712, 2584, 2455, 2324, 2187, 2053, 1923, 1794, 1668, 1554, 1449, 1366, 1281, 1200, 1127, 1036, 945,
840, 723, 604, 471, 328, 193, 53, -96, -244, -386, -535, -676, -827, -963, -1106, -1238, -1365, -1478, -1577, -1671,
-1766, -1852, -1949, -2047, -2161, -2284, -2416, -2547, -2693, -2833, -2980, -3116, -3254, -3392, -3518, -3639, -3767, -3884, -4001, -4112,
-4209, -4292, -4370, -4437, -4500, -4559, -4621, -4694, -4774, -4870, -4971, -5091, -5204, -5325, -5434, -5553, -5663, -5758, -5859, -5951,
-6038, -6126, -6205, -6279, -6346, -6406, -6451, -6495, -6528, -6564, -6600, -6645, -6692, -6757, -6836, -6917, -7001, -7086, -7158, -7210,
-7258, -7288, -7308, -7309, -7298, -7276, -7236, -7186, -7115, -7030, -6926, -6805, -6667, -6513, -6357, -6177, -6008, -5830, -5647, -5461,
-5255, -5030, -4784, -4512, -4211, -3881, -3535, -3161, -2768, -2358, -1944, -1501, -1068, -616, -155, 305, 764, 1237, 1699, 2157,
2605, 3045, 3476, 3895, 4310, 4717, 5113, 5503, 5887, 6258, 6624, 6970, 7300, 7602, 7893, 8157, 8416, 8637, 8846, 9029,
9197, 9353, 9495, 9628, 9754, 9860, 9968, 10060, 10149, 10222, 10280, 10320, 10353, 10367, 10367, 10347, 10313, 10267, 10216, 10152,
10076, 9999, 9909, 9814, 9711, 9605, 9505, 9405, 9306, 9219, 9127, 9040, 8946, 8850, 8749, 8631, 8501, 8361, 8214, 8059,
7895, 7730, 7563, 7398, 7236, 7080, 6916, 6758, 6599, 6442, 6298, 6160, 6029, 5900, 5790, 5675, 5564, 5448, 5337, 5217,
5080, 4945, 4801, 4654, 4503, 4351, 4204, 4072, 3931, 3802, 3678, 3556, 3433, 3320, 3217, 3116, 3018, 2928, 2846, 2760,
2685, 2595, 2506, 2413, 2313, 2193, 2076, 1954, 1829, 1700, 1576, 1463, 1353, 1236, 1134, 1030, 931, 832, 734, 641,
554, 465, 384, 298, 209, 132, 37, -62, -164, -281, -404, -525, -656, -780, -903, -1018, -1129, -1237, -1344, -1435,
-1529, -1616, -1713, -1798, -1878, -1959, -2044, -2116, -2196, -2277, -2366, -2458, -2558, -2669, -2789, -2905, -3023, -3147, -3262, -3369,
-3473, -3574, -3669, -3759, -3846, -3936, -4025, -4113, -4198, -4280, -4367, -4451, -4536, -4631, -4724, -4839, -4956, -5073, -5210, -5349,
-5481, -5621, -5751, -5882, -6009, -6124, -6229, -6338, -6440, -6548, -6651, -6764, -6872, -6981, -7085, -7202, -7308, -7425, -7550, -7682,
-7821, -7966, -8114, -8269, -8424, -8573, -8714, -8845, -8966, -9067, -9169, -9264, -9349, -9423, -9507, -9584, -9653, -9719, -9780, -9842,
-9897, -9942, -10000, -10044, -10099, -10134, -10176, -10217, -10244, -10248, -10239, -10200, -10142, -10070, -9973, -9865, -9739, -9594, -9443, -9274,
-9098, -8907, -8694, -8470, -8236, -7979, -7717, -7436, -7144, -6834, -6514, -6164, -5801, -5418, -5007, -4573, -4123, -3663, -3189, -2714,
-2229, -1745, -1256, -767, -277, 211, 707, 1197, 1682, 2156, 2628, 3087, 3534, 3968, 4392, 4818, 5216, 5606, 5980, 6324,
6644, 6925, 7182, 7413, 7624, 7803, 7972, 8123, 8265, 8396, 8520, 8626, 8723, 8791, 8856, 8907, 8942, 8970, 8987, 8989,
8990, 8973, 8939, 8886, 8805, 8708, 8582, 8454, 8318, 8176, 8033, 7904, 7774, 7659, 7541, 7425, 7314, 7199, 7084, 6973,
6854, 6748, 6632, 6517, 6394, 6278, 6137, 6002, 5849, 5687, 5510, 5337, 5162, 4995, 4829, 4680, 4546, 4424, 4308, 4191,
4087, 3983, 3871, 3760, 3656, 3544, 3431, 3322, 3212, 3095, 2977, 2844, 2711, 2563, 2408, 2244, 2086, 1937, 1795, 1660,
1544, 1430, 1331, 1225, 1132, 1036, 929, 819, 719, 605, 487, 371, 257, 139, 14, -125, -262, -412, -566, -722,
-874, -1024, -1162, -1292, -1405, -1511, -1605, -1699, -1787, -1875, -1967, -2062, -2159, -2263, -2366, -2466, -2576, -2684, -2796, -2917,
-3042, -3170, -3302, -3430, -3566, -3691, -3807, -3911, -4009, -4091, -4164, -4229, -4300, -4368, -4446, -4518, -4608, -4695, -4791, -4887,
-4991, -5094, -5206, -5304, -5422, -5542, -5662, -5784, -5902, -6019, -6123, -6211, -6289, -6355, -6405, -6451, -6493, -6543, -6592, -6643,
-6709, -6783, -6849, -6923, -6996, -7069, -7139, -7202, -7261, -7328, -7376, -7422, -7460, -7487, -7501, -7492, -7456, -7412, -7336, -7248,
-7150, -7047, -6936, -6829, -6712, -6595, -6474, -6337, -6191, -6032, -5857, -5652, -5430, -5194, -4936, -4661, -4364, -4041, -3708, -3344,
-2954, -2551, -2120, -1683, -1237, -777, -323, 134, 583, 1033, 1475, 1927, 2370, 2818, 3256, 3698, 4135, 4575, 4995, 5417,
5817, 6215, 6590, 6949, 7287, 7608, 7901, 8186, 8445, 8690, 8914, 9125, 9325, 9505, 9662, 9820, 9953, 10073, 10180, 10264,
10346, 10410, 10461, 10497, 10527, 10529, 10522, 10493, 10446, 10382, 10306, 10219, 10136, 10040, 9949, 9859, 9769, 9684, 9606, 9511,
9422, 9321, 9226, 9107, 8988, 8867, 8738, 8600, 8465, 8326, 8173, 8016, 7846, 7681, 7512, 7342, 7174, 7015, 6867, 6732,
6597, 6475, 6360, 6245, 6128, 6020, 5899, 5772, 5638, 5503, 5374, 5234, 5098, 4959, 4820, 4677, 4525, 4382, 4234, 4087,
3945, 3816, 3690, 3576, 3473, 3371, 3282, 3190, 3096, 3004, 2899, 2797, 2690, 2566, 2447, 2334, 2210, 2090, 1968, 1844,
1721, 1593, 1465, 1346, 1227, 1113, 1007, 907, 818, 727, 651, 571, 493, 401, 313, 212, 110, -1, -110, -230,
-342, -458, -565, -685, -793, -914, -1028, -1139, -1246, -1351, -1441, -1530, -1611, -1689, -1766, -1831, -1904, -1982, -2068, -2162,
-2258, -2367, -2473, -2582, -2692, -2802, -2908, -3014, -3124, -3226, -3342, -3442, -3543, -3653, -3742, -3828, -3907, -3992, -4066, -4143,
-4220, -4304, -4399, -4499, -4611, -4731, -4850, -4979, -5107, -5228, -5352, -5470, -5588, -5705, -5823, -5945, -6054, -6163, -6274, -6376,
-6474, -6564, -6658, -6751, -6847, -6950, -7068, -7190, -7317, -7456, -7599, -7747, -7888, -8032, -8167, -8301, -8424, -8550, -8670, -8792,
-8904, -9012, -9111, -9209, -9284, -9362, -9432, -9503, -9571, -9637, -9718, -9802, -9885, -9974, -10056, -10129, -10200, -10252, -10285, -10316,
-10320, -10321, -10303, -10276, -10236, -10177, -10099, -10009, -9903, -9778, -9638, -9492, -9331, -9156, -8982, -8793, -8593, -8384, -8158, -7902,
-7637, -7337, -7010, -6668, -6299, -5914, -5511, -5091, -4662, -4214, -3752, -3278, -2799, -2309, -1809, -1317, -817, -324, 169, 663,
1152, 1647, 2148, 2633, 3113, 3582, 4039, 4481, 4885, 5274, 5640, 5984, 6300, 6595, 6872, 7133, 7370, 7590, 7789, 7963,
8127, 8268, 8403, 8530, 8648, 8756, 8858, 8941, 9010, 9054, 9080, 9084, 9063, 9019, 8961, 8887, 8804, 8718, 8621, 8525,
8430, 8324, 8223, 8114, 8007, 7900, 7798, 7707, 7616, 7531, 7451, 7371, 7280, 7179, 7061, 6936, 6800, 6647, 6490, 6333,
6177, 6022, 5874, 5730, 5593, 5460, 5325, 5200, 5074, 4953, 4842, 4733, 4638, 4545, 4450, 4357, 4259, 4155, 4036, 3905,
3768, 3618, 3460, 3313, 3159, 3014, 2867, 2728, 2607, 2478, 2352, 2235, 2115, 2001, 1891, 1783, 1680, 1587, 1485, 1385,
1278, 1166, 1041, 899, 753, 606, 443, 280, 126, -24, -166, -310, -436, -559, -680, -801, -912, -1027, -1133, -1242,
-1344, -1439, -1538, -1647, -1744, -1857, -1973, -2109, -2251, -2391, -2541, -2699, -2845, -2985, -3113, -3235, -3352, -3460, -3557, -3665,
-3757, -3848, -3946, -4046, -4134, -4223, -4314, -4400, -4500, -4597, -4706, -4827, -4960, -5096, -5233, -5366, -5506, -5626, -5743, -5845,
-5938, -6023, -6097, -6164, -6235, -6305, -6374, -6438, -6508, -6569, -6631, -6691, -6756, -6818, -6893, -6967, -7052, -7135, -7218, -7291,
-7361, -7408, -7439, -7454, -7447, -7423, -7385, -7328, -7269, -7211, -7127, -7050, -6961, -6866, -6762, -6641, -6514, -6376, -6232, -6079,
-5918, -5745, -5559, -5354, -5126, -4881, -4602, -4298, -3975, -3620, -3261, -2868, -2476, -2073, -1667, -1257, -840, -432, -7, 416,
845, 1264, 1699, 2128, 2555, 2984, 3403, 3825, 4246, 4647, 5045, 5441, 5816, 6183, 6534, 6866, 7190, 7491, 7773, 8042,
8290, 8520, 8728, 8923, 9107, 9277, 9427, 9575, 9711, 9836, 9944, 10039, 10117, 10171, 10205, 10221, 10218, 10195, 10156, 10112,
10065, 10009, 9945, 9878, 9806, 9731, 9650, 9565, 9476, 9386, 9289, 9198, 9102, 9004, 8906, 8793, 8679, 8551, 8414, 8260,
8102, 7937, 7765, 7591, 7426, 7274, 7124, 6984, 6850, 6716, 6591, 6460, 6327, 6202, 6078, 5949, 5833, 5712, 5595, 5467,
5345, 5205, 5074, 4920, 4768, 4611, 4456, 4306, 4154, 4017, 3896, 3775, 3661, 3556, 3456, 3346, 3243, 3142, 3044, 2941,
2840, 2738, 2639, 2538, 2426, 2312, 2194, 2064, 1934, 1805, 1668, 1542, 1416, 1297, 1196, 1097, 1003, 919, 834, 751,
665, 574, 487, 401, 306, 213, 120, 24, -79, -185, -295, -404, -523, -641, -761, -875, -988, -1092, -1185, -1271,
-1354, -1425, -1497, -1570, -1648, -1728, -1806, -1890, -1975, -2066, -2146, -2244, -2340, -2439, -2543, -2650, -2760, -2878, -2986, -3101,
-3207, -3310, -3406, -3487, -3560, -3647, -3721, -3796, -3878, -3963, -4059, -4159, -4261, -4369, -4473, -4575, -4692, -4813, -4936, -5062,
-5188, -5327, -5459, -5590, -5713, -5828, -5944, -6049, -6144, -6236, -6332, -6422, -6526, -6637, -6750, -6865, -6991, -7122, -7251, -7376,
-7507, -7643, -7777, -7922, -8061, -8197, -8335, -8465, -8586, -8702, -8806, -8898, -8974, -9046, -9120, -9192, -9262, -9341, -9420, -9508,
-9593, -9666, -9752, -9820, -9889, -9948, -10003, -10050, -10091, -10123, -10144, -10154, -10144, -10117, -10063, -10000, -9912, -9809, -9699, -9579,
-9450, -9320, -9175, -9025, -8867, -8683, -8485, -8275, -8037, -7788, -7514, -7221, -6917, -6587, -6237, -5874, -5484, -5078, -4644, -4203,
-3750, -3288, -2818, -2350, -1875, -1394, -915, -440, 39, 530, 1016, 1500, 1977, 2454, 2912, 3361, 3783, 4198, 4591, 4970,
5330, 5665, 5977, 6268, 6529, 6770, 6985, 7189, 7365, 7543, 7700, 7857, 7993, 8132, 8259, 8367, 8460, 8534, 8581, 8611,
8630, 8627, 8611, 8588, 8541, 8491, 8419, 8342, 8243, 8134, 8026, 7923, 7804, 7704, 7614, 7527, 7450, 7371, 7297, 7219,
7131, 7023, 6921, 6804, 6682, 6548, 6412, 6273, 6135, 5981, 5838, 5680, 5529, 5370, 5213, 5062, 4924, 4788, 4674, 4562,
4468, 4374, 4277, 4181, 4082, 3963, 3847, 3723, 3586, 3453, 3311, 3168, 3028, 2884, 2738, 2593, 2447, 2302, 2159, 2017,
1891, 1765, 1655, 1559, 1458, 1370, 1277, 1178, 1080, 969, 848, 725, 592, 454, 311, 167, 24, -112, -251, -387,
-526, -665, -800, -930, -1053, -1161, -1272, -1360, -1445, -1529, -1612, -1708, -1800, -1902, -2015, -2134, -2262, -2393, -2530, -2662,
-2795, -2921, -3046, -3170, -3291, -3413, -3526, -3642, -3748, -3847, -3935, -4019, -4092, -4168, -4241, -4321, -4407, -4501, -4607, -4720,
-4841, -4967, -5096, -5216, -5336, -5457, -5560, -5667, -5764, -5866, -5955, -6044, -6129, -6198, -6254, -6317, -6364, -6410, -6455, -6499,
-6549, -6601, -6660, -6739, -6818, -6890, -6962, -7029, -7084, -7132, -7156, -7175, -7184, -7174, -7155, -7122, -7083, -7027, -6953, -6866,
-6770, -6659, -6538, -6412, -6277, -6145, -6002, -5857, -5714, -5550, -5373, -5182, -4968, -4732, -4474, -4185, -3878, -3556, -3215, -2849,
-2475, -2098, -1701, -1292, -880, -466, -41, 387, 812, 1234, 1660, 2083, 2499, 2911, 3327, 3740, 4151, 4543, 4938, 5330,
5713, 6077, 6441, 6783, 7112, 7419, 7702, 7972, 8224, 8449, 8665, 8862, 9046, 9220, 9381, 9537, 9682, 9810, 9927, 10029,
10107, 10174, 10211, 10245, 10259, 10258, 10247, 10229, 10193, 10149, 10094, 10028, 9954, 9875, 9786, 9703, 9611, 9534, 9446, 9364,
9292, 9209, 9116, 9027, 8918, 8802, 8668, 8528, 8385, 8235, 8082, 7931, 7780, 7628, 7480, 7323, 7177, 7032, 6882, 6741,
6612, 6483, 6359, 6241, 6132, 6026, 5913, 5796, 5673, 5537, 5400, 5245, 5100, 4951, 4800, 4646, 4511, 4374, 4240, 4109,
3976, 3858, 3737, 3616, 3510, 3397, 3302, 3204, 3115, 3024, 2936, 2834, 2734, 2618, 2501, 2376, 2241, 2111, 1985, 1856,
1737, 1622, 1512, 1408, 1300, 1195, 1104, 1002, 909, 817, 733, 648, 559, 483, 404, 309, 209, 111, -1, -120,
-238, -358, -480, -595, -705, -811, -907, -1002, -1096, -1191, -1282, -1358, -1451, -1527, -1615, -1685, -1765, -1848, -1930, -2015,
-2112, -2209, -2321, -2436, -2548, -2675, -2799, -2908, -3022, -3129, -3225, -3319, -3415, -3513, -3603, -3695, -3790, -3883, -3969, -4065,
-4152, -4249, -4342, -4446, -4557, -4679, -4796, -4932, -5072, -5214, -5355, -5488, -5611, -5738, -5854, -5957, -6069, -6178, -6284, -6389,
-6494, -6608, -6719, -6828, -6945, -7053, -7171, -7289, -7419, -7554, -7699, -7843, -7995, -8147, -8290, -8431, -8562, -8683, -8790, -8887,
-8983, -9069, -9160, -9244, -9330, -9411, -9493, -9562, -9634, -9702, -9775, -9841, -9900, -9969, -10035, -10092, -10155, -10200, -10242, -10258,
-10252, -10229, -10191, -10138, -10063, -9970, -9876, -9770, -9650, -9524, -9385, -9228, -9060, -8873, -8669, -8458, -8229, -7978, -7723, -7448,
-7150, -6837, -6497, -6137, -5750, -5341, -4910, -4470, -4015, -3550, -3072, -2599, -2122, -1635, -1149, -662, -164, 329, 829, 1314,
1802, 2281, 2756, 3207, 3656, 4089, 4509, 4906, 5280, 5641, 5972, 6278, 6554, 6809, 7038, 7247, 7445, 7627, 7805, 7957,
8104, 8233, 8352, 8452, 8540, 8615, 8679, 8731, 8763, 8793, 8794, 8789, 8763, 8716, 8652, 8570, 8471, 8370, 8260, 8154,
8043, 7940, 7847, 7756, 7662, 7578, 7486, 7394, 7297, 7204, 7097, 7001, 6890, 6778, 6673, 6550, 6415, 6266, 6113, 5960,
5787, 5628, 5467, 5318, 5170, 5029, 4908, 4795, 4680, 4569, 4468, 4355, 4245, 4132, 4015, 3903, 3784, 3663, 3544, 3418,
3279, 3133, 2975, 2825, 2663, 2505, 2355, 2208, 2072, 1948, 1825, 1720, 1621, 1512, 1418, 1313, 1206, 1093, 979, 865,
751, 626, 511, 386, 252, 112, -37, -182, -331, -480, -618, -749, -880, -993, -1097, -1197, -1284, -1372, -1466, -1551,
-1652, -1753, -1854, -1965, -2073, -2186, -2307, -2422, -2548, -2679, -2811, -2942, -3079, -3217, -3346, -3469, -3585, -3688, -3780, -3865,
-3949, -4024, -4107, -4195, -4281, -4377, -4482, -4589, -4699, -4811, -4930, -5041, -5154, -5281, -5401, -5529, -5652, -5768, -5885, -5993,
-6083, -6171, -6241, -6303, -6359, -6410, -6464, -6522, -6574, -6646, -6712, -6788, -6865, -6941, -7015, -7088, -7146, -7210, -7271, -7322,
-7370, -7401, -7417, -7428, -7418, -7382, -7336, -7275, -7201, -7110, -7014, -6918, -6822, -6708, -6602, -6483, -6363, -6224, -6076, -5911,
-5732, -5530, -5315, -5074, -4827, -4558, -4256, -3939, -3607, -3249, -2879, -2486, -2088, -1677, -1255, -826, -407, 22, 449, 880,
1307, 1732, 2164, 2601, 3024, 3452, 3875, 4299, 4712, 5118, 5514, 5900, 6266, 6620, 6953, 7265, 7554, 7825, 8083, 8326,
8556, 8766, 8970, 9161, 9332, 9484, 9628, 9753, 9861, 9953, 10036, 10108, 10165, 10210, 10238, 10258, 10251, 10227, 10198, 10146,
10095, 10017, 9950, 9880, 9813, 9741, 9674, 9608, 9538, 9457, 9371, 9276, 9177, 9062, 8943, 8819, 8697, 8566, 8424, 8284,
8134, 7979, 7820, 7657, 7491, 7329, 7171, 7017, 6882, 6750, 6623, 6509, 6391, 6283, 6155, 6026, 5896, 5760, 5617, 5483,
5336, 5198, 5055, 4905, 4764, 4619, 4467, 4320, 4169, 4024, 3883, 3745, 3626, 3518, 3411, 3319, 3229, 3127, 3032, 2922,
2821, 2713, 2597, 2486, 2374, 2257, 2148, 2029, 1923, 1808, 1692, 1574, 1460, 1346, 1241, 1129, 1041, 951, 875, 793,
724, 650, 572, 485, 386, 293, 196, 83, -22, -128, -237, -342, -452, -562, -674, -782, -894, -1003, -1107, -1208,
-1305, -1394, -1472, -1552, -1628, -1708, -1793, -1877, -1976, -2081, -2186, -2296, -2411, -2518, -2630, -2737, -2852, -2961, -3074, -3187,
-3300, -3410, -3516, -3618, -3718, -3809, -3896, -3980, -4062, -4143, -4235, -4324, -4432, -4542, -4657, -4773, -4902, -5025, -5143, -5260,
-5376, -5496, -5608, -5723, -5848, -5968, -6084, -6188, -6300, -6406, -6497, -6585, -6680, -6774, -6869, -6979, -7094, -7220, -7355, -7492,
-7632, -7769, -7902, -8040, -8166, -8290, -8420, -8539, -8660, -8785, -8896, -9011, -9108, -9211, -9301, -9380, -9459, -9539, -9612, -9692,
-9783, -9880, -9978, -10072, -10163, -10245, -10319, -10374, -10414, -10448, -10465, -10479, -10475, -10464, -10436, -10393, -10330, -10253, -10157, -10040,
-9904, -9762, -9605, -9434, -9262, -9075, -8887, -8678, -8443, -8187, -7910, -7595, -7266, -6914, -6545, -6153, -5745, -5324, -4892, -4442,
-3982, -3505, -3016, -2527, -2026, -1525, -1027, -528, -33, 463, 947, 1434, 1921, 2401, 2868, 3329, 3776, 4199, 4603, 4985,
5349, 5699, 6020, 6317, 6604, 6869, 7122, 7344, 7549, 7739, 7923, 8082, 8237, 8382, 8518, 8632, 8739, 8835, 8909, 8962,
8999, 9008, 9000, 8977, 8941, 8896, 8837, 8768, 8696, 8615, 8522, 8425, 8322, 8215, 8110, 8005, 7902, 7807, 7711, 7614,
7518, 7415, 7306, 7185, 7046, 6904, 6745, 6588, 6419, 6254, 6094, 5937, 5778, 5627, 5472, 5324, 5171, 5023, 4883, 4756,
4626, 4515, 4406, 4305, 4206, 4104, 3996, 3883, 3750, 3617, 3473, 3328, 3177, 3030, 2893, 2759, 2627, 2502, 2383, 2259,
2139, 2021, 1904, 1800, 1699, 1596, 1512, 1421, 1330, 1236, 1135, 1029, 909, 775, 633, 488, 348, 198, 52, -82,
-214, -344, -472, -595, -715, -842, -965, -1085, -1200, -1319, -1424, -1529, -1634, -1741, -1862, -1979, -2114, -2255, -2406, -2554,
-2707, -2860, -3010, -3151, -3278, -3403, -3529, -3643, -3759, -3869, -3992, -4097, -4203, -4305, -4400, -4486, -4576, -4662, -4762, -4864,
-4967, -5085, -5210, -5333, -5464, -5584, -5699, -5810, -5902, -5986, -6068, -6141, -6214, -6284, -6353, -6428, -6490, -6552, -6609, -6660,
-6719, -6772, -6835, -6900, -6976, -7053, -7134, -7219, -7298, -7367, -7429, -7480, -7508, -7524, -7529, -7535, -7514, -7496, -7467, -7438,
-7398, -7347, -7284, -7215, -7128, -7040, -6935, -6834, -6718, -6596, -6461, -6319, -6152, -5966, -5753, -5517, -5255, -4961, -4652, -4319,
-3972, -3603, -3217, -2820, -2417, -1991, -1558, -1120, -665, -218, 241, 701, 1160, 1623, 2083, 2547, 3001, 3454, 3902, 4341,
4759, 5174, 5566, 5949, 6308, 6665, 6992, 7310, 7608, 7885, 8149, 8389, 8605, 8804, 8982, 9149, 9300, 9438, 9574, 9703,
9807, 9902, 9980, 10033, 10067, 10077, 10078, 10063, 10037, 10007, 9974, 9935, 9895, 9846, 9794, 9739, 9677, 9603, 9529, 9450,
9375, 9298, 9223, 9148, 9067, 8980, 8885, 8775, 8647, 8506, 8361, 8212, 8057, 7900, 7757, 7611, 7474, 7339, 7206, 7073,
6938, 6794, 6656, 6518, 6379, 6245, 6111, 5979, 5849, 5707, 5567, 5419, 5260, 5096, 4922, 4751, 4580, 4413, 4257, 4117,
3980, 3849, 3723, 3600, 3481, 3357, 3237, 3120, 2999, 2890, 2775, 2668, 2569, 2457, 2348, 2236, 2113, 1987, 1856, 1722,
1603, 1486, 1374, 1274, 1184, 1099, 1015, 927, 851, 766, 683, 592, 500, 418, 330, 244, 162, 82, -8, -103,
-201, -308, -418, -535, -647, -758, -858, -959, -1050, -1132, -1215, -1308, -1390, -1478, -1571, -1670, -1767, -1867, -1965, -2061,
-2156, -2251, -2353, -2463, -2575, -2691, -2810, -2935, -3059, -3180, -3291, -3397, -3500, -3591, -3679, -3766, -3859, -3952, -4044, -4148,
-4248, -4351, -4452, -4550, -4651, -4750, -4850, -4957, -5064, -5175, -5295, -5411, -5534, -5646, -5746, -5849, -5941, -6019, -6099, -6177,
-6262, -6346, -6438, -6534, -6642, -6746, -6858, -6963, -7073, -7181, -7292, -7410, -7529, -7654, -7787, -7918, -8044, -8179, -8300, -8409,
-8519, -8612, -8701, -8790, -8880, -8979, -9076, -9182, -9289, -9396, -9503, -9604, -9690, -9782, -9864, -9935, -10011, -10076, -10142, -10201,
-10247, -10284, -10304, -10301, -10278, -10232, -10169, -10088, -10001, -9904, -9801, -9683, -9556, -9420, -9266, -9093, -8893, -8681, -8445, -8190,
-7916, -7625, -7319, -6994, -6653, -6292, -5915, -5517, -5100, -4670, -4230, -3777, -3325, -2861, -2410, -1952, -1492, -1032, -575, -108,
344, 808, 1263, 1718, 2164, 2605, 3023, 3440, 3840, 4224, 4586, 4933, 5261, 5568, 5852, 6120, 6377, 6612, 6836, 7045,
7249, 7449, 7627, 7795, 7947, 8086, 8206, 8312, 8404, 8484, 8545, 8596, 8631, 8650, 8649, 8629, 8592, 8536, 8462, 8371,
8280, 8178, 8081, 7983, 7882, 7792, 7692, 7588, 7481, 7361, 7237, 7107, 6967, 6827, 6692, 6547, 6406, 6255, 6104, 5945,
5776, 5602, 5430, 5250, 5078, 4906, 4755, 4611, 4472, 4358, 4246, 4129, 4017, 3903, 3785, 3667, 3543, 3427, 3314, 3197,
3083, 2970, 2854, 2745, 2619, 2499, 2367, 2236, 2111, 1998, 1881, 1782, 1687, 1599, 1518, 1437, 1348, 1252, 1150, 1044,
927, 804, 687, 568, 441, 315, 194, 63, -72, -212, -359, -508, -658, -805, -942, -1069, -1190, -1308, -1423, -1530,
-1647, -1764, -1889, -2018, -2154, -2293, -2432, -2564, -2701, -2835, -2963, -3096, -3220, -3356, -3498, -3631, -3763, -3895, -4006, -4115,
-4208, -4299, -4381, -4455, -4527, -4609, -4692, -4783, -4872, -4969, -5067, -5160, -5250, -5339, -5428, -5510, -5599, -5687, -5779, -5870,
-5958, -6042, -6118, -6180, -6237, -6282, -6326, -6360, -6399, -6442, -6486, -6542, -6604, -6670, -6738, -6804, -6861, -6913, -6964, -7007,
-7044, -7079, -7114, -7145, -7166, -7172, -7172, -7154, -7120, -7065, -7004, -6928, -6841, -6751, -6655, -6554, -6447, -6334, -6203, -6061,
-5895, -5711, -5508, -5285, -5042, -4780, -4502, -4206, -3889, -3547, -3192, -2817, -2418, -2007, -1585, -1160, -720, -280, 165, 604,
1047, 1490, 1932, 2367, 2802, 3231, 3652, 4064, 4466, 4856, 5241, 5613, 5977, 6329, 6671, 6992, 7301, 7584, 7843, 8084,
8304, 8512, 8704, 8884, 9053, 9211, 9361, 9495, 9618, 9723, 9817, 9887, 9944, 9993, 10027, 10061, 10077, 10095, 10103, 10094,
10072, 10032, 9975, 9917, 9835, 9753, 9675, 9596, 9515, 9436, 9359, 9279, 9184, 9081, 8973, 8852, 8722, 8581, 8444, 8303,
8163, 8019, 7875, 7729, 7571, 7407, 7238, 7068, 6895, 6721, 6557, 6403, 6252, 6114, 5978, 5844, 5714, 5577, 5434, 5288,
5140, 4989, 4838, 4693, 4548, 4411, 4275, 4150, 4016, 3883, 3748, 3618, 3490, 3360, 3243, 3137, 3041, 2946, 2862, 2777,
2692, 2603, 2508, 2411, 2305, 2200, 2092, 1991, 1890, 1791, 1689, 1593, 1499, 1404, 1298, 1197, 1094, 993, 889, 793,
706, 625, 542, 466, 381, 295, 193, 92, -13, -123, -237, -345, -455, -563, -673, -783, -884, -992, -1098, -1213,
-1321, -1433, -1542, -1646, -1738, -1827, -1916, -1998, -2087, -2177, -2266, -2371, -2472, -2582, -2696, -2804, -2910, -3017, -3119, -3224,
-3324, -3419, -3524, -3626, -3731, -3837, -3936, -4034, -4125, -4210, -4292, -4374, -4454, -4540, -4633, -4730, -4839, -4950, -5064, -5184,
-5299, -5411, -5517, -5625, -5732, -5831, -5937, -6050, -6157, -6269, -6376, -6482, -6585, -6680, -6773, -6867, -6963, -7065, -7166, -7280,
-7410, -7537, -7670, -7803, -7933, -8061, -8182, -8296, -8414, -8525, -8630, -8744, -8855, -8964, -9074, -9174, -9266, -9361, -9438, -9510,
-9584, -9650, -9720, -9785, -9857, -9934, -10001, -10057, -10108, -10142, -10156, -10152, -10140, -10109, -10067, -10011, -9942, -9864, -9769, -9658,
-9523, -9376, -9208, -9014, -8810, -8591, -8352, -8105, -7842, -7570, -7279, -6969, -6643, -6300, -5930, -5544, -5137, -4719, -4289, -3850,
-3400, -2945, -2488, -2026, -1564, -1101, -638, -180, 284, 735, 1191, 1634, 2074, 2512, 2932, 3343, 3741, 4126, 4492, 4842,
5174, 5481, 5773, 6055, 6314, 6560, 6785, 7001, 7188, 7365, 7516, 7654, 7776, 7893, 7994, 8093, 8184, 8270, 8339, 8398,
8445, 8475, 8481, 8472, 8446, 8404, 8348, 8285, 8215, 8141, 8063, 7976, 7886, 7785, 7677, 7561, 7443, 7328, 7212, 7103,
6995, 6891, 6788, 6680, 6571, 6453, 6321, 6177, 6027, 5869, 5710, 5548, 5392, 5241, 5096, 4951, 4811, 4673, 4535, 4397,
4265, 4138, 4019, 3904, 3800, 3701, 3611, 3517, 3421, 3327, 3224, 3107, 2983, 2853, 2725, 2601, 2475, 2364, 2253, 2145,
2041, 1938, 1839, 1735, 1632, 1531, 1431, 1337, 1243, 1151, 1068, 981, 888, 786, 677, 554, 423, 283, 146, 0,
-144, -284, -417, -552, -685, -815, -948, -1077, -1216, -1354, -1489, -1619, -1751, -1878, -1998, -2121, -2246, -2381, -2518, -2664,
-2819, -2977, -3133, -3291, -3445, -3593, -3735, -3866, -3991, -4112, -4229, -4346, -4455, -4572, -4680, -4783, -4879, -4973, -5058, -5141,
-5220, -5311, -5404, -5503, -5610, -5723, -5836, -5949, -6052, -6150, -6244, -6320, -6388, -6457, -6520, -6583, -6641, -6703, -6766, -6824,
-6877, -6927, -6977, -7019, -7067, -7119, -7178, -7239, -7308, -7379, -7453, -7518, -7577, -7613, -7645, -7651, -7644, -7623, -7598, -7556,
-7508, -7451, -7390, -7306, -7214, -7098, -6972, -6826, -6668, -6494, -6315, -6118, -5907, -5680, -5432, -5164, -4869, -4541, -4187, -3812,
-3405, -2982, -2546, -2102, -1641, -1170, -691, -208, 284, 779, 1270, 1757, 2243, 2720, 3181, 3632, 4076, 4511, 4934, 5345,
5746, 6138, 6510, 6860, 7193, 7501, 7785, 8046, 8291, 8512, 8722, 8913, 9092, 9257, 9405, 9534, 9648, 9754, 9845, 9928,
10003, 10077, 10144, 10202, 10251, 10279, 10299, 10300, 10280, 10254, 10212, 10154, 10093, 10034, 9971, 9907, 9836, 9765, 9690, 9608,
9514, 9418, 9317, 9218, 9112, 9014, 8910, 8803, 8678, 8553, 8418, 8267, 8101, 7932, 7754, 7568, 7387, 7211, 7039, 6877,
6716, 6556, 6400, 6244, 6085, 5926, 5775, 5625, 5479, 5330, 5191, 5054, 4915, 4771, 4626, 4475, 4324, 4160, 4007, 3853,
3706, 3570, 3439, 3323, 3217, 3108, 3011, 2916, 2820, 2725, 2635, 2543, 2455, 2366, 2280, 2198, 2113, 2025, 1932, 1832,
1731, 1618, 1507, 1397, 1290, 1188, 1096, 1005, 925, 842, 758, 677, 593, 501, 410, 311, 219, 119, 23, -72,
-168, -272, -381, -496, -618, -744, -875, -999, -1122, -1240, -1349, -1452, -1554, -1648, -1747, -1838, -1933, -2027, -2128, -2227,
-2329, -2425, -2527, -2626, -2723, -2823, -2931, -3035, -3152, -3263, -3385, -3502, -3606, -3712, -3810, -3900, -3985, -4062, -4137, -4219,
-4297, -4379, -4468, -4557, -4650, -4739, -4834, -4928, -5026, -5121, -5227, -5338, -5452, -5574, -5693, -5811, -5937, -6047, -6154, -6262,
-6357, -6448, -6535, -6633, -6728, -6834, -6943, -7064, -7187, -7305, -7431, -7559, -7688, -7814, -7947, -8082, -8220, -8366, -8508, -8648,
-8789, -8917, -9035, -9147, -9246, -9340, -9426, -9508, -9596, -9685, -9772, -9857, -9945, -10028, -10105, -10172, -10236, -10289, -10332, -10368,
-10395, -10414, -10423, -10419, -10397, -10358, -10293, -10209, -10106, -9981, -9841, -9685, -9517, -9342, -9148, -8948, -8730, -8504, -8260, -7995,
-7713, -7418, -7097, -6759, -6403, -6031, -5648, -5243, -4822, -4394, -3945, -3488, -3024, -2554, -2082, -1601, -1120, -644, -164, 314,
788, 1262, 1722, 2181, 2630, 3063, 3495, 3912, 4319, 4713, 5092, 5453, 5798, 6120, 6414, 6690, 6939, 7159, 7361, 7544,
7720, 7877, 8024, 8164, 8291, 8402, 8504, 8578, 8640, 8690, 8715, 8735, 8739, 8736, 8715, 8685, 8636, 8575, 8490, 8392,
8282, 8155, 8016, 7880, 7747, 7620, 7491, 7375, 7263, 7154, 7043, 6926, 6803, 6680, 6543, 6414, 6280, 6150, 6009, 5874,
5731, 5591, 5436, 5276, 5118, 4952, 4792, 4634, 4486, 4349, 4226, 4107, 4009, 3911, 3816, 3711, 3613, 3506, 3398, 3279,
3164, 3052, 2929, 2813, 2693, 2575, 2449, 2314, 2187, 2051, 1912, 1779, 1655, 1540, 1429, 1327, 1233, 1148, 1057, 966,
867, 760, 649, 532, 402, 282, 157, 33, -96, -230, -360, -499, -641, -785, -931, -1067, -1207, -1341, -1454, -1564,
-1670, -1764, -1862, -1964, -2072, -2182, -2304, -2422, -2554, -2683, -2811, -2940, -3066, -3197, -3326, -3453, -3592, -3723, -3855, -3979,
-4105, -4218, -4323, -4414, -4499, -4579, -4652, -4733, -4818, -4907, -5005, -5111, -5218, -5333, -5436, -5549, -5651, -5756, -5861, -5967,
-6066, -6176, -6276, -6372, -6465, -6553, -6628, -6692, -6743, -6794, -6839, -6885, -6940, -7003, -7077, -7158, -7238, -7328, -7411, -7485,
-7548, -7607, -7667, -7714, -7757, -7794, -7829, -7851, -7864, -7856, -7831, -7787, -7728, -7650, -7561, -7464, -7364, -7260, -7157, -7044,
-6922, -6783, -6632, -6450, -6253, -6029, -5787, -5521, -5235, -4927, -4613, -4260, -3891, -3501, -3091, -2656, -2203, -1734, -1267, -794,
-320, 154, 624, 1095, 1568, 2042, 2505, 2979, 3449, 3904, 4353, 4792, 5219, 5632, 6023, 6400, 6768, 7113, 7441, 7749,
8038, 8311, 8557, 8783, 8997, 9195, 9374, 9541, 9693, 9837, 9967, 10084, 10186, 10277, 10344, 10400, 10436, 10460, 10468, 10458,
10446, 10419, 10386, 10336, 10279, 10209, 10142, 10059, 9975, 9898, 9819, 9738, 9657, 9578, 9500, 9407, 9306, 9201, 9084, 8951,
8814, 8670, 8524, 8371, 8220, 8067, 7913, 7755, 7588, 7426, 7261, 7100, 6938, 6789, 6647, 6516, 6381, 6253, 6126, 6001,
5861, 5719, 5573, 5418, 5259, 5102, 4944, 4796, 4644, 4497, 4353, 4211, 4068, 3929, 3795, 3664, 3539, 3416, 3315, 3211,
3120, 3029, 2941, 2853, 2759, 2656, 2559, 2442, 2329, 2218, 2105, 1993, 1884, 1777, 1676, 1573, 1473, 1369, 1274, 1179,
1089, 991, 911, 830, 752, 674, 594, 511, 423, 323, 221, 113, -3, -117, -236, -352, -466, -579, -692, -801,
-910, -1021, -1128, -1234, -1337, -1437, -1536, -1627, -1717, -1799, -1893, -1990, -2088, -2189, -2302, -2409, -2532, -2655, -2776, -2895,
-3005, -3116, -3226, -3328, -3428, -3532, -3629, -3728, -3827, -3916, -4006, -4086, -4166, -4246, -4325, -4410, -4500, -4591, -4698, -4807,
-4917, -5033, -5150, -5261, -5375, -5483, -5585, -5688, -5788, -5891, -5989, -6093, -6197, -6293, -6389, -6489, -6584, -6681, -6780, -6886,
-7002, -7120, -7245, -7387, -7534, -7680, -7829, -7971, -8117, -8250, -8381, -8502, -8620, -8732, -8846, -8961, -9067, -9172, -9266, -9366,
-9456, -9534, -9619, -9696, -9778, -9857, -9936, -10009, -10091, -10153, -10213, -10255, -10283, -10295, -10285, -10260, -10224, -10165, -10095, -10010,
-9913, -9798, -9668, -9518, -9366, -9187, -9000, -8800, -8585, -8360, -8114, -7860, -7587, -7299, -6984, -6657, -6305, -5939, -5558, -5156,
-4743, -4318, -3877, -3426, -2968, -2509, -2046, -1578, -1113, -647, -183, 284, 743, 1205, 1660, 2125, 2579, 3024, 3464, 3885,
4291, 4674, 5031, 5375, 5702, 6001, 6289, 6561, 6816, 7050, 7270, 7474, 7659, 7815, 7968, 8101, 8226, 8336, 8443, 8540,
8635, 8705, 8758, 8796, 8810, 8799, 8759, 8701, 8627, 8543, 8449, 8351, 8244, 8145, 8034, 7920, 7805, 7684, 7558, 7441,
7316, 7203, 7087, 6980, 6873, 6771, 6655, 6534, 6404, 6262, 6104, 5939, 5769, 5607, 5432, 5274, 5119, 4975, 4841, 4702,
4579, 4454, 4328, 4217, 4103, 3997, 3893, 3799, 3705, 3620, 3520, 3415, 3302, 3185, 3047, 2913, 2759, 2611, 2465, 2320,
2193, 2065, 1946, 1825, 1709, 1593, 1479, 1358, 1248, 1134, 1025, 911, 800, 692, 575, 451, 320, 181, 26, -133,
-299, -471, -629, -793, -935, -1078, -1207, -1341, -1463, -1584, -1697, -1816, -1931, -2038, -2149, -2251, -2358, -2457, -2554, -2662,
-2781, -2899, -3027, -3167, -3307, -3445, -3575, -3695, -3813, -3916, -4014, -4094, -4174, -4250, -4325, -4393, -4475, -4549, -4619, -4690,
-4763, -4831, -4904, -4979, -5072, -5164, -5268, -5382, -5497, -5618, -5728, -5827, -5923, -6005, -6077, -6137, -6193, -6250, -6302, -6354,
-6412, -6474, -6534, -6590, -6646, -6706, -6761, -6816, -6874, -6945, -7012, -7088, -7155, -7225, -7278, -7312, -7333, -7333, -7305, -7265,
-7204, -7140, -7059, -6978, -6884, -6793, -6677, -6563, -6422, -6271, -6110, -5931, -5745, -5552, -5343, -5118, -4882, -4627, -4350, -4053,
-3722, -3368, -2995, -2586, -2166, -1741, -1316, -881, -447, -13, 419, 860, 1298, 1738, 2173, 2603, 3036, 3461, 3872, 4280,
4678, 5070, 5449, 5822, 6187, 6537, 6870, 7189, 7487, 7768, 8030, 8271, 8491, 8700, 8892, 9070, 9234, 9385, 9524, 9653,
9765, 9868, 9959, 10041, 10112, 10168, 10213, 10231, 10245, 10234, 10211, 10165, 10111, 10047, 9976, 9891, 9804, 9719, 9633, 9547,
9454, 9358, 9265, 9161, 9054, 8950, 8834, 8719, 8602, 8480, 8348, 8209, 8054, 7895, 7731, 7549, 7370, 7196, 7024, 6851,
6689, 6537, 6394, 6253, 6121, 5994, 5863, 5735, 5610, 5485, 5359, 5240, 5113, 4995, 4871, 4742, 4604, 4463, 4321, 4174,
4026, 3888, 3749, 3621, 3499, 3388, 3287, 3189, 3098, 3011, 2923, 2823, 2738, 2644, 2550, 2456, 2356, 2260, 2159, 2051,
1941, 1823, 1702, 1577, 1452, 1326, 1212, 1098, 988, 889, 800, 716, 628, 550, 470, 378, 292, 198, 104, 10,
-84, -185, -283, -389, -498, -614, -733, -853, -967, -1087, -1195, -1298, -1395, -1486, -1563, -1638, -1707, -1788, -1860, -1936,
-2014, -2099, -2191, -2279, -2368, -2465, -2565, -2661, -2761, -2869, -2983, -3100, -3208, -3329, -3432, -3534, -3628, -3714, -3797, -3875,
-3952, -4024, -4106, -4189, -4274, -4369, -4474, -4580, -4687, -4794, -4910, -5022, -5141, -5263, -5392, -5515, -5651, -5773, -5898, -6014,
-6119, -6218, -6319, -6412, -6505, -6592, -6689, -6786, -6894, -7014, -7134, -7263, -7385, -7512, -7644, -7774, -7907, -8042, -8178, -8312,
-8444, -8573, -8687, -8800, -8893, -8984, -9060, -9135, -9197, -9255, -9316, -9381, -9450, -9520, -9584, -9654, -9717, -9774, -9820, -9864,
-9896, -9918, -9933, -9938, -9927, -9899, -9850, -9791, -9700, -9592, -9465, -9325, -9169, -9001, -8822, -8631, -8437, -8226, -8002, -7761,
-7507, -7240, -6945, -6639, -6319, -5977, -5617, -5240, -4845, -4436, -4005, -3565, -3118, -2656, -2192, -1727, -1268, -810, -350, 109,
560, 1025, 1479, 1939, 2386, 2821, 3254, 3667, 4065, 4445, 4817, 5168, 5505, 5814, 6117, 6396, 6646, 6877, 7080, 7253,
7412, 7547, 7680, 7798, 7913, 8020, 8132, 8227, 8320, 8390, 8442, 8478, 8498, 8496, 8477, 8447, 8407, 8355, 8289, 8209,
8121, 8014, 7897, 7772, 7643, 7508, 7378, 7260, 7155, 7051, 6959, 6876, 6790, 6703, 6607, 6503, 6386, 6260, 6125, 5990,
5857, 5716, 5569, 5427, 5281, 5127, 4973, 4820, 4670, 4523, 4380, 4257, 4152, 4051, 3961, 3888, 3808, 3730, 3643, 3548,
3446, 3331, 3214, 3090, 2966, 2841, 2711, 2583, 2455, 2323, 2186, 2053, 1923, 1793, 1668, 1554, 1449, 1366, 1281, 1199,
1126, 1035, 944, 839, 722, 603, 470, 327, 193, -5, 31, 176, 288, 481, 714, 1005, 1326, 1706, 2109, 2526,
2921, 3308, 3667, 4002, 4320, 4629, 4910, 5160, 5378, 5574, 5744, 5883, 5995, 6111, 6246, 6415, 6602, 6803, 7011, 7239,
7474, 7727, 7983, 8246, 8504, 8755, 8991, 9231, 9477, 9723, 9954, 10158, 10311, 10400, 10417, 10380, 10291, 10164, 10013, 9831,
9623, 9385, 9121, 8837, 8534, 8212, 7876, 7507, 7107, 6698, 6296, 5912, 5558, 5240, 4948, 4676, 4408, 4148, 3899, 3655,
3424, 3204, 3004, 2824, 2650, 2492, 2354, 2235, 2111, 1992, 1877, 1747, 1611, 1476, 1346, 1226, 1116, 1023, 936, 849,
766, 692, 625, 561, 508, 476, 457, 450, 455, 482, 511, 546, 585, 611, 624, 613, 592, 569, 541, 515,
498, 486, 479, 482, 482, 484, 484, 477, 472, 461, 439, 429, 422, 416, 410, 407, 394, 375, 336, 284,
219, 137, 45, -51, -142, -229, -325, -414, -492, -572, -650, -730, -803, -877, -954, -1032, -1092, -1144, -1194, -1247,
-1301, -1366, -1438, -1530, -1618, -1704, -1786, -1866, -1933, -2003, -2060, -2118, -2172, -2226, -2275, -2330, -2389, -2451, -2504, -2554,
-2589, -2611, -2628, -2645, -2664, -2688, -2717, -2748, -2782, -2818, -2861, -2907, -2951, -2989, -3019, -3040, -3052, -3057, -3066, -3086,
-3109, -3138, -3177, -3215, -3252, -3286, -3331, -3385, -3455, -3526, -3606, -3703, -3823, -3953, -4105, -4270, -4444, -4620, -4784, -4929,
-5071, -5210, -5360, -5531, -5712, -5914, -6116, -6325, -6530, -6736, -6939, -7150, -7361, -7574, -7793, -8024, -8264, -8520, -8787, -9061,
-9322, -9556, -9750, -9914, -10053, -10163, -10257, -10346, -10415, -10470, -10505, -10506, -10484, -10435, -10359, -10260, -10121, -9956, -9777, -9581,
-9371, -9148, -8895, -8605, -8258, -7854, -7383, -6846, -6259, -5643, -5002, -4347, -3680, -3006, -2336, -1666, -1004, -350, 295, 934,
1557, 2157, 2737, 3307, 3859, 4400, 4919, 5421, 5895, 6329, 6721, 7062, 7356, 7610, 7821, 8000, 8149, 8281, 8401, 8502,
8590, 8660, 8702, 8712, 8701, 8673, 8634, 8594, 8563, 8532, 8485, 8423, 8333, 8216, 8070, 7891, 7687, 7462, 7216, 6971,
6735, 6510, 6300, 6103, 5917, 5728, 5531, 5322, 5112, 4899, 4691, 4499, 4317, 4146, 3980, 3826, 3672, 3516, 3350, 3178,
2994, 2803, 2612, 2427, 2261, 2116, 1993, 1892, 1804, 1718, 1643, 1571, 1506, 1444, 1394, 1358, 1329, 1308, 1294, 1275,
1256, 1229, 1192, 1144, 1074, 998, 922, 850, 784, 737, 700, 685, 666, 655, 643, 626, 602, 579, 550, 517,
476, 438, 400, 363, 316, 267, 210, 137, 47, -59, -167, -276, -382, -476, -561, -637, -705, -773, -840, -914,
-994, -1075, -1161, -1260, -1352, -1446, -1536, -1621, -1703, -1784, -1867, -1965, -2065, -2176, -2283, -2384, -2474, -2557, -2624, -2681,
-2727, -2760, -2794, -2826, -2854, -2897, -2938, -2985, -3029, -3076, -3109, -3134, -3155, -3183, -3219, -3259, -3316, -3379, -3455, -3525,
-3598, -3667, -3723, -3765, -3795, -3810, -3834, -3851, -3879, -3926, -3991, -4071, -4164, -4255, -4358, -4462, -4580, -4703, -4848, -5004,
-5184, -5372, -5574, -5779, -5990, -6194, -6382, -6546, -6692, -6826, -6950, -7077, -7222, -7380, -7554, -7743, -7938, -8127, -8307, -8481,
-8634, -8772, -8894, -8999, -9090, -9168, -9230, -9268, -9270, -9225, -9119, -8955, -8727, -8445, -8114, -7754, -7361, -6940, -6487, -5998,
-5467, -4893, -4273, -3609, -2900, -2155, -1387, -613, 167, 937, 1706, 2456, 3188, 3894, 4574, 5207, 5798, 6329, 6815, 7247,
7639, 7993, 8314, 8595, 8845, 9064, 9247, 9397, 9506, 9577, 9610, 9613, 9588, 9556, 9515, 9479, 9431, 9368, 9286, 9172,
9038, 8893, 8734, 8572, 8412, 8255, 8110, 7981, 7851, 7732, 7610, 7477, 7328, 7158, 6970, 6780, 6586, 6404, 6224, 6058,
5886, 5710, 5529, 5339, 5138, 4933, 4729, 4528, 4339, 4162, 4003, 3865, 3744, 3632, 3530, 3424, 3310, 3186, 3060, 2934,
2812, 2701, 2602, 2501, 2408, 2316, 2222, 2126, 2026, 1926, 1827, 1728, 1637, 1553, 1486, 1434, 1393, 1359, 1328, 1291,
1251, 1201, 1143, 1081, 1025, 962, 909, 857, 803, 755, 708, 664, 613, 562, 510, 459, 413, 377, 350, 332,
315, 303, 287, 269, 244, 208, 165, 122, 73, 27, -25, -66, -108, -147, -190, -229, -274, -322, -378, -435,
-491, -542, -594, -642, -686, -730, -782, -829, -885, -947, -1013, -1086, -1158, -1228, -1298, -1363, -1421, -1474, -1528, -1582,
-1638, -1698, -1766, -1837, -1905, -1975, -2029, -2088, -2131, -2173, -2210, -2251, -2292, -2334, -2384, -2439, -2499, -2559, -2618, -2678,
-2728, -2777, -2825, -2873, -2930, -2993, -3056, -3126, -3194, -3260, -3318, -3374, -3427, -3476, -3518, -3570, -3625, -3690, -3769, -3858,
-3960, -4074, -4182, -4296, -4405, -4513, -4618, -4731, -4849, -4978, -5110, -5248, -5390, -5534, -5682, -5825, -5969, -6107, -6239, -6380,
-6532, -6691, -6873, -7067, -7274, -7488, -7693, -7890, -8071, -8242, -8400, -8551, -8701, -8844, -8984, -9117, -9249, -9364, -9460, -9532,
-9574, -9586, -9564, -9515, -9447, -9372, -9276, -9172, -9042, -8891, -8699, -8466, -8186, -7867, -7507, -7108, -6675, -6212, -5719, -5198,
-4662, -4110, -3536, -2943, -2340, -1725, -1107, -488, 127, 732, 1335, 1930, 2518, 3092, 3651, 4186, 4687, 5154, 5588, 5984,
6348, 6683, 6986, 7270, 7527, 7752, 7948, 8115, 8248, 8348, 8423, 8484, 8531, 8570, 8609, 8650, 8684, 8709, 8716, 8698,
8655, 8577, 8466, 8330, 8178, 8009, 7837, 7662, 7482, 7301, 7110, 6907, 6695, 6468, 6236, 5999, 5771, 5552, 5345, 5154,
4974, 4800, 4633, 4463, 4286, 4105, 3914, 3720, 3528, 3343, 3166, 3002, 2852, 2717, 2581, 2452, 2329, 2206, 2090, 1968,
1868, 1778, 1707, 1647, 1607, 1569, 1548, 1524, 1489, 1453, 1405, 1343, 1282, 1218, 1159, 1105, 1062, 1020, 988, 950,
917, 881, 843, 801, 759, 718, 682, 652, 618, 591, 556, 519, 472, 408, 332, 245, 151, 51, -54, -147,
-243, -334, -420, -506, -590, -671, -766, -859, -955, -1050, -1139, -1227, -1309, -1380, -1449, -1525, -1607, -1693, -1780, -1877,
-1982, -2080, -2177, -2268, -2349, -2430, -2495, -2558, -2617, -2677, -2736, -2800, -2865, -2931, -2986, -3031, -3072, -3105, -3129, -3153,
-3180, -3215, -3260, -3312, -3375, -3440, -3507, -3577, -3640, -3698, -3752, -3802, -3849, -3900, -3957, -4021, -4090, -4168, -4241, -4312,
-4378, -4447, -4510, -4587, -4673, -4775, -4893, -5032, -5188, -5358, -5535, -5715, -5893, -6058, -6214, -6362, -6503, -6645, -6793, -6942,
-7099, -7260, -7415, -7562, -7698, -7823, -7940, -8043, -8145, -8242, -8340, -8438, -8528, -8612, -8681, -8712, -8706, -8653, -8551, -8397,
-8199, -7960, -7696, -7393, -7062, -6695, -6288, -5841, -5349, -4815, -4243, -3638, -3008, -2364, -1706, -1042, -360, 331, 1029, 1733,
2435, 3122, 3791, 4433, 5036, 5601, 6126, 6601, 7038, 7434, 7793, 8117, 8406, 8653, 8857, 9013, 9143, 9242, 9320, 9387,
9445, 9498, 9536, 9556, 9557, 9526, 9473, 9398, 9297, 9179, 9052, 8908, 8766, 8623, 8483, 8339, 8191, 8029, 7854, 7666,
7475, 7285, 7099, 6921, 6751, 6587, 6425, 6253, 6073, 5889, 5688, 5479, 5264, 5042, 4826, 4616, 4417, 4232, 4060, 3897,
3738, 3578, 3422, 3271, 3124, 2986, 2860, 2746, 2643, 2549, 2460, 2380, 2296, 2209, 2125, 2032, 1935, 1835, 1744, 1658,
1583, 1517, 1465, 1418, 1377, 1339, 1294, 1261, 1224, 1194, 1165, 1141, 1116, 1100, 1080, 1061, 1044, 1012, 978, 935,
885, 832, 774, 726, 678, 634, 599, 569, 536, 505, 470, 438, 400, 361, 323, 281, 239, 195, 150, 105,
58, 5, -54, -121, -192, -271, -343, -409, -473, -530, -587, -631, -681, -722, -771, -815, -862, -905, -960, -1003,
-1051, -1093, -1137, -1176, -1214, -1259, -1304, -1357, -1410, -1466, -1523, -1577, -1628, -1668, -1710, -1745, -1782, -1812, -1843, -1882,
-1918, -1961, -2008, -2055, -2098, -2143, -2186, -2232, -2276, -2328, -2387, -2455, -2525, -2602, -2680, -2760, -2835, -2910, -2975, -3037,
-3093, -3150, -3205, -3265, -3333, -3409, -3490, -3579, -3666, -3754, -3844, -3941, -4042, -4159, -4277, -4411, -4548, -4694, -4842, -4993,
-5144, -5289, -5426, -5558, -5677, -5797, -5922, -6054, -6199, -6356, -6513, -6681, -6848, -7010, -7174, -7337, -7504, -7669, -7829, -7991,
-8158, -8317, -8479, -8625, -8770, -8885, -8969, -9031, -9071, -9085, -9089, -9084, -9063, -9032, -8987, -8917, -8833, -8716, -8578, -8414,
-8214, -7982, -7717, -7419, -7089, -6729, -6331, -5897, -5423, -4904, -4348, -3759, -3148, -2513, -1862, -1201, -528, 145, 823, 1495,
2154, 2794, 3412, 4005, 4568, 5098, 5593, 6060, 6492, 6894, 7263, 7596, 7882, 8116, 8301, 8437, 8538, 8603, 8649, 8675,
8690, 8693, 8688, 8674, 8654, 8616, 8566, 8493, 8396, 8286, 8162, 8033, 7908, 7776, 7640, 7500, 7337, 7158, 6967, 6766,
6556, 6349, 6141, 5940, 5747, 5570, 5405, 5256, 5115, 4976, 4834, 4692, 4543, 4396, 4245, 4107, 3974, 3846, 3719, 3597,
3470, 3341, 3206, 3072, 2935, 2802, 2667, 2545, 2432, 2336, 2253, 2184, 2128, 2073, 2017, 1960, 1900, 1846, 1787, 1729,
1676, 1621, 1568, 1511, 1456, 1397, 1334, 1263, 1196, 1123, 1051, 982, 924, 880, 846, 815, 789, 766, 738, 702,
664, 618, 568, 510, 452, 391, 329, 260, 199, 129, 61, -18, -99, -188, -271, -358, -437, -507, -575, -637,
-700, -761, -825, -897, -969, -1048, -1131, -1220, -1310, -1402, -1492, -1576, -1662, -1745, -1828, -1918, -2011, -2110, -2203, -2287,
-2372, -2442, -2506, -2562, -2613, -2660, -2707, -2751, -2803, -2857, -2918, -2988, -3055, -3126, -3194, -3259, -3327, -3389, -3458, -3532,
-3613, -3697, -3781, -3859, -3937, -4004, -4066, -4123, -4174, -4226, -4280, -4334, -4406, -4492, -4592, -4712, -4838, -4974, -5110, -5244,
-5380, -5525, -5666, -5821, -5974, -6132, -6290, -6445, -6595, -6739, -6873, -6996, -7108, -7215, -7315, -7421, -7533, -7663, -7800, -7945,
-8082, -8210, -8317, -8404, -8465, -8507, -8522, -8508, -8474, -8401, -8301, -8163, -7988, -7770, -7503, -7177, -6805, -6379, -5920, -5430,
-4905, -4359, -3779, -3172, -2528, -1843, -1128, -377, 399, 1188, 1976, 2757, 3515, 4245, 4937, 5592, 6208, 6779, 7305, 7781,
8199, 8560, 8877, 9143, 9373, 9568, 9731, 9873, 9987, 10079, 10146, 10188, 10204, 10190, 10148, 10077, 9991, 9889, 9776, 9654,
9523, 9382, 9225, 9053, 8871, 8681, 8492, 8307, 8125, 7955, 7788, 7631, 7480, 7330, 7177, 7011, 6838, 6651, 6453, 6247,
6043, 5841, 5646, 5452, 5259, 5073, 4884, 4693, 4512, 4334, 4164, 4001, 3845, 3705, 3574, 3456, 3347, 3245, 3142, 3040,
2927, 2815, 2700, 2582, 2470, 2363, 2258, 2158, 2064, 1972, 1886, 1803, 1724, 1651, 1579, 1516, 1456, 1406, 1365, 1328,
1298, 1270, 1241, 1209, 1167, 1117, 1069, 1015, 957, 901, 851, 800, 751, 701, 658, 616, 572, 531, 489, 445,
408, 371, 337, 310, 275, 243, 209, 164, 115, 59, -3, -66, -133, -199, -266, -329, -391, -451, -507, -558,
-612, -668, -720, -777, -826, -876, -924, -962, -1006, -1048, -1095, -1140, -1189, -1240, -1297, -1355, -1408, -1469, -1525, -1574,
-1623, -1668, -1712, -1753, -1791, -1833, -1875, -1913, -1955, -1988, -2022, -2059, -2086, -2121, -2159, -2196, -2237, -2289, -2345, -2409,
-2475, -2541, -2612, -2674, -2739, -2801, -2859, -2924, -2985, -3049, -3116, -3186, -3256, -3327, -3395, -3471, -3543, -3625, -3704, -3796,
-3892, -3998, -4115, -4242, -4378, -4513, -4653, -4789, -4917, -5044, -5171, -5300, -5428, -5559, -5690, -5826, -5958, -6097, -6233, -6379,
-6521, -6660, -6805, -6956, -7111, -7274, -7447, -7632, -7817, -8002, -8171, -8337, -8484, -8620, -8742, -8853, -8958, -9050, -9126, -9197,
-9261, -9311, -9352, -9382, -9396, -9389, -9367, -9327, -9278, -9214, -9136, -9040, -8920, -8764, -8572, -8336, -8061, -7735, -7376, -6971,
-6522, -6035, -5515, -4959, -4372, -3754, -3111, -2449, -1765, -1067, -359, 358, 1077, 1800, 2515, 3220, 3902, 4557, 5181, 5762,
6294, 6778, 7211, 7588, 7913, 8191, 8436, 8644, 8813, 8951, 9058, 9125, 9163, 9167, 9152, 9121, 9075, 9022, 8958, 8881,
8795, 8693, 8575, 8440, 8277, 8096, 7899, 7683, 7465, 7246, 7030, 6829, 6632, 6442, 6257, 6071, 5892, 5716, 5541, 5379,
5220, 5071, 4931, 4796, 4667, 4539, 4414, 4287, 4155, 4006, 3860, 3710, 3560, 3420, 3289, 3169, 3061, 2961, 2864, 2778,
2693, 2616, 2542, 2469, 2403, 2338, 2275, 2222, 2169, 2117, 2060, 1998, 1928, 1852, 1764, 1676, 1590, 1503, 1422, 1346,
1278, 1217, 1157, 1102, 1054, 1003, 951, 900, 849, 797, 745, 694, 642, 591, 537, 473, 403, 332, 251, 167,
84, 2, -74, -145, -215, -274, -329, -382, -429, -477, -525, -582, -635, -689, -742, -792, -840, -890, -946, -1003,
-1066, -1136, -1206, -1279, -1356, -1431, -1502, -1575, -1638, -1698, -1746, -1796, -1844, -1895, -1945, -2000, -2059, -2112, -2171, -2230,
-2286, -2344, -2411, -2474, -2554, -2633, -2721, -2811, -2909, -3005, -3103, -3194, -3280, -3358, -3432, -3499, -3570, -3641, -3718, -3799,
-3887, -3979, -4073, -4171, -4275, -4383, -4494, -4612, -4736, -4869, -5009, -5156, -5310, -5464, -5616, -5760, -5893, -6017, -6132, -6233,
-6341, -6444, -6551, -6665, -6780, -6904, -7026, -7146, -7272, -7392, -7505, -7616, -7720, -7822, -7922, -8016, -8102, -8178, -8223, -8244,
-8234, -8189, -8112, -8003, -7872, -7717, -7536, -7338, -7120, -6881, -6617, -6316, -5980, -5603, -5182, -4718, -4219, -3687, -3121, -2522,
-1887, -1222, -524, 198, 935, 1681, 2424, 3156, 3864, 4538, 5174, 5774, 6333, 6854, 7337, 7787, 8201, 8574, 8903, 9188,
9434, 9637, 9806, 9938, 10041, 10111, 10143, 10146, 10120, 10058, 9974, 9865, 9733, 9593, 9440, 9284, 9127, 8974, 8823, 8669,
8516, 8356, 8186, 8013, 7835, 7655, 7475, 7290, 7105, 6920, 6728, 6537, 6341, 6139, 5937, 5732, 5533, 5338, 5152, 4977,
4819, 4671, 4534, 4402, 4275, 4152, 4027, 3903, 3782, 3663, 3546, 3425, 3312, 3201, 3092, 2979, 2873, 2766, 2658, 2546,
2443, 2340, 2250, 2161, 2088, 2022, 1963, 1906, 1848, 1795, 1739, 1685, 1624, 1569, 1505, 1445, 1382, 1321, 1261, 1201,
1138, 1079, 1011, 949, 882, 823, 766, 715, 669, 632, 596, 562, 528, 491, 457, 420, 377, 332, 286, 237,
188, 142, 93, 47, -2, -50, -101, -150, -199, -249, -294, -333, -371, -407, -438, -470, -497, -528, -566, -602,
-642, -689, -730, -777, -821, -867, -914, -961, -1006, -1057, -1104, -1155, -1201, -1253, -1300, -1344, -1388, -1429, -1465, -1500,
-1537, -1574, -1614, -1659, -1707, -1760, -1813, -1869, -1930, -1990, -2049, -2110, -2170, -2234, -2300, -2364, -2435, -2502, -2570, -2635,
-2697, -2755, -2813, -2869, -2927, -2987, -3055, -3130, -3210, -3296, -3395, -3492, -3596, -3700, -3808, -3919, -4029, -4143, -4266, -4383,
-4504, -4626, -4751, -4876, -4996, -5112, -5232, -5349, -5466, -5590, -5720, -5864, -6010, -6167, -6334, -6502, -6676, -6845, -7014, -7184,
-7343, -7503, -7661, -7814, -7964, -8107, -8244, -8372, -8483, -8588, -8676, -8756, -8819, -8880, -8936, -8991, -9039, -9077, -9109, -9123,
-9118, -9095, -9042, -8964, -8853, -8710, -8533, -8324, -8075, -7793, -7467, -7105, -6702, -6258, -5770, -5254, -4704, -4121, -3513, -2875,
-2210, -1515, -801, -69, 671, 1419, 2152, 2877, 3575, 4250, 4888, 5491, 6051, 6571, 7040, 7469, 7842, 8167, 8440, 8667,
8844, 8991, 9107, 9203, 9279, 9338, 9382, 9405, 9403, 9377, 9322, 9246, 9141, 9019, 8880, 8734, 8576, 8410, 8242, 8067,
7885, 7695, 7503, 7306, 7109, 6919, 6742, 6569, 6412, 6259, 6120, 5985, 5849, 5711, 5564, 5417, 5262, 5098, 4936, 4777,
4621, 4467, 4321, 4176, 4034, 3895, 3759, 3626, 3497, 3375, 3265, 3164, 3072, 2988, 2908, 2838, 2765, 2692, 2615, 2531,
2445, 2348, 2251, 2153, 2060, 1969, 1879, 1795, 1710, 1627, 1544, 1465, 1389, 1316, 1245, 1181, 1123, 1069, 1015, 966,
913, 859, 795, 728, 649, 572, 487, 400, 315, 232, 151, 71, -5, -82, -160, -234, -305, -377, -447, -512,
-574, -629, -685, -739, -792, -844, -908, -973, -1042, -1116, -1192, -1271, -1345, -1415, -1490, -1558, -1620, -1682, -1742, -1799,
-1856, -1913, -1968, -2019, -2067, -2110, -2149, -2190, -2236, -2276, -2327, -2387, -2449, -2516, -2592, -2673, -2754, -2833, -2909, -2989,
-3062, -3130, -3206, -3276, -3352, -3429, -3505, -3580, -3658, -3728, -3802, -3881, -3957, -4042, -4139, -4240, -4355, -4478, -4614, -4749,
-4896, -5034, -5170, -5300, -5428, -5544, -5661, -5775, -5896, -6012, -6123, -6236, -6343, -6443, -6541, -6637, -6732, -6822, -6921, -7016,
-7123, -7227, -7336, -7442, -7539, -7616, -7676, -7710, -7719, -7704, -7667, -7612, -7540, -7450, -7336, -7202, -7045, -6863, -6648, -6410,
-6142, -5849, -5528, -5181, -4811, -4418, -3995, -3544, -3050, -2522, -1951, -1339, -699, -38, 641, 1321, 1996, 2660, 3305, 3928,
4530, 5095, 5642, 6152, 6629, 7073, 7481, 7854, 8193, 8497, 8767, 9005, 9204, 9372, 9503, 9602, 9667, 9697, 9693, 9661,
9604, 9530, 9435, 9328, 9216, 9088, 8950, 8807, 8654, 8501, 8344, 8188, 8033, 7882, 7724, 7569, 7402, 7236, 7062, 6878,
6689, 6493, 6292, 6094, 5897, 5706, 5522, 5345, 5178, 5018, 4860, 4707, 4562, 4422, 4288, 4162, 4041, 3928, 3819, 3707,
3606, 3502, 3396, 3287, 3171, 3059, 2943, 2827, 2724, 2624, 2530, 2442, 2362, 2283, 2214, 2144, 2082, 2018, 1958, 1904,
1851, 1799, 1748, 1696, 1650, 1597, 1543, 1483, 1417, 1348, 1279, 1209, 1141, 1079, 1019, 965, 911, 860, 816, 770,
726, 683, 642, 596, 552, 512, 470, 428, 383, 338, 289, 236, 179, 120, 62, -1, -59, -112, -163, -209,
-258, -299, -339, -375, -412, -451, -485, -523, -563, -601, -638, -675, -713, -754, -797, -841, -891, -944, -997, -1048,
-1099, -1148, -1196, -1241, -1281, -1321, -1359, -1396, -1432, -1473, -1514, -1553, -1599, -1645, -1690, -1738, -1786, -1840, -1894, -1958,
-2020, -2093, -2166, -2236, -2310, -2380, -2451, -2518, -2582, -2642, -2706, -2765, -2828, -2897, -2964, -3038, -3110, -3193, -3272, -3355,
-3443, -3537, -3635, -3739, -3848, -3962, -4081, -4204, -4326, -4447, -4568, -4679, -4794, -4898, -5010, -5116, -5228, -5346, -5466, -5589,
-5720, -5853, -5993, -6136, -6282, -6430, -6582, -6735, -6896, -7059, -7227, -7390, -7551, -7702, -7847, -7973, -8089, -8195, -8296, -8388,
-8473, -8554, -8634, -8704, -8767, -8823, -8870, -8906, -8930, -8936, -8926, -8898, -8849, -8780, -8680, -8556, -8393, -8185, -7941, -7649,
-7317, -6946, -6537, -6091, -5608, -5083, -4529, -3940, -3317, -2663, -1987, -1288, -573, 154, 890, 1619, 2344, 3056, 3752, 4415,
5049, 5641, 6184, 6674, 7111, 7495, 7825, 8107, 8344, 8547, 8713, 8853, 8963, 9049, 9111, 9141, 9148, 9127, 9080, 9020,
8944, 8862, 8761, 8658, 8527, 8390, 8234, 8066, 7883, 7694, 7500, 7304, 7106, 6918, 6742, 6578, 6423, 6281, 6137, 5999,
5858, 5713, 5573, 5434, 5295, 5161, 5031, 4895, 4759, 4623, 4486, 4347, 4202, 4059, 3916, 3779, 3642, 3521, 3410, 3313,
3222, 3140, 3065, 2985, 2907, 2831, 2756, 2682, 2606, 2528, 2453, 2372, 2294, 2211, 2129, 2046, 1960, 1863, 1775, 1685,
1602, 1524, 1454, 1391, 1337, 1285, 1234, 1183, 1132, 1075, 1020, 962, 900, 832, 766, 699, 629, 564, 490, 418,
338, 259, 178, 101, 26, -43, -107, -167, -220, -271, -322, -370, -421, -472, -532, -592, -652, -717, -788, -853,
-921, -989, -1058, -1131, -1206, -1283, -1361, -1437, -1508, -1578, -1644, -1704, -1759, -1813, -1866, -1913, -1967, -2020, -2086, -2153,
-2227, -2300, -2383, -2462, -2544, -2625, -2712, -2799, -2891, -2983, -3079, -3173, -3264, -3355, -3441, -3524, -3600, -3677, -3745, -3821,
-3893, -3980, -4072, -4173, -4284, -4397, -4514, -4635, -4755, -4880, -5004, -5134, -5264, -5395, -5525, -5656, -5785, -5908, -6027, -6137,
-6238, -6329, -6417, -6500, -6587, -6680, -6780, -6884, -6992, -7103, -7209, -7310, -7402, -7485, -7555, -7611, -7656, -7683, -7696, -7692,
-7669, -7623, -7553, -7452, -7318, -7153, -6956, -6734, -6494, -6229, -5947, -5644, -5313, -4956, -4563, -4134, -3669, -3160, -2614, -2027,
-1410, -765, -101, 577, 1262, 1949, 2627, 3297, 3946, 4572, 5172, 5738, 6274, 6765, 7223, 7645, 8028, 8375, 8685, 8962,
9206, 9411, 9586, 9721, 9820, 9888, 9928, 9938, 9922, 9879, 9814, 9720, 9611, 9488, 9351, 9207, 9061, 8906, 8759, 8610,
8463, 8321, 8170, 8023, 7871, 7708, 7542, 7367, 7192, 7010, 6826, 6642, 6467, 6282, 6097, 5917, 5742, 5563, 5393, 5226,
5072, 4922, 4779, 4653, 4533, 4421, 4307, 4199, 4087, 3976, 3860, 3745, 3628, 3512, 3398, 3283, 3172, 3064, 2958, 2859,
2755, 2658, 2563, 2473, 2385, 2308, 2233, 2166, 2105, 2047, 1988, 1928, 1869, 1807, 1743, 1672, 1604, 1533, 1463, 1388,
1318, 1252, 1186, 1123, 1062, 1002, 945, 886, 833, 784, 736, 692, 654, 615, 582, 538, 501, 457, 410, 360,
304, 251, 195, 138, 86, 32, -18, -67, -116, -161, -208, -253, -299, -336, -374, -413, -447, -479, -513, -550,
-589, -629, -675, -720, -771, -819, -874, -928, -980, -1029, -1077, -1125, -1175, -1219, -1266, -1313, -1359, -1403, -1444, -1485,
-1530, -1566, -1610, -1651, -1698, -1747, -1799, -1859, -1922, -1986, -2055, -2123, -2189, -2256, -2322, -2383, -2449, -2515, -2577, -2644,
-2710, -2776, -2843, -2906, -2973, -3041, -3109, -3181, -3259, -3346, -3437, -3533, -3641, -3753, -3865, -3980, -4090, -4207, -4323, -4438,
-4550, -4668, -4782, -4898, -5015, -5133, -5254, -5375, -5496, -5620, -5742, -5871, -6005, -6147, -6299, -6459, -6625, -6795, -6966, -7135,
-7299, -7459, -7615, -7763, -7903, -8042, -8171, -8292, -8411, -8527, -8633, -8729, -8815, -8897, -8969, -9029, -9083, -9134, -9179, -9216,
-9237, -9239, -9221, -9168, -9089, -8974, -8823, -8634, -8403, -8138, -7830, -7480, -7090, -6657, -6187, -5666, -5107, -4507, -3873, -3207,
-2511, -1790, -1048, -288, 490, 1275, 2065, 2845, 3600, 4328, 5012, 5645, 6233, 6767, 7248, 7680, 8065, 8402, 8688, 8924,
9123, 9271, 9385, 9464, 9515, 9539, 9544, 9523, 9494, 9448, 9388, 9306, 9205, 9080, 8936, 8768, 8588, 8397, 8201, 8007,
7815, 7623, 7435, 7250, 7068, 6892, 6717, 6547, 6382, 6222, 6068, 5922, 5780, 5645, 5513, 5377, 5237, 5092, 4940, 4784,
4623, 4465, 4313, 4166, 4021, 3891, 3761, 3643, 3526, 3416, 3312, 3214, 3117, 3025, 2940, 2856, 2781, 2707, 2633, 2558,
2476, 2390, 2298, 2203, 2107, 2006, 1908, 1817, 1730, 1647, 1568, 1492, 1424, 1359, 1288, 1227, 1163, 1099, 1042, 987,
931, 873, 816, 757, 695, 621, 551, 475, 396, 313, 233, 159, 81, 10, -56, -117, -173, -230, -286, -340,
-393, -452, -500, -552, -603, -656, -706, -759, -811, -874, -936, -1004, -1072, -1145, -1221, -1288, -1353, -1415, -1473, -1526,
-1576, -1624, -1673, -1725, -1773, -1823, -1874, -1926, -1977, -2032, -2087, -2148, -2211, -2273, -2348, -2427, -2510, -2596, -2681, -2771,
-2852, -2933, -3009, -3079, -3148, -3216, -3289, -3362, -3435, -3512, -3593, -3673, -3763, -3853, -3947, -4046, -4146, -4252, -4374, -4493,
-4624, -4754, -4887, -5020, -5149, -5265, -5379, -5488, -5589, -5687, -5786, -5884, -5985, -6088, -6192, -6304, -6410, -6519, -6621, -6728,
-6835, -6934, -7037, -7145, -7248, -7346, -7435, -7510, -7573, -7610, -7625, -7621, -7590, -7544, -7474, -7392, -7293, -7185, -7059, -6918,
-6754, -6563, -6346, -6098, -5820, -5507, -5161, -4788, -4377, -3925, -3438, -2909, -2345, -1744, -1106, -439, 248, 950, 1651, 2347,
3027, 3680, 4312, 4917, 5489, 6038, 6553, 7034, 7482, 7892, 8265, 8607, 8906, 9166, 9385, 9561, 9699, 9792, 9850, 9873,
9862, 9828, 9766, 9687, 9594, 9486, 9370, 9248, 9116, 8978, 8832, 8685, 8530, 8371, 8210, 8048, 7882, 7713, 7541, 7363,
7183, 6994, 6798, 6603, 6407, 6207, 6018, 5833, 5658, 5493, 5335, 5190, 5051, 4910, 4780, 4653, 4523, 4398, 4274, 4154,
4037, 3917, 3803, 3687, 3569, 3454, 3333, 3214, 3100, 2983, 2873, 2773, 2676, 2590, 2506, 2433, 2358, 2293, 2227, 2161,
2097, 2028, 1963, 1895, 1828, 1764, 1697, 1633, 1564, 1498, 1422, 1354, 1282, 1213, 1144, 1083, 1026, 971, 923, 877,
833, 794, 754, 714, 674, 628, 583, 539, 492, 446, 398, 354, 308, 256, 208, 156, 106, 56, 6, -36,
-76, -117, -149, -182, -212, -240, -268, -298, -331, -365, -402, -442, -481, -520, -560, -604, -642, -686, -732, -776,
-821, -868, -915, -960, -999, -1039, -1075, -1111, -1146, -1182, -1215, -1259, -1297, -1344, -1391, -1443, -1496, -1550, -1604, -1663,
-1724, -1782, -1846, -1909, -1978, -2045, -2111, -2176, -2243, -2301, -2361, -2418, -2479, -2536, -2597, -2661, -2732, -2804, -2883, -2970,
-3056, -3151, -3244, -3336, -3436, -3536, -3639, -3741, -3853, -3964, -4076, -4184, -4296, -4404, -4507, -4612, -4715, -4822, -4931, -5044,
-5166, -5298, -5432, -5580, -5728, -5884, -6038, -6193, -6352, -6512, -6672, -6835, -6997, -7158, -7319, -7476, -7625, -7771, -7903, -8032,
-8155, -8273, -8390, -8501, -8621, -8739, -8858, -8975, -9083, -9180, -9267, -9338, -9390, -9424, -9437, -9426, -9396, -9335, -9249, -9124,
-8963, -8766, -8526, -8245, -7922, -7560, -7165, -6731, -6257, -5746, -5192, -4595, -3954, -3269, -2549, -1797, -1013, -216, 588, 1397,
2198, 2981, 3739, 4462, 5149, 5788, 6375, 6908, 7384, 7808, 8178, 8499, 8781, 9027, 9231, 9406, 9548, 9654, 9724, 9760,
9764, 9738, 9680, 9599, 9500, 9385, 9254, 9113, 8956, 8799, 8626, 8444, 8259, 8072, 7887, 7708, 7539, 7378, 7230, 7082,
6944, 6808, 6670, 6528, 6384, 6233, 6077, 5917, 5760, 5604, 5450, 5300, 5150, 5000, 4856, 4709, 4568, 4431, 4299, 4179,
4059, 3956, 3860, 3768, 3684, 3599, 3516, 3430, 3340, 3242, 3142, 3040, 2938, 2842, 2738, 2643, 2546, 2452, 2358, 2269,
2175, 2091, 2008, 1928, 1851, 1782, 1721, 1663, 1603, 1549, 1490, 1426, 1359, 1289, 1212, 1131, 1051, 968, 887, 805,
729, 647, 573, 495, 422, 348, 278, 207, 139, 76, 16, -38, -93, -147, -202, -262, -327, -397, -470, -547,
-621, -703, -776, -855, -927, -1001, -1071, -1140, -1207, -1278, -1343, -1408, -1469, -1531, -1584, -1637, -1687, -1742, -1795, -1857,
-1920, -1992, -2067, -2150, -2231, -2316, -2405, -2487, -2572, -2651, -2732, -2811, -2889, -2968, -3050, -3127, -3202, -3278, -3350, -3424,
-3494, -3567, -3648, -3731, -3819, -3918, -4028, -4142, -4259, -4378, -4504, -4620, -4736, -4846, -4955, -5068, -5174, -5274, -5381, -5485,
-5583, -5685, -5778, -5875, -5966, -6053, -6147, -6241, -6340, -6450, -6560, -6674, -6791, -6902, -7009, -7105, -7188, -7253, -7306, -7347,
-7374, -7383, -7387, -7376, -7348, -7311, -7254, -7179, -7087, -6975, -6845, -6697, -6531, -6348, -6146, -5929, -5682, -5403, -5083, -4730,
-4324, -3883, -3399, -2877, -2323, -1736, -1124, -500, 142, 791, 1439, 2087, 2727, 3353, 3964, 4554, 5117, 5660, 6173, 6655,
7105, 7524, 7904, 8247, 8552, 8815, 9036, 9224, 9366, 9476, 9551, 9598, 9611, 9603, 9565, 9508, 9431, 9341, 9238, 9132,
9013, 8895, 8769, 8643, 8508, 8369, 8220, 8063, 7892, 7714, 7529, 7340, 7145, 6953, 6764, 6576, 6396, 6218, 6044, 5874,
5708, 5545, 5393, 5243, 5099, 4965, 4837, 4710, 4591, 4468, 4346, 4222, 4097, 3964, 3838, 3699, 3570, 3441, 3319, 3202,
3095, 2991, 2891, 2792, 2705, 2615, 2532, 2450, 2373, 2299, 2233, 2162, 2095, 2030, 1961, 1891, 1821, 1739, 1658, 1581,
1500, 1426, 1346, 1282, 1215, 1154, 1095, 1042, 987, 935, 885, 834, 788, 744, 697, 656, 614, 570, 525, 475,
427, 373, 316, 261, 203, 150, 91, 45, -4, -45, -88, -126, -164, -199, -235, -273, -309, -344, -379, -414,
-448, -485, -518, -562, -604, -650, -697, -750, -794, -845, -890, -937, -980, -1020, -1058, -1096, -1130, -1167, -1203, -1247,
-1288, -1325, -1367, -1413, -1455, -1500, -1548, -1600, -1657, -1717, -1780, -1844, -1909, -1977, -2045, -2112, -2177, -2235, -2292, -2352,
-2408, -2469, -2529, -2591, -2659, -2730, -2795, -2866, -2944, -3017, -3098, -3182, -3273, -3368, -3465, -3569, -3677, -3783, -3888, -3993,
-4098, -4196, -4291, -4386, -4486, -4586, -4688, -4793, -4908, -5024, -5140, -5259, -5386, -5513, -5646, -5782, -5923, -6073, -6230, -6383,
-6548, -6707, -6868, -7020, -7167, -7305, -7438, -7567, -7693, -7816, -7939, -8065, -8187, -8311, -8433, -8548, -8663, -8773, -8870, -8965,
-9053, -9132, -9205, -9260, -9306, -9322, -9315, -9279, -9206, -9106, -8973, -8802, -8602, -8371, -8105, -7811, -7476, -7108, -6700, -6247,
-5750, -5209, -4629, -4007, -3353, -2663, -1946, -1201, -435, 343, 1126, 1909, 2674, 3412, 4114, 4772, 5383, 5943, 6458, 6931,
7357, 7741, 8084, 8388, 8647, 8862, 9032, 9170, 9269, 9338, 9374, 9386, 9371, 9333, 9270, 9187, 9078, 8954, 8801, 8640,
8470, 8295, 8117, 7949, 7787, 7629, 7480, 7330, 7184, 7037, 6890, 6741, 6593, 6442, 6297, 6149, 6001, 5854, 5706, 5554,
5397, 5240, 5080, 4916, 4754, 4601, 4453, 4320, 4195, 4080, 3970, 3869, 3767, 3670, 3571, 3475, 3380, 3285, 3190, 3093,
2999, 2905, 2814, 2717, 2619, 2516, 2414, 2309, 2210, 2112, 2022, 1937, 1861, 1791, 1725, 1665, 1603, 1546, 1485, 1424,
1360, 1294, 1231, 1161, 1093, 1026, 959, 887, 813, 739, 660, 581, 503, 428, 356, 289, 227, 172, 119, 67,
21, -31, -79, -134, -194, -253, -315, -377, -445, -507, -575, -638, -708, -779, -858, -928, -1000, -1077, -1145, -1211,
-1273, -1332, -1386, -1436, -1486, -1542, -1595, -1655, -1721, -1790, -1862, -1935, -2009, -2089, -2166, -2249, -2326, -2416, -2501, -2589,
-2682, -2770, -2857, -2943, -3022, -3094, -3166, -3236, -3304, -3376, -3454, -3538, -3623, -3720, -3815, -3921, -4027, -4134, -4247, -4357,
-4470, -4583, -4699, -4816, -4933, -5049, -5166, -5278, -5380, -5480, -5568, -5652, -5740, -5827, -5920, -6016, -6120, -6226, -6332, -6446,
-6557, -6668, -6771, -6875, -6966, -7049, -7126, -7198, -7263, -7316, -7357, -7380, -7384, -7368, -7336, -7283, -7210, -7127, -7031, -6924,
-6800, -6665, -6517, -6345, -6151, -5926, -5668, -5380, -5043, -4674, -4268, -3824, -3345, -2836, -2288, -1718, -1118, -493, 147, 796,
1454, 2104, 2746, 3372, 3980, 4564, 5127, 5658, 6170, 6644, 7093, 7506, 7887, 8235, 8545, 8814, 9048, 9242, 9399, 9518,
9594, 9648, 9661, 9650, 9617, 9565, 9498, 9422, 9338, 9247, 9152, 9047, 8930, 8811, 8677, 8533, 8382, 8227, 8065, 7897,
7727, 7556, 7380, 7203, 7019, 6838, 6655, 6475, 6293, 6124, 5958, 5801, 5652, 5514, 5380, 5257, 5128, 5003, 4875, 4746,
4615, 4477, 4349, 4219, 4087, 3961, 3839, 3714, 3593, 3477, 3360, 3250, 3141, 3035, 2940, 2853, 2767, 2686, 2617, 2548,
2477, 2405, 2333, 2260, 2185, 2104, 2024, 1943, 1866, 1787, 1715, 1641, 1570, 1497, 1426, 1357, 1294, 1231, 1172, 1119,
1069, 1020, 972, 930, 889, 840, 794, 744, 695, 634, 580, 520, 464, 406, 350, 299, 245, 194, 142, 93,
47, -2, -44, -86, -126, -163, -198, -234, -267, -303, -343, -381, -425, -469, -521, -573, -624, -672, -721, -763,
-814, -856, -901, -946, -989, -1034, -1076, -1116, -1155, -1197, -1233, -1269, -1310, -1352, -1396, -1442, -1500, -1555, -1615, -1680,
-1743, -1804, -1865, -1928, -1991, -2054, -2114, -2176, -2240, -2300, -2360, -2428, -2488, -2548, -2610, -2673, -2739, -2805, -2879, -2959,
-3043, -3133, -3230, -3329, -3433, -3534, -3634, -3737, -3838, -3937, -4039, -4144, -4247, -4352, -4459, -4568, -4674, -4782, -4888, -4999,
-5115, -5230, -5356, -5487, -5630, -5774, -5928, -6085, -6246, -6403, -6557, -6711, -6862, -7001, -7145, -7285, -7425, -7567, -7701, -7834,
-7967, -8088, -8206, -8318, -8428, -8536, -8648, -8753, -8860, -8960, -9056, -9142, -9215, -9270, -9297, -9301, -9280, -9232, -9150, -9048,
-8914, -8752, -8558, -8326, -8058, -7753, -7404, -7017, -6589, -6123, -5619, -5075, -4493, -3874, -3214, -2519, -1787, -1033, -256, 529,
1315, 2092, 2850, 3573, 4265, 4917, 5521, 6088, 6610, 7080, 7508, 7883, 8212, 8496, 8733, 8934, 9104, 9235, 9343, 9418,
9464, 9477, 9462, 9414, 9337, 9236, 9119, 8981, 8834, 8680, 8517, 8356, 8194, 8029, 7869, 7707, 7545, 7384, 7221, 7070,
6925, 6780, 6642, 6503, 6366, 6225, 6075, 5921, 5762, 5602, 5434, 5271, 5107, 4951, 4801, 4657, 4519, 4392, 4263, 4143,
4023, 3908, 3799, 3689, 3591, 3497, 3403, 3311, 3221, 3128, 3031, 2930, 2822, 2717, 2610, 2501, 2395, 2292, 2194, 2102,
2016, 1936, 1856, 1780, 1706, 1637, 1562, 1498, 1433, 1373, 1314, 1252, 1193, 1130, 1064, 991, 915, 837, 755, 674,
596, 519, 447, 378, 313, 253, 194, 134, 82, 24, -31, -85, -140, -192, -243, -298, -353, -408, -465, -530,
-595, -671, -743, -816, -889, -955, -1027, -1087, -1152, -1210, -1265, -1317, -1374, -1425, -1480, -1536, -1593, -1656, -1713, -1772,
-1835, -1900, -1967, -2039, -2122, -2204, -2289, -2376, -2467, -2552, -2635, -2717, -2791, -2869, -2938, -3005, -3078, -3153, -3228, -3306,
-3387, -3469, -3556, -3640, -3730, -3825, -3918, -4025, -4130, -4246, -4365, -4484, -4606, -4725, -4842, -4951, -5054, -5155, -5249, -5342,
-5436, -5533, -5629, -5730, -5832, -5934, -6045, -6153, -6256, -6366, -6475, -6584, -6697, -6811, -6924, -7032, -7134, -7230, -7311, -7378,
-7428, -7461, -7479, -7482, -7470, -7454, -7426, -7388, -7340, -7279, -7206, -7108, -6993, -6857, -6699, -6515, -6297, -6053, -5780, -5473,
-5129, -4744, -4320, -3848, -3338, -2789, -2207, -1593, -959, -305, 351, 1022, 1682, 2343, 2989, 3621, 4230, 4824, 5386, 5929,
6445, 6926, 7375, 7788, 8159, 8491, 8777, 9020, 9222, 9377, 9494, 9574, 9624, 9648, 9649, 9625, 9588, 9529, 9459, 9373,
9273, 9163, 9045, 8911, 8780, 8641, 8499, 8346, 8188, 8028, 7854, 7672, 7486, 7290, 7097, 6901, 6712, 6528, 6350, 6179,
6019, 5865, 5716, 5571, 5427, 5285, 5144, 5006, 4872, 4741, 4606, 4481, 4347, 4221, 4092, 3966, 3830, 3697, 3568, 3441,
3319, 3202, 3094, 2994, 2900, 2815, 2732, 2654, 2574, 2496, 2421, 2344, 2263, 2190, 2117, 2042, 1969, 1893, 1818, 1744,
1666, 1587, 1515, 1440, 1368, 1301, 1240, 1186, 1131, 1088, 1042, 999, 957, 909, 865, 820, 772, 723, 676, 629,
584, 531, 482, 432, 384, 328, 276, 227, 177, 128, 85, 47, 9, -26, -56, -88, -119, -154, -190, -229,
-268, -311, -352, -394, -437, -482, -524, -572, -617, -666, -710, -760, -802, -848, -890, -929, -963, -1001, -1034, -1067,
-1103, -1141, -1184, -1225, -1270, -1320, -1372, -1422, -1474, -1529, -1584, -1641, -1698, -1760, -1821, -1881, -1943, -2004, -2063, -2119,
-2173, -2225, -2283, -2334, -2391, -2455, -2516, -2589, -2663, -2740, -2823, -2908, -2991, -3079, -3170, -3264, -3359, -3454, -3551, -3655,
-3754, -3857, -3955, -4058, -4153, -4247, -4343, -4439, -4542, -4651, -4767, -4889, -5017, -5151, -5289, -5430, -5574, -5719, -5865, -6014,
-6167, -6317, -6473, -6629, -6781, -6934, -7083, -7224, -7363, -7499, -7626, -7757, -7884, -8015, -8153, -8289, -8433, -8573, -8710, -8842,
-8968, -9075, -9173, -9260, -9331, -9391, -9431, -9453, -9454, -9429, -9377, -9292, -9179, -9034, -8854, -8644, -8405, -8129, -7823, -7480,
-7105, -6684, -6215, -5697, -5136, -4527, -3870, -3174, -2447, -1697, -921, -133, 663, 1459, 2244, 3009, 3743, 4438, 5090, 5700,
6258, 6773, 7242, 7667, 8050, 8388, 8689, 8946, 9162, 9327, 9457, 9543, 9588, 9600, 9582, 9539, 9474, 9388, 9284, 9164,
9027, 8881, 8721, 8561, 8402, 8238, 8080, 7931, 7783, 7641, 7505, 7368, 7224, 7077, 6924, 6766, 6602, 6442, 6272, 6108,
5947, 5784, 5621, 5467, 5309, 5151, 5000, 4857, 4712, 4579, 4452, 4336, 4225, 4125, 4024, 3928, 3833, 3728, 3626, 3519,
3411, 3297, 3187, 3076, 2971, 2865, 2760, 2660, 2563, 2467, 2370, 2278, 2189, 2106, 2025, 1953, 1887, 1824, 1760, 1699,
1633, 1568, 1497, 1424, 1347, 1269, 1186, 1105, 1027, 951, 876, 799, 726, 655, 584, 516, 444, 380, 314, 260,
206, 155, 108, 55, -2, -56, -117, -183, -249, -318, -392, -465, -539, -608, -677, -742, -813, -877, -942, -1008,
-1068, -1130, -1184, -1247, -1298, -1350, -1403, -1456, -1515, -1575, -1637, -1709, -1783, -1864, -1944, -2027, -2114, -2195, -2274, -2352,
-2433, -2508, -2586, -2663, -2743, -2819, -2895, -2965, -3041, -3112, -3183, -3258, -3334, -3418, -3506, -3601, -3704, -3810, -3921, -4035,
-4146, -4258, -4367, -4472, -4578, -4680, -4782, -4883, -4985, -5087, -5186, -5285, -5387, -5481, -5574, -5671, -5766, -5870, -5979, -6092,
-6212, -6338, -6461, -6587, -6705, -6817, -6924, -7017, -7102, -7178, -7242, -7298, -7346, -7388, -7422, -7443, -7456, -7456, -7436, -7409,
-7368, -7321, -7263, -7191, -7107, -7004, -6876, -6727, -6546, -6332, -6078, -5786, -5450, -5079, -4665, -4217, -3735, -3218, -2680, -2111,
-1514, -901, -267, 375, 1029, 1684, 2335, 2974, 3605, 4219, 4808, 5383, 5923, 6436, 6912, 7351, 7755, 8115, 8433, 8711,
8947, 9149, 9305, 9425, 9515, 9572, 9600, 9604, 9583, 9548, 9499, 9437, 9364, 9279, 9182, 9076, 8962, 8827, 8681, 8519,
8348, 8173, 7991, 7806, 7623, 7439, 7261, 7081, 6902, 6729, 6559, 6388, 6230, 6070, 5914, 5764, 5619, 5481, 5349, 5212,
5075, 4934, 4792, 4644, 4497, 4351, 4203, 4061, 3924, 3796, 3671, 3554, 3434, 3326, 3222, 3118, 3018, 2926, 2837, 2745,
2662, 2581, 2505, 2426, 2345, 2262, 2180, 2092, 2003, 1911, 1828, 1738, 1657, 1579, 1507, 1439, 1373, 1309, 1251, 1191,
1132, 1078, 1024, 971, 919, 872, 821, 774, 719, 670, 616, 556, 497, 435, 376, 320, 261, 210, 163, 113,
71, 29, -13, -54, -92, -131, -172, -209, -245, -287, -323, -364, -404, -451, -496, -543, -591, -646, -696, -745,
-796, -844, -883, -924, -962, -999, -1039, -1074, -1112, -1150, -1189, -1232, -1268, -1313, -1357, -1400, -1445, -1495, -1547, -1600,
-1657, -1715, -1777, -1839, -1896, -1956, -2011, -2063, -2114, -2165, -2220, -2271, -2324, -2378, -2439, -2498, -2559, -2623, -2691, -2761,
-2832, -2906, -2985, -3065, -3153, -3240, -3335, -3429, -3522, -3611, -3700, -3788, -3870, -3958, -4046, -4136, -4228, -4324, -4425, -4528,
-4636, -4746, -4861, -4981, -5101, -5226, -5358, -5497, -5638, -5785, -5932, -6084, -6233, -6376, -6515, -6651, -6785, -6916, -7044, -7176,
-7308, -7442, -7580, -7721, -7862, -8001, -8138, -8275, -8406, -8534, -8662, -8788, -8908, -9017, -9119, -9208, -9279, -9331, -9356, -9361,
-9340, -9294, -9227, -9136, -9025, -8892, -8732, -8545, -8328, -8072, -7778, -7443, -7070, -6656, -6194, -5689, -5146, -4558, -3927, -3255,
-2557, -1819, -1061, -292, 484, 1256, 2008, 2743, 3450, 4123, 4762, 5367, 5930, 6453, 6932, 7368, 7757, 8100, 8401, 8652,
8865, 9034, 9165, 9261, 9320, 9343, 9332, 9290, 9219, 9126, 9018, 8893, 8765, 8629, 8499, 8366, 8232, 8098, 7962, 7825,
7683, 7539, 7391, 7242, 7091, 6939, 6788, 6632, 6479, 6320, 6152, 5982, 5814, 5643, 5477, 5315, 5158, 5013, 4877, 4746,
4628, 4508, 4398, 4290, 4181, 4071, 3962, 3850, 3741, 3634, 3529, 3420, 3313, 3206, 3094, 2981, 2872, 2760, 2651, 2546,
2447, 2358, 2272, 2193, 2121, 2053, 1988, 1922, 1855, 1789, 1715, 1643, 1574, 1500, 1427, 1359, 1282, 1212, 1132, 1055,
973, 900, 821, 749, 677, 609, 550, 490, 438, 387, 335, 285, 233, 183, 122, 59, -3, -61, -126, -193,
-254, -326, -395, -465, -534, -603, -673, -744, -807, -869, -927, -983, -1034, -1082, -1134, -1182, -1238, -1294, -1355, -1418,
-1490, -1555, -1626, -1702, -1770, -1849, -1928, -2005, -2085, -2168, -2250, -2330, -2411, -2487, -2559, -2632, -2696, -2763, -2828, -2900,
-2972, -3047, -3129, -3216, -3312, -3405, -3502, -3606, -3707, -3808, -3911, -4016, -4124, -4235, -4342, -4449, -4556, -4658, -4756, -4849,
-4943, -5029, -5120, -5209, -5306, -5404, -5507, -5621, -5736, -5858, -5978, -6093, -6211, -6322, -6435, -6542, -6644, -6750, -6846, -6932,
-7012, -7081, -7137, -7186, -7217, -7242, -7257, -7256, -7253, -7246, -7232, -7209, -7179, -7141, -7081, -7000, -6896, -6767, -6608, -6420,
-6200, -5952, -5666, -5345, -4988, -4594, -4163, -3699, -3201, -2676, -2119, -1539, -943, -329, 295, 922, 1558, 2188, 2816, 3433,
4034, 4618, 5180, 5720, 6230, 6709, 7149, 7560, 7925, 8249, 8530, 8773, 8969, 9134, 9254, 9350, 9414, 9460, 9478, 9482,
9473, 9443, 9393, 9329, 9250, 9152, 9036, 8917, 8782, 8639, 8484, 8324, 8164, 7993, 7818, 7646, 7456, 7277, 7095, 6914,
6743, 6582, 6421, 6270, 6124, 5981, 5842, 5697, 5556, 5412, 5265, 5116, 4967, 4815, 4672, 4526, 4384, 4249, 4113, 3977,
3848, 3719, 3596, 3475, 3362, 3260, 3160, 3067, 2983, 2896, 2818, 2733, 2648, 2562, 2477, 2384, 2298, 2206, 2119, 2033,
1949, 1867, 1788, 1709, 1633, 1562, 1490, 1425, 1356, 1300, 1244, 1190, 1139, 1093, 1046, 995, 942, 891, 836, 780,
719, 661, 604, 545, 487, 431, 380, 329, 277, 230, 182, 136, 89, 45, 9, -33, -71, -105, -140, -179,
-220, -263, -309, -355, -407, -458, -507, -556, -608, -655, -703, -746, -791, -835, -876, -919, -960, -1003, -1042, -1078,
-1115, -1154, -1188, -1232, -1276, -1323, -1376, -1430, -1486, -1542, -1601, -1659, -1714, -1775, -1832, -1885, -1940, -1998, -2053, -2112,
-2165, -2226, -2284, -2338, -2395, -2455, -2510, -2577, -2639, -2710, -2787, -2868, -2949, -3036, -3126, -3215, -3303, -3393, -3483, -3572,
-3655, -3747, -3839, -3929, -4023, -4114, -4211, -4305, -4401, -4500, -4606, -4708, -4821, -4939, -5067, -5196, -5332, -5472, -5616, -5759,
-5905, -6041, -6180, -6317, -6452, -6586, -6726, -6858, -6994, -7128, -7263, -7394, -7524, -7652, -7783, -7911, -8040, -8172, -8306, -8444,
-8575, -8704, -8825, -8935, -9023, -9103, -9160, -9202, -9223, -9225, -9210, -9177, -9120, -9043, -8941, -8809, -8650, -8461, -8238, -7986,
-7699, -7377, -7019, -6628, -6188, -5710, -5181, -4612, -3998, -3340, -2653, -1937, -1205, -459, 295, 1045, 1787, 2514, 3218, 3893,
4532, 5135, 5698, 6221, 6702, 7141, 7536, 7893, 8207, 8484, 8717, 8904, 9051, 9159, 9225, 9254, 9247, 9214, 9158, 9083,
8991, 8893, 8784, 8670, 8543, 8413, 8278, 8142, 8004, 7867, 7730, 7595, 7459, 7321, 7184, 7038, 6883, 6728, 6566, 6400,
6227, 6053, 5884, 5718, 5557, 5404, 5258, 5115, 4979, 4842, 4713, 4588, 4467, 4349, 4237, 4129, 4021, 3917, 3809, 3702,
3595, 3482, 3368, 3248, 3130, 3007, 2894, 2783, 2680, 2577, 2484, 2393, 2306, 2223, 2143, 2064, 1987, 1914, 1841, 1769,
1703, 1632, 1564, 1492, 1423, 1343, 1265, 1179, 1098, 1013, 931, 853, 778, 707, 640, 579, 515, 457, 397, 341,
283, 228, 170, 113, 56, 1, -58, -118, -182, -244, -316, -386, -463, -535, -610, -680, -747, -812, -875, -934,
-987, -1041, -1097, -1152, -1210, -1262, -1324, -1379, -1437, -1498, -1559, -1623, -1694, -1762, -1838, -1917, -1998, -2082, -2164, -2246,
-2323, -2402, -2473, -2546, -2612, -2676, -2745, -2820, -2888, -2963, -3036, -3119, -3195, -3277, -3363, -3450, -3543, -3641, -3739, -3846,
-3954, -4065, -4178, -4285, -4392, -4497, -4592, -4687, -4780, -4870, -4962, -5054, -5152, -5252, -5353, -5457, -5564, -5666, -5781, -5891,
-6009, -6122, -6238, -6358, -6478, -6593, -6709, -6815, -6918, -7005, -7082, -7144, -7201, -7247, -7285, -7316, -7349, -7367, -7380, -7387,
-7383, -7373, -7343, -7303, -7247, -7171, -7077, -6960, -6821, -6653, -6457, -6223, -5957, -5647, -5301, -4910, -4487, -4030, -3535, -3014,
-2465, -1893, -1300, -689, -61, 574, 1223, 1872, 2518, 3155, 3781, 4388, 4978, 5540, 6079, 6582, 7049, 7478, 7863, 8206,
8506, 8765, 8978, 9160, 9308, 9420, 9508, 9568, 9600, 9610, 9600, 9568, 9517, 9449, 9366, 9273, 9172, 9055, 8928, 8791,
8646, 8485, 8311, 8132, 7953, 7767, 7581, 7397, 7222, 7054, 6886, 6723, 6571, 6415, 6261, 6111, 5961, 5812, 5664, 5517,
5371, 5230, 5083, 4942, 4799, 4656, 4510, 4362, 4221, 4082, 3948, 3821, 3699, 3588, 3479, 3382, 3283, 3194, 3100, 3012,
2924, 2836, 2748, 2658, 2573, 2489, 2400, 2318, 2234, 2146, 2061, 1975, 1893, 1810, 1734, 1657, 1590, 1525, 1466, 1407,
1354, 1303, 1252, 1199, 1146, 1093, 1041, 982, 928, 874, 821, 763, 711, 656, 595, 542, 486, 429, 380, 323,
276, 235, 192, 153, 113, 78, 41, 3, -38, -75, -123, -165, -213, -258, -306, -350, -399, -447, -498, -547,
-596, -645, -690, -736, -778, -819, -856, -891, -931, -967, -1000, -1039, -1083, -1125, -1173, -1219, -1268, -1321, -1373, -1425,
-1480, -1535, -1588, -1646, -1704, -1763, -1818, -1872, -1928, -1984, -2035, -2084, -2135, -2185, -2242, -2295, -2356, -2421, -2486, -2556,
-2632, -2705, -2785, -2863, -2943, -3027, -3108, -3195, -3281, -3371, -3459, -3547, -3636, -3724, -3809, -3897, -3986, -4069, -4168, -4259,
-4368, -4474, -4588, -4704, -4829, -4956, -5091, -5219, -5354, -5489, -5623, -5764, -5904, -6045, -6187, -6327, -6465, -6603, -6734, -6864,
-6993, -7123, -7258, -7392, -7530, -7672, -7823, -7969, -8115, -8261, -8406, -8539, -8665, -8785, -8894, -8989, -9073, -9147, -9209, -9253,
-9272, -9273, -9255, -9210, -9140, -9053, -8940, -8804, -8640, -8459, -8242, -7993, -7705, -7378, -7008, -6592, -6123, -5611, -5055, -4458,
-3818, -3146, -2444, -1718, -972, -208, 555, 1313, 2065, 2797, 3502, 4168, 4806, 5405, 5966, 6487, 6971, 7409, 7803, 8150,
8446, 8701, 8903, 9063, 9187, 9266, 9310, 9325, 9308, 9269, 9207, 9122, 9026, 8916, 8794, 8673, 8538, 8414, 8286, 8159,
8028, 7898, 7759, 7617, 7465, 7308, 7145, 6982, 6811, 6646, 6474, 6307, 6137, 5972, 5811, 5648, 5486, 5336, 5183, 5043,
4908, 4774, 4658, 4541, 4426, 4318, 4209, 4097, 3982, 3863, 3744, 3626, 3503, 3389, 3270, 3156, 3041, 2932, 2825, 2723,
2621, 2527, 2428, 2340, 2255, 2178, 2102, 2031, 1963, 1894, 1826, 1751, 1681, 1604, 1524, 1445, 1364, 1277, 1203, 1123,
1045, 968, 896, 824, 754, 684, 621, 556, 498, 439, 387, 331, 279, 228, 176, 118, 59, -4, -72, -143,
-212, -287, -357, -428, -493, -561, -632, -696, -755, -817, -878, -935, -994, -1049, -1103, -1157, -1211, -1264, -1319, -1377,
-1443, -1509, -1582, -1659, -1735, -1816, -1893, -1968, -2046, -2117, -2198, -2270, -2342, -2412, -2485, -2558, -2628, -2695, -2768, -2836,
-2905, -2973, -3053, -3130, -3215, -3304, -3400, -3498, -3603, -3702, -3808, -3910, -4012, -4114, -4213, -4309, -4407, -4503, -4598, -4697,
-4791, -4887, -4983, -5077, -5176, -5270, -5369, -5477, -5587, -5702, -5824, -5945, -6071, -6197, -6321, -6441, -6553, -6664, -6763, -6859,
-6946, -7030, -7106, -7180, -7246, -7303, -7357, -7402, -7441, -7472, -7497, -7516, -7530, -7530, -7527, -7509, -7478, -7431, -7358, -7263,
-7135, -6972, -6781, -6554, -6299, -6009, -5685, -5326, -4939, -4515, -4061, -3573, -3057, -2518, -1949, -1355, -745, -112, 530, 1182,
1833, 2491, 3135, 3770, 4384, 4976, 5540, 6074, 6570, 7026, 7445, 7830, 8168, 8465, 8731, 8945, 9127, 9271, 9386, 9468,
9525, 9561, 9578, 9573, 9549, 9504, 9441, 9357, 9258, 9137, 9006, 8861, 8706, 8540, 8372, 8203, 8032, 7857, 7688, 7516,
7348, 7179, 7012, 6850, 6688, 6529, 6377, 6228, 6080, 5930, 5779, 5624, 5471, 5314, 5152, 4994, 4836, 4684, 4532, 4388,
4252, 4118, 3992, 3873, 3757, 3643, 3533, 3425, 3326, 3228, 3130, 3039, 2951, 2863, 2772, 2681, 2591, 2499, 2402, 2307,
2216, 2124, 2036, 1950, 1873, 1801, 1729, 1664, 1600, 1534, 1475, 1412, 1353, 1301, 1246, 1192, 1138, 1085, 1028, 969,
913, 857, 796, 730, 671, 613, 554, 497, 448, 401, 355, 309, 269, 225, 184, 141, 100, 61, 22, -21,
-63, -104, -146, -192, -240, -287, -338, -391, -441, -489, -540, -589, -633, -675, -714, -758, -791, -831, -870, -908,
-946, -987, -1026, -1069, -1111, -1155, -1199, -1248, -1298, -1352, -1406, -1464, -1520, -1576, -1634, -1687, -1738, -1790, -1841, -1890,
-1938, -1988, -2041, -2094, -2150, -2209, -2267, -2329, -2391, -2457, -2525, -2593, -2670, -2749, -2828, -2909, -2995, -3081, -3166, -3248,
-3332, -3416, -3498, -3574, -3656, -3742, -3825, -3916, -4006, -4105, -4207, -4308, -4413, -4524, -4637, -4754, -4876, -5005, -5132, -5266,
-5403, -5541, -5674, -5811, -5941, -6075, -6205, -6332, -6457, -6587, -6716, -6851, -6989, -7132, -7275, -7419, -7560, -7708, -7853, -8000,
-8144, -8290, -8430, -8568, -8695, -8817, -8931, -9027, -9107, -9174, -9223, -9253, -9269, -9269, -9255, -9224, -9178, -9109, -9025, -8912,
-8770, -8602, -8398, -8159, -7886, -7569, -7219, -6820, -6381, -5891, -5361, -4781, -4164, -3507, -2821, -2112, -1379, -634, 112, 862,
1608, 2338, 3047, 3736, 4395, 5022, 5606, 6151, 6657, 7117, 7527, 7893, 8212, 8489, 8717, 8900, 9039, 9134, 9192, 9214,
9210, 9183, 9138, 9072, 9000, 8916, 8825, 8727, 8624, 8513, 8395, 8266, 8137, 7999, 7857, 7710, 7561, 7405, 7250, 7084,
6917, 6747, 6576, 6400, 6230, 6063, 5905, 5746, 5599, 5463, 5330, 5200, 5076, 4956, 4834, 4714, 4591, 4472, 4353, 4234,
4112, 3991, 3871, 3753, 3632, 3510, 3389, 3269, 3152, 3040, 2935, 2832, 2736, 2649, 2569, 2488, 2405, 2327, 2256, 2179,
2101, 2025, 1945, 1865, 1788, 1704, 1624, 1546, 1461, 1381, 1301, 1217, 1135, 1055, 985, 916, 849, 786, 730, 675,
620, 562, 508, 451, 390, 326, 264, 200, 135, 67, -1, -71, -139, -211, -280, -352, -425, -494, -557, -620,
-678, -734, -787, -837, -891, -940, -995, -1055, -1111, -1174, -1240, -1307, -1377, -1448, -1520, -1593, -1667, -1743, -1820, -1895,
-1969, -2043, -2117, -2192, -2256, -2324, -2390, -2452, -2516, -2581, -2651, -2722, -2798, -2881, -2966, -3050, -3141, -3233, -3328, -3424,
-3520, -3618, -3717, -3810, -3912, -4007, -4104, -4202, -4292, -4381, -4468, -4554, -4643, -4733, -4825, -4921, -5026, -5130, -5244, -5361,
-5479, -5596, -5714, -5832, -5948, -6061, -6175, -6284, -6386, -6490, -6584, -6672, -6758, -6831, -6896, -6958, -7012, -7066, -7113, -7161,
-7204, -7246, -7282, -7310, -7326, -7333, -7323, -7295, -7250, -7184, -7089, -6977, -6831, -6664, -6460, -6233, -5977, -5680, -5353, -4992,
-4601, -4184, -3738, -3260, -2763, -2236, -1683, -1110, -512, 102, 730, 1372, 2013, 2650, 3283, 3899, 4496, 5072, 5614, 6130,
6608, 7048, 7450, 7812, 8132, 8419, 8663, 8878, 9057, 9208, 9332, 9425, 9492, 9535, 9555, 9545, 9512, 9461, 9391, 9300,
9194, 9080, 8952, 8814, 8667, 8510, 8348, 8181, 8013, 7844, 7679, 7516, 7357, 7199, 7048, 6898, 6748, 6598, 6445, 6290,
6133, 5969, 5806, 5648, 5488, 5324, 5172, 5019, 4869, 4721, 4576, 4434, 4299, 4165, 4042, 3924, 3809, 3702, 3600, 3500,
3404, 3308, 3208, 3112, 3016, 2916, 2815, 2716, 2619, 2523, 2427, 2340, 2249, 2167, 2076, 1997, 1919, 1847, 1774, 1708,
1643, 1582, 1524, 1465, 1413, 1357, 1299, 1241, 1178, 1119, 1051, 989, 924, 863, 800, 744, 685, 629, 576, 523,
471, 423, 377, 328, 288, 245, 203, 163, 122, 82, 38, -9, -55, -106, -157, -213, -262, -313, -365, -415,
-461, -508, -554, -601, -645, -689, -729, -775, -811, -851, -892, -925, -971, -1012, -1052, -1102, -1150, -1201, -1253, -1308,
-1367, -1423, -1477, -1533, -1587, -1641, -1690, -1745, -1801, -1854, -1902, -1958, -2011, -2062, -2112, -2168, -2225, -2284, -2345, -2411,
-2481, -2551, -2630, -2709, -2790, -2873, -2950, -3033, -3112, -3191, -3272, -3350, -3435, -3514, -3597, -3682, -3769, -3853, -3943, -4034,
-4128, -4226, -4331, -4438, -4553, -4668, -4794, -4917, -5051, -5184, -5309, -5438, -5570, -5697, -5824, -5952, -6079, -6208, -6339, -6465,
-6597, -6732, -6861, -6994, -7130, -7269, -7405, -7549, -7692, -7842, -7991, -8137, -8275, -8413, -8541, -8658, -8764, -8860, -8937, -9008,
-9063, -9107, -9140, -9158, -9159, -9145, -9110, -9059, -8982, -8888, -8771, -8628, -8457, -8264, -8029, -7761, -7453, -7099, -6704, -6262,
-5773, -5249, -4675, -4072, -3439, -2772, -2088, -1383, -665, 61, 787, 1510, 2219, 2913, 3581, 4218, 4827, 5399, 5933, 6427,
6882, 7289, 7650, 7963, 8230, 8451, 8625, 8764, 8859, 8924, 8954, 8961, 8953, 8921, 8871, 8811, 8734, 8650, 8555, 8455,
8350, 8239, 8119, 8001, 7874, 7741, 7600, 7448, 7289, 7127, 6957, 6787, 6622, 6457, 6294, 6134, 5979, 5830, 5688, 5544,
5413, 5279, 5152, 5024, 4898, 4781, 4666, 4547, 4432, 4315, 4195, 4072, 3945, 3819, 3694, 3567, 3446, 3328, 3212, 3104,
2998, 2896, 2804, 2712, 2624, 2540, 2454, 2373, 2291, 2212, 2140, 2064, 1986, 1910, 1828, 1747, 1661, 1574, 1488, 1404,
1317, 1235, 1158, 1082, 1011, 942, 876, 814, 749, 693, 631, 571, 513, 451, 392, 336, 269, 208, 139, 71,
-1, -77, -148, -226, -298, -373, -442, -510, -574, -634, -694, -749, -806, -862, -915, -977, -1030, -1091, -1153, -1213,
-1275, -1342, -1408, -1481, -1551, -1629, -1706, -1788, -1864, -1944, -2018, -2088, -2160, -2230, -2295, -2363, -2427, -2496, -2563, -2634,
-2706, -2782, -2860, -2938, -3021, -3108, -3193, -3283, -3376, -3473, -3575, -3676, -3774, -3876, -3976, -4067, -4159, -4247, -4337, -4424,
-4510, -4600, -4690, -4781, -4878, -4973, -5079, -5183, -5290, -5395, -5510, -5621, -5739, -5855, -5976, -6090, -6207, -6314, -6423, -6518,
-6606, -6691, -6768, -6838, -6902, -6962, -7024, -7080, -7133, -7183, -7226, -7265, -7294, -7316, -7329, -7331, -7315, -7293, -7246, -7185,
-7096, -6983, -6844, -6677, -6474, -6241, -5976, -5681, -5355, -4998, -4615, -4204, -3759, -3289, -2791, -2273, -1721, -1147, -549, 60,
693, 1332, 1975, 2612, 3246, 3864, 4464, 5036, 5581, 6096, 6576, 7018, 7421, 7787, 8116, 8403, 8662, 8882, 9068, 9223,
9345, 9439, 9506, 9545, 9562, 9558, 9531, 9484, 9419, 9337, 9238, 9124, 8994, 8855, 8699, 8542, 8378, 8211, 8049, 7890,
7729, 7570, 7412, 7257, 7100, 6944, 6791, 6635, 6475, 6318, 6163, 6008, 5849, 5689, 5532, 5375, 5213, 5058, 4903, 4752,
4605, 4463, 4327, 4201, 4078, 3962, 3855, 3745, 3642, 3534, 3434, 3336, 3237, 3135, 3038, 2941, 2843, 2746, 2651, 2555,
2459, 2367, 2276, 2188, 2105, 2023, 1942, 1871, 1806, 1737, 1681, 1620, 1563, 1505, 1442, 1384, 1326, 1266, 1208, 1148,
1086, 1024, 962, 902, 842, 782, 727, 667, 613, 564, 510, 465, 419, 377, 334, 294, 257, 214, 171, 126,
79, 32, -14, -62, -110, -160, -212, -263, -311, -360, -412, -458, -507, -552, -595, -640, -679, -715, -755, -793,
-830, -871, -914, -959, -1001, -1048, -1100, -1152, -1199, -1252, -1306, -1361, -1413, -1468, -1522, -1578, -1629, -1684, -1737, -1788,
-1843, -1887, -1941, -1992, -2045, -2101, -2157, -2217, -2284, -2350, -2417, -2492, -2562, -2638, -2712, -2793, -2871, -2950, -3030, -3110,
-3195, -3272, -3354, -3434, -3518, -3597, -3679, -3762, -3849, -3938, -4034, -4135, -4240, -4349, -4459, -4579, -4700, -4822, -4945, -5070,
-5201, -5328, -5459, -5587, -5718, -5848, -5977, -6104, -6235, -6360, -6489, -6621, -6754, -6886, -7025, -7167, -7313, -7465, -7614, -7763,
-7913, -8058, -8198, -8333, -8462, -8585, -8697, -8802, -8895, -8974, -9046, -9102, -9142, -9167, -9177, -9169, -9141, -9105, -9044, -8969,
-8872, -8753, -8602, -8422, -8205, -7951, -7656, -7321, -6938, -6517, -6049, -5539, -4986, -4401, -3776, -3116, -2433, -1725, -1004, -268,
473, 1205, 1935, 2652, 3343, 4011, 4647, 5251, 5817, 6336, 6816, 7252, 7636, 7974, 8264, 8507, 8708, 8861, 8981, 9065,
9114, 9135, 9126, 9102, 9056, 8993, 8922, 8844, 8758, 8661, 8557, 8448, 8330, 8207, 8069, 7927, 7777, 7622, 7460, 7296,
7129, 6965, 6792, 6628, 6462, 6301, 6137, 5981, 5827, 5686, 5542, 5409, 5279, 5156, 5036, 4909, 4789, 4668, 4545, 4421,
4293, 4163, 4037, 3907, 3783, 3657, 3536, 3417, 3305, 3192, 3086, 2976, 2879, 2782, 2691, 2600, 2520, 2441, 2362, 2285,
2208, 2130, 2049, 1963, 1882, 1796, 1711, 1625, 1539, 1454, 1374, 1293, 1215, 1140, 1069, 997, 926, 863, 804, 739,
683, 625, 569, 512, 454, 394, 330, 265, 196, 127, 56, -14, -89, -162, -228, -299, -365, -425, -490, -551,
-615, -675, -731, -784, -842, -894, -949, -1003, -1058, -1120, -1182, -1248, -1320, -1390, -1462, -1537, -1612, -1689, -1761, -1833,
-1906, -1975, -2046, -2114, -2181, -2252, -2316, -2385, -2450, -2518, -2584, -2654, -2728, -2808, -2887, -2970, -3059, -3153, -3246, -3341,
-3438, -3537, -3631, -3727, -3818, -3907, -3998, -4088, -4179, -4270, -4362, -4451, -4540, -4636, -4726, -4823, -4924, -5027, -5135, -5247,
-5362, -5482, -5604, -5726, -5845, -5964, -6083, -6193, -6300, -6400, -6501, -6594, -6683, -6768, -6855, -6933, -7006, -7078, -7148, -7213,
-7275, -7329, -7384, -7439, -7478, -7515, -7544, -7558, -7554, -7529, -7488, -7422, -7331, -7216, -7073, -6905, -6711, -6487, -6237, -5957,
-5647, -5307, -4938, -4536, -4106, -3645, -3153, -2637, -2086, -1506, -905, -284, 361, 1016, 1684, 2341, 2995, 3636, 4255, 4849,
5412, 5947, 6450, 6910, 7340, 7724, 8076, 8385, 8656, 8891, 9094, 9260, 9398, 9508, 9591, 9638, 9666, 9661, 9637, 9585,
9510, 9420, 9314, 9189, 9057, 8916, 8770, 8617, 8461, 8302, 8144, 7981, 7820, 7657, 7497, 7340, 7180, 7021, 6866, 6705,
6543, 6384, 6217, 6048, 5878, 5709, 5541, 5375, 5212, 5060, 4906, 4761, 4619, 4482, 4353, 4231, 4105, 3989, 3874, 3764,
3651, 3548, 3443, 3340, 3237, 3132, 3033, 2927, 2824, 2720, 2621, 2522, 2424, 2333, 2250, 2167, 2088, 2010, 1941, 1871,
1805, 1742, 1678, 1616, 1553, 1492, 1433, 1376, 1314, 1252, 1194, 1129, 1064, 1002, 938, 877, 819, 761, 709, 658,
609, 563, 517, 474, 434, 389, 347, 305, 260, 219, 176, 130, 85, 39, -8, -57, -105, -160, -209, -262,
-308, -352, -401, -440, -482, -521, -560, -597, -638, -673, -716, -752, -793, -832, -880, -925, -967, -1015, -1064, -1112,
-1164, -1215, -1266, -1320, -1372, -1422, -1475, -1522, -1571, -1615, -1663, -1713, -1762, -1812, -1865, -1918, -1971, -2031, -2090, -2153,
-2214, -2281, -2349, -2423, -2495, -2567, -2643, -2724, -2801, -2873, -2952, -3028, -3101, -3176, -3249, -3328, -3408, -3489, -3575, -3660,
-3751, -3850, -3945, -4052, -4156, -4265, -4376, -4494, -4611, -4732, -4856, -4985, -5111, -5234, -5357, -5482, -5607, -5728, -5850, -5976,
-6104, -6234, -6367, -6505, -6646, -6790, -6938, -7084, -7238, -7387, -7537, -7690, -7843, -7989, -8135, -8276, -8412, -8537, -8647, -8753,
-8849, -8928, -9004, -9063, -9116, -9158, -9185, -9205, -9210, -9197, -9167, -9116, -9044, -8944, -8817, -8655, -8470, -8240, -7980, -7670,
-7325, -6937, -6499, -6019, -5500, -4935, -4336, -3706, -3044, -2360, -1654, -928, -191, 549, 1294, 2032, 2754, 3451, 4127, 4771,
5374, 5930, 6455, 6925, 7354, 7728, 8057, 8338, 8572, 8757, 8911, 9020, 9102, 9149, 9175, 9178, 9168, 9135, 9089, 9030,
8955, 8871, 8770, 8659, 8544, 8411, 8279, 8135, 7985, 7828, 7662, 7499, 7332, 7159, 6991, 6824, 6661, 6502, 6351, 6205,
6066, 5928, 5791, 5662, 5532, 5400, 5272, 5142, 5011, 4883, 4748, 4620, 4488, 4359, 4228, 4094, 3968, 3841, 3715, 3596,
3485, 3374, 3268, 3172, 3080, 2992, 2902, 2816, 2736, 2649, 2567, 2480, 2393, 2308, 2220, 2127, 2044, 1958, 1869, 1779,
1693, 1610, 1525, 1444, 1370, 1296, 1227, 1156, 1095, 1034, 971, 909, 854, 792, 729, 662, 597, 530, 459, 390,
320, 247, 178, 104, 31, -41, -107, -179, -242, -306, -370, -425, -486, -542, -594, -650, -709, -763, -822, -887,
-948, -1019, -1083, -1154, -1224, -1295, -1368, -1442, -1519, -1589, -1663, -1733, -1805, -1871, -1938, -2001, -2066, -2131, -2195, -2260,
-2328, -2400, -2471, -2550, -2628, -2715, -2799, -2886, -2975, -3067, -3159, -3248, -3343, -3433, -3529, -3616, -3707, -3794, -3883, -3967,
-4050, -4138, -4225, -4311, -4404, -4497, -4596, -4701, -4805, -4918, -5033, -5148, -5263, -5381, -5495, -5613, -5724, -5835, -5948, -6052,
-6154, -6252, -6345, -6436, -6521, -6601, -6682, -6761, -6838, -6915, -6988, -7064, -7138, -7202, -7270, -7325, -7374, -7409, -7430, -7435,
-7428, -7400, -7357, -7292, -7203, -7097, -6959, -6797, -6614, -6401, -6165, -5905, -5614, -5300, -4957, -4583, -4181, -3747, -3283, -2786,
-2256, -1696, -1109, -499, 135, 776, 1424, 2073, 2720, 3349, 3959, 4550, 5112, 5645, 6145, 6610, 7043, 7440, 7799, 8126,
8422, 8679, 8903, 9088, 9246, 9367, 9458, 9517, 9550, 9554, 9535, 9492, 9426, 9349, 9252, 9140, 9024, 8890, 8752, 8609,
8461, 8314, 8163, 8012, 7865, 7716, 7565, 7407, 7250, 7091, 6927, 6761, 6589, 6423, 6252, 6078, 5910, 5743, 5577, 5414,
5257, 5108, 4955, 4810, 4668, 4533, 4410, 4283, 4166, 4050, 3935, 3825, 3707, 3596, 3484, 3371, 3259, 3151, 3036, 2928,
2821, 2720, 2619, 2527, 2430, 2342, 2254, 2174, 2093, 2019, 1946, 1878, 1806, 1745, 1679, 1615, 1549, 1480, 1415, 1348,
1278, 1210, 1147, 1084, 1013, 948, 887, 830, 768, 715, 662, 613, 564, 514, 469, 425, 380, 335, 295, 250,
205, 158, 107, 58, 9, -46, -98, -151, -200, -252, -302, -348, -393, -442, -485, -526, -569, -610, -649, -689,
-730, -770, -808, -849, -892, -936, -985, -1031, -1081, -1136, -1183, -1237, -1286, -1338, -1386, -1436, -1484, -1530, -1579, -1625,
-1672, -1718, -1770, -1820, -1867, -1920, -1972, -2023, -2081, -2145, -2209, -2272, -2342, -2410, -2484, -2557, -2629, -2702, -2775, -2850,
-2922, -2993, -3065, -3140, -3211, -3290, -3362, -3446, -3524, -3605, -3691, -3779, -3871, -3971, -4071, -4177, -4285, -4398, -4513, -4632,
-4746, -4861, -4980, -5101, -5217, -5331, -5450, -5569, -5687, -5811, -5930, -6059, -6187, -6312, -6449, -6585, -6725, -6866, -7014, -7164,
-7315, -7466, -7616, -7766, -7906, -8042, -8174, -8298, -8414, -8522, -8622, -8718, -8801, -8877, -8943, -9001, -9050, -9086, -9109, -9120,
-9117, -9093, -9057, -9000, -8919, -8812, -8675, -8506, -8303, -8062, -7783, -7463, -7101, -6705, -6263, -5789, -5275, -4724, -4142, -3529,
-2886, -2223, -1536, -832, -121, 598, 1315, 2027, 2722, 3396, 4044, 4662, 5236, 5774, 6267, 6713, 7116, 7469, 7777, 8047,
8272, 8457, 8609, 8726, 8811, 8875, 8910, 8925, 8917, 8891, 8854, 8801, 8731, 8654, 8555, 8448, 8333, 8202, 8067, 7918,
7769, 7609, 7448, 7285, 7125, 6966, 6811, 6661, 6515, 6365, 6222, 6084, 5950, 5814, 5685, 5555, 5427, 5297, 5168, 5040,
4909, 4774, 4638, 4503, 4370, 4235, 4101, 3973, 3852, 3731, 3616, 3507, 3403, 3303, 3205, 3109, 3020, 2930, 2837, 2754,
2668, 2584, 2494, 2405, 2318, 2228, 2137, 2044, 1954, 1864, 1776, 1684, 1604, 1523, 1446, 1373, 1304, 1233, 1170, 1106,
1043, 980, 917, 856, 794, 729, 663, 596, 526, 458, 383, 310, 238, 162, 87, 15, -55, -123, -186, -250,
-310, -372, -427, -489, -548, -603, -661, -723, -779, -841, -904, -969, -1037, -1109, -1178, -1253, -1328, -1400, -1473, -1549,
-1621, -1690, -1759, -1825, -1889, -1951, -2014, -2079, -2146, -2213, -2280, -2354, -2423, -2497, -2574, -2657, -2743, -2829, -2915, -3007,
-3103, -3195, -3289, -3376, -3468, -3559, -3649, -3735, -3816, -3896, -3984, -4070, -4158, -4243, -4339, -4433, -4531, -4630, -4733, -4839,
-4952, -5064, -5177, -5289, -5407, -5519, -5631, -5744, -5853, -5955, -6051, -6145, -6236, -6325, -6405, -6489, -6569, -6651, -6731, -6809,
-6889, -6957, -7032, -7099, -7161, -7218, -7265, -7303, -7329, -7342, -7340, -7317, -7278, -7219, -7138, -7033, -6903, -6753, -6578, -6379,
-6156, -5916, -5644, -5347, -5021, -4667, -4283, -3865, -3417, -2938, -2428, -1890, -1320, -729, -114, 513, 1152, 1794, 2427, 3056,
3669, 4263, 4827, 5366, 5876, 6355, 6796, 7215, 7590, 7937, 8239, 8518, 8755, 8964, 9134, 9273, 9381, 9458, 9511, 9537,
9533, 9507, 9458, 9392, 9301, 9204, 9089, 8971, 8844, 8711, 8573, 8437, 8297, 8153, 8006, 7861, 7708, 7555, 7397, 7239,
7079, 6917, 6752, 6584, 6420, 6249, 6078, 5908, 5743, 5577, 5420, 5264, 5117, 4973, 4837, 4703, 4578, 4452, 4331, 4214,
4099, 3982, 3868, 3752, 3637, 3526, 3416, 3304, 3196, 3087, 2980, 2876, 2773, 2676, 2584, 2489, 2403, 2322, 2242, 2168,
2094, 2021, 1956, 1888, 1822, 1752, 1685, 1622, 1550, 1481, 1414, 1345, 1279, 1211, 1146, 1079, 1017, 955, 894, 840,
783, 732, 684, 640, 593, 550, 502, 461, 413, 370, 321, 279, 226, 180, 126, 79, 24, -24, -76, -125,
-176, -227, -274, -318, -362, -408, -445, -487, -526, -569, -609, -647, -692, -739, -779, -826, -872, -921, -975, -1023,
-1075, -1126, -1179, -1230, -1282, -1334, -1386, -1434, -1483, -1535, -1578, -1628, -1674, -1723, -1777, -1827, -1877, -1939, -1998, -2058,
-2122, -2188, -2258, -2327, -2397, -2470, -2542, -2613, -2691, -2763, -2840, -2914, -2984, -3059, -3136, -3207, -3284, -3363, -3444, -3525,
-3617, -3705, -3803, -3902, -4005, -4109, -4222, -4332, -4447, -4559, -4679, -4794, -4914, -5030, -5149, -5271, -5389, -5507, -5631, -5748,
-5871, -5994, -6123, -6255, -6388, -6525, -6667, -6812, -6957, -7109, -7255, -7408, -7553, -7695, -7835, -7971, -8098, -8222, -8339, -8446,
-8548, -8639, -8718, -8794, -8854, -8907, -8948, -8984, -9005, -9013, -9007, -8987, -8942, -8881, -8790, -8678, -8535, -8355, -8142, -7896,
-7608, -7286, -6919, -6516, -6074, -5595, -5074, -4524, -3936, -3318, -2679, -2014, -1335, -633, 74, 783, 1494, 2195, 2881, 3542,
4174, 4773, 5334, 5858, 6333, 6772, 7161, 7505, 7807, 8062, 8280, 8459, 8598, 8712, 8794, 8850, 8881, 8888, 8884, 8861,
8822, 8771, 8703, 8621, 8525, 8414, 8294, 8165, 8026, 7885, 7735, 7579, 7423, 7264, 7105, 6949, 6794, 6639, 6491, 6348,
6207, 6069, 5933, 5806, 5675, 5549, 5417, 5288, 5160, 5028, 4894, 4759, 4625, 4490, 4358, 4228, 4099, 3970, 3846, 3729,
3614, 3501, 3394, 3296, 3192, 3097, 3005, 2914, 2830, 2741, 2658, 2570, 2481, 2389, 2299, 2205, 2116, 2022, 1931, 1842,
1758, 1668, 1582, 1503, 1431, 1350, 1281, 1213, 1144, 1082, 1015, 952, 895, 831, 767, 704, 634, 568, 494, 420,
348, 276, 202, 127, 55, -14, -86, -154, -219, -281, -346, -406, -467, -522, -583, -641, -702, -756, -820, -877,
-944, -1010, -1081, -1152, -1222, -1296, -1368, -1441, -1510, -1585, -1652, -1724, -1792, -1857, -1923, -1990, -2052, -2117, -2180, -2250,
-2316, -2385, -2455, -2531, -2608, -2690, -2773, -2861, -2952, -3041, -3133, -3224, -3315, -3403, -3493, -3578, -3667, -3757, -3836, -3925,
-4012, -4099, -4186, -4274, -4366, -4460, -4556, -4658, -4762, -4868, -4981, -5095, -5211, -5325, -5448, -5561, -5675, -5781, -5890, -5994,
-6094, -6193, -6290, -6377, -6472, -6558, -6644, -6731, -6818, -6901, -6979, -7060, -7143, -7217, -7289, -7355, -7419, -7468, -7507, -7529,
-7543, -7537, -7510, -7465, -7401, -7320, -7213, -7084, -6935, -6761, -6564, -6344, -6094, -5818, -5512, -5177, -4809, -4413, -3982, -3516,
-3021, -2490, -1926, -1333, -713, -75, 583, 1248, 1916, 2575, 3221, 3854, 4464, 5043, 5600, 6123, 6615, 7072, 7490, 7875,
8225, 8536, 8809, 9050, 9254, 9424, 9557, 9659, 9730, 9765, 9776, 9759, 9720, 9661, 9580, 9485, 9379, 9264, 9134, 9006,
8868, 8724, 8577, 8429, 8279, 8127, 7969, 7816, 7655, 7494, 7326, 7159, 6989, 6817, 6642, 6467, 6291, 6118, 5947, 5779,
5618, 5462, 5309, 5160, 5019, 4883, 4746, 4617, 4489, 4369, 4248, 4127, 4012, 3895, 3778, 3662, 3546, 3432, 3320, 3202,
3094, 2990, 2884, 2783, 2686, 2598, 2507, 2425, 2342, 2265, 2191, 2118, 2045, 1976, 1908, 1837, 1774, 1705, 1638, 1568,
1500, 1428, 1363, 1292, 1228, 1162, 1099, 1035, 977, 919, 869, 818, 767, 722, 672, 628, 581, 535, 492, 445,
396, 351, 303, 253, 201, 150, 98, 48, -4, -52, -102, -151, -197, -244, -286, -327, -370, -410, -450, -488,
-530, -573, -610, -651, -700, -743, -788, -833, -882, -932, -985, -1031, -1084, -1133, -1183, -1230, -1281, -1329, -1376, -1418,
-1467, -1515, -1560, -1608, -1657, -1708, -1761, -1813, -1871, -1933, -1994, -2056, -2122, -2190, -2259, -2327, -2397, -2470, -2539, -2607,
-2680, -2748, -2819, -2888, -2960, -3031, -3104, -3178, -3257, -3339, -3424, -3513, -3603, -3698, -3795, -3896, -3996, -4105, -4217, -4328,
-4439, -4553, -4667, -4780, -4895, -5009, -5127, -5239, -5355, -5474, -5596, -5716, -5844, -5976, -6111, -6252, -6389, -6534, -6680, -6828,
-6979, -7129, -7281, -7431, -7577, -7722, -7864, -7997, -8125, -8249, -8362, -8471, -8573, -8666, -8756, -8835, -8906, -8977, -9032, -9079,
-9117, -9135, -9139, -9127, -9094, -9036, -8952, -8847, -8706, -8531, -8326, -8082, -7801, -7479, -7118, -6723, -6286, -5810, -5296, -4750,
-4164, -3550, -2905, -2238, -1545, -835, -108, 617, 1350, 2072, 2780, 3463, 4122, 4743, 5325, 5863, 6359, 6809, 7213, 7570,
7880, 8156, 8385, 8578, 8736, 8864, 8960, 9029, 9072, 9091, 9092, 9070, 9027, 8972, 8896, 8807, 8705, 8588, 8465, 8329,
8181, 8036, 7878, 7721, 7558, 7397, 7242, 7090, 6936, 6791, 6647, 6507, 6367, 6229, 6094, 5961, 5822, 5688, 5553, 5412,
5274, 5136, 4995, 4857, 4718, 4579, 4445, 4313, 4183, 4055, 3937, 3823, 3713, 3606, 3505, 3406, 3311, 3218, 3123, 3032,
2940, 2847, 2757, 2663, 2570, 2473, 2380, 2288, 2193, 2103, 2015, 1924, 1840, 1755, 1673, 1596, 1527, 1455, 1387, 1323,
1258, 1195, 1130, 1064, 998, 930, 864, 793, 725, 652, 578, 502, 430, 359, 287, 216, 144, 77, 9, -56,
-114, -175, -236, -292, -349, -403, -464, -524, -584, -649, -715, -780, -850, -913, -989, -1062, -1129, -1201, -1275, -1340,
-1413, -1479, -1546, -1613, -1678, -1739, -1803, -1866, -1929, -1994, -2064, -2131, -2203, -2277, -2358, -2437, -2517, -2600, -2687, -2775,
-2862, -2951, -3038, -3128, -3213, -3300, -3388, -3475, -3558, -3639, -3722, -3811, -3893, -3982, -4070, -4167, -4263, -4361, -4467, -4577,
-4688, -4797, -4910, -5027, -5143, -5259, -5367, -5486, -5592, -5702, -5811, -5912, -6016, -6116, -6213, -6310, -6403, -6500, -6594, -6692,
-6786, -6888, -6984, -7081, -7176, -7261, -7346, -7422, -7489, -7546, -7594, -7626, -7644, -7648, -7635, -7606, -7562, -7498, -7415, -7311,
-7192, -7044, -6885, -6698, -6492, -6256, -5995, -5701, -5374, -5013, -4616, -4182, -3712, -3209, -2667, -2095, -1495, -869, -224, 430,
1101, 1761, 2425, 3074, 3705, 4312, 4899, 5456, 5983, 6477, 6943, 7375, 7770, 8129, 8454, 8734, 8979, 9181, 9346, 9481,
9579, 9644, 9680, 9689, 9675, 9632, 9575, 9499, 9411, 9311, 9199, 9080, 8959, 8829, 8693, 8553, 8412, 8261, 8107, 7949,
7788, 7615, 7445, 7268, 7091, 6916, 6736, 6562, 6386, 6212, 6038, 5876, 5714, 5558, 5407, 5260, 5119, 4980, 4849, 4714,
4588, 4459, 4332, 4205, 4081, 3955, 3827, 3704, 3582, 3463, 3343, 3231, 3117, 3012, 2907, 2808, 2709, 2619, 2534, 2446,
2366, 2289, 2211, 2134, 2060, 1990, 1912, 1840, 1769, 1692, 1619, 1541, 1472, 1394, 1322, 1253, 1187, 1124, 1060, 1003,
946, 890, 838, 786, 737, 689, 640, 589, 543, 495, 448, 395, 346, 289, 239, 187, 130, 81, 29, -26,
-75, -124, -172, -214, -263, -309, -348, -394, -434, -471, -514, -551, -598, -641, -684, -730, -776, -824, -870, -919,
-969, -1022, -1069, -1119, -1164, -1211, -1255, -1302, -1350, -1395, -1437, -1481, -1527, -1573, -1619, -1663, -1717, -1767, -1820, -1876,
-1933, -1993, -2053, -2115, -2178, -2246, -2310, -2376, -2441, -2505, -2571, -2636, -2702, -2769, -2835, -2899, -2969, -3042, -3114, -3187,
-3265, -3346, -3433, -3518, -3609, -3708, -3799, -3901, -4003, -4106, -4211, -4316, -4419, -4526, -4631, -4736, -4845, -4954, -5065, -5174,
-5285, -5406, -5523, -5645, -5773, -5902, -6040, -6175, -6314, -6459, -6605, -6751, -6898, -7046, -7192, -7335, -7471, -7608, -7739, -7867,
-7988, -8107, -8219, -8331, -8435, -8533, -8627, -8714, -8799, -8872, -8940, -8996, -9044, -9073, -9093, -9091, -9069, -9023, -8957, -8860,
-8739, -8582, -8395, -8175, -7921, -7635, -7309, -6953, -6558, -6124, -5660, -5155, -4615, -4043, -3440, -2808, -2147, -1465, -766, -58,
661, 1377, 2081, 2766, 3429, 4060, 4660, 5216, 5737, 6212, 6645, 7036, 7385, 7696, 7966, 8197, 8401, 8560, 8693, 8795,
8867, 8920, 8942, 8940, 8917, 8875, 8814, 8735, 8636, 8529, 8406, 8277, 8141, 8001, 7857, 7712, 7564, 7419, 7277, 7132,
6991, 6852, 6713, 6578, 6444, 6309, 6176, 6036, 5901, 5763, 5620, 5479, 5334, 5189, 5047, 4905, 4763, 4631, 4497, 4373,
4247, 4128, 4015, 3904, 3798, 3695, 3596, 3497, 3400, 3303, 3207, 3114, 3015, 2920, 2821, 2725, 2627, 2528, 2428, 2336,
2240, 2150, 2063, 1977, 1896, 1814, 1739, 1669, 1596, 1528, 1460, 1393, 1328, 1258, 1191, 1123, 1055, 981, 913, 837,
766, 686, 611, 540, 464, 390, 325, 257, 191, 126, 64, 5, -54, -114, -171, -231, -288, -349, -414, -474,
-537, -607, -673, -742, -812, -884, -958, -1029, -1101, -1170, -1237, -1307, -1372, -1435, -1502, -1565, -1623, -1688, -1752, -1816,
-1886, -1952, -2024, -2099, -2172, -2248, -2332, -2411, -2498, -2580, -2669, -2759, -2836, -2927, -3011, -3093, -3175, -3255, -3338, -3418,
-3499, -3578, -3662, -3746, -3835, -3925, -4021, -4119, -4219, -4322, -4429, -4537, -4645, -4757, -4867, -4980, -5092, -5201, -5308, -5416,
-5514, -5616, -5714, -5811, -5909, -6006, -6104, -6201, -6295, -6392, -6489, -6589, -6687, -6784, -6879, -6973, -7059, -7137, -7215, -7281,
-7339, -7386, -7415, -7434, -7439, -7426, -7400, -7360, -7304, -7233, -7140, -7037, -6918, -6769, -6604, -6418, -6206, -5965, -5693, -5392,
-5059, -4686, -4284, -3841, -3366, -2854, -2311, -1740, -1144, -526, 107, 753, 1395, 2037, 2676, 3299, 3901, 4488, 5047, 5584,
6089, 6568, 7017, 7430, 7807, 8150, 8455, 8721, 8952, 9143, 9297, 9420, 9506, 9561, 9595, 9598, 9578, 9541, 9488, 9421,
9341, 9247, 9147, 9040, 8923, 8797, 8666, 8530, 8387, 8238, 8085, 7927, 7764, 7593, 7423, 7252, 7077, 6901, 6729, 6557,
6387, 6224, 6062, 5907, 5755, 5605, 5463, 5321, 5186, 5052, 4916, 4785, 4655, 4521, 4392, 4262, 4136, 4006, 3877, 3754,
3634, 3514, 3393, 3281, 3175, 3069, 2968, 2875, 2786, 2699, 2611, 2531, 2451, 2372, 2294, 2215, 2140, 2064, 1982, 1909,
1830, 1755, 1677, 1601, 1530, 1462, 1388, 1319, 1257, 1194, 1131, 1076, 1019, 966, 914, 862, 814, 761, 715, 661,
611, 559, 504, 449, 397, 343, 287, 233, 178, 126, 75, 24, -23, -71, -115, -164, -209, -250, -291, -338,
-378, -420, -462, -508, -554, -600, -652, -700, -747, -797, -850, -898, -952, -1002, -1048, -1103, -1152, -1196, -1241, -1293,
-1339, -1386, -1428, -1479, -1525, -1576, -1625, -1680, -1734, -1791, -1853, -1915, -1977, -2039, -2105, -2171, -2242, -2306, -2373, -2439,
-2509, -2572, -2640, -2706, -2773, -2843, -2910, -2981, -3056, -3129, -3209, -3294, -3379, -3469, -3560, -3651, -3755, -3849, -3953, -4055,
-4160, -4266, -4369, -4476, -4580, -4688, -4793, -4900, -5008, -5120, -5230, -5345, -5462, -5584, -5707, -5836, -5965, -6102, -6240, -6380,
-6518, -6664, -6804, -6945, -7082, -7221, -7359, -7485, -7613, -7737, -7852, -7964, -8073, -8178, -8276, -8371, -8460, -8546, -8625, -8698,
-8760, -8813, -8858, -8887, -8905, -8899, -8878, -8836, -8764, -8673, -8551, -8406, -8223, -8018, -7779, -7500, -7193, -6849, -6477, -6065,
-5620, -5142, -4631, -4088, -3516, -2911, -2286, -1638, -971, -293, 393, 1079, 1757, 2424, 3064, 3683, 4269, 4819, 5329, 5804,
6238, 6634, 6991, 7308, 7590, 7833, 8044, 8226, 8377, 8496, 8589, 8652, 8694, 8712, 8703, 8677, 8631, 8565, 8482, 8389,
8282, 8170, 8044, 7914, 7782, 7648, 7513, 7372, 7234, 7101, 6968, 6834, 6705, 6575, 6445, 6316, 6185, 6050, 5914, 5777,
5638, 5500, 5354, 5214, 5073, 4934, 4797, 4662, 4529, 4401, 4280, 4159, 4039, 3930, 3824, 3716, 3617, 3520, 3420, 3322,
3228, 3127, 3031, 2932, 2832, 2737, 2631, 2535, 2435, 2338, 2242, 2153, 2062, 1977, 1894, 1812, 1732, 1659, 1586, 1519,
1448, 1382, 1310, 1245, 1176, 1103, 1032, 959, 887, 812, 735, 658, 581, 508, 433, 362, 288, 220, 151, 84,
21, -42, -105, -162, -223, -284, -342, -405, -468, -534, -602, -667, -737, -810, -882, -953, -1025, -1098, -1169, -1240,
-1309, -1379, -1443, -1508, -1574, -1639, -1703, -1765, -1830, -1894, -1961, -2027, -2102, -2173, -2250, -2330, -2409, -2494, -2580, -2664,
-2749, -2832, -2925, -3008, -3092, -3177, -3261, -3339, -3421, -3503, -3588, -3671, -3753, -3840, -3933, -4016, -4113, -4209, -4311, -4414,
-4524, -4629, -4740, -4851, -4959, -5074, -5185, -5292, -5398, -5500, -5607, -5706, -5803, -5901, -5998, -6097, -6191, -6283, -6384, -6478,
-6576, -6671, -6770, -6867, -6965, -7054, -7141, -7224, -7296, -7363, -7416, -7455, -7487, -7499, -7501, -7490, -7459, -7415, -7356, -7279,
-7185, -7072, -6937, -6789, -6611, -6412, -6183, -5933, -5649, -5332, -4983, -4597, -4171, -3709, -3213, -2681, -2122, -1532, -916, -285,
361, 1017, 1673, 2327, 2967, 3593, 4201, 4786, 5345, 5882, 6384, 6859, 7296, 7698, 8068, 8403, 8688, 8946, 9158, 9335,
9477, 9584, 9657, 9704, 9720, 9715, 9681, 9636, 9572, 9494, 9406, 9306, 9196, 9081, 8957, 8831, 8694, 8550, 8405, 8252,
8091, 7927, 7760, 7591, 7413, 7237, 7061, 6883, 6706, 6536, 6366, 6201, 6039, 5879, 5725, 5579, 5433, 5287, 5151, 5013,
4882, 4745, 4615, 4483, 4355, 4223, 4095, 3967, 3841, 3714, 3591, 3476, 3364, 3246, 3144, 3036, 2941, 2845, 2752, 2664,
2580, 2495, 2414, 2335, 2259, 2183, 2104, 2026, 1952, 1875, 1798, 1724, 1648, 1574, 1498, 1424, 1355, 1288, 1224, 1162,
1105, 1047, 991, 937, 885, 835, 783, 735, 684, 630, 579, 527, 474, 419, 363, 312, 256, 203, 150, 94,
46, -7, -56, -98, -144, -188, -232, -275, -318, -359, -402, -443, -485, -529, -575, -623, -671, -717, -768, -817,
-865, -915, -965, -1015, -1063, -1111, -1159, -1203, -1247, -1294, -1335, -1383, -1430, -1475, -1523, -1573, -1623, -1673, -1731, -1783,
-1844, -1903, -1961, -2028, -2091, -2156, -2221, -2285, -2353, -2419, -2482, -2548, -2614, -2678, -2743, -2809, -2878, -2947, -3019, -3094,
-3174, -3251, -3335, -3420, -3511, -3605, -3697, -3794, -3897, -3994, -4097, -4198, -4304, -4406, -4508, -4614, -4719, -4824, -4932, -5038,
-5149, -5263, -5380, -5498, -5627, -5749, -5881, -6016, -6154, -6295, -6434, -6574, -6721, -6862, -7003, -7143, -7278, -7410, -7544, -7668,
-7787, -7903, -8016, -8125, -8230, -8332, -8426, -8519, -8606, -8684, -8755, -8815, -8870, -8909, -8933, -8940, -8932, -8898, -8842, -8759,
-8658, -8525, -8360, -8168, -7939, -7680, -7387, -7063, -6702, -6307, -5881, -5416, -4914, -4385, -3814, -3217, -2591, -1942, -1273, -589,
107, 801, 1497, 2184, 2846, 3488, 4096, 4673, 5209, 5708, 6167, 6588, 6968, 7307, 7609, 7877, 8111, 8308, 8467, 8604,
8708, 8784, 8835, 8854, 8854, 8835, 8791, 8734, 8657, 8564, 8458, 8342, 8221, 8091, 7954, 7821, 7683, 7542, 7406, 7267,
7130, 6997, 6864, 6730, 6595, 6463, 6326, 6189, 6048, 5909, 5771, 5628, 5485, 5339, 5199, 5056, 4915, 4780, 4646, 4515,
4390, 4270, 4157, 4040, 3930, 3828, 3727, 3623, 3526, 3422, 3328, 3227, 3128, 3031, 2930, 2830, 2732, 2631, 2533, 2438,
2339, 2250, 2162, 2071, 1989, 1909, 1834, 1761, 1685, 1617, 1551, 1481, 1411, 1344, 1276, 1208, 1134, 1062, 989, 916,
844, 768, 693, 623, 548, 476, 405, 340, 270, 209, 146, 88, 29, -34, -87, -149, -212, -268, -331, -396,
-465, -533, -600, -666, -737, -808, -879, -945, -1016, -1087, -1155, -1220, -1284, -1354, -1414, -1478, -1538, -1604, -1664, -1730,
-1794, -1861, -1930, -2003, -2077, -2158, -2237, -2318, -2399, -2483, -2565, -2652, -2736, -2820, -2905, -2986, -3066, -3148, -3230, -3310,
-3389, -3472, -3558, -3642, -3730, -3821, -3914, -4013, -4114, -4216, -4324, -4432, -4542, -4651, -4765, -4875, -4987, -5097, -5208, -5316,
-5420, -5527, -5631, -5730, -5833, -5935, -6036, -6140, -6245, -6353, -6460, -6567, -6678, -6787, -6895, -7003, -7101, -7198, -7289, -7372,
-7446, -7514, -7569, -7617, -7652, -7668, -7678, -7670, -7650, -7613, -7567, -7508, -7426, -7327, -7214, -7075, -6914, -6726, -6512, -6265,
-5987, -5669, -5317, -4925, -4491, -4025, -3521, -2981, -2409, -1807, -1180, -533, 132, 800, 1479, 2154, 2818, 3470, 4107, 4716,
5307, 5869, 6400, 6900, 7361, 7791, 8180, 8525, 8834, 9098, 9322, 9506, 9651, 9760, 9841, 9887, 9904, 9905, 9874, 9827,
9768, 9691, 9606, 9505, 9395, 9279, 9150, 9014, 8870, 8721, 8565, 8398, 8228, 8056, 7878, 7699, 7517, 7333, 7153, 6975,
6798, 6621, 6452, 6286, 6122, 5964, 5811, 5663, 5513, 5368, 5229, 5085, 4945, 4804, 4663, 4528, 4389, 4255, 4119, 3988,
3859, 3733, 3613, 3495, 3382, 3267, 3168, 3066, 2970, 2875, 2786, 2699, 2619, 2530, 2450, 2369, 2288, 2208, 2127, 2045,
1965, 1884, 1809, 1730, 1657, 1582, 1507, 1439, 1375, 1307, 1249, 1191, 1136, 1077, 1020, 970, 920, 864, 814, 764,
709, 657, 599, 547, 491, 439, 383, 328, 274, 222, 168, 117, 69, 23, -24, -65, -110, -152, -196, -239,
-282, -323, -368, -411, -458, -503, -552, -604, -652, -700, -754, -801, -852, -899, -951, -995, -1042, -1089, -1137, -1178,
-1224, -1264, -1311, -1359, -1404, -1450, -1499, -1552, -1603, -1656, -1712, -1771, -1831, -1889, -1950, -2016, -2075, -2138, -2198, -2264,
-2325, -2385, -2447, -2514, -2575, -2640, -2701, -2773, -2842, -2910, -2985, -3061, -3142, -3224, -3307, -3399, -3487, -3578, -3674, -3772,
-3865, -3961, -4059, -4159, -4261, -4360, -4461, -4562, -4665, -4768, -4877, -4988, -5100, -5211, -5332, -5456, -5581, -5713, -5850, -5984,
-6122, -6264, -6402, -6545, -6688, -6826, -6963, -7101, -7234, -7369, -7497, -7620, -7745, -7869, -7987, -8107, -8220, -8336, -8441, -8549,
-8651, -8746, -8833, -8911, -8981, -9040, -9082, -9103, -9112, -9098, -9063, -9008, -8928, -8825, -8693, -8532, -8346, -8129, -7879, -7600,
-7283, -6937, -6555, -6135, -5680, -5188, -4660, -4098, -3504, -2881, -2227, -1555, -864, -169, 536, 1230, 1920, 2589, 3232, 3852,
4439, 4988, 5506, 5982, 6422, 6821, 7186, 7509, 7798, 8043, 8263, 8444, 8588, 8704, 8787, 8840, 8865, 8864, 8841, 8798,
8733, 8655, 8564, 8461, 8355, 8235, 8113, 7988, 7860, 7732, 7599, 7469, 7336, 7203, 7070, 6936, 6800, 6661, 6520, 6375,
6231, 6086, 5937, 5788, 5641, 5492, 5347, 5201, 5063, 4927, 4792, 4666, 4540, 4422, 4304, 4188, 4078, 3970, 3863, 3756,
3653, 3549, 3444, 3338, 3232, 3125, 3020, 2914, 2811, 2707, 2610, 2507, 2413, 2322, 2233, 2145, 2067, 1984, 1907, 1832,
1758, 1686, 1618, 1544, 1475, 1401, 1329, 1252, 1177, 1100, 1027, 948, 874, 798, 724, 650, 578, 511, 445, 377,
316, 255, 192, 133, 70, 11, -48, -108, -172, -235, -298, -366, -435, -507, -574, -644, -716, -783, -850, -918,
-986, -1052, -1117, -1175, -1239, -1298, -1362, -1421, -1482, -1548, -1610, -1674, -1741, -1810, -1881, -1953, -2028, -2108, -2187, -2265,
-2349, -2427, -2508, -2589, -2667, -2745, -2822, -2901, -2974, -3053, -3131, -3208, -3288, -3371, -3452, -3540, -3628, -3721, -3813, -3911,
-4009, -4114, -4215, -4322, -4426, -4536, -4639, -4746, -4849, -4953, -5056, -5156, -5256, -5355, -5458, -5560, -5658, -5764, -5868, -5976,
-6080, -6192, -6300, -6410, -6522, -6635, -6744, -6852, -6953, -7051, -7143, -7223, -7301, -7368, -7428, -7479, -7517, -7548, -7569, -7578,
-7577, -7563, -7543, -7506, -7456, -7389, -7304, -7198, -7071, -6918, -6744, -6541, -6300, -6030, -5725, -5382, -5001, -4587, -4138, -3655,
-3131, -2586, -2015, -1414, -798, -168, 478, 1128, 1780, 2430, 3069, 3696, 4308, 4896, 5459, 5996, 6502, 6977, 7413, 7811,
8172, 8495, 8773, 9014, 9212, 9380, 9512, 9612, 9685, 9728, 9750, 9748, 9731, 9690, 9637, 9566, 9486, 9391, 9282, 9164,
9035, 8897, 8750, 8593, 8432, 8269, 8097, 7926, 7746, 7571, 7398, 7227, 7055, 6885, 6723, 6560, 6402, 6245, 6096, 5943,
5792, 5645, 5499, 5354, 5210, 5062, 4920, 4776, 4637, 4498, 4359, 4225, 4092, 3965, 3844, 3723, 3611, 3503, 3395, 3295,
3196, 3102, 3007, 2918, 2828, 2741, 2653, 2567, 2480, 2395, 2309, 2224, 2143, 2060, 1979, 1900, 1822, 1751, 1675, 1609,
1540, 1478, 1416, 1361, 1302, 1243, 1188, 1132, 1079, 1023, 970, 913, 857, 801, 742, 688, 632, 574, 519, 464,
411, 357, 305, 258, 211, 162, 121, 75, 30, -13, -58, -102, -146, -193, -237, -286, -335, -384, -432, -485,
-534, -587, -637, -686, -733, -781, -833, -878, -922, -966, -1012, -1052, -1098, -1143, -1187, -1236, -1283, -1332, -1387, -1438,
-1492, -1547, -1606, -1665, -1724, -1782, -1846, -1900, -1962, -2023, -2086, -2147, -2209, -2264, -2325, -2388, -2449, -2514, -2581, -2649,
-2723, -2793, -2867, -2946, -3025, -3108, -3194, -3283, -3368, -3457, -3550, -3645, -3734, -3830, -3924, -4022, -4116, -4211, -4308, -4409,
-4506, -4611, -4716, -4828, -4943, -5057, -5175, -5297, -5422, -5551, -5680, -5816, -5950, -6084, -6219, -6355, -6486, -6620, -6750, -6883,
-7008, -7135, -7258, -7381, -7503, -7622, -7740, -7858, -7975, -8088, -8196, -8305, -8406, -8498, -8584, -8663, -8730, -8785, -8825, -8853,
-8863, -8851, -8821, -8773, -8701, -8610, -8487, -8344, -8179, -7984, -7758, -7512, -7228, -6912, -6566, -6185, -5767, -5315, -4829, -4306,
-3758, -3177, -2575, -1943, -1301, -641, 22, 687, 1345, 1990, 2626, 3235, 3815, 4369, 4895, 5384, 5844, 6267, 6655, 7006,
7325, 7602, 7848, 8054, 8228, 8365, 8470, 8549, 8596, 8617, 8617, 8595, 8556, 8496, 8422, 8338, 8248, 8147, 8045, 7931,
7823, 7706, 7586, 7466, 7342, 7212, 7084, 6955, 6817, 6680, 6538, 6396, 6254, 6105, 5956, 5810, 5669, 5525, 5378, 5237,
5100, 4968, 4838, 4716, 4593, 4478, 4363, 4249, 4136, 4029, 3918, 3808, 3701, 3591, 3479, 3370, 3263, 3155, 3043, 2941,
2834, 2731, 2633, 2535, 2438, 2350, 2260, 2176, 2094, 2018, 1940, 1862, 1785, 1711, 1636, 1559, 1484, 1406, 1330, 1248,
1168, 1090, 1013, 933, 860, 781, 707, 632, 563, 494, 428, 366, 300, 240, 175, 116, 52, -10, -74, -139,
-207, -272, -343, -414, -486, -554, -623, -696, -765, -833, -902, -971, -1036, -1103, -1163, -1230, -1292, -1352, -1412, -1475,
-1541, -1606, -1672, -1741, -1812, -1887, -1964, -2040, -2119, -2197, -2278, -2359, -2440, -2519, -2599, -2680, -2760, -2836, -2914, -2993,
-3072, -3147, -3229, -3305, -3386, -3476, -3560, -3649, -3746, -3839, -3937, -4035, -4139, -4245, -4348, -4449, -4556, -4657, -4761, -4862,
-4967, -5068, -5167, -5265, -5364, -5463, -5561, -5662, -5759, -5864, -5970, -6073, -6184, -6295, -6401, -6510, -6614, -6719, -6820, -6917,
-7005, -7089, -7165, -7235, -7296, -7347, -7394, -7426, -7447, -7467, -7465, -7455, -7436, -7406, -7362, -7305, -7226, -7136, -7020, -6883,
-6720, -6529, -6312, -6062, -5777, -5461, -5108, -4723, -4305, -3851, -3366, -2854, -2315, -1749, -1164, -560, 55, 684, 1312, 1941,
2566, 3184, 3786, 4370, 4934, 5474, 5987, 6470, 6922, 7339, 7719, 8062, 8366, 8634, 8864, 9057, 9218, 9345, 9441, 9512,
9558, 9579, 9579, 9559, 9527, 9476, 9407, 9328, 9236, 9130, 9012, 8883, 8745, 8603, 8451, 8291, 8131, 7964, 7799, 7628,
7454, 7283, 7118, 6949, 6787, 6624, 6465, 6314, 6158, 6007, 5860, 5711, 5565, 5421, 5274, 5130, 4982, 4842, 4698, 4560,
4421, 4287, 4156, 4028, 3901, 3779, 3663, 3549, 3443, 3338, 3237, 3141, 3044, 2955, 2863, 2775, 2685, 2598, 2509, 2425,
2334, 2247, 2165, 2079, 1998, 1920, 1842, 1766, 1691, 1621, 1554, 1488, 1422, 1361, 1304, 1245, 1187, 1131, 1072, 1022,
964, 908, 852, 794, 736, 678, 623, 564, 508, 452, 401, 350, 298, 245, 195, 151, 103, 55, 12, -30,
-77, -121, -167, -209, -258, -305, -348, -399, -450, -500, -554, -602, -652, -702, -748, -798, -843, -892, -937, -981,
-1026, -1074, -1114, -1159, -1205, -1250, -1300, -1350, -1398, -1449, -1502, -1557, -1614, -1673, -1731, -1795, -1851, -1910, -1973, -2029,
-2088, -2150, -2211, -2274, -2332, -2392, -2455, -2520, -2585, -2650, -2720, -2791, -2864, -2938, -3017, -3095, -3180, -3268, -3355, -3443,
-3532, -3625, -3715, -3806, -3899, -3991, -4085, -4180, -4279, -4375, -4477, -4576, -4684, -4789, -4899, -5012, -5127, -5247, -5367, -5493,
-5621, -5749, -5881, -6016, -6148, -6279, -6411, -6541, -6669, -6796, -6923, -7049, -7170, -7290, -7411, -7527, -7645, -7759, -7869, -7979,
-8085, -8186, -8282, -8378, -8457, -8535, -8598, -8656, -8698, -8723, -8725, -8717, -8689, -8637, -8567, -8479, -8364, -8227, -8063, -7872,
-7654, -7408, -7126, -6822, -6485, -6112, -5707, -5272, -4803, -4304, -3774, -3217, -2638, -2035, -1416, -783, -149, 494, 1130, 1756,
2371, 2963, 3537, 4087, 4607, 5103, 5566, 5999, 6399, 6763, 7093, 7389, 7651, 7876, 8072, 8233, 8363, 8460, 8530, 8571,
8588, 8582, 8559, 8512, 8456, 8384, 8302, 8213, 8115, 8010, 7906, 7791, 7674, 7554, 7429, 7305, 7179, 7049, 6919, 6784,
6645, 6502, 6357, 6213, 6068, 5921, 5774, 5629, 5489, 5347, 5209, 5076, 4948, 4819, 4697, 4578, 4459, 4343, 4226, 4115,
4009, 3900, 3788, 3682, 3574, 3466, 3354, 3247, 3140, 3033, 2926, 2825, 2724, 2626, 2531, 2441, 2354, 2270, 2184, 2107,
2024, 1947, 1868, 1794, 1721, 1647, 1569, 1493, 1419, 1342, 1264, 1186, 1106, 1032, 953, 877, 802, 730, 659, 589,
522, 458, 394, 330, 269, 205, 144, 80, 17, -44, -111, -177, -243, -314, -381, -453, -524, -595, -665, -737,
-803, -872, -932, -999, -1065, -1128, -1189, -1253, -1313, -1376, -1439, -1507, -1573, -1642, -1710, -1784, -1855, -1929, -2004, -2085,
-2163, -2245, -2324, -2406, -2486, -2562, -2639, -2719, -2798, -2874, -2951, -3030, -3108, -3187, -3271, -3355, -3445, -3531, -3619, -3713,
-3811, -3907, -4006, -4112, -4217, -4320, -4425, -4528, -4634, -4741, -4842, -4942, -5043, -5143, -5245, -5344, -5449, -5551, -5655, -5759,
-5867, -5978, -6088, -6196, -6308, -6417, -6528, -6636, -6746, -6848, -6947, -7039, -7127, -7209, -7279, -7345, -7398, -7446, -7482, -7510,
-7530, -7539, -7539, -7525, -7501, -7462, -7410, -7336, -7246, -7134, -6996, -6838, -6647, -6429, -6181, -5898, -5583, -5234, -4847, -4429,
-3975, -3491, -2982, -2444, -1880, -1299, -700, -85, 539, 1169, 1796, 2417, 3036, 3637, 4224, 4793, 5337, 5857, 6347, 6806,
7235, 7623, 7977, 8296, 8576, 8819, 9026, 9201, 9348, 9461, 9548, 9610, 9647, 9663, 9654, 9628, 9583, 9523, 9444, 9356,
9254, 9141, 9015, 8880, 8737, 8586, 8425, 8263, 8096, 7927, 7753, 7579, 7407, 7238, 7069, 6904, 6740, 6580, 6421, 6262,
6108, 5954, 5801, 5647, 5499, 5351, 5203, 5054, 4906, 4764, 4618, 4478, 4342, 4206, 4075, 3944, 3821, 3706, 3591, 3481,
3376, 3275, 3178, 3078, 2980, 2888, 2795, 2704, 2613, 2524, 2439, 2348, 2262, 2178, 2095, 2011, 1930, 1854, 1778, 1701,
1630, 1558, 1495, 1431, 1370, 1311, 1255, 1195, 1139, 1079, 1025, 970, 910, 857, 801, 744, 684, 627, 574, 521,
464, 412, 357, 307, 254, 205, 163, 117, 72, 28, -14, -59, -103, -149, -194, -236, -288, -333, -382, -429,
-478, -527, -579, -626, -675, -723, -770, -816, -862, -910, -953, -994, -1039, -1086, -1127, -1173, -1220, -1268, -1315, -1367,
-1413, -1469, -1521, -1575, -1630, -1688, -1743, -1804, -1860, -1922, -1978, -2037, -2096, -2155, -2213, -2272, -2330, -2392, -2453, -2517,
-2582, -2649, -2724, -2794, -2870, -2947, -3027, -3107, -3191, -3273, -3362, -3448, -3536, -3628, -3716, -3807, -3899, -3991, -4085, -4181,
-4276, -4373, -4473, -4577, -4682, -4788, -4904, -5020, -5141, -5262, -5387, -5513, -5641, -5768, -5899, -6032, -6164, -6296, -6429, -6559,
-6689, -6817, -6945, -7074, -7200, -7322, -7446, -7570, -7691, -7813, -7934, -8055, -8171, -8279, -8385, -8483, -8575, -8656, -8726, -8786,
-8834, -8864, -8881, -8880, -8862, -8826, -8765, -8686, -8583, -8457, -8303, -8129, -7921, -7687, -7426, -7134, -6812, -6452, -6060, -5634,
-5171, -4678, -4154, -3600, -3024, -2426, -1810, -1183, -542, 103, 747, 1385, 2011, 2621, 3216, 3785, 4332, 4853, 5342, 5804,
6230, 6628, 6987, 7313, 7596, 7850, 8067, 8248, 8393, 8506, 8592, 8653, 8681, 8693, 8681, 8648, 8599, 8534, 8461, 8378,
8285, 8187, 8082, 7973, 7858, 7738, 7616, 7491, 7358, 7222, 7081, 6941, 6794, 6646, 6497, 6350, 6201, 6049, 5901, 5754,
5613, 5468, 5329, 5196, 5064, 4937, 4813, 4691, 4575, 4455, 4339, 4225, 4113, 3996, 3883, 3768, 3656, 3541, 3427, 3317,
3211, 3099, 2999, 2893, 2795, 2699, 2601, 2509, 2424, 2334, 2253, 2176, 2091, 2015, 1933, 1856, 1780, 1706, 1625, 1549,
1466, 1388, 1307, 1230, 1151, 1077, 999, 928, 855, 785, 713, 644, 580, 515, 452, 392, 328, 271, 204, 141,
80, 12, -53, -122, -193, -259, -329, -401, -468, -535, -605, -668, -734, -798, -866, -929, -989, -1049, -1110, -1171,
-1230, -1292, -1356, -1420, -1486, -1552, -1622, -1695, -1767, -1841, -1919, -1996, -2070, -2145, -2222, -2299, -2371, -2446, -2518, -2593,
-2669, -2745, -2817, -2893, -2972, -3050, -3128, -3211, -3297, -3384, -3475, -3570, -3666, -3762, -3861, -3959, -4060, -4162, -4259, -4361,
-4459, -4557, -4655, -4756, -4855, -4958, -5057, -5155, -5260, -5359, -5465, -5571, -5684, -5796, -5908, -6021, -6137, -6254, -6368, -6479,
-6591, -6696, -6795, -6890, -6979, -7064, -7142, -7214, -7282, -7340, -7396, -7437, -7478, -7506, -7528, -7538, -7539, -7530, -7505, -7467,
-7412, -7335, -7237, -7113, -6967, -6789, -6584, -6345, -6073, -5771, -5433, -5065, -4660, -4232, -3768, -3274, -2749, -2204, -1633, -1042,
-437, 186, 816, 1451, 2084, 2709, 3330, 3930, 4521, 5086, 5626, 6139, 6623, 7070, 7484, 7860, 8197, 8500, 8765, 8996,
9193, 9354, 9488, 9590, 9667, 9717, 9742, 9745, 9731, 9693, 9640, 9570, 9481, 9381, 9260, 9133, 8998, 8850, 8696, 8539,
8379, 8213, 8047, 7877, 7711, 7542, 7373, 7207, 7045, 6882, 6719, 6559, 6402, 6245, 6089, 5934, 5776, 5620, 5464, 5307,
5157, 5006, 4856, 4713, 4572, 4437, 4303, 4173, 4050, 3929, 3810, 3695, 3589, 3481, 3377, 3274, 3175, 3079, 2983, 2887,
2794, 2699, 2607, 2513, 2423, 2333, 2247, 2161, 2078, 1999, 1923, 1850, 1775, 1707, 1639, 1576, 1510, 1449, 1387, 1327,
1265, 1206, 1150, 1089, 1029, 971, 911, 851, 791, 734, 676, 616, 563, 509, 460, 409, 361, 309, 265, 217,
172, 128, 84, 37, -11, -55, -101, -151, -200, -246, -295, -345, -397, -449, -497, -546, -594, -641, -685, -729,
-773, -821, -863, -906, -951, -996, -1041, -1086, -1134, -1180, -1233, -1279, -1331, -1387, -1438, -1492, -1549, -1609, -1666, -1720,
-1777, -1834, -1887, -1945, -1999, -2061, -2116, -2174, -2231, -2294, -2355, -2418, -2482, -2551, -2622, -2691, -2766, -2843, -2922, -2999,
-3084, -3165, -3250, -3338, -3418, -3504, -3589, -3674, -3762, -3849, -3943, -4034, -4128, -4226, -4327, -4426, -4532, -4640, -4751, -4868,
-4983, -5104, -5225, -5351, -5476, -5603, -5735, -5867, -5992, -6121, -6250, -6376, -6503, -6631, -6758, -6888, -7016, -7145, -7276, -7406,
-7536, -7663, -7792, -7919, -8040, -8158, -8277, -8387, -8489, -8583, -8671, -8748, -8811, -8860, -8899, -8921, -8923, -8914, -8888, -8845,
-8779, -8698, -8595, -8466, -8312, -8134, -7924, -7687, -7419, -7113, -6778, -6411, -6007, -5569, -5094, -4589, -4053, -3485, -2892, -2281,
-1647, -1003, -354, 302, 952, 1597, 2232, 2845, 3442, 4015, 4561, 5079, 5562, 6009, 6423, 6798, 7137, 7435, 7698, 7922,
8111, 8260, 8383, 8470, 8529, 8565, 8576, 8566, 8535, 8495, 8442, 8374, 8299, 8215, 8120, 8018, 7910, 7795, 7675, 7552,
7420, 7289, 7151, 7011, 6865, 6717, 6567, 6416, 6264, 6116, 5967, 5823, 5683, 5544, 5408, 5279, 5150, 5021, 4902, 4778,
4655, 4535, 4415, 4298, 4180, 4063, 3947, 3832, 3715, 3599, 3482, 3368, 3253, 3144, 3040, 2936, 2839, 2742, 2647, 2558,
2474, 2386, 2305, 2221, 2140, 2056, 1973, 1894, 1813, 1732, 1651, 1570, 1487, 1410, 1326, 1244, 1167, 1087, 1011, 938,
867, 797, 727, 665, 598, 535, 471, 409, 344, 280, 213, 147, 80, 13, -58, -126, -197, -267, -339, -408,
-479, -548, -617, -683, -749, -811, -874, -936, -995, -1054, -1118, -1180, -1240, -1306, -1373, -1441, -1510, -1579, -1651, -1725,
-1798, -1873, -1947, -2025, -2099, -2175, -2252, -2325, -2400, -2471, -2545, -2619, -2690, -2764, -2837, -2917, -2994, -3074, -3160, -3245,
-3335, -3423, -3514, -3610, -3703, -3799, -3893, -3993, -4091, -4190, -4287, -4387, -4482, -4577, -4672, -4767, -4864, -4958, -5058, -5159,
-5260, -5361, -5470, -5576, -5688, -5799, -5911, -6022, -6133, -6242, -6348, -6458, -6561, -6659, -6755, -6845, -6931, -7009, -7081, -7148,
-7209, -7264, -7312, -7356, -7391, -7420, -7442, -7453, -7455, -7445, -7418, -7374, -7315, -7234, -7131, -7006, -6855, -6677, -6470, -6234,
-5967, -5669, -5336, -4974, -4581, -4157, -3704, -3223, -2715, -2185, -1627, -1055, -464, 143, 763, 1389, 2011, 2633, 3246, 3847,
4431, 4991, 5527, 6038, 6518, 6959, 7368, 7743, 8080, 8382, 8644, 8876, 9071, 9235, 9375, 9478, 9559, 9610, 9635, 9641,
9626, 9586, 9532, 9459, 9372, 9269, 9155, 9031, 8899, 8756, 8608, 8456, 8294, 8133, 7971, 7806, 7647, 7485, 7325, 7167,
7010, 6853, 6693, 6536, 6379, 6221, 6061, 5907, 5749, 5595, 5437, 5286, 5136, 4990, 4843, 4703, 4564, 4432, 4300, 4174,
4053, 3937, 3824, 3716, 3607, 3504, 3402, 3299, 3198, 3100, 3001, 2902, 2805, 2711, 2616, 2523, 2435, 2347, 2258, 2177,
2096, 2017, 1943, 1868, 1798, 1731, 1667, 1602, 1540, 1478, 1418, 1355, 1293, 1233, 1170, 1108, 1050, 989, 927, 869,
808, 752, 694, 639, 588, 536, 484, 435, 386, 338, 294, 248, 202, 159, 113, 64, 16, -34, -81, -135,
-183, -232, -284, -335, -387, -435, -482, -530, -577, -623, -669, -712, -760, -805, -847, -890, -935, -978, -1025, -1072,
-1121, -1173, -1222, -1276, -1329, -1384, -1438, -1493, -1551, -1608, -1660, -1716, -1773, -1827, -1886, -1940, -1998, -2057, -2115, -2170,
-2236, -2295, -2358, -2426, -2493, -2565, -2638, -2713, -2789, -2867, -2946, -3027, -3107, -3189, -3273, -3356, -3439, -3524, -3611, -3697,
-3785, -3875, -3969, -4060, -4155, -4253, -4353, -4456, -4565, -4679, -4793, -4909, -5027, -5151, -5273, -5396, -5521, -5645, -5771, -5894,
-6020, -6146, -6269, -6396, -6522, -6646, -6773, -6895, -7020, -7150, -7275, -7398, -7526, -7650, -7772, -7894, -8009, -8123, -8227, -8325,
-8412, -8489, -8559, -8614, -8658, -8691, -8708, -8708, -8698, -8667, -8620, -8552, -8464, -8352, -8220, -8064, -7881, -7673, -7438, -7173,
-6874, -6543, -6179, -5779, -5347, -4882, -4385, -3860, -3308, -2726, -2133, -1519, -892, -254, 386, 1021, 1652, 2274, 2883, 3469,
4035, 4578, 5089, 5568, 6015, 6429, 6805, 7139, 7440, 7703, 7927, 8113, 8267, 8388, 8479, 8538, 8577, 8592, 8589, 8564,
8522, 8471, 8407, 8327, 8244, 8153, 8055, 7949, 7834, 7717, 7594, 7464, 7328, 7188, 7045, 6898, 6747, 6596, 6446, 6298,
6150, 6005, 5863, 5722, 5581, 5446, 5314, 5187, 5060, 4935, 4816, 4697, 4576, 4455, 4338, 4219, 4099, 3980, 3858, 3740,
3621, 3506, 3393, 3281, 3172, 3070, 2968, 2870, 2774, 2680, 2588, 2502, 2412, 2330, 2246, 2167, 2083, 2002, 1920, 1840,
1756, 1672, 1590, 1506, 1424, 1342, 1261, 1184, 1104, 1030, 959, 888, 821, 750, 682, 620, 555, 486, 426, 359,
295, 228, 162, 95, 27, -45, -117, -190, -261, -331, -404, -472, -540, -610, -672, -734, -798, -862, -924, -988,
-1050, -1109, -1175, -1237, -1303, -1368, -1437, -1506, -1576, -1650, -1726, -1798, -1877, -1951, -2027, -2105, -2178, -2252, -2327, -2400,
-2475, -2545, -2619, -2695, -2769, -2848, -2926, -3005, -3087, -3170, -3257, -3347, -3439, -3530, -3625, -3721, -3821, -3917, -4016, -4114,
-4211, -4308, -4403, -4499, -4592, -4688, -4786, -4884, -4983, -5080, -5183, -5288, -5391, -5496, -5606, -5717, -5829, -5941, -6054, -6166,
-6275, -6384, -6491, -6593, -6692, -6783, -6870, -6952, -7029, -7099, -7164, -7225, -7283, -7332, -7373, -7410, -7439, -7457, -7463, -7460,
-7444, -7414, -7365, -7302, -7218, -7110, -6980, -6819, -6636, -6420, -6177, -5903, -5599, -5265, -4905, -4514, -4098, -3655, -3184, -2688,
-2170, -1627, -1067, -493, 92, 686, 1285, 1884, 2477, 3066, 3649, 4213, 4766, 5292, 5797, 6271, 6715, 7126, 7502, 7850,
8160, 8433, 8678, 8888, 9068, 9216, 9335, 9426, 9491, 9528, 9548, 9544, 9519, 9475, 9415, 9334, 9239, 9132, 9008, 8879,
8739, 8592, 8442, 8286, 8131, 7971, 7809, 7651, 7489, 7328, 7169, 7008, 6847, 6687, 6527, 6370, 6211, 6051, 5894, 5737,
5578, 5422, 5263, 5111, 4960, 4812, 4669, 4533, 4398, 4268, 4142, 4021, 3904, 3791, 3678, 3568, 3461, 3357, 3251, 3150,
3050, 2950, 2851, 2752, 2659, 2564, 2470, 2376, 2290, 2202, 2116, 2038, 1961, 1888, 1815, 1745, 1680, 1615, 1549, 1488,
1425, 1361, 1300, 1237, 1178, 1117, 1056, 996, 939, 878, 819, 759, 702, 645, 592, 540, 489, 441, 392, 347,
302, 258, 212, 168, 123, 75, 30, -17, -64, -112, -160, -209, -255, -305, -353, -406, -451, -500, -547, -591,
-635, -677, -720, -763, -805, -845, -888, -932, -977, -1023, -1067, -1117, -1168, -1219, -1268, -1318, -1371, -1424, -1477, -1533,
-1585, -1642, -1694, -1746, -1801, -1854, -1909, -1961, -2015, -2073, -2132, -2189, -2254, -2317, -2381, -2448, -2518, -2589, -2661, -2735,
-2810, -2890, -2968, -3044, -3126, -3209, -3292, -3370, -3455, -3537, -3620, -3704, -3793, -3883, -3975, -4068, -4167, -4266, -4371, -4480,
-4587, -4704, -4817, -4933, -5052, -5171, -5292, -5415, -5539, -5667, -5791, -5913, -6037, -6162, -6286, -6408, -6531, -6658, -6784, -6911,
-7039, -7172, -7300, -7430, -7556, -7684, -7809, -7925, -8038, -8150, -8253, -8344, -8432, -8508, -8577, -8631, -8670, -8698, -8711, -8707,
-8690, -8654, -8602, -8533, -8440, -8333, -8198, -8042, -7856, -7645, -7406, -7134, -6833, -6496, -6131, -5731, -5305, -4845, -4357, -3842,
-3298, -2734, -2151, -1551, -938, -317, 308, 926, 1543, 2154, 2754, 3338, 3903, 4452, 4971, 5459, 5919, 6344, 6730, 7078,
7394, 7670, 7911, 8113, 8283, 8422, 8526, 8602, 8655, 8680, 8689, 8674, 8646, 8603, 8549, 8480, 8403, 8316, 8218, 8113,
7996, 7873, 7746, 7610, 7472, 7331, 7184, 7035, 6881, 6733, 6582, 6428, 6283, 6135, 5994, 5851, 5715, 5583, 5454, 5326,
5199, 5076, 4952, 4826, 4703, 4580, 4457, 4332, 4208, 4088, 3966, 3846, 3727, 3612, 3500, 3388, 3278, 3175, 3077, 2979,
2883, 2793, 2705, 2620, 2533, 2449, 2368, 2283, 2197, 2114, 2028, 1944, 1858, 1772, 1691, 1610, 1528, 1444, 1368, 1290,
1213, 1140, 1069, 1001, 933, 863, 801, 739, 671, 607, 545, 478, 411, 340, 274, 204, 132, 62, -7, -80,
-148, -218, -289, -355, -419, -488, -549, -612, -678, -737, -799, -863, -921, -983, -1048, -1112, -1177, -1248, -1316, -1390,
-1462, -1535, -1608, -1681, -1755, -1828, -1906, -1978, -2050, -2123, -2197, -2267, -2339, -2410, -2483, -2557, -2630, -2708, -2786, -2868,
-2950, -3038, -3126, -3218, -3309, -3404, -3495, -3589, -3686, -3779, -3876, -3969, -4065, -4158, -4255, -4346, -4443, -4536, -4632, -4730,
-4829, -4929, -5035, -5138, -5249, -5359, -5471, -5588, -5703, -5817, -5930, -6043, -6153, -6261, -6365, -6466, -6567, -6659, -6750, -6836,
-6917, -6995, -7067, -7133, -7198, -7255, -7308, -7355, -7392, -7426, -7448, -7460, -7459, -7444, -7410, -7360, -7285, -7191, -7072, -6929,
-6763, -6568, -6345, -6098, -5816, -5509, -5171, -4806, -4417, -3997, -3550, -3079, -2583, -2063, -1523, -964, -392, 191, 785, 1383,
1981, 2577, 3170, 3748, 4313, 4859, 5384, 5880, 6348, 6787, 7192, 7563, 7902, 8206, 8479, 8719, 8924, 9103, 9252, 9370,
9463, 9524, 9564, 9576, 9568, 9536, 9486, 9418, 9332, 9233, 9121, 9002, 8869, 8732, 8592, 8441, 8288, 8132, 7974, 7817,
7659, 7498, 7342, 7185, 7025, 6862, 6700, 6537, 6374, 6209, 6043, 5883, 5719, 5556, 5399, 5246, 5095, 4946, 4804, 4667,
4529, 4397, 4268, 4143, 4026, 3908, 3795, 3682, 3574, 3466, 3354, 3248, 3142, 3036, 2931, 2832, 2729, 2629, 2533, 2442,
2353, 2267, 2183, 2102, 2023, 1949, 1873, 1801, 1735, 1666, 1597, 1533, 1469, 1404, 1339, 1271, 1209, 1142, 1078, 1015,
954, 894, 828, 770, 715, 660, 603, 555, 503, 453, 405, 355, 310, 265, 217, 171, 125, 77, 28, -20,
-71, -120, -172, -220, -272, -322, -371, -420, -468, -513, -557, -604, -646, -687, -733, -776, -818, -861, -905, -951,
-995, -1040, -1089, -1136, -1189, -1237, -1289, -1345, -1395, -1448, -1498, -1553, -1603, -1654, -1706, -1756, -1808, -1860, -1911, -1966,
-2022, -2079, -2135, -2195, -2254, -2316, -2381, -2450, -2521, -2590, -2662, -2737, -2813, -2888, -2963, -3041, -3116, -3197, -3274, -3352,
-3430, -3513, -3594, -3681, -3767, -3858, -3950, -4041, -4141, -4238, -4340, -4449, -4560, -4673, -4786, -4902, -5022, -5140, -5260, -5376,
-5498, -5620, -5741, -5859, -5984, -6105, -6228, -6356, -6482, -6613, -6742, -6872, -7005, -7140, -7273, -7406, -7540, -7674, -7804, -7931,
-8056, -8173, -8281, -8384, -8478, -8564, -8638, -8704, -8757, -8803, -8832, -8852, -8857, -8851, -8828, -8786, -8725, -8646, -8544, -8418,
-8268, -8092, -7888, -7652, -7385, -7085, -6751, -6382, -5979, -5544, -5075, -4578, -4049, -3499, -2926, -2328, -1715, -1091, -457, 181,
820, 1456, 2082, 2697, 3296, 3876, 4428, 4954, 5448, 5907, 6327, 6713, 7058, 7362, 7630, 7860, 8054, 8219, 8347, 8448,
8524, 8572, 8600, 8608, 8596, 8571, 8525, 8466, 8398, 8317, 8223, 8122, 8009, 7889, 7763, 7628, 7491, 7345, 7200, 7048,
6897, 6746, 6598, 6452, 6309, 6168, 6031, 5893, 5757, 5626, 5495, 5366, 5239, 5111, 4985, 4857, 4731, 4604, 4478, 4350,
4223, 4098, 3975, 3851, 3730, 3614, 3505, 3393, 3288, 3187, 3092, 2996, 2902, 2809, 2722, 2633, 2542, 2458, 2372, 2287,
2197, 2110, 2024, 1936, 1849, 1763, 1678, 1593, 1511, 1428, 1355, 1277, 1204, 1136, 1066, 998, 934, 869, 802, 738,
670, 606, 540, 471, 402, 332, 263, 193, 120, 49, -22, -94, -165, -234, -301, -366, -429, -491, -552, -614,
-674, -737, -799, -859, -922, -988, -1050, -1116, -1183, -1252, -1323, -1395, -1466, -1540, -1613, -1685, -1759, -1832, -1904, -1973,
-2045, -2112, -2180, -2247, -2317, -2388, -2461, -2534, -2609, -2690, -2767, -2848, -2932, -3019, -3108, -3198, -3286, -3379, -3476, -3568,
-3660, -3752, -3844, -3936, -4028, -4120, -4206, -4296, -4388, -4483, -4580, -4676, -4777, -4881, -4985, -5092, -5199, -5309, -5423, -5536,
-5648, -5760, -5872, -5979, -6085, -6192, -6296, -6393, -6484, -6575, -6664, -6747, -6826, -6904, -6979, -7053, -7122, -7187, -7249, -7299,
-7348, -7386, -7416, -7434, -7437, -7427, -7401, -7356, -7293, -7206, -7100, -6971, -6816, -6634, -6426, -6193, -5930, -5641, -5325, -4984,
-4613, -4214, -3786, -3331, -2848, -2337, -1802, -1241, -663, -69, 540, 1152, 1771, 2387, 2997, 3599, 4179, 4743, 5283, 5796,
6278, 6725, 7143, 7527, 7873, 8191, 8473, 8722, 8934, 9120, 9270, 9393, 9482, 9546, 9585, 9595, 9588, 9558, 9507, 9438,
9353, 9257, 9142, 9024, 8892, 8761, 8621, 8478, 8329, 8182, 8033, 7880, 7726, 7572, 7413, 7254, 7089, 6927, 6765, 6601,
6436, 6271, 6109, 5944, 5783, 5621, 5465, 5311, 5162, 5019, 4878, 4743, 4611, 4483, 4361, 4239, 4119, 4004, 3891, 3775,
3662, 3549, 3438, 3330, 3224, 3117, 3016, 2912, 2811, 2715, 2621, 2530, 2443, 2355, 2276, 2197, 2121, 2048, 1975, 1904,
1838, 1769, 1703, 1634, 1567, 1502, 1431, 1364, 1300, 1233, 1170, 1105, 1043, 980, 921, 863, 806, 753, 699, 650,
601, 555, 506, 460, 411, 365, 316, 271, 219, 175, 121, 73, 21, -27, -81, -127, -178, -227, -277, -327,
-372, -417, -462, -507, -546, -591, -633, -677, -720, -763, -810, -860, -904, -952, -1002, -1054, -1107, -1157, -1211, -1260,
-1314, -1365, -1418, -1471, -1523, -1573, -1627, -1679, -1727, -1781, -1834, -1890, -1948, -2004, -2061, -2128, -2190, -2255, -2323, -2393,
-2465, -2536, -2610, -2685, -2757, -2830, -2909, -2984, -3064, -3141, -3216, -3296, -3378, -3457, -3541, -3627, -3716, -3804, -3902, -3999,
-4100, -4204, -4311, -4418, -4533, -4646, -4760, -4875, -4993, -5108, -5228, -5344, -5465, -5588, -5705, -5826, -5949, -6070, -6197, -6320,
-6451, -6582, -6713, -6847, -6983, -7119, -7255, -7392, -7525, -7659, -7785, -7906, -8023, -8134, -8238, -8333, -8422, -8500, -8571, -8629,
-8677, -8716, -8740, -8753, -8750, -8738, -8707, -8659, -8590, -8505, -8392, -8257, -8092, -7902, -7679, -7420, -7129, -6807, -6444, -6052,
-5622, -5162, -4669, -4144, -3590, -3014, -2412, -1791, -1156, -510, 139, 797, 1448, 2088, 2723, 3338, 3929, 4492, 5025, 5523,
5985, 6409, 6790, 7139, 7442, 7706, 7937, 8128, 8287, 8414, 8508, 8582, 8628, 8654, 8658, 8642, 8614, 8570, 8515, 8447,
8365, 8272, 8166, 8050, 7926, 7796, 7658, 7521, 7375, 7228, 7079, 6930, 6781, 6637, 6490, 6347, 6207, 6071, 5936, 5801,
5669, 5544, 5414, 5290, 5159, 5032, 4905, 4775, 4644, 4515, 4387, 4258, 4132, 4010, 3889, 3768, 3652, 3542, 3434, 3327,
3226, 3130, 3031, 2937, 2845, 2755, 2669, 2578, 2493, 2405, 2315, 2223, 2133, 2043, 1955, 1864, 1777, 1691, 1610, 1524,
1442, 1367, 1295, 1217, 1149, 1079, 1011, 945, 877, 811, 749, 680, 612, 546, 474, 404, 330, 256, 184, 111,
40, -34, -104, -172, -242, -310, -373, -439, -503, -564, -626, -687, -750, -814, -877, -938, -1006, -1067, -1139, -1207,
-1281, -1353, -1424, -1498, -1573, -1645, -1715, -1790, -1858, -1931, -2001, -2069, -2139, -2209, -2277, -2346, -2417, -2493, -2566, -2641,
-2718, -2800, -2883, -2968, -3055, -3146, -3238, -3329, -3422, -3514, -3606, -3696, -3788, -3875, -3968, -4059, -4145, -4239, -4331, -4425,
-4519, -4615, -4714, -4814, -4916, -5024, -5132, -5240, -5354, -5467, -5583, -5694, -5809, -5921, -6027, -6129, -6234, -6333, -6428, -6522,
-6612, -6696, -6784, -6863, -6944, -7020, -7095, -7166, -7228, -7290, -7347, -7395, -7435, -7465, -7488, -7494, -7485, -7457, -7416, -7352,
-7266, -7158, -7029, -6878, -6700, -6497, -6271, -6015, -5736, -5430, -5095, -4733, -4341, -3922, -3472, -2995, -2492, -1961, -1412, -836,
-244, 362, 979, 1600, 2225, 2845, 3455, 4048, 4621, 5174, 5699, 6192, 6657, 7088, 7486, 7849, 8176, 8471, 8732, 8957,
9150, 9312, 9441, 9541, 9609, 9652, 9670, 9658, 9628, 9575, 9506, 9420, 9318, 9207, 9086, 8959, 8822, 8684, 8540, 8390,
8240, 8086, 7933, 7774, 7614, 7457, 7295, 7131, 6964, 6797, 6630, 6462, 6293, 6125, 5958, 5793, 5633, 5474, 5322, 5173,
5029, 4889, 4754, 4624, 4492, 4366, 4243, 4125, 4007, 3888, 3776, 3662, 3547, 3434, 3324, 3216, 3106, 2998, 2895, 2798,
2698, 2604, 2513, 2429, 2342, 2264, 2184, 2110, 2037, 1963, 1892, 1823, 1756, 1685, 1621, 1552, 1485, 1416, 1349, 1281,
1218, 1150, 1088, 1025, 965, 905, 847, 792, 743, 691, 642, 595, 545, 499, 450, 402, 357, 308, 260, 212,
162, 111, 59, 8, -42, -92, -141, -189, -236, -286, -331, -378, -420, -464, -506, -548, -590, -632, -677, -723,
-763, -808, -857, -903, -951, -999, -1049, -1101, -1153, -1201, -1254, -1304, -1356, -1405, -1457, -1506, -1554, -1602, -1654, -1704,
-1755, -1808, -1862, -1918, -1975, -2033, -2096, -2160, -2224, -2290, -2359, -2429, -2500, -2570, -2641, -2716, -2788, -2859, -2933, -3007,
-3082, -3155, -3233, -3310, -3389, -3469, -3556, -3643, -3735, -3830, -3925, -4025, -4127, -4232, -4336, -4446, -4558, -4671, -4783, -4899,
-5013, -5127, -5243, -5359, -5479, -5592, -5711, -5833, -5955, -6079, -6205, -6336, -6470, -6606, -6738, -6878, -7013, -7151, -7288, -7423,
-7558, -7687, -7813, -7936, -8053, -8160, -8262, -8358, -8442, -8521, -8588, -8647, -8697, -8735, -8763, -8782, -8786, -8776, -8751, -8703,
-8639, -8552, -8441, -8304, -8139, -7950, -7724, -7466, -7180, -6857, -6501, -6108, -5684, -5230, -4744, -4225, -3681, -3113, -2518, -1905,
-1274, -635, 15, 670, 1328, 1975, 2618, 3245, 3852, 4429, 4980, 5494, 5970, 6407, 6805, 7162, 7479, 7755, 7993, 8201,
8369, 8507, 8616, 8700, 8755, 8789, 8801, 8792, 8769, 8725, 8665, 8594, 8506, 8407, 8297, 8177, 8051, 7917, 7773, 7632,
7481, 7331, 7179, 7027, 6880, 6736, 6591, 6451, 6313, 6178, 6042, 5907, 5776, 5645, 5510, 5379, 5246, 5111, 4976, 4843,
4709, 4578, 4446, 4315, 4189, 4065, 3943, 3824, 3712, 3604, 3498, 3396, 3299, 3202, 3109, 3016, 2923, 2833, 2740, 2649,
2559, 2468, 2376, 2283, 2192, 2104, 2013, 1927, 1843, 1757, 1675, 1595, 1516, 1441, 1372, 1301, 1233, 1168, 1102, 1036,
969, 903, 833, 764, 696, 624, 555, 481, 409, 335, 263, 193, 123, 54, -16, -83, -150, -215, -274, -336,
-398, -457, -517, -574, -639, -701, -764, -832, -900, -968, -1038, -1105, -1181, -1254, -1322, -1395, -1468, -1535, -1607, -1675,
-1742, -1812, -1879, -1945, -2013, -2079, -2147, -2217, -2292, -2365, -2440, -2520, -2604, -2685, -2769, -2854, -2945, -3034, -3122, -3212,
-3300, -3391, -3479, -3567, -3658, -3747, -3834, -3922, -4010, -4103, -4192, -4287, -4382, -4484, -4585, -4687, -4796, -4908, -5020, -5130,
-5243, -5359, -5472, -5584, -5692, -5805, -5908, -6015, -6120, -6219, -6318, -6415, -6507, -6598, -6686, -6776, -6861, -6948, -7030, -7114,
-7191, -7266, -7334, -7391, -7443, -7484, -7512, -7527, -7530, -7514, -7480, -7430, -7360, -7270, -7163, -7032, -6878, -6701, -6504, -6276,
-6033, -5762, -5468, -5144, -4793, -4413, -4002, -3562, -3093, -2596, -2073, -1530, -962, -377, 222, 835, 1451, 2066, 2684, 3286,
3881, 4456, 5008, 5532, 6031, 6499, 6936, 7339, 7714, 8056, 8363, 8635, 8878, 9079, 9250, 9382, 9485, 9561, 9606, 9624,
9619, 9591, 9545, 9476, 9394, 9300, 9194, 9079, 8955, 8825, 8694, 8553, 8409, 8262, 8114, 7957, 7799, 7637, 7474, 7301,
7132, 6958, 6785, 6614, 6440, 6272, 6104, 5937, 5772, 5616, 5462, 5313, 5168, 5027, 4890, 4755, 4627, 4497, 4373, 4247,
4123, 4000, 3880, 3759, 3636, 3519, 3403, 3288, 3175, 3070, 2963, 2862, 2763, 2669, 2576, 2490, 2407, 2323, 2244, 2169,
2091, 2017, 1942, 1873, 1797, 1726, 1655, 1582, 1509, 1436, 1366, 1293, 1225, 1158, 1096, 1035, 974, 918, 862, 808,
756, 704, 655, 606, 555, 504, 457, 407, 359, 306, 257, 201, 151, 99, 45, -4, -56, -108, -156, -204,
-251, -294, -342, -389, -429, -476, -517, -556, -600, -641, -688, -734, -778, -826, -872, -922, -968, -1018, -1070, -1122,
-1170, -1221, -1267, -1315, -1361, -1409, -1460, -1508, -1552, -1600, -1649, -1698, -1749, -1797, -1855, -1908, -1965, -2024, -2084, -2147,
-2210, -2273, -2340, -2409, -2475, -2544, -2611, -2678, -2747, -2815, -2884, -2957, -3027, -3097, -3172, -3250, -3328, -3407, -3490, -3577,
-3667, -3758, -3854, -3954, -4050, -4154, -4260, -4365, -4472, -4579, -4685, -4795, -4902, -5010, -5123, -5235, -5350, -5463, -5578, -5702,
-5822, -5947, -6076, -6206, -6342, -6476, -6612, -6751, -6891, -7030, -7168, -7305, -7441, -7570, -7695, -7818, -7934, -8046, -8150, -8250,
-8344, -8433, -8512, -8586, -8651, -8707, -8758, -8794, -8822, -8832, -8832, -8811, -8775, -8717, -8635, -8527, -8398, -8235, -8048, -7826,
-7573, -7290, -6973, -6627, -6244, -5834, -5391, -4915, -4416, -3882, -3322, -2740, -2136, -1514, -876, -226, 431, 1088, 1744, 2392,
3023, 3632, 4215, 4766, 5286, 5766, 6211, 6613, 6978, 7303, 7590, 7846, 8062, 8245, 8404, 8522, 8618, 8685, 8727, 8752,
8749, 8726, 8685, 8628, 8554, 8464, 8359, 8247, 8122, 7992, 7856, 7719, 7577, 7434, 7290, 7148, 7010, 6868, 6730, 6592,
6456, 6322, 6188, 6054, 5922, 5784, 5650, 5514, 5375, 5238, 5097, 4956, 4821, 4685, 4549, 4423, 4294, 4175, 4054, 3940,
3830, 3723, 3619, 3518, 3420, 3322, 3226, 3130, 3035, 2942, 2845, 2751, 2654, 2559, 2463, 2368, 2271, 2182, 2090, 2003,
1919, 1836, 1756, 1676, 1602, 1533, 1459, 1392, 1324, 1255, 1188, 1117, 1050, 980, 911, 838, 769, 694, 622, 545,
472, 402, 327, 255, 190, 124, 58, -8, -70, -128, -188, -249, -308, -369, -429, -491, -557, -619, -684, -755,
-822, -891, -961, -1033, -1107, -1177, -1249, -1318, -1385, -1456, -1521, -1586, -1654, -1719, -1780, -1847, -1914, -1981, -2053, -2123,
-2198, -2275, -2351, -2429, -2514, -2594, -2683, -2765, -2855, -2944, -3023, -3114, -3200, -3282, -3367, -3450, -3535, -3619, -3703, -3787,
-3875, -3962, -4057, -4150, -4249, -4350, -4453, -4558, -4666, -4775, -4884, -4996, -5107, -5218, -5329, -5437, -5542, -5650, -5748, -5849,
-5947, -6045, -6141, -6238, -6334, -6429, -6520, -6614, -6705, -6799, -6888, -6975, -7058, -7139, -7210, -7271, -7328, -7375, -7411, -7432,
-7438, -7429, -7407, -7363, -7306, -7233, -7140, -7029, -6897, -6749, -6582, -6385, -6169, -5929, -5662, -5366, -5039, -4683, -4297, -3875,
-3426, -2943, -2433, -1893, -1330, -748, -149, 464, 1083, 1709, 2327, 2938, 3541, 4124, 4683, 5224, 5734, 6220, 6673, 7099,
7493, 7853, 8178, 8469, 8725, 8943, 9129, 9280, 9395, 9484, 9538, 9565, 9574, 9555, 9517, 9462, 9394, 9313, 9222, 9117,
9008, 8892, 8767, 8633, 8495, 8354, 8206, 8053, 7897, 7736, 7572, 7401, 7232, 7063, 6890, 6718, 6548, 6380, 6215, 6055,
5897, 5746, 5597, 5450, 5311, 5171, 5037, 4904, 4770, 4641, 4513, 4381, 4255, 4127, 4004, 3877, 3752, 3634, 3518, 3401,
3285, 3177, 3075, 2972, 2874, 2784, 2696, 2611, 2524, 2445, 2366, 2288, 2211, 2133, 2058, 1982, 1903, 1830, 1753, 1679,
1604, 1529, 1460, 1393, 1323, 1255, 1195, 1133, 1072, 1017, 961, 907, 855, 804, 754, 703, 654, 600, 550, 498,
443, 388, 336, 284, 228, 176, 122, 70, 20, -30, -76, -124, -168, -217, -262, -304, -345, -392, -434, -477,
-520, -567, -613, -660, -711, -761, -808, -858, -911, -959, -1012, -1063, -1110, -1164, -1213, -1258, -1304, -1357, -1404, -1452,
-1497, -1549, -1596, -1650, -1701, -1757, -1814, -1872, -1934, -1997, -2060, -2124, -2190, -2257, -2328, -2393, -2461, -2527, -2598, -2663,
-2732, -2800, -2870, -2942, -3011, -3085, -3163, -3239, -3321, -3408, -3496, -3587, -3680, -3772, -3877, -3972, -4077, -4179, -4286, -4392,
-4496, -4603, -4708, -4818, -4925, -5033, -5143, -5257, -5369, -5485, -5605, -5727, -5851, -5980, -6110, -6246, -6381, -6519, -6656, -6798,
-6934, -7071, -7203, -7337, -7469, -7589, -7711, -7829, -7937, -8042, -8143, -8240, -8328, -8412, -8490, -8564, -8629, -8686, -8731, -8766,
-8791, -8798, -8793, -8762, -8715, -8647, -8548, -8430, -8280, -8106, -7894, -7660, -7392, -7087, -6753, -6384, -5986, -5552, -5087, -4592,
-4067, -3514, -2936, -2329, -1707, -1066, -412, 248, 911, 1570, 2219, 2853, 3461, 4046, 4596, 5113, 5589, 6031, 6435, 6801,
7130, 7420, 7678, 7898, 8087, 8249, 8380, 8482, 8559, 8608, 8637, 8643, 8624, 8590, 8537, 8465, 8378, 8282, 8173, 8060,
7934, 7805, 7673, 7541, 7406, 7267, 7130, 6998, 6865, 6732, 6603, 6474, 6344, 6214, 6083, 5949, 5813, 5677, 5539, 5402,
5259, 5120, 4982, 4846, 4711, 4579, 4448, 4324, 4204, 4085, 3969, 3860, 3755, 3649, 3549, 3452, 3353, 3254, 3161, 3061,
2965, 2866, 2767, 2672, 2568, 2473, 2375, 2280, 2186, 2098, 2009, 1925, 1842, 1761, 1683, 1610, 1537, 1469, 1397, 1330,
1259, 1193, 1123, 1049, 978, 904, 832, 758, 681, 605, 528, 455, 382, 311, 239, 170, 101, 35, -29, -91,
-155, -212, -275, -336, -396, -460, -524, -590, -658, -724, -795, -867, -939, -1010, -1082, -1155, -1226, -1297, -1366, -1436,
-1500, -1566, -1632, -1698, -1764, -1827, -1893, -1960, -2028, -2096, -2172, -2244, -2322, -2403, -2483, -2569, -2654, -2739, -2825, -2908,
-3001, -3084, -3168, -3254, -3338, -3418, -3501, -3585, -3671, -3756, -3840, -3928, -4023, -4108, -4206, -4305, -4407, -4511, -4621, -4727,
-4838, -4948, -5056, -5171, -5281, -5387, -5493, -5594, -5701, -5799, -5897, -5993, -6090, -6188, -6282, -6374, -6473, -6565, -6660, -6753,
-6848, -6940, -7032, -7116, -7195, -7270, -7334, -7391, -7434, -7462, -7483, -7483, -7473, -7449, -7405, -7346, -7271, -7178, -7066, -6934,
-6780, -6610, -6411, -6189, -5936, -5664, -5356, -5016, -4645, -4238, -3793, -3315, -2805, -2263, -1696, -1101, -485, 143, 781, 1427,
2071, 2710, 3333, 3942, 4530, 5094, 5632, 6146, 6625, 7076, 7490, 7869, 8215, 8528, 8792, 9029, 9222, 9382, 9508, 9600,
9660, 9695, 9702, 9688, 9647, 9595, 9526, 9442, 9350, 9246, 9133, 9014, 8887, 8759, 8619, 8472, 8326, 8172, 8009, 7846,
7678, 7509, 7332, 7157, 6983, 6807, 6632, 6463, 6295, 6132, 5972, 5814, 5661, 5515, 5371, 5226, 5091, 4953, 4823, 4687,
4558, 4427, 4299, 4169, 4042, 3915, 3791, 3666, 3545, 3432, 3321, 3205, 3104, 2998, 2903, 2808, 2716, 2629, 2545, 2461,
2380, 2301, 2224, 2149, 2070, 1993, 1919, 1842, 1766, 1692, 1617, 1544, 1468, 1395, 1327, 1261, 1198, 1136, 1079, 1022,
965, 912, 860, 809, 757, 709, 657, 603, 551, 500, 447, 392, 336, 286, 231, 178, 125, 69, 22, -30,
-79, -121, -168, -211, -256, -299, -343, -384, -427, -468, -511, -556, -602, -650, -699, -745, -796, -845, -893, -943,
-993, -1044, -1091, -1140, -1188, -1233, -1277, -1325, -1366, -1415, -1463, -1509, -1557, -1608, -1659, -1710, -1768, -1821, -1882, -1942,
-2001, -2067, -2131, -2196, -2261, -2326, -2395, -2461, -2525, -2591, -2657, -2722, -2788, -2855, -2925, -2996, -3069, -3145, -3226, -3304,
-3388, -3474, -3567, -3661, -3754, -3851, -3954, -4051, -4155, -4256, -4362, -4465, -4567, -4674, -4779, -4885, -4993, -5100, -5212, -5327,
-5444, -5562, -5691, -5813, -5945, -6079, -6217, -6357, -6494, -6633, -6778, -6917, -7055, -7193, -7326, -7455, -7586, -7707, -7823, -7935,
-8045, -8151, -8252, -8349, -8437, -8525, -8606, -8678, -8742, -8794, -8841, -8871, -8885, -8882, -8864, -8820, -8752, -8658, -8547, -8401,
-8225, -8023, -7782, -7513, -7210, -6875, -6505, -6102, -5668, -5196, -4689, -4157, -3584, -2988, -2363, -1718, -1055, -378, 307, 990,
1674, 2348, 2995, 3624, 4218, 4780, 5303, 5789, 6236, 6644, 7013, 7341, 7633, 7892, 8118, 8306, 8458, 8588, 8686, 8757,
8803, 8818, 8814, 8792, 8746, 8686, 8609, 8515, 8408, 8292, 8171, 8041, 7905, 7773, 7636, 7496, 7360, 7222, 7085, 6953,
6820, 6687, 6551, 6419, 6283, 6146, 6006, 5867, 5730, 5587, 5446, 5300, 5162, 5020, 4880, 4746, 4613, 4484, 4359, 4240,
4128, 4012, 3902, 3800, 3699, 3595, 3498, 3394, 3301, 3200, 3102, 3004, 2904, 2804, 2706, 2606, 2509, 2414, 2317, 2228,
2140, 2050, 1968, 1888, 1813, 1741, 1665, 1597, 1531, 1460, 1390, 1323, 1255, 1187, 1113, 1041, 968, 895, 823, 747,
672, 603, 528, 457, 386, 322, 251, 191, 127, 69, 10, -52, -105, -168, -231, -287, -351, -415, -485, -553,
-619, -686, -757, -827, -899, -965, -1036, -1106, -1174, -1239, -1303, -1373, -1434, -1498, -1559, -1625, -1685, -1751, -1816, -1883,
-1952, -2025, -2100, -2181, -2260, -2342, -2423, -2506, -2588, -2675, -2760, -2844, -2928, -3009, -3089, -3172, -3254, -3335, -3414, -3497,
-3583, -3668, -3756, -3847, -3941, -4040, -4141, -4244, -4351, -4459, -4569, -4678, -4792, -4902, -5013, -5123, -5233, -5341, -5445, -5551,
-5655, -5754, -5857, -5958, -6060, -6163, -6267, -6375, -6481, -6587, -6697, -6804, -6912, -7017, -7114, -7209, -7298, -7378, -7449, -7515,
-7568, -7613, -7644, -7657, -7664, -7652, -7629, -7588, -7538, -7475, -7389, -7285, -7166, -7022, -6857, -6664, -6444, -6192, -5909, -5587,
-5230, -4834, -4398, -3930, -3423, -2883, -2310, -1709, -1084, -439, 223, 888, 1563, 2233, 2893, 3540, 4172, 4776, 5362, 5918,
6444, 6939, 7395, 7820, 8204, 8545, 8849, 9110, 9330, 9510, 9653, 9760, 9838, 9882, 9898, 9898, 9865, 9817, 9757, 9680,
9593, 9492, 9382, 9265, 9136, 9000, 8856, 8707, 8551, 8383, 8214, 8042, 7864, 7686, 7504, 7320, 7141, 6963, 6786, 6610,
6442, 6276, 6112, 5955, 5802, 5655, 5505, 5360, 5221, 5077, 4937, 4796, 4656, 4521, 4382, 4249, 4113, 3982, 3854, 3728,
3608, 3490, 3377, 3263, 3164, 3062, 2966, 2871, 2783, 2696, 2616, 2527, 2447, 2367, 2286, 2206, 2125, 2043, 1963, 1882,
1807, 1729, 1655, 1581, 1506, 1438, 1374, 1306, 1248, 1190, 1135, 1076, 1019, 969, 919, 863, 813, 763, 708, 656,
598, 546, 490, 438, 382, 328, 10, -534, -1077, -759, -710, -459, -349, -49, 162, 490, 782, 1100, 1365, 1683,
1934, 2205, 2435, 2680, 2868, 3051, 3183, 3325, 3428, 3565, 3678, 3833, 3973, 4098, 4189, 4288, 4363, 4451, 4518, 4635,
4730, 4856, 4980, 5135, 5275, 5464, 5644, 5889, 6124, 6370, 6568, 6802, 6972, 7180, 7334, 7498, 7675, 7858, 8016, 8162,
8270, 8364, 8430, 8484, 8523, 8536, 8499, 8465, 8370, 8277, 8155, 8028, 7926, 7831, 7732, 7642, 7542, 7432, 7313, 7214,
7114, 7022, 6928, 6844, 6759, 6660, 6564, 6469, 6409, 6352, 6290, 6216, 6139, 6029, 5899, 5739, 5569, 5389, 5191, 4953,
4723, 4457, 4199, 3905, 3610, 3333, 3048, 2752, 2444, 2110, 1735, 1356, 969, 590, 216, -159, -514, -849, -1177, -1502,
-1809, -2093, -2354, -2598, -2818, -3010, -3208, -3386, -3559, -3697, -3815, -3900, -3981, -4005, -4038, -4053, -4094, -4131, -4150, -4182,
-4215, -4261, -4346, -4431, -4554, -4686, -4842, -5003, -5197, -5352, -5539, -5740, -5970, -6217, -6474, -6737, -7004, -7278, -7560, -7845,
-8122, -8410, -8685, -8939, -9189, -9391, -9566, -9734, -9869, -9998, -10115, -10198, -10253, -10298, -10309, -10307, -10280, -10265, -10222, -10181,
-10138, -10084, -10001, -9904, -9820, -9745, -9678, -9587, -9527, -9476, -9409, -9366, -9315, -9284, -9256, -9246, -9246, -9255, -9253, -9249,
-9254, -9226, -9212, -9192, -9143, -9102, -9037, -8943, -8833, -8696, -8568, -8423, -8268, -8104, -7942, -7761, -7566, -7336, -7138, -6892,
-6635, -6378, -6131, -5867, -5616, -5352, -5131, -4903, -4689, -4503, -4334, -4162, -4009, -3854, -3702, -3535, -3348, -3167, -2997, -2824,
-2666, -2503, -2350, -2220, -2072, -1942, -1837, -1724, -1633, -1532, -1409, -1294, -1132, -981, -826, -667, -523, -386, -274, -206,
-115, -34, 17, 50, 88, 94, 115, 127, 154, 187, 227, 242, 259, 251, 221, 160, 98, 30, -33, -100,
-155, -220, -283, -327, -357, -367, -353, -332, -317, -304, -312, -323, -355, -359, -356, -334, -306, -261, -220, -136,
-69, 37, 149, 262, 376, 510, 610, 698, 756, 816, 901, 999, 1084, 1200, 1301, 1413, 1528, 1636, 1771, 1897,
2014, 2136, 2236, 2320, 2380, 2428, 2478, 2558, 2629, 2725, 2829, 2948, 3079, 3199, 3343, 3493, 3650, 3813, 3996, 4148,
4306, 4457, 4619, 4815, 5020, 5232, 5488, 5722, 5993, 6239, 6503, 6768, 7029, 7289, 7515, 7761, 7949, 8148, 8306, 8470,
8624, 8775, 8913, 9049, 9165, 9248, 9328, 9403, 9460, 9487, 9503, 9503, 9472, 9426, 9355, 9292, 9233, 9157, 9107, 9059,
9010, 8944, 8885, 8841, 8803, 8739, 8707, 8679, 8624, 8572, 8516, 8455, 8416, 8373, 8338, 8314, 8283, 8244, 8198, 8147,
8089, 8030, 7966, 7891, 7791, 7698, 7556, 7398, 7233, 7097, 6939, 6764, 6594, 6418, 6216, 6005, 5803, 5603, 5384, 5182,
4970, 4751, 4516, 4281, 4042, 3824, 3596, 3387, 3190, 2982, 2776, 2563, 2364, 2152, 1958, 1768, 1580, 1384, 1201, 992,
775, 570, 367, 163, -30, -228, -430, -649, -866, -1087, -1308, -1538, -1737, -1946, -2161, -2384, -2614, -2828, -3044, -3256,
-3451, -3640, -3846, -4019, -4227, -4407, -4596, -4786, -4953, -5096, -5243, -5385, -5527, -5668, -5802, -5930, -6061, -6178, -6283, -6402,
-6531, -6655, -6801, -6940, -7079, -7211, -7317, -7434, -7568, -7688, -7819, -7936, -8086, -8203, -8333, -8459, -8586, -8730, -8860, -8996,
-9135, -9242, -9334, -9402, -9475, -9526, -9561, -9580, -9612, -9625, -9635, -9627, -9595, -9583, -9563, -9514, -9464, -9405, -9313, -9216,
-9094, -8972, -8844, -8688, -8560, -8446, -8322, -8217, -8105, -8010, -7918, -7823, -7725, -7654, -7549, -7448, -7346, -7227, -7108, -6982,
-6876, -6779, -6673, -6600, -6528, -6450, -6373, -6288, -6174, -6063, -5921, -5761, -5583, -5382, -5184, -4968, -4740, -4530, -4317, -4119,
-3927, -3726, -3544, -3346, -3132, -2903, -2679, -2428, -2188, -1951, -1728, -1520, -1323, -1137, -989, -854, -749, -667, -602, -554,
-500, -430, -373, -300, -244, -169, -121, -93, -78, -64, -62, -77, -79, -112, -137, -174, -188, -177, -162, -121,
-50, 3, 70, 104, 146, 176, 208, 219, 254, 273, 295, 295, 328, 355, 396, 444, 511, 568, 608, 652,
658, 652, 642, 608, 590, 564, 551, 537, 520, 508, 525, 540, 581, 650, 711, 771, 805, 842, 877, 921,
957, 1035, 1108, 1202, 1308, 1427, 1575, 1723, 1880, 2065, 2242, 2419, 2576, 2727, 2863, 2996, 3128, 3281, 3411, 3576,
3738, 3908, 4069, 4244, 4413, 4602, 4760, 4935, 5082, 5213, 5349, 5475, 5603, 5730, 5884, 6030, 6200, 6347, 6526, 6710,
6896, 7068, 7264, 7427, 7586, 7735, 7872, 7999, 8136, 8265, 8396, 8524, 8647, 8762, 8877, 8960, 9058, 9131, 9215, 9257,
9294, 9299, 9286, 9256, 9235, 9194, 9172, 9121, 9086, 9014, 8940, 8863, 8779, 8692, 8605, 8518, 8426, 8317, 8195, 8073,
7972, 7867, 7768, 7692, 7596, 7516, 7409, 7307, 7208, 7099, 7000, 6913, 6804, 6683, 6567, 6437, 6309, 6173, 6037, 5922,
5780, 5656, 5493, 5329, 5149, 4966, 4755, 4574, 4371, 4171, 3948, 3734, 3512, 3299, 3040, 2833, 2633, 2409, 2202, 1958,
1733, 1493, 1249, 1026, 813, 591, 366, 158, -54, -264, -477, -681, -860, -1059, -1225, -1413, -1625, -1808, -2003, -2206,
-2393, -2580, -2747, -2921, -3100, -3269, -3466, -3652, -3814, -3980, -4133, -4308, -4492, -4672, -4853, -5049, -5232, -5416, -5584, -5746,
-5907, -6074, -6235, -6416, -6560, -6707, -6848, -6998, -7132, -7279, -7414, -7571, -7714, -7853, -7980, -8089, -8202, -8302, -8394, -8488,
-8591, -8669, -8753, -8812, -8873, -8931, -8986, -9045, -9119, -9162, -9224, -9264, -9289, -9302, -9297, -9297, -9308, -9285, -9265, -9249,
-9223, -9202, -9167, -9146, -9131, -9114, -9078, -9038, -8976, -8916, -8828, -8727, -8635, -8524, -8404, -8290, -8166, -8060, -7945, -7806,
-7677, -7557, -7417, -7289, -7118, -6961, -6761, -6553, -6332, -6133, -5898, -5680, -5461, -5259, -5068, -4872, -4683, -4519, -4324, -4140,
-3955, -3750, -3558, -3357, -3153, -2975, -2783, -2611, -2453, -2308, -2210, -2105, -2005, -1920, -1832, -1724, -1622, -1515, -1397, -1284,
-1160, -1063, -957, -851, -767, -682, -631, -572, -530, -483, -445, -370, -307, -223, -149, -70, 5, 68, 111, 155,
178, 193, 186, 163, 120, 90, 34, 14, -7, -25, -22, -46, -61, -76, -134, -174, -225, -282, -327, -402,
-460, -517, -569, -619, -621, -629, -599, -565, -522, -495, -460, -448, -404, -398, -366, -337, -298, -237, -179, -119,
-44, 50, 160, 282, 401, 517, 630, 723, 811, 892, 984, 1053, 1136, 1247, 1367, 1473, 1601, 1755, 1897, 2064,
2236, 2402, 2562, 2727, 2893, 3045, 3196, 3375, 3541, 3731, 3941, 4166, 4382, 4630, 4870, 5122, 5363, 5611, 5859, 6089,
6310, 6530, 6724, 6939, 7132, 7341, 7547, 7755, 7946, 8156, 8359, 8549, 8720, 8858, 9018, 9143, 9244, 9339, 9444, 9525,
9584, 9660, 9724, 9785, 9842, 9915, 9967, 10003, 10048, 10062, 10060, 10048, 10043, 10016, 10009, 9975, 9963, 9926, 9891, 9846,
9805, 9749, 9701, 9658, 9616, 9533, 9444, 9344, 9250, 9125, 9009, 8895, 8789, 8669, 8539, 8404, 8266, 8087, 7961, 7802,
7648, 7488, 7304, 7113, 6918, 6693, 6484, 6283, 6067, 5866, 5663, 5451, 5220, 4987, 4757, 4533, 4314, 4107, 3867, 3634,
3407, 3166, 2919, 2670, 2440, 2229, 2002, 1788, 1573, 1347, 1113, 900, 691, 474, 281, 67, -150, -362, -586, -806,
-1024, -1230, -1425, -1615, -1808, -1998, -2210, -2415, -2615, -2822, -3006, -3206, -3415, -3609, -3816, -4040, -4239, -4457, -4634, -4810,
-4982, -5161, -5337, -5522, -5704, -5888, -6062, -6238, -6405, -6568, -6737, -6917, -7072, -7240, -7389, -7511, -7635, -7731, -7848, -7980,
-8092, -8208, -8325, -8440, -8544, -8664, -8744, -8854, -8951, -9056, -9136, -9206, -9253, -9307, -9348, -9408, -9463, -9507, -9572, -9623,
-9692, -9731, -9750, -9775, -9785, -9788, -9790, -9750, -9734, -9689, -9622, -9562, -9515, -9449, -9400, -9342, -9286, -9235, -9137, -9034,
-8926, -8809, -8685, -8557, -8411, -8268, -8120, -7975, -7839, -7706, -7569, -7471, -7344, -7221, -7085, -6924, -6773, -6605, -6436, -6247,
-6070, -5889, -5706, -5520, -5360, -5208, -5044, -4885, -4723, -4565, -4379, -4190, -3968, -3770, -3552, -3328, -3106, -2887, -2686, -2492,
-2309, -2146, -1990, -1855, -1715, -1568, -1416, -1275, -1107, -985, -839, -709, -591, -479, -404, -334, -268, -240, -228, -216,
-212, -203, -200, -151, -110, -83, -44, -10, 7, 29, 41, 37, 49, 36, 12, -6, -26, -32, -19, 0,
48, 92, 124, 163, 184, 207, 208, 212, 209, 202, 164, 153, 138, 109, 100, 108, 125, 164, 181, 183,
195, 188, 185, 148, 142, 137, 128, 108, 116, 135, 161, 211, 290, 378, 470, 567, 672, 767, 864, 955,
1048, 1145, 1279, 1407, 1564, 1711, 1878, 2055, 2246, 2449, 2671, 2873, 3078, 3268, 3449, 3612, 3774, 3928, 4102, 4274,
4461, 4653, 4849, 5036, 5222, 5433, 5625, 5804, 5985, 6164, 6332, 6476, 6618, 6746, 6906, 7030, 7185, 7371, 7533, 7720,
7885, 8058, 8214, 8366, 8476, 8621, 8739, 8849, 8948, 9021, 9110, 9193, 9256, 9337, 9417, 9497, 9566, 9619, 9648, 9666,
9655, 9651, 9619, 9589, 9558, 9507, 9446, 9383, 9311, 9239, 9180, 9119, 9054, 8978, 8903, 8797, 8679, 8561, 8431, 8304,
8186, 8053, 7926, 7807, 7677, 7541, 7413, 7273, 7163, 7031, 6899, 6743, 6583, 6405, 6233, 6058, 5864, 5680, 5502, 5326,
5146, 4956, 4755, 4564, 4365, 4182, 3979, 3775, 3570, 3346, 3104, 2866, 2633, 2412, 2174, 1959, 1751, 1544, 1329, 1105,
882, 690, 478, 273, 76, -143, -365, -580, -787, -1013, -1222, -1414, -1588, -1761, -1956, -2139, -2325, -2518, -2709, -2883,
-3051, -3228, -3427, -3617, -3819, -4012, -4202, -4384, -4562, -4724, -4876, -5048, -5226, -5410, -5576, -5751, -5923, -6072, -6235, -6414,
-6585, -6752, -6922, -7090, -7223, -7346, -7459, -7588, -7695, -7816, -7927, -8054, -8154, -8248, -8336, -8436, -8512, -8596, -8675, -8764,
-8823, -8863, -8889, -8920, -8945, -8997, -9018, -9048, -9094, -9122, -9151, -9179, -9191, -9203, -9220, -9231, -9244, -9223, -9189, -9160,
-9117, -9069, -9040, -9008, -8983, -8957, -8904, -8857, -8793, -8709, -8637, -8536, -8434, -8312, -8159, -8013, -7851, -7701, -7551, -7404,
-7255, -7120, -6953, -6783, -6622, -6421, -6227, -6032, -5842, -5644, -5430, -5207, -5005, -4806, -4628, -4469, -4311, -4168, -4024, -3867,
-3705, -3550, -3385, -3236, -3077, -2921, -2765, -2596, -2467, -2334, -2209, -2103, -2006, -1930, -1838, -1738, -1620, -1515, -1375, -1259,
-1143, -1037, -922, -793, -683, -596, -510, -455, -397, -365, -328, -284, -235, -181, -113, -60, 0, 33, 70, 99,
124, 127, 117, 106, 74, 14, -37, -69, -93, -101, -90, -72, -63, -64, -64, -64, -72, -72, -92, -85,
-104, -106, -114, -114, -87, -33, 24, 95, 187, 269, 335, 417, 472, 535, 590, 644, 716, 774, 847, 915,
1000, 1102, 1218, 1336, 1473, 1595, 1719, 1815, 1927, 2024, 2110, 2205, 2318, 2437, 2557, 2695, 2831, 2981, 3161, 3334,
3529, 3726, 3916, 4107, 4285, 4464, 4641, 4799, 4990, 5174, 5392, 5589, 5809, 6019, 6254, 6461, 6678, 6882, 7085, 7286,
7445, 7602, 7753, 7875, 8003, 8142, 8274, 8404, 8523, 8659, 8780, 8878, 8964, 9059, 9123, 9195, 9252, 9293, 9325, 9343,
9361, 9372, 9376, 9405, 9426, 9447, 9480, 9489, 9478, 9477, 9450, 9427, 9402, 9367, 9324, 9276, 9199, 9140, 9067, 8990,
8914, 8848, 8783, 8720, 8617, 8505, 8388, 8252, 8135, 8000, 7851, 7717, 7558, 7394, 7237, 7071, 6880, 6716, 6553, 6407,
6236, 6046, 5860, 5656, 5466, 5256, 5067, 4873, 4680, 4469, 4275, 4061, 3849, 3643, 3447, 3264, 3075, 2885, 2675, 2467,
2252, 2026, 1812, 1599, 1400, 1185, 987, 763, 538, 320, 89, -117, -302, -505, -708, -922, -1157, -1375, -1602, -1830,
-2036, -2246, -2448, -2656, -2875, -3082, -3300, -3502, -3683, -3868, -4069, -4245, -4437, -4637, -4838, -5046, -5225, -5406, -5562, -5735,
-5901, -6063, -6229, -6386, -6536, -6670, -6818, -6952, -7091, -7237, -7387, -7552, -7695, -7815, -7933, -8045, -8145, -8259, -8366, -8492,
-8590, -8684, -8782, -8859, -8937, -9028, -9107, -9210, -9294, -9363, -9418, -9450, -9468, -9500, -9522, -9546, -9560, -9576, -9567, -9557,
-9533, -9524, -9488, -9477, -9445, -9401, -9323, -9241, -9140, -9030, -8917, -8813, -8719, -8613, -8500, -8384, -8270, -8139, -8020, -7899,
-7766, -7637, -7481, -7322, -7154, -6969, -6805, -6642, -6486, -6351, -6210, -6068, -5926, -5747, -5604, -5448, -5295, -5128, -4954, -4756,
-4551, -4344, -4153, -3963, -3777, -3624, -3459, -3304, -3157, -2989, -2820, -2650, -2482, -2326, -2163, -1977, -1809, -1632, -1461, -1321,
-1205, -1113, -1025, -962, -898, -839, -765, -693, -622, -553, -508, -432, -380, -319, -278, -242, -230, -235, -263, -286,
-310, -340, -334, -335, -315, -302, -308, -284, -261, -252, -229, -231, -226, -239, -271, -314, -334, -362, -363, -354,
-342, -318, -284, -271, -252, -238, -235, -230, -236, -231, -262, -283, -292, -309, -312, -287, -251, -191, -137, -84,
-29, 38, 81, 148, 197, 268, 326, 387, 475, 566, 667, 789, 936, 1112, 1294, 1468, 1649, 1841, 1985, 2159,
2333, 2493, 2665, 2844, 3022, 3221, 3411, 3600, 3827, 4044, 4278, 4497, 4720, 4938, 5132, 5301, 5451, 5630, 5807, 5988,
6157, 6349, 6531, 6711, 6913, 7109, 7293, 7497, 7680, 7875, 8045, 8183, 8319, 8449, 8570, 8703, 8828, 8978, 9109, 9238,
9363, 9480, 9584, 9686, 9778, 9868, 9944, 10000, 10031, 10048, 10035, 10034, 10032, 10030, 10029, 10016, 9997, 9966, 9918, 9869,
9800, 9732, 9658, 9577, 9471, 9363, 9236, 9110, 8976, 8859, 8731, 8641, 8516, 8408, 8276, 8136, 7983, 7834, 7700, 7549,
7394, 7239, 7071, 6904, 6719, 6537, 6365, 6213, 6038, 5886, 5715, 5522, 5335, 5130, 4938, 4745, 4542, 4336, 4135, 3922,
3706, 3474, 3254, 3040, 2842, 2637, 2438, 2225, 2013, 1765, 1535, 1311, 1100, 874, 660, 441, 219, -15, -245, -467,
-667, -874, -1062, -1267, -1465, -1685, -1896, -2118, -2314, -2519, -2703, -2896, -3107, -3300, -3500, -3696, -3886, -4065, -4236, -4407,
-4594, -4777, -4980, -5177, -5365, -5551, -5732, -5892, -6060, -6233, -6402, -6576, -6739, -6905, -7061, -7197, -7339, -7483, -7649, -7796,
-7959, -8106, -8240, -8353, -8463, -8551, -8663, -8770, -8864, -8954, -9042, -9107, -9173, -9237, -9301, -9376, -9449, -9501, -9558, -9599,
-9604, -9628, -9616, -9639, -9647, -9644, -9652, -9659, -9626, -9609, -9592, -9581, -9564, -9541, -9507, -9480, -9407, -9321, -9228, -9140,
-9044, -8951, -8865, -8767, -8654, -8527, -8409, -8284, -8165, -8031, -7884, -7732, -7550, -7349, -7135, -6925, -6719, -6519, -6323, -6132,
-5952, -5760, -5569, -5376, -5201, -5009, -4822, -4632, -4440, -4229, -4012, -3806, -3607, -3429, -3258, -3112, -2987, -2852, -2728, -2588,
-2465, -2333, -2207, -2071, -1948, -1805, -1656, -1498, -1369, -1257, -1144, -1055, -981, -915, -847, -767, -677, -599, -519, -423,
-344, -257, -164, -81, 2, 50, 89, 124, 114, 107, 107, 96, 101, 95, 89, 111, 110, 111, 124, 112,
113, 99, 68, 37, -20, -90, -137, -192, -211, -226, -241, -230, -214, -197, -174, -166, -141, -124, -100, -86,
-69, -61, -51, -29, 16, 71, 136, 230, 336, 432, 529, 619, 701, 789, 868, 944, 1030, 1106, 1178, 1268,
1355, 1470, 1605, 1747, 1917, 2078, 2238, 2377, 2518, 2662, 2796, 2938, 3090, 3254, 3415, 3586, 3755, 3939, 4133, 4356,
4588, 4822, 5052, 5270, 5471, 5678, 5869, 6041, 6228, 6437, 6627, 6823, 7018, 7205, 7383, 7572, 7755, 7955, 8132, 8293,
8439, 8559, 8665, 8758, 8848, 8952, 9055, 9137, 9227, 9299, 9379, 9428, 9493, 9556, 9623, 9666, 9713, 9724, 9729, 9714,
9687, 9685, 9685, 9672, 9660, 9652, 9625, 9593, 9540, 9498, 9458, 9396, 9345, 9276, 9188, 9080, 8968, 8844, 8737, 8620,
8508, 8408, 8274, 8142, 7992, 7835, 7692, 7533, 7388, 7228, 7060, 6889, 6691, 6491, 6295, 6119, 5941, 5773, 5591, 5411,
5217, 5024, 4823, 4639, 4449, 4259, 4073, 3879, 3675, 3470, 3261, 3051, 2862, 2672, 2485, 2296, 2106, 1887, 1692, 1483,
1271, 1072, 880, 678, 475, 251, 22, -189, -408, -617, -812, -1024, -1205, -1419, -1639, -1840, -2049, -2274, -2459, -2659,
-2857, -3051, -3257, -3460, -3645, -3847, -4028, -4208, -4379, -4547, -4731, -4911, -5082, -5261, -5431, -5591, -5739, -5908, -6069, -6213,
-6361, -6529, -6671, -6801, -6934, -7048, -7188, -7316, -7456, -7596, -7735, -7867, -7985, -8090, -8207, -8312, -8424, -8518, -8643, -8713,
-8803, -8876, -8952, -9029, -9106, -9189, -9270, -9328, -9390, -9419, -9452, -9473, -9483, -9490, -9496, -9488, -9464, -9448, -9415, -9383,
-9342, -9309, -9274, -9243, -9174, -9113, -9018, -8927, -8815, -8706, -8604, -8506, -8400, -8276, -8162, -8051, -7938, -7836, -7716, -7615,
-7497, -7366, -7227, -7063, -6898, -6719, -6542, -6399, -6239, -6090, -5932, -5770, -5623, -5463, -5304, -5160, -5000, -4809, -4640, -4441,
-4238, -4024, -3803, -3634, -3457, -3286, -3145, -2987, -2858, -2699, -2564, -2439, -2317, -2184, -2051, -1910, -1779, -1632, -1501, -1397,
-1319, -1240, -1197, -1147, -1112, -1080, -1034, -993, -971, -928, -889, -840, -786, -735, -675, -628, -608, -602, -597, -605,
-617, -622, -605, -572, -572, -534, -496, -462, -423, -398, -350, -319, -310, -298, -293, -305, -328, -349, -353, -345,
-330, -307, -268, -243, -220, -182, -154, -122, -90, -82, -68, -65, -60, -52, -30, 25, 102, 186, 283, 387,
492, 597, 708, 822, 940, 1057, 1163, 1290, 1392, 1515, 1653, 1801, 1986, 2175, 2374, 2592, 2760, 2947, 3134, 3314,
3492, 3676, 3851, 4022, 4183, 4355, 4509, 4688, 4878, 5098, 5278, 5503, 5698, 5875, 6051, 6205, 6363, 6524, 6680, 6846,
7003, 7146, 7291, 7441, 7589, 7770, 7935, 8110, 8270, 8424, 8556, 8662, 8777, 8878, 8974, 9058, 9163, 9244, 9316, 9379,
9441, 9508, 9574, 9625, 9681, 9712, 9726, 9722, 9693, 9666, 9643, 9587, 9573, 9534, 9498, 9430, 9368, 9295, 9229, 9155,
9090, 9015, 8933, 8832, 8717, 8590, 8478, 8343, 8234, 8120, 8003, 7875, 7742, 7610, 7479, 7326, 7185, 7055, 6909, 6766,
6591, 6421, 6230, 6057, 5864, 5696, 5515, 5349, 5157, 4962, 4767, 4577, 4372, 4188, 3985, 3797, 3582, 3364, 3141, 2918,
2689, 2479, 2271, 2065, 1857, 1639, 1432, 1226, 989, 788, 581, 373, 172, -44, -260, -481, -701, -902, -1098, -1297,
-1483, -1693, -1881, -2072, -2274, -2478, -2660, -2854, -3047, -3243, -3435, -3620, -3823, -4022, -4203, -4377, -4548, -4718, -4893, -5058,
-5225, -5420, -5596, -5769, -5946, -6100, -6272, -6441, -6594, -6750, -6903, -7044, -7179, -7291, -7415, -7522, -7636, -7767, -7886, -7999,
-8097, -8199, -8280, -8368, -8447, -8520, -8589, -8647, -8703, -8737, -8762, -8795, -8804, -8847, -8892, -8913, -8956, -8961, -8983, -8986,
-8968, -8947, -8938, -8914, -8874, -8833, -8787, -8727, -8664, -8603, -8567, -8510, -8462, -8385, -8313, -8222, -8111, -7994, -7866, -7736,
-7586, -7447, -7289, -7131, -6971, -6801, -6645, -6506, -6340, -6209, -6036, -5860, -5666, -5465, -5256, -5058, -4850, -4660, -4469, -4297,
-4123, -3949, -3776, -3637, -3496, -3350, -3213, -3076, -2936, -2761, -2591, -2427, -2272, -2135, -2001, -1892, -1786, -1687, -1582, -1502,
-1408, -1319, -1243, -1156, -1078, -968, -845, -715, -626, -524, -450, -398, -364, -311, -285, -248, -235, -201, -179, -145,
-118, -104, -63, -31, 10, 42, 39, 13, -28, -74, -112, -160, -199, -244, -264, -288, -317, -328, -342, -327,
-327, -324, -333, -354, -385, -426, -460, -478, -486, -482, -439, -413, -372, -337, -281, -211, -152, -82, -19, 34,
84, 119, 160, 203, 275, 345, 455, 550, 666, 777, 877, 1012, 1139, 1250, 1377, 1505, 1603, 1714, 1800, 1917,
2036, 2165, 2336, 2518, 2694, 2888, 3061, 3250, 3446, 3627, 3822, 4013, 4196, 4383, 4551, 4733, 4917, 5107, 5315, 5556,
5785, 6004, 6214, 6419, 6602, 6789, 6941, 7115, 7284, 7439, 7571, 7698, 7825, 7955, 8073, 8220, 8362, 8484, 8585, 8681,
8749, 8831, 8877, 8934, 8982, 9028, 9054, 9071, 9104, 9102, 9123, 9137, 9153, 9184, 9188, 9170, 9152, 9118, 9077, 9029,
8984, 8928, 8887, 8803, 8732, 8663, 8566, 8484, 8420, 8320, 8250, 8141, 8026, 7899, 7770, 7606, 7485, 7335, 7194, 7045,
6900, 6745, 6575, 6401, 6255, 6087, 5925, 5756, 5586, 5398, 5214, 5026, 4819, 4633, 4440, 4266, 4062, 3876, 3696, 3500,
3304, 3118, 2923, 2734, 2533, 2347, 2166, 1939, 1727, 1523, 1304, 1107, 911, 713, 515, 314, 105, -111, -314, -509,
-728, -921, -1129, -1327, -1564, -1772, -1987, -2183, -2380, -2593, -2779, -2977, -3183, -3369, -3569, -3759, -3944, -4132, -4316, -4494,
-4683, -4878, -5057, -5238, -5405, -5579, -5737, -5885, -6042, -6210, -6368, -6518, -6673, -6819, -6956, -7110, -7245, -7391, -7517, -7660,
-7787, -7925, -8035, -8132, -8240, -8347, -8439, -8549, -8663, -8760, -8868, -8942, -9035, -9116, -9189, -9265, -9324, -9388, -9428, -9450,
-9464, -9484, -9498, -9513, -9536, -9544, -9552, -9537, -9516, -9489, -9444, -9400, -9348, -9275, -9202, -9117, -9010, -8897, -8810, -8697,
-8607, -8510, -8420, -8314, -8189, -8052, -7931, -7770, -7626, -7459, -7317, -7151, -6972, -6788, -6619, -6437, -6299, -6128, -5996, -5842,
-5673, -5498, -5309, -5104, -4894, -4694, -4480, -4285, -4076, -3864, -3661, -3466, -3275, -3108, -2933, -2780, -2614, -2425, -2244, -2050,
-1840, -1659, -1466, -1298, -1151, -997, -857, -757, -631, -531, -440, -364, -295, -214, -126, -38, 53, 151, 232, 291,
327, 375, 402, 402, 418, 430, 429, 436, 416, 426, 446, 454, 487, 535, 560, 575, 594, 587, 581, 553,
521, 506, 487, 477, 455, 444, 441, 450, 456, 476, 493, 522, 516, 503, 471, 452, 409, 384, 365, 367,
367, 367, 380, 418, 447, 505, 548, 606, 648, 705, 733, 779, 813, 854, 914, 1022, 1104, 1197, 1329, 1463,
1599, 1736, 1909, 2063, 2224, 2372, 2519, 2660, 2799, 2932, 3084, 3248, 3438, 3623, 3809, 4012, 4203, 4394, 4595, 4790,
4982, 5156, 5327, 5480, 5638, 5789, 5949, 6114, 6310, 6500, 6676, 6866, 7071, 7230, 7401, 7577, 7737, 7897, 8035, 8160,
8307, 8418, 8526, 8660, 8784, 8923, 9056, 9182, 9291, 9399, 9464, 9555, 9610, 9668, 9718, 9743, 9772, 9776, 9764, 9781,
9773, 9764, 9763, 9745, 9719, 9691, 9614, 9568, 9498, 9419, 9330, 9242, 9156, 9058, 8937, 8823, 8708, 8612, 8496, 8386,
8268, 8151, 8023, 7876, 7737, 7578, 7424, 7264, 7115, 6946, 6795, 6612, 6440, 6264, 6108, 5927, 5768, 5596, 5405, 5216,
5013, 4798, 4590, 4384, 4179, 3974, 3765, 3548, 3329, 3104, 2901, 2687, 2469, 2262, 2056, 1826, 1596, 1382, 1145, 916,
690, 460, 246, 24, -203, -412, -633, -840, -1049, -1263, -1449, -1662, -1883, -2079, -2295, -2500, -2724, -2920, -3125, -3303,
-3504, -3695, -3896, -4087, -4277, -4466, -4647, -4818, -5015, -5200, -5393, -5585, -5782, -5968, -6140, -6302, -6478, -6644, -6806, -6968,
-7127, -7292, -7446, -7580, -7731, -7881, -8026, -8174, -8317, -8451, -8577, -8686, -8777, -8877, -8972, -9063, -9159, -9250, -9344, -9405,
-9473, -9550, -9602, -9678, -9740, -9803, -9851, -9867, -9884, -9890, -9906, -9901, -9906, -9912, -9927, -9936, -9913, -9908, -9901, -9869,
-9845, -9809, -9759, -9711, -9626, -9565, -9454, -9356, -9256, -9164, -9079, -8988, -8881, -8766, -8644, -8505, -8367, -8215, -8066, -7890,
-7712, -7521, -7331, -7121, -6929, -6734, -6567, -6390, -6221, -6058, -5900, -5712, -5522, -5324, -5140, -4936, -4732, -4535, -4356, -4155,
-3973, -3803, -3662, -3518, -3375, -3245, -3109, -2982, -2830, -2668, -2511, -2360, -2205, -2056, -1920, -1791, -1657, -1548, -1436, -1346,
-1267, -1178, -1104, -1024, -925, -823, -717, -622, -523, -433, -358, -290, -246, -197, -174, -146, -147, -142, -120, -118,
-109, -73, -54, -22, 3, 29, 49, 38, 34, 17, -3, -29, -55, -64, -64, -85, -88, -56, -35, 17,
60, 100, 155, 195, 201, 231, 249, 282, 302, 349, 399, 466, 530, 620, 708, 836, 928, 1041, 1143, 1233,
1303, 1385, 1464, 1562, 1641, 1741, 1847, 1983, 2111, 2250, 2412, 2566, 2731, 2883, 3056, 3205, 3353, 3495, 3644, 3784,
3947, 4115, 4303, 4500, 4702, 4906, 5119, 5325, 5550, 5755, 5947, 6145, 6334, 6501, 6676, 6839, 7011, 7179, 7364, 7548,
7738, 7892, 8060, 8238, 8379, 8520, 8652, 8776, 8887, 8971, 9061, 9130, 9190, 9268, 9345, 9421, 9503, 9574, 9632, 9681,
9717, 9756, 9769, 9786, 9799, 9794, 9769, 9746, 9717, 9706, 9679, 9654, 9635, 9604, 9555, 9515, 9447, 9394, 9311, 9228,
9137, 9050, 8931, 8825, 8704, 8579, 8460, 8333, 8223, 8092, 7949, 7809, 7668, 7518, 7345, 7163, 7011, 6846, 6652, 6466,
6300, 6112, 5926, 5745, 5558, 5399, 5219, 5023, 4841, 4649, 4455, 4241, 4041, 3860, 3664, 3451, 3272, 3052, 2866, 2662,
2463, 2275, 2095, 1885, 1705, 1495, 1291, 1068, 852, 642, 448, 230, 33, -175, -387, -606, -813, -1006, -1196, -1397,
-1604, -1805, -2015, -2228, -2443, -2653, -2829, -3028, -3222, -3415, -3611, -3792, -3994, -4163, -4343, -4503, -4676, -4848, -5028, -5201,
-5386, -5556, -5726, -5870, -6037, -6171, -6326, -6456, -6616, -6763, -6883, -7017, -7146, -7275, -7409, -7538, -7668, -7808, -7938, -8038,
-8153, -8247, -8338, -8435, -8520, -8605, -8691, -8763, -8839, -8898, -8962, -9031, -9094, -9165, -9209, -9247, -9271, -9281, -9281, -9266,
-9238, -9243, -9228, -9196, -9170, -9138, -9093, -9044, -9013, -8950, -8902, -8836, -8743, -8664, -8546, -8437, -8317, -8201, -8084, -7965,
-7848, -7739, -7619, -7506, -7384, -7260, -7123, -6987, -6824, -6673, -6507, -6324, -6146, -5969, -5796, -5627, -5458, -5302, -5156, -4988,
-4837, -4649, -4498, -4317, -4124, -3929, -3736, -3527, -3344, -3141, -2970, -2797, -2641, -2503, -2368, -2238, -2115, -1973, -1849, -1723,
-1573, -1436, -1311, -1196, -1078, -968, -887, -813, -735, -682, -646, -616, -582, -555, -513, -465, -410, -357, -302, -269,
-223, -194, -171, -172, -154, -150, -152, -171, -171, -174, -155, -145, -127, -77, -47, -14, 13, 23, 29, 18,
5, -4, -13, -31, -39, -32, -30, -24, 7, 42, 95, 121, 154, 191, 196, 212, 223, 207, 253, 274,
313, 367, 434, 508, 587, 691, 813, 928, 1034, 1156, 1264, 1364, 1464, 1566, 1699, 1834, 1961, 2118, 2280, 2452,
2637, 2820, 3009, 3205, 3387, 3570, 3755, 3919, 4077, 4228, 4403, 4582, 4750, 4948, 5136, 5318, 5524, 5705, 5908, 6096,
6282, 6453, 6614, 6765, 6917, 7037, 7184, 7340, 7502, 7646, 7791, 7939, 8086, 8222, 8364, 8490, 8635, 8720, 8824, 8911,
8992, 9051, 9112, 9177, 9250, 9298, 9355, 9390, 9432, 9456, 9471, 9498, 9507, 9490, 9464, 9439, 9383, 9335, 9272, 9215,
9162, 9091, 9025, 8960, 8883, 8806, 8707, 8611, 8527, 8427, 8315, 8196, 8073, 7942, 7810, 7678, 7551, 7432, 7301, 7167,
7025, 6892, 6735, 6579, 6432, 6262, 6084, 5928, 5742, 5562, 5375, 5185, 5004, 4827, 4636, 4460, 4282, 4082, 3886, 3677,
3476, 3267, 3067, 2862, 2661, 2442, 2226, 2001, 1794, 1587, 1394, 1191, 1001, 797, 579, 357, 148, -48, -263, -470,
-671, -887, -1095, -1310, -1526, -1730, -1930, -2126, -2311, -2498, -2710, -2909, -3124, -3319, -3515, -3722, -3909, -4096, -4285, -4489,
-4686, -4859, -5037, -5220, -5384, -5550, -5714, -5890, -6069, -6235, -6409, -6568, -6728, -6870, -7022, -7162, -7316, -7454, -7577, -7704,
-7835, -7936, -8063, -8173, -8290, -8409, -8519, -8619, -8731, -8819, -8903, -8980, -9071, -9156, -9222, -9276, -9340, -9383, -9427, -9476,
-9516, -9571, -9619, -9647, -9693, -9716, -9699, -9702, -9686, -9676, -9661, -9622, -9585, -9538, -9485, -9438, -9377, -9334, -9277, -9204,
-9129, -9042, -8939, -8823, -8695, -8564, -8424, -8275, -8137, -7990, -7844, -7692, -7545, -7400, -7254, -7104, -6943, -6768, -6592, -6404,
-6206, -6021, -5821, -5606, -5414, -5229, -5044, -4862, -4689, -4523, -4369, -4199, -4017, -3846, -3669, -3486, -3294, -3108, -2930, -2755,
-2569, -2413, -2264, -2131, -2001, -1873, -1761, -1641, -1515, -1388, -1261, -1123, -998, -867, -752, -630, -524, -428, -348, -267,
-218, -162, -121, -82, -28, 39, 82, 144, 211, 268, 300, 337, 368, 385, 401, 401, 391, 367, 351, 335,
322, 326, 330, 338, 362, 363, 383, 375, 366, 355, 354, 337, 328, 327, 307, 300, 315, 320, 372, 397,
454, 503, 559, 591, 641, 675, 732, 764, 803, 852, 901, 964, 1036, 1122, 1225, 1322, 1441, 1569, 1682, 1795,
1898, 2004, 2119, 2221, 2327, 2447, 2570, 2698, 2841, 3003, 3171, 3346, 3521, 3711, 3893, 4074, 4234, 4406, 4579, 4745,
4902, 5073, 5240, 5426, 5604, 5791, 5987, 6176, 6371, 6559, 6743, 6918, 7076, 7233, 7383, 7522, 7659, 7792, 7931, 8064,
8204, 8325, 8451, 8585, 8714, 8833, 8940, 9032, 9116, 9185, 9258, 9326, 9392, 9429, 9487, 9526, 9564, 9593, 9631, 9649,
9678, 9675, 9697, 9673, 9647, 9605, 9552, 9500, 9460, 9392, 9333, 9257, 9181, 9097, 9001, 8910, 8821, 8722, 8626, 8514,
8388, 8260, 8113, 7979, 7851, 7689, 7562, 7423, 7269, 7120, 6963, 6808, 6656, 6495, 6342, 6189, 6016, 5846, 5660, 5470,
5283, 5119, 4931, 4772, 4589, 4409, 4201, 4011, 3830, 3626, 3428, 3242, 3035, 2834, 2613, 2390, 2173, 1967, 1754, 1559,
1356, 1147, 939, 717, 502, 296, 86, -123, -337, -541, -757, -973, -1201, -1408, -1612, -1810, -2004, -2213, -2399, -2605,
-2796, -3002, -3201, -3395, -3587, -3784, -3969, -4167, -4370, -4565, -4739, -4929, -5104, -5276, -5443, -5616, -5790, -5957, -6133, -6306,
-6462, -6618, -6771, -6935, -7090, -7236, -7393, -7536, -7658, -7774, -7897, -8013, -8133, -8252, -8381, -8495, -8608, -8712, -8823, -8911,
-9017, -9102, -9196, -9282, -9345, -9397, -9457, -9497, -9558, -9612, -9657, -9706, -9745, -9783, -9805, -9827, -9831, -9846, -9839, -9819,
-9793, -9756, -9710, -9657, -9609, -9561, -9505, -9438, -9386, -9324, -9227, -9145, -9050, -8946, -8829, -8705, -8571, -8439, -8297, -8136,
-7992, -7846, -7709, -7564, -7423, -7286, -7135, -6981, -6820, -6649, -6481, -6300, -6118, -5931, -5739, -5567, -5388, -5218, -5048, -4897,
-4727, -4589, -4424, -4269, -4098, -3932, -3765, -3587, -3404, -3236, -3056, -2888, -2739, -2593, -2446, -2330, -2201, -2083, -1969, -1843,
-1721, -1601, -1485, -1352, -1232, -1111, -1009, -896, -807, -735, -676, -618, -567, -523, -486, -428, -389, -327, -283, -230,
-177, -131, -97, -70, -39, -24, -25, -30, -23, -30, -25, -19, -1, 11, 45, 68, 106, 114, 146, 162,
196, 192, 212, 213, 225, 229, 253, 278, 325, 371, 429, 482, 547, 608, 677, 724, 788, 840, 896, 943,
1011, 1071, 1143, 1226, 1334, 1436, 1553, 1671, 1798, 1918, 2045, 2175, 2300, 2431, 2555, 2672, 2804, 2936, 3080, 3245,
3401, 3576, 3751, 3933, 4102, 4288, 4465, 4640, 4804, 4978, 5138, 5295, 5436, 5598, 5775, 5943, 6107, 6292, 6466, 6643,
6807, 6963, 7128, 7278, 7419, 7560, 7693, 7810, 7919, 8039, 8161, 8288, 8413, 8535, 8654, 8760, 8856, 8955, 9031, 9116,
9185, 9242, 9289, 9347, 9372, 9395, 9427, 9461, 9476, 9496, 9518, 9519, 9523, 9491, 9456, 9425, 9387, 9320, 9279, 9209,
9140, 9047, 8963, 8876, 8791, 8696, 8606, 8513, 8400, 8282, 8155, 8024, 7888, 7754, 7628, 7480, 7346, 7187, 7034, 6884,
6738, 6589, 6435, 6304, 6142, 5987, 5813, 5643, 5469, 5295, 5121, 4949, 4780, 4600, 4405, 4221, 4040, 3856, 3665, 3496,
3296, 3105, 2905, 2693, 2476, 2269, 2055, 1850, 1638, 1442, 1232, 1019, 789, 594, 379, 174, -29, -232, -435, -656,
-873, -1077, -1290, -1488, -1695, -1888, -2080, -2273, -2475, -2665, -2847, -3038, -3214, -3394, -3586, -3778, -3968, -4153, -4347, -4545,
-4702, -4875, -5036, -5208, -5382, -5545, -5707, -5872, -6024, -6182, -6336, -6501, -6652, -6811, -6955, -7109, -7245, -7378, -7498, -7622,
-7738, -7849, -7950, -8069, -8172, -8275, -8367, -8464, -8556, -8649, -8737, -8804, -8887, -8942, -8997, -9040, -9072, -9112, -9145, -9169,
-9209, -9215, -9250, -9262, -9265, -9272, -9268, -9256, -9254, -9223, -9184, -9127, -9070, -9013, -8950, -8875, -8814, -8741, -8670, -8594,
-8506, -8419, -8319, -8207, -8098, -7967, -7833, -7688, -7543, -7382, -7230, -7073, -6929, -6781, -6624, -6490, -6330, -6174, -6008, -5841,
-5683, -5516, -5318, -5144, -4950, -4759, -4580, -4402, -4228, -4071, -3903, -3753, -3594, -3440, -3286, -3133, -2967, -2817, -2650, -2495,
-2334, -2182, -2042, -1911, -1784, -1681, -1575, -1484, -1401, -1306, -1217, -1130, -1037, -952, -867, -784, -698, -619, -563, -511,
-463, -429, -399, -375, -360, -324, -314, -288, -257, -226, -202, -160, -132, -105, -82, -85, -77, -84, -98, -110,
-130, -136, -148, -145, -145, -130, -118, -113, -90, -77, -71, -66, -73, -74, -79, -78, -64, -57, -31, 1,
41, 89, 156, 208, 273, 335, 414, 464, 533, 597, 669, 736, 819, 902, 1010, 1122, 1242, 1369, 1503, 1630,
1777, 1922, 2060, 2192, 2326, 2466, 2605, 2742, 2898, 3042, 3198, 3375, 3550, 3732, 3917, 4097, 4285, 4474, 4649, 4815,
4982, 5150, 5321, 5484, 5653, 5834, 6012, 6197, 6371, 6557, 6733, 6916, 7089, 7263, 7418, 7573, 7709, 7839, 7973, 8109,
8226, 8361, 8473, 8598, 8711, 8818, 8917, 9015, 9106, 9184, 9252, 9301, 9348, 9384, 9405, 9428, 9442, 9458, 9467, 9478,
9482, 9469, 9456, 9438, 9406, 9367, 9329, 9274, 9214, 9134, 9056, 8976, 8892, 8802, 8728, 8630, 8541, 8442, 8338, 8223,
8105, 7981, 7865, 7730, 7593, 7446, 7308, 7144, 6998, 6835, 6689, 6528, 6377, 6211, 6044, 5859, 5695, 5511, 5331, 5151,
4957, 4768, 4571, 4368, 4168, 3964, 3757, 3560, 3364, 3163, 2950, 2735, 2523, 2309, 2087, 1896, 1667, 1450, 1235, 1013,
800, 573, 352, 151, -62, -267, -465, -677, -889, -1098, -1316, -1523, -1719, -1912, -2119, -2317, -2517, -2711, -2913, -3101,
-3281, -3466, -3645, -3828, -4005, -4190, -4383, -4574, -4733, -4913, -5087, -5256, -5427, -5596, -5762, -5938, -6091, -6243, -6391, -6545,
-6692, -6835, -6983, -7142, -7281, -7425, -7553, -7688, -7798, -7927, -8035, -8159, -8261, -8356, -8447, -8539, -8626, -8704, -8784, -8865,
-8941, -9010, -9072, -9127, -9167, -9201, -9232, -9268, -9290, -9305, -9305, -9316, -9316, -9314, -9309, -9298, -9297, -9268, -9256, -9213,
-9167, -9109, -9045, -8973, -8915, -8820, -8750, -8666, -8573, -8474, -8378, -8274, -8173, -8060, -7942, -7828, -7684, -7537, -7381, -7221,
-7069, -6913, -6752, -6597, -6435, -6283, -6124, -5961, -5797, -5645, -5482, -5311, -5141, -4953, -4768, -4580, -4410, -4230, -4063, -3898,
-3740, -3578, -3436, -3280, -3133, -2990, -2831, -2694, -2529, -2380, -2211, -2060, -1908, -1766, -1625, -1499, -1381, -1277, -1164, -1068,
-964, -879, -783, -689, -595, -504, -402, -318, -234, -176, -119, -72, -37, -17, 14, 29, 55, 60, 72, 103,
122, 148, 171, 195, 215, 232, 226, 237, 223, 223, 210, 206, 202, 213, 212, 234, 252, 276, 313, 344,
364, 398, 420, 435, 444, 458, 476, 498, 515, 561, 597, 642, 694, 757, 819, 891, 955, 1007, 1067, 1130,
1183, 1232, 1299, 1368, 1447, 1532, 1629, 1738, 1853, 1975, 2098, 2227, 2350, 2484, 2621, 2744, 2882, 3010, 3147, 3286,
3445, 3606, 3780, 3946, 4134, 4309, 4494, 4680, 4860, 5035, 5209, 5369, 5538, 5693, 5848, 5999, 6157, 6316, 6475, 6639,
6806, 6975, 7119, 7275, 7409, 7537, 7661, 7777, 7885, 7993, 8087, 8183, 8278, 8366, 8457, 8553, 8639, 8736, 8816, 8891,
8951, 8999, 9025, 9060, 9084, 9106, 9118, 9124, 9133, 9134, 9120, 9115, 9108, 9095, 9071, 9041, 8994, 8937, 8868, 8794,
8702, 8615, 8525, 8427, 8336, 8229, 8118, 8009, 7891, 7779, 7661, 7533, 7412, 7268, 7114, 6976, 6809, 6642, 6494, 6327,
6171, 6014, 5860, 5700, 5535, 5353, 5203, 5025, 4861, 4677, 4486, 4300, 4109, 3902, 3701, 3507, 3308, 3124, 2924, 2735,
2538, 2324, 2118, 1928, 1718, 1512, 1300, 1089, 872, 646, 426, 212, -8, -216, -413, -613, -809, -1020, -1233, -1423,
-1635, -1832, -2026, -2229, -2430, -2626, -2830, -3027, -3226, -3409, -3585, -3756, -3939, -4110, -4287, -4474, -4655, -4823, -4996, -5167,
-5340, -5504, -5681, -5846, -6007, -6166, -6319, -6466, -6607, -6740, -6891, -7040, -7181, -7327, -7468, -7594, -7717, -7846, -7968, -8088,
-8203, -8316, -8412, -8512, -8582, -8666, -8742, -8825, -8895, -8982, -9048, -9111, -9161, -9209, -9238, -9277, -9300, -9330, -9346, -9356,
-9356, -9346, -9327, -9337, -9316, -9299, -9291, -9273, -9247, -9213, -9156, -9102, -9044, -8988, -8924, -8849, -8766, -8680, -8589, -8494,
-8405, -8311, -8226, -8127, -8018, -7910, -7771, -7631, -7494, -7344, -7197, -7040, -6878, -6722, -6548, -6386, -6226, -6065, -5904, -5751,
-5581, -5406, -5227, -5034, -4841, -4649, -4463, -4286, -4104, -3927, -3760, -3585, -3432, -3285, -3140, -3004, -2866, -2722, -2572, -2426,
-2274, -2139, -1995, -1874, -1748, -1634, -1534, -1433, -1340, -1258, -1173, -1111, -1028, -955, -862, -778, -672, -584, -509, -438,
-377, -302, -252, -210, -162, -136, -99, -78, -47, -21, 17, 63, 107, 145, 187, 209, 230, 244, 248, 246,
243, 247, 244, 234, 223, 236, 242, 267, 298, 334, 362, 393, 412, 435, 448, 473, 490, 524, 544, 594,
632, 692, 751, 835, 918, 1010, 1107, 1207, 1290, 1387, 1471, 1553, 1641, 1737, 1839, 1944, 2061, 2180, 2313, 2444,
2587, 2735, 2883, 3025, 3168, 3304, 3437, 3567, 3692, 3826, 3969, 4116, 4273, 4435, 4601, 4764, 4946, 5117, 5297, 5466,
5637, 5803, 5967, 6126, 6284, 6423, 6590, 6737, 6920, 7082, 7255, 7417, 7587, 7742, 7892, 8030, 8167, 8300, 8404, 8506,
8610, 8690, 8781, 8862, 8948, 9025, 9092, 9174, 9236, 9288, 9323, 9356, 9365, 9382, 9390, 9388, 9373, 9353, 9333, 9309,
9274, 9255, 9228, 9196, 9169, 9128, 9074, 9018, 8938, 8869, 8788, 8705, 8617, 8524, 8419, 8329, 8215, 8102, 7991, 7880,
7771, 7658, 7528, 7388, 7243, 7082, 6936, 6775, 6606, 6447, 6278, 6107, 5937, 5761, 5569, 5386, 5212, 5040, 4858, 4665,
4469, 4260, 4066, 3852, 3655, 3451, 3259, 3050, 2855, 2643, 2435, 2223, 2022, 1825, 1625, 1430, 1220, 1011, 799, 576,
361, 150, -55, -258, -453, -667, -875, -1085, -1302, -1501, -1700, -1897, -2090, -2298, -2515, -2713, -2925, -3133, -3331, -3523,
-3711, -3901, -4099, -4287, -4483, -4675, -4848, -5025, -5210, -5373, -5547, -5722, -5899, -6081, -6248, -6406, -6554, -6695, -6849, -6986,
-7132, -7271, -7412, -7539, -7671, -7784, -7908, -8026, -8144, -8270, -8383, -8481, -8573, -8651, -8729, -8809, -8885, -8970, -9041, -9112,
-9177, -9223, -9272, -9324, -9352, -9398, -9433, -9458, -9473, -9470, -9452, -9443, -9429, -9418, -9400, -9382, -9345, -9310, -9248, -9202,
-9126, -9070, -8997, -8916, -8818, -8713, -8597, -8472, -8344, -8222, -8110, -7989, -7864, -7730, -7597, -7449, -7304, -7151, -6992, -6840,
-6673, -6505, -6332, -6152, -5985, -5820, -5659, -5513, -5364, -5218, -5065, -4886, -4737, -4566, -4401, -4232, -4063, -3888, -3710, -3538,
-3375, -3217, -3058, -2925, -2787, -2655, -2530, -2387, -2247, -2100, -1958, -1824, -1695, -1557, -1433, -1302, -1184, -1079, -1005, -932,
-867, -815, -763, -711, -652, -589, -528, -471, -430, -376, -341, -302, -281, -264, -251, -259, -273, -283, -301, -309,
-297, -291, -262, -249, -244, -231, -216, -208, -189, -196, -188, -193, -208, -223, -222, -225, -199, -180, -148, -105,
-61, -36, 1, 29, 58, 76, 99, 135, 146, 175, 211, 247, 294, 362, 428, 521, 607, 694, 775, 867,
952, 1041, 1122, 1224, 1318, 1421, 1542, 1668, 1804, 1952, 2110, 2293, 2476, 2648, 2828, 3013, 3164, 3340, 3508, 3674,
3850, 4026, 4209, 4405, 4594, 4786, 4994, 5193, 5404, 5592, 5790, 5978, 6155, 6311, 6451, 6611, 6771, 6932, 7080, 7249,
7405, 7560, 7727, 7881, 8026, 8178, 8313, 8455, 8577, 8679, 8776, 8864, 8951, 9043, 9126, 9220, 9302, 9385, 9467, 9527,
9583, 9632, 9670, 9700, 9731, 9741, 9738, 9719, 9686, 9654, 9616, 9582, 9548, 9504, 9453, 9395, 9322, 9245, 9151, 9057,
8956, 8855, 8733, 8615, 8477, 8343, 8199, 8069, 7927, 7812, 7675, 7550, 7400, 7247, 7080, 6916, 6762, 6596, 6431, 6268,
6088, 5914, 5726, 5539, 5358, 5191, 5006, 4842, 4660, 4466, 4272, 4066, 3869, 3665, 3463, 3259, 3060, 2853, 2642, 2418,
2202, 1990, 1789, 1587, 1392, 1182, 975, 744, 522, 301, 95, -120, -327, -534, -743, -958, -1176, -1389, -1587, -1785,
-1970, -2171, -2357, -2566, -2768, -2974, -3169, -3360, -3537, -3724, -3912, -4091, -4282, -4464, -4645, -4820, -4980, -5143, -5318, -5486,
-5667, -5846, -6018, -6186, -6347, -6493, -6639, -6788, -6935, -7085, -7230, -7376, -7515, -7634, -7760, -7880, -8018, -8138, -8272, -8394,
-8504, -8591, -8679, -8745, -8834, -8911, -8983, -9055, -9123, -9170, -9222, -9261, -9302, -9345, -9387, -9412, -9444, -9453, -9440, -9436,
-9403, -9395, -9378, -9355, -9340, -9318, -9268, -9228, -9180, -9136, -9085, -9031, -8965, -8900, -8804, -8700, -8583, -8475, -8360, -8251,
-8146, -8036, -7907, -7776, -7640, -7502, -7365, -7215, -7059, -6896, -6714, -6521, -6317, -6116, -5923, -5732, -5550, -5375, -5200, -5022,
-4844, -4658, -4482, -4300, -4120, -3941, -3757, -3568, -3376, -3191, -3014, -2855, -2707, -2575, -2456, -2335, -2222, -2090, -1978, -1854,
-1738, -1614, -1503, -1378, -1259, -1128, -1026, -937, -848, -778, -721, -662, -610, -542, -470, -401, -336, -258, -195, -124,
-57, 4, 64, 94, 118, 142, 133, 129, 132, 123, 134, 136, 136, 157, 166, 170, 184, 174, 180, 169,
149, 130, 96, 51, 29, -2, -1, 4, 8, 32, 66, 95, 129, 147, 182, 211, 244, 276, 308, 339,
375, 417, 481, 554, 635, 739, 852, 960, 1066, 1166, 1259, 1358, 1453, 1545, 1642, 1741, 1837, 1949, 2057, 2190,
2334, 2488, 2658, 2818, 2983, 3125, 3270, 3421, 3558, 3705, 3854, 4018, 4182, 4355, 4518, 4699, 4881, 5088, 5297, 5505,
5710, 5907, 6085, 6267, 6436, 6589, 6752, 6933, 7099, 7274, 7443, 7607, 7759, 7915, 8067, 8228, 8368, 8502, 8617, 8710,
8794, 8868, 8933, 9012, 9088, 9151, 9218, 9266, 9323, 9351, 9390, 9421, 9457, 9473, 9496, 9483, 9468, 9435, 9392, 9368,
9343, 9310, 9280, 9247, 9202, 9150, 9081, 9016, 8954, 8871, 8803, 8714, 8614, 8496, 8374, 8243, 8122, 7995, 7872, 7758,
7617, 7478, 7322, 7160, 7007, 6841, 6688, 6522, 6350, 6176, 5979, 5780, 5585, 5405, 5225, 5053, 4866, 4687, 4491, 4296,
4095, 3907, 3713, 3521, 3331, 3137, 2936, 2734, 2525, 2316, 2124, 1936, 1746, 1555, 1366, 1153, 957, 748, 541, 342,
149, -50, -248, -464, -682, -888, -1101, -1302, -1494, -1701, -1879, -2086, -2296, -2491, -2693, -2909, -3089, -3285, -3473, -3658,
-3852, -4045, -4226, -4416, -4589, -4764, -4928, -5090, -5265, -5434, -5599, -5767, -5930, -6082, -6222, -6378, -6527, -6659, -6798, -6952,
-7081, -7206, -7330, -7436, -7563, -7680, -7804, -7931, -8051, -8167, -8272, -8361, -8459, -8546, -8639, -8717, -8820, -8877, -8951, -9008,
-9068, -9127, -9184, -9244, -9303, -9341, -9384, -9393, -9405, -9407, -9400, -9390, -9379, -9357, -9321, -9291, -9245, -9200, -9144, -9095,
-9043, -8991, -8910, -8835, -8728, -8626, -8503, -8385, -8274, -8164, -8051, -7922, -7800, -7681, -7559, -7446, -7316, -7201, -7072, -6933,
-6785, -6618, -6451, -6275, -6098, -5952, -5794, -5645, -5491, -5332, -5187, -5029, -4870, -4724, -4568, -4384, -4219, -4028, -3842, -3642,
-3438, -3281, -3117, -2959, -2828, -2682, -2561, -2415, -2287, -2169, -2053, -1928, -1804, -1674, -1556, -1423, -1307, -1212, -1143, -1072,
-1034, -986, -952, -923, -879, -839, -816, -774, -737, -690, -643, -596, -545, -505, -489, -482, -479, -487, -493, -496,
-479, -447, -444, -405, -368, -335, -298, -274, -230, -201, -190, -176, -167, -173, -186, -196, -192, -177, -152, -121,
-76, -44, -13, 31, 64, 101, 140, 159, 185, 199, 220, 241, 277, 340, 424, 516, 620, 728, 838, 947,
1061, 1176, 1297, 1416, 1528, 1659, 1767, 1895, 2038, 2188, 2371, 2557, 2754, 2966, 3131, 3314, 3498, 3672, 3846, 4024,
4195, 4364, 4523, 4692, 4846, 5020, 5204, 5414, 5587, 5801, 5986, 6156, 6323, 6470, 6618, 6769, 6915, 7072, 7219, 7354,
7491, 7631, 7769, 7934, 8085, 8245, 8389, 8529, 8648, 8742, 8844, 8931, 9016, 9088, 9180, 9251, 9312, 9365, 9416, 9471,
9524, 9564, 9608, 9628, 9632, 9620, 9586, 9550, 9519, 9459, 9436, 9390, 9350, 9277, 9209, 9131, 9059, 8979, 8907, 8825,
8739, 8633, 8515, 8385, 8269, 8130, 8019, 7899, 7779, 7648, 7512, 7378, 7243, 7087, 6944, 6809, 6660, 6515, 6340, 6169,
5976, 5803, 5610, 5440, 5259, 5092, 4900, 4707, 4511, 4322, 4116, 3933, 3730, 3543, 3330, 3114, 2893, 2672, 2446, 2239,
2031, 1827, 1621, 1406, 1200, 996, 762, 562, 358, 150, -49, -260, -473, -691, -909, -1107, -1302, -1498, -1682, -1890,
-2076, -2265, -2464, -2665, -2846, -3038, -3227, -3421, -3609, -3791, -3990, -4185, -4363, -4534, -4703, -4870, -5040, -5203, -5367, -5557,
-5730, -5899, -6072, -6222, -6390, -6554, -6703, -6854, -7003, -7140, -7271, -7380, -7501, -7605, -7715, -7842, -7957, -8067, -8161, -8259,
-8337, -8420, -8496, -8565, -8629, -8684, -8736, -8767, -8790, -8820, -8828, -8867, -8907, -8926, -8965, -8967, -8985, -8983, -8963, -8938,
-8925, -8898, -8856, -8812, -8763, -8702, -8637, -8574, -8535, -8475, -8424, -8345, -8271, -8178, -8066, -7947, -7818, -7688, -7538, -7399,
-7241, -7083, -6924, -6755, -6600, -6460, -6295, -6164, -5991, -5816, -5622, -5423, -5215, -5018, -4813, -4624, -4435, -4265, -4093, -3922,
-3751, -3612, -3472, -3328, -3193, -3056, -2917, -2743, -2575, -2413, -2259, -2123, -1991, -1882, -1777, -1679, -1575, -1496, -1402, -1314,
-1238, -1151, -1074, -965, -842, -713, -624, -522, -449, -397, -363, -310, -284, -247, -234, -200, -178, -144, -117, -103,
-62, -30, 9, 41, 39, -3, 45, 96, 5, -114, -316, -539, -783, -1012, -1204, -1334, -1413, -1438, -1420, -1365,
-1267, -1135, -983, -810, -635, -463, -277, -108, 80, 298, 559, 863, 1193, 1543, 1898, 2227, 2540, 2833, 3099, 3345,
3565, 3764, 3949, 4098, 4233, 4373, 4509, 4662, 4828, 4992, 5145, 5272, 5381, 5487, 5586, 5711, 5858, 6041, 6251, 6486,
6725, 6985, 7250, 7535, 7820, 8102, 8357, 8585, 8766, 8916, 9029, 9116, 9191, 9242, 9278, 9287, 9245, 9161, 9044, 8887,
8706, 8504, 8290, 8064, 7812, 7554, 7294, 7036, 6797, 6583, 6390, 6220, 6053, 5884, 5719, 5541, 5377, 5215, 5070, 4939,
4813, 4685, 4554, 4419, 4288, 4160, 4036, 3914, 3782, 3633, 3463, 3269, 3068, 2847, 2609, 2370, 2130, 1879, 1641, 1407,
1175, 937, 703, 480, 249, 6, -251, -510, -763, -1007, -1234, -1441, -1625, -1796, -1925, -2032, -2130, -2203, -2261, -2313,
-2349, -2390, -2450, -2514, -2577, -2643, -2703, -2759, -2814, -2855, -2899, -2939, -2989, -3045, -3116, -3197, -3298, -3417, -3572, -3747,
-3945, -4165, -4395, -4634, -4875, -5111, -5346, -5573, -5803, -6027, -6246, -6469, -6691, -6909, -7131, -7363, -7600, -7830, -8053, -8255,
-8440, -8591, -8722, -8829, -8919, -8997, -9069, -9141, -9200, -9251, -9297, -9354, -9410, -9468, -9535, -9604, -9669, -9719, -9756, -9788,
-9808, -9831, -9857, -9874, -9886, -9893, -9890, -9882, -9867, -9841, -9803, -9734, -9638, -9507, -9326, -9099, -8826, -8521, -8186, -7811,
-7399, -6957, -6471, -5961, -5438, -4896, -4353, -3800, -3252, -2688, -2114, -1541, -974, -420, 113, 630, 1118, 1590, 2051, 2485,
2891, 3276, 3638, 3968, 4274, 4570, 4866, 5141, 5392, 5636, 5862, 6064, 6250, 6413, 6557, 6664, 6745, 6794, 6794, 6756,
6690, 6600, 6499, 6380, 6245, 6095, 5915, 5722, 5509, 5270, 5010, 4737, 4459, 4165, 3865, 3562, 3264, 2976, 2708, 2466,
2243, 2019, 1816, 1635, 1462, 1285, 1114, 954, 794, 627, 468, 306, 143, -19, -150, -272, -390, -502, -600, -702,
-827, -959, -1116, -1290, -1484, -1686, -1905, -2134, -2375, -2609, -2840, -3069, -3279, -3476, -3674, -3863, -4045, -4230, -4434, -4636,
-4835, -5036, -5234, -5420, -5585, -5734, -5867, -5962, -6025, -6064, -6084, -6071, -6048, -6019, -5991, -5962, -5935, -5904, -5857, -5799,
-5732, -5644, -5529, -5396, -5234, -5054, -4849, -4630, -4386, -4129, -3859, -3589, -3312, -3013, -2694, -2351, -1970, -1557, -1104, -619,
-99, 442, 998, 1574, 2163, 2759, 3354, 3944, 4523, 5081, 5632, 6151, 6660, 7149, 7612, 8040, 8415, 8754, 9050, 9284,
9480, 9644, 9777, 9879, 9960, 10015, 10043, 10037, 10013, 9981, 9923, 9847, 9761, 9667, 9560, 9440, 9319, 9201, 9071, 8965,
8865, 8768, 8669, 8563, 8454, 8337, 8202, 8065, 7913, 7749, 7584, 7421, 7243, 7062, 6885, 6712, 6545, 6374, 6206, 6038,
5853, 5666, 5474, 5271, 5061, 4854, 4652, 4461, 4263, 4079, 3903, 3729, 3567, 3416, 3273, 3130, 2988, 2848, 2714, 2560,
2418, 2273, 2125, 1990, 1860, 1723, 1587, 1446, 1309, 1169, 1025, 881, 734, 577, 419, 254, 82, -100, -281, -457,
-632, -817, -998, -1184, -1368, -1551, -1735, -1910, -2083, -2252, -2404, -2557, -2714, -2863, -3003, -3138, -3264, -3385, -3508, -3628,
-3747, -3866, -3985, -4104, -4220, -4336, -4440, -4547, -4653, -4765, -4888, -5010, -5133, -5261, -5409, -5557, -5720, -5893, -6073, -6270,
-6464, -6652, -6847, -7032, -7210, -7397, -7584, -7770, -7949, -8121, -8292, -8461, -8624, -8788, -8940, -9085, -9212, -9317, -9394, -9445,
-9469, -9480, -9476, -9460, -9431, -9384, -9325, -9270, -9200, -9124, -9043, -8951, -8854, -8729, -8580, -8413, -8217, -8014, -7810, -7613,
-7401, -7192, -6973, -6751, -6515, -6270, -6012, -5730, -5436, -5105, -4746, -4349, -3924, -3479, -3032, -2572, -2123, -1666, -1197, -723,
-236, 255, 744, 1240, 1719, 2192, 2653, 3098, 3505, 3894, 4241, 4540, 4799, 5018, 5208, 5374, 5513, 5642, 5747, 5834,
5893, 5927, 5947, 5936, 5894, 5834, 5749, 5648, 5518, 5377, 5229, 5081, 4933, 4797, 4663, 4520, 4383, 4242, 4093, 3936,
3761, 3586, 3400, 3202, 3010, 2808, 2608, 2412, 2232, 2058, 1885, 1712, 1547, 1373, 1200, 1022, 832, 629, 431, 228,
22, -195, -401, -607, -806, -1002, -1191, -1377, -1565, -1750, -1930, -2118, -2314, -2516, -2714, -2910, -3112, -3309, -3506, -3701,
-3882, -4054, -4219, -4376, -4528, -4662, -4797, -4935, -5062, -5191, -5314, -5430, -5537, -5638, -5730, -5814, -5869, -5915, -5944, -5958,
-5952, -5925, -5882, -5820, -5747, -5667, -5571, -5462, -5334, -5188, -5021, -4833, -4613, -4377, -4127, -3847, -3536, -3189, -2804, -2388,
-1953, -1493, -1020, -526, -16, 515, 1062, 1630, 2223, 2819, 3411, 4006, 4597, 5178, 5746, 6297, 6827, 7322, 7782, 8207,
8593, 8937, 9257, 9554, 9825, 10059, 10261, 10415, 10534, 10608, 10657, 10657, 10625, 10569, 10495, 10384, 10254, 10115, 9966, 9815,
9667, 9530, 9387, 9234, 9076, 8913, 8747, 8563, 8378, 8202, 8023, 7844, 7671, 7500, 7325, 7167, 7023, 6880, 6738, 6600,
6461, 6315, 6160, 6000, 5825, 5646, 5467, 5296, 5113, 4933, 4748, 4577, 4398, 4222, 4047, 3877, 3695, 3520, 3339, 3147,
2951, 2750, 2555, 2367, 2173, 1990, 1811, 1641, 1473, 1315, 1160, 1011, 857, 722, 576, 427, 277, 126, -20, -165,
-306, -443, -580, -713, -836, -967, -1096, -1222, -1347, -1483, -1611, -1748, -1889, -2041, -2193, -2340, -2488, -2641, -2788, -2933,
-3073, -3223, -3364, -3505, -3645, -3794, -3931, -4078, -4224, -4378, -4529, -4680, -4822, -4971, -5111, -5240, -5375, -5500, -5627, -5751,
-5883, -6011, -6126, -6255, -6389, -6524, -6673, -6811, -6951, -7090, -7227, -7355, -7482, -7602, -7726, -7844, -7966, -8089, -8209, -8321,
-8438, -8556, -8678, -8797, -8903, -9006, -9102, -9175, -9238, -9282, -9317, -9339, -9360, -9365, -9358, -9332, -9293, -9237, -9167, -9084,
-8981, -8851, -8696, -8516, -8300, -8051, -7769, -7474, -7164, -6824, -6474, -6098, -5690, -5264, -4818, -4362, -3884, -3388, -2880, -2365,
-1834, -1284, -741, -203, 317, 813, 1291, 1743, 2183, 2601, 2999, 3376, 3727, 4057, 4364, 4641, 4902, 5146, 5355, 5553,
5710, 5841, 5936, 6003, 6047, 6072, 6084, 6079, 6057, 6022, 5984, 5929, 5867, 5791, 5710, 5614, 5505, 5385, 5251, 5095,
4930, 4759, 4580, 4400, 4212, 4028, 3845, 3664, 3479, 3304, 3121, 2935, 2745, 2556, 2361, 2160, 1947, 1735, 1525, 1306,
1094, 883, 684, 492, 308, 130, -43, -223, -393, -567, -745, -921, -1104, -1294, -1477, -1663, -1844, -2029, -2207, -2373,
-2527, -2685, -2833, -2988, -3137, -3295, -3454, -3617, -3787, -3966, -4137, -4316, -4492, -4662, -4823, -4975, -5112, -5254, -5377, -5502,
-5624, -5742, -5854, -5965, -6066, -6164, -6249, -6323, -6386, -6416, -6436, -6423, -6383, -6315, -6224, -6111, -5985, -5831, -5657, -5451,
-5220, -4963, -4683, -4370, -4027, -3644, -3225, -2757, -2254, -1721, -1177, -611, -41, 530, 1106, 1690, 2284, 2890, 3489, 4083,
4667, 5238, 5792, 6325, 6841, 7340, 7794, 8228, 8620, 8981, 9303, 9597, 9873, 10127, 10358, 10559, 10726, 10854, 10957, 11024,
11062, 11071, 11055, 11020, 10958, 10876, 10775, 10656, 10526, 10392, 10259, 10107, 9949, 9777, 9601, 9410, 9216, 9020, 8821, 8621,
8424, 8229, 8026, 7818, 7616, 7425, 7236, 7040, 6849, 6662, 6469, 6280, 6093, 5907, 5722, 5540, 5368, 5193, 5012, 4838,
4656, 4470, 4289, 4110, 3924, 3734, 3547, 3361, 3171, 2989, 2800, 2621, 2433, 2265, 2084, 1904, 1716, 1530, 1351, 1174,
987, 812, 642, 476, 314, 151, -3, -152, -301, -437, -581, -721, -871, -1017, -1163, -1300, -1444, -1582, -1713, -1844,
-1966, -2090, -2214, -2329, -2450, -2577, -2697, -2830, -2969, -3113, -3260, -3406, -3556, -3715, -3863, -4007, -4150, -4296, -4439, -4583,
-4729, -4878, -5026, -5182, -5345, -5515, -5682, -5848, -6014, -6183, -6342, -6495, -6641, -6781, -6925, -7065, -7201, -7340, -7483, -7620,
-7770, -7913, -8062, -8209, -8348, -8487, -8619, -8737, -8843, -8940, -9037, -9129, -9216, -9300, -9387, -9467, -9541, -9609, -9675, -9724,
-9765, -9797, -9817, -9812, -9788, -9744, -9689, -9613, -9527, -9428, -9320, -9192, -9042, -8873, -8678, -8454, -8204, -7929, -7637, -7323,
-6974, -6600, -6202, -5784, -5343, -4881, -4405, -3916, -3406, -2882, -2330, -1767, -1192, -617, -52, 491, 1026, 1535, 2032, 2500,
2949, 3377, 3781, 4150, 4496, 4814, 5110, 5382, 5625, 5831, 6005, 6136, 6233, 6290, 6315, 6320, 6298, 6267, 6225, 6161,
6087, 6005, 5913, 5802, 5684, 5565, 5423, 5277, 5116, 4948, 4767, 4577, 4392, 4204, 4030, 3850, 3677, 3505, 3334, 3159,
2978, 2797, 2615, 2435, 2249, 2058, 1865, 1667, 1465, 1273, 1081, 899, 712, 534, 362, 177, -9, -199, -387, -572,
-761, -950, -1136, -1329, -1515, -1703, -1887, -2064, -2244, -2414, -2582, -2752, -2923, -3100, -3274, -3447, -3619, -3787, -3946, -4111,
-4265, -4420, -4568, -4709, -4839, -4968, -5076, -5184, -5295, -5402, -5510, -5604, -5686, -5762, -5825, -5873, -5911, -5938, -5946, -5937,
-5909, -5868, -5802, -5714, -5614, -5508, -5388, -5242, -5076, -4882, -4657, -4400, -4118, -3806, -3474, -3110, -2722, -2298, -1842, -1347,
-836, -307, 230, 773, 1325, 1891, 2462, 3042, 3611, 4176, 4726, 5268, 5796, 6310, 6795, 7267, 7699, 8101, 8456, 8772,
9052, 9301, 9509, 9703, 9864, 9994, 10092, 10169, 10224, 10267, 10283, 10285, 10269, 10228, 10173, 10095, 9994, 9884, 9765, 9641,
9513, 9372, 9236, 9085, 8940, 8796, 8652, 8505, 8357, 8199, 8043, 7875, 7698, 7516, 7333, 7148, 6967, 6787, 6604, 6416,
6236, 6061, 5891, 5722, 5555, 5390, 5223, 5046, 4865, 4682, 4499, 4316, 4137, 3961, 3779, 3601, 3425, 3258, 3094, 2929,
2769, 2611, 2449, 2287, 2120, 1945, 1776, 1607, 1432, 1270, 1105, 943, 777, 619, 474, 328, 179, 40, -105, -243,
-392, -542, -692, -843, -995, -1136, -1278, -1419, -1553, -1692, -1827, -1951, -2080, -2210, -2333, -2461, -2592, -2732, -2880, -3025,
-3174, -3321, -3467, -3614, -3760, -3908, -4055, -4198, -4349, -4503, -4652, -4801, -4955, -5113, -5276, -5436, -5600, -5768, -5924, -6083,
-6235, -6391, -6537, -6679, -6826, -6976, -7115, -7253, -7390, -7526, -7663, -7798, -7923, -8052, -8169, -8282, -8393, -8494, -8589, -8682,
-8771, -8857, -8943, -9012, -9079, -9133, -9183, -9223, -9242, -9255, -9254, -9243, -9222, -9179, -9127, -9054, -8963, -8861, -8743, -8600,
-8433, -8240, -8022, -7770, -7485, -7174, -6841, -6482, -6113, -5723, -5320, -4897, -4454, -4003, -3542, -3066, -2586, -2101, -1610, -1113,
-609, -98, 400, 875, 1334, 1767, 2173, 2546, 2905, 3238, 3558, 3856, 4130, 4383, 4618, 4826, 5023, 5202, 5358, 5488,
5605, 5685, 5741, 5766, 5769, 5761, 5739, 5703, 5656, 5597, 5518, 5430, 5321, 5211, 5089, 4959, 4818, 4679, 4521, 4350,
4167, 3977, 3791, 3602, 3415, 3228, 3037, 2844, 2643, 2443, 2240, 2037, 1840, 1648, 1452, 1256, 1055, 849, 650, 447,
253, 62, -129, -316, -504, -690, -880, -1071, -1256, -1431, -1610, -1782, -1961, -2140, -2318, -2492, -2671, -2840, -3005, -3165,
-3326, -3486, -3649, -3814, -3981, -4135, -4286, -4429, -4585, -4728, -4869, -5008, -5138, -5259, -5365, -5464, -5551, -5630, -5703, -5771,
-5831, -5881, -5910, -5923, -5917, -5903, -5862, -5799, -5717, -5610, -5461, -5291, -5085, -4857, -4602, -4335, -4048, -3759, -3432, -3079,
-2697, -2280, -1839, -1370, -875, -364, 170, 724, 1285, 1846, 2402, 2943, 3469, 3968, 4463, 4944, 5413, 5868, 6301, 6721,
7121, 7494, 7856, 8192, 8505, 8784, 9036, 9246, 9431, 9584, 9708, 9812, 9894, 9960, 9999, 10020, 10020, 10008, 9974, 9938,
9883, 9811, 9727, 9621, 9508, 9384, 9247, 9115, 8972, 8827, 8677, 8517, 8351, 8181, 8005, 7832, 7665, 7488, 7313, 7130,
6952, 6777, 6602, 6426, 6259, 6089, 5926, 5752, 5580, 5403, 5230, 5054, 4886, 4718, 4557, 4387, 4222, 4062, 3899, 3737,
3581, 3429, 3277, 3117, 2954, 2784, 2618, 2445, 2284, 2122, 1965, 1809, 1652, 1499, 1345, 1191, 1039, 888, 742, 593,
433, 275, 116, -40, -194, -345, -493, -631, -773, -911, -1047, -1184, -1318, -1454, -1590, -1720, -1865, -2006, -2153, -2295,
-2442, -2581, -2719, -2854, -2989, -3117, -3247, -3384, -3528, -3664, -3809, -3953, -4097, -4252, -4405, -4560, -4717, -4874, -5027, -5178,
-5325, -5470, -5611, -5754, -5906, -6056, -6208, -6364, -6516, -6675, -6831, -6984, -7135, -7293, -7438, -7586, -7720, -7854, -7976, -8093,
-8213, -8331, -8442, -8555, -8657, -8752, -8845, -8923, -8995, -9060, -9110, -9157, -9188, -9203, -9208, -9188, -9160, -9116, -9057, -8985,
-8892, -8787, -8661, -8518, -8348, -8164, -7956, -7729, -7481, -7219, -6924, -6609, -6258, -5884, -5488, -5058, -4615, -4151, -3680, -3185,
-2686, -2180, -1672, -1153, -640, -126, 373, 868, 1359, 1843, 2317, 2777, 3217, 3627, 4009, 4353, 4663, 4939, 5184, 5407,
5596, 5758, 5897, 6007, 6089, 6161, 6206, 6243, 6259, 6256, 6233, 6183, 6115, 6022, 5911, 5797, 5675, 5545, 5414, 5274,
5127, 4978, 4825, 4668, 4518, 4361, 4197, 4028, 3853, 3669, 3473, 3276, 3081, 2890, 2706, 2519, 2333, 2148, 1960, 1769,
1579, 1386, 1196, 1003, 804, 607, 402, 186, -23, -222, -422, -612, -800, -990, -1170, -1355, -1546, -1734, -1920, -2103,
-2288, -2477, -2668, -2863, -3055, -3241, -3419, -3586, -3753, -3904, -4055, -4203, -4364, -4514, -4669, -4812, -4962, -5097, -5240, -5368,
-5504, -5617, -5730, -5822, -5896, -5957, -5999, -6036, -6065, -6094, -6111, -6118, -6105, -6077, -6035, -5975, -5901, -5804, -5679, -5527,
-5339, -5116, -4866, -4584, -4288, -3984, -3660, -3316, -2941, -2534, -2095, -1624, -1131, -617, -74, 488, 1078, 1672, 2279, 2880,
3481, 4053, 4613, 5156, 5681, 6183, 6659, 7118, 7546, 7943, 8309, 8651, 8962, 9239, 9484, 9699, 9878, 10015, 10133, 10218,
10276, 10310, 10319, 10312, 10281, 10232, 10162, 10089, 10003, 9907, 9798, 9683, 9558, 9425, 9285, 9144, 9001, 8852, 8695, 8534,
8366, 8192, 8011, 7829, 7645, 7465, 7284, 7102, 6917, 6731, 6544, 6363, 6180, 6001, 5819, 5637, 5456, 5268, 5074, 4882,
4694, 4507, 4330, 4152, 3980, 3810, 3642, 3468, 3304, 3141, 2977, 2814, 2652, 2489, 2318, 2149, 1985, 1820, 1666, 1509,
1360, 1208, 1061, 907, 758, 605, 457, 308, 156, 6, -147, -310, -464, -623, -774, -919, -1068, -1209, -1354, -1499,
-1642, -1788, -1934, -2074, -2219, -2362, -2506, -2657, -2803, -2952, -3099, -3242, -3389, -3531, -3668, -3804, -3952, -4100, -4249, -4400,
-4552, -4705, -4847, -5000, -5156, -5310, -5464, -5616, -5765, -5916, -6067, -6209, -6360, -6505, -6665, -6822, -6979, -7129, -7275, -7413,
-7563, -7706, -7847, -7988, -8128, -8263, -8394, -8518, -8644, -8771, -8891, -9010, -9128, -9235, -9331, -9419, -9495, -9566, -9626, -9684,
-9737, -9776, -9809, -9825, -9833, -9820, -9794, -9749, -9685, -9596, -9483, -9340, -9171, -8979, -8763, -8519, -8257, -7971, -7660, -7331,
-6969, -6579, -6154, -5704, -5222, -4713, -4184, -3631, -3069, -2501, -1927, -1360, -798, -236, 302, 829, 1349, 1845, 2330, 2801,
3257, 3696, 4110, 4496, 4843, 5160, 5437, 5687, 5901, 6093, 6259, 6395, 6512, 6602, 6660, 6712, 6745, 6767, 6766, 6752,
6710, 6650, 6556, 6456, 6332, 6206, 6072, 5932, 5786, 5635, 5474, 5309, 5137, 4968, 4795, 4623, 4445, 4268, 4073, 3873,
3666, 3461, 3260, 3063, 2871, 2684, 2492, 2297, 2104, 1915, 1723, 1532, 1345, 1161, 968, 768, 570, 367, 170, -27,
-210, -394, -568, -751, -933, -1107, -1294, -1463, -1647, -1825, -1991, -2165, -2342, -2525, -2704, -2881, -3050, -3212, -3366, -3516,
-3665, -3815, -3963, -4108, -4255, -4392, -4520, -4649, -4778, -4902, -5027, -5142, -5251, -5341, -5410, -5466, -5512, -5543, -5569, -5579,
-5580, -5561, -5523, -5469, -5397, -5306, -5200, -5074, -4918, -4735, -4514, -4256, -3971, -3658, -3324, -2974, -2603, -2214, -1806, -1373,
-929, -467, 5, 493, 999, 1512, 2044, 2584, 3129, 3663, 4193, 4702, 5190, 5658, 6112, 6541, 6951, 7330, 7699, 8041,
8360, 8656, 8929, 9180, 9404, 9600, 9758, 9893, 9994, 10069, 10119, 10144, 10156, 10141, 10110, 10069, 10012, 9945, 9862, 9773,
9673, 9553, 9420, 9282, 9132, 8981, 8821, 8659, 8493, 8323, 8150, 7971, 7791, 7613, 7430, 7253, 7080, 6901, 6708, 6516,
6329, 6147, 5962, 5779, 5603, 5423, 5243, 5062, 4882, 4704, 4520, 4343, 4175, 4004, 3827, 3652, 3473, 3302, 3132, 2967,
2806, 2649, 2490, 2333, 2172, 2005, 1844, 1685, 1528, 1379, 1223, 1065, 917, 756, 611, 458, 310, 171, 30, -117,
-261, -415, -563, -720, -869, -1013, -1156, -1299, -1447, -1591, -1737, -1886, -2030, -2171, -2302, -2449, -2587, -2741, -2892, -3044,
-3198, -3345, -3496, -3644, -3789, -3943, -4095, -4243, -4401, -4553, -4697, -4850, -4997, -5150, -5308, -5467, -5630, -5787, -5940, -6093,
-6252, -6404, -6553, -6712, -6871, -7026, -7177, -7323, -7470, -7614, -7761, -7906, -8054, -8196, -8333, -8463, -8598, -8717, -8837, -8952,
-9065, -9175, -9273, -9359, -9438, -9501, -9560, -9614, -9656, -9689, -9715, -9727, -9726, -9714, -9682, -9641, -9578, -9502, -9408, -9286,
-9145, -8976, -8788, -8574, -8345, -8089, -7814, -7516, -7194, -6856, -6489, -6095, -5676, -5238, -4769, -4274, -3759, -3233, -2696, -2153,
-1607, -1067, -531, -5, 510, 1003, 1482, 1939, 2381, 2803, 3206, 3596, 3956, 4290, 4585, 4853, 5077, 5273, 5439, 5577,
5689, 5769, 5823, 5852, 5865, 5856, 5841, 5816, 5781, 5733, 5660, 5578, 5468, 5347, 5214, 5075, 4928, 4780, 4619, 4457,
4289, 4117, 3949, 3783, 3623, 3468, 3300, 3130, 2949, 2763, 2571, 2369, 2177, 1989, 1801, 1607, 1421, 1234, 1040, 854,
673, 500, 322, 149, -31, -218, -413, -606, -801, -990, -1174, -1358, -1536, -1713, -1886, -2061, -2235, -2401, -2555, -2713,
-2874, -3033, -3203, -3377, -3552, -3719, -3866, -4020, -4155, -4288, -4412, -4538, -4655, -4760, -4856, -4950, -5031, -5109, -5185, -5263,
-5336, -5393, -5431, -5451, -5451, -5428, -5392, -5334, -5266, -5183, -5077, -4954, -4816, -4650, -4476, -4280, -4070, -3844, -3578, -3281,
-2956, -2596, -2203, -1792, -1366, -920, -461, 9, 497, 991, 1497, 2004, 2518, 3027, 3540, 4055, 4560, 5069, 5563, 6034,
6491, 6918, 7318, 7689, 8032, 8346, 8630, 8882, 9114, 9312, 9489, 9645, 9778, 9878, 9965, 10021, 10058, 10068, 10065, 10047,
10011, 9959, 9898, 9821, 9742, 9646, 9548, 9446, 9334, 9215, 9088, 8954, 8817, 8667, 8519, 8375, 8228, 8068, 7911, 7751,
7583, 7413, 7239, 7066, 6901, 6731, 6553, 6379, 6197, 6014, 5833, 5660, 5493, 5323, 5151, 4985, 4810, 4634, 4457, 4279,
4110, 3946, 3776, 3607, 3437, 3267, 3099, 2935, 2777, 2624, 2466, 2314, 2155, 1999, 1834, 1669, 1506, 1349, 1192, 1040,
888, 732, 576, 425, 273, 128, -19, -164, -311, -458, -613, -770, -927, -1076, -1225, -1370, -1507, -1653, -1795, -1942,
-2086, -2231, -2372, -2514, -2651, -2799, -2947, -3102, -3261, -3416, -3564, -3712, -3855, -4000, -4150, -4301, -4455, -4609, -4762, -4917,
-5065, -5216, -5372, -5531, -5692, -5853, -6004, -6156, -6302, -6441, -6586, -6726, -6879, -7026, -7169, -7316, -7454, -7585, -7724, -7852,
-7986, -8114, -8235, -8354, -8458, -8561, -8656, -8751, -8838, -8932, -9008, -9087, -9154, -9203, -9243, -9266, -9278, -9282, -9268, -9237,
-9189, -9122, -9034, -8934, -8817, -8683, -8521, -8339, -8129, -7886, -7611, -7310, -6976, -6622, -6241, -5829, -5401, -4959, -4492, -4017,
-3533, -3039, -2533, -2012, -1480, -944, -396, 137, 667, 1175, 1669, 2147, 2605, 3029, 3426, 3797, 4136, 4444, 4733, 5001,
5261, 5493, 5709, 5895, 6057, 6186, 6284, 6359, 6413, 6440, 6445, 6432, 6398, 6337, 6267, 6188, 6108, 6018, 5919, 5818,
5691, 5552, 5401, 5241, 5070, 4895, 4714, 4538, 4346, 4153, 3953, 3753, 3561, 3375, 3185, 3004, 2813, 2622, 2419, 2210,
2001, 1797, 1587, 1389, 1192, 988, 784, 580, 382, 187, 2, -184, -363, -548, -733, -926, -1120, -1317, -1504, -1693,
-1868, -2048, -2225, -2407, -2586, -2759, -2927, -3096, -3249, -3410, -3568, -3733, -3901, -4070, -4232, -4390, -4540, -4682, -4814, -4948,
-5076, -5197, -5308, -5414, -5503, -5582, -5654, -5719, -5786, -5839, -5887, -5920, -5921, -5906, -5863, -5800, -5719, -5611, -5478, -5327,
-5148, -4942, -4715, -4463, -4194, -3903, -3593, -3258, -2891, -2489, -2065, -1613, -1143, -654, -141, 378, 906, 1441, 1974, 2509,
3029, 3542, 4049, 4540, 5018, 5492, 5950, 6393, 6818, 7224, 7604, 7956, 8281, 8570, 8827, 9051, 9245, 9412, 9556, 9678,
9772, 9847, 9904, 9933, 9950, 9941, 9920, 9882, 9830, 9757, 9677, 9572, 9459, 9329, 9197, 9059, 8916, 8768, 8619, 8460,
8300, 8126, 7950, 7781, 7610, 7431, 7259, 7076, 6894, 6707, 6513, 6331, 6149, 5966, 5791, 5614, 5432, 5250, 5065, 4884,
4708, 4537, 4372, 4198, 4028, 3854, 3675, 3505, 3332, 3168, 3001, 2840, 2679, 2512, 2347, 2183, 2018, 1862, 1704, 1557,
1402, 1251, 1089, 936, 779, 622, 469, 321, 178, 28, -121, -275, -423, -570, -717, -861, -1000, -1141, -1282, -1426,
-1574, -1720, -1865, -2004, -2140, -2277, -2414, -2558, -2702, -2840, -2986, -3123, -3258, -3400, -3538, -3681, -3825, -3975, -4125, -4273,
-4416, -4561, -4707, -4852, -4998, -5150, -5297, -5449, -5599, -5744, -5892, -6044, -6202, -6354, -6510, -6670, -6822, -6973, -7119, -7266,
-7418, -7567, -7715, -7869, -8013, -8154, -8294, -8428, -8562, -8691, -8817, -8941, -9062, -9164, -9269, -9355, -9444, -9524, -9599, -9672,
-9734, -9777, -9816, -9832, -9841, -9833, -9808, -9773, -9721, -9646, -9554, -9442, -9316, -9168, -9004, -8820, -8605, -8368, -8100, -7800,
-7468, -7110, -6720, -6304, -5864, -5396, -4905, -4400, -3881, -3351, -2813, -2258, -1699, -1130, -552, 30, 610, 1175, 1723, 2258,
2770, 3249, 3710, 4128, 4514, 4858, 5172, 5452, 5707, 5936, 6146, 6335, 6494, 6622, 6720, 6795, 6839, 6861, 6863, 6842,
6796, 6729, 6643, 6540, 6427, 6307, 6189, 6067, 5940, 5806, 5657, 5501, 5349, 5176, 5005, 4834, 4656, 4479, 4286, 4095,
3901, 3708, 3514, 3335, 3156, 2976, 2789, 2606, 2422, 2221, 2030, 1836, 1645, 1455, 1258, 1056, 862, 663, 465, 281,
96, -79, -258, -437, -622, -808, -994, -1179, -1356, -1537, -1717, -1898, -2073, -2248, -2428, -2597, -2757, -2916, -3069, -3220,
-3369, -3520, -3679, -3831, -3976, -4121, -4255, -4386, -4507, -4623, -4736, -4837, -4926, -5003, -5068, -5127, -5172, -5214, -5250, -5280,
-5297, -5303, -5288, -5250, -5195, -5118, -5015, -4896, -4751, -4585, -4391, -4175, -3938, -3674, -3388, -3096, -2773, -2426, -2052, -1648,
-1215, -749, -260, 243, 759, 1289, 1824, 2366, 2899, 3433, 3960, 4475, 4972, 5465, 5935, 6396, 6834, 7263, 7665, 8045,
8391, 8710, 8991, 9247, 9461, 9640, 9800, 9931, 10031, 10115, 10176, 10213, 10229, 10228, 10209, 10181, 10129, 10070, 10001, 9914,
9815, 9699, 9577, 9446, 9312, 9179, 9040, 8896, 8744, 8577, 8414, 8246, 8073, 7898, 7729, 7556, 7380, 7200, 7015, 6828,
6648, 6467, 6287, 6107, 5929, 5741, 5556, 5371, 5189, 5002, 4823, 4652, 4482, 4310, 4138, 3971, 3798, 3624, 3458, 3293,
3128, 2964, 2796, 2634, 2464, 2300, 2134, 1975, 1822, 1676, 1521, 1369, 1216, 1056, 897, 740, 590, 437, 279, 125,
-34, -187, -346, -496, -645, -787, -935, -1081, -1231, -1374, -1536, -1681, -1835, -1985, -2132, -2281, -2430, -2582, -2736, -2887,
-3028, -3177, -3319, -3471, -3620, -3774, -3932, -4096, -4253, -4414, -4575, -4734, -4888, -5044, -5202, -5366, -5528, -5685, -5841, -5997,
-6156, -6313, -6477, -6646, -6808, -6975, -7132, -7293, -7448, -7594, -7746, -7900, -8053, -8198, -8344, -8487, -8626, -8762, -8895, -9031,
-9165, -9289, -9406, -9516, -9612, -9706, -9787, -9867, -9940, -10005, -10057, -10095, -10124, -10137, -10131, -10114, -10078, -10027, -9952, -9849,
-9730, -9587, -9422, -9234, -9034, -8805, -8552, -8268, -7954, -7610, -7240, -6843, -6423, -5972, -5497, -5007, -4498, -3980, -3454, -2927,
-2405, -1881, -1350, -827, -299, 222, 736, 1235, 1714, 2178, 2616, 3029, 3414, 3766, 4088, 4382, 4631, 4861, 5064, 5247,
5414, 5558, 5684, 5780, 5857, 5909, 5941, 5948, 5943, 5905, 5849, 5777, 5684, 5574, 5460, 5336, 5211, 5080, 4948, 4807,
4658, 4500, 4340, 4168, 3996, 3816, 3630, 3444, 3253, 3044, 2855, 2650, 2470, 2284, 2104, 1919, 1739, 1550, 1361, 1176,
987, 795, 603, 412, 221, 30, -166, -351, -535, -714, -891, -1056, -1225, -1398, -1572, -1745, -1922, -2093, -2265, -2440,
-2606, -2771, -2943, -3105, -3268, -3422, -3570, -3710, -3850, -3983, -4123, -4258, -4395, -4532, -4661, -4785, -4896, -4999, -5097, -5187,
-5267, -5330, -5378, -5409, -5427, -5434, -5423, -5407, -5377, -5339, -5281, -5203, -5099, -4970, -4816, -4635, -4429, -4198, -3935, -3655,
-3342, -3006, -2651, -2278, -1888, -1486, -1068, -635, -189, 284, 774, 1270, 1785, 2301, 2821, 3330, 3836, 4333, 4823, 5293,
5746, 6181, 6597, 6989, 7360, 7711, 8045, 8354, 8649, 8923, 9165, 9382, 9564, 9724, 9852, 9960, 10034, 10093, 10134, 10153,
10150, 10130, 10098, 10049, 9988, 9924, 9849, 9763, 9659, 9552, 9430, 9299, 9159, 9018, 8870, 8722, 8567, 8410, 8244, 8083,
7909, 7744, 7575, 7413, 7243, 7077, 6910, 6737, 6564, 6387, 6220, 6048, 5879, 5708, 5540, 5363, 5195, 5022, 4850, 4686,
4522, 4356, 4203, 4040, 3877, 3709, 3550, 3381, 3230, 3067, 2904, 2751, 2591, 2433, 2275, 2118, 1965, 1814, 1664, 1513,
1368, 1215, 1061, 912, 757, 607, 453, 306, 161, 9, -140, -290, -445, -584, -730, -869, -1012, -1155, -1305, -1447,
-1595, -1741, -1892, -2035, -2185, -2327, -2482, -2629, -2780, -2930, -3081, -3224, -3369, -3518, -3673, -3826, -3981, -4137, -4297, -4455,
-4610, -4764, -4919, -5078, -5235, -5395, -5550, -5709, -5863, -6015, -6171, -6333, -6490, -6648, -6808, -6959, -7107, -7251, -7397, -7539,
-7678, -7820, -7952, -8092, -8216, -8335, -8449, -8566, -8667, -8773, -8863, -8953, -9027, -9084, -9134, -9177, -9208, -9238, -9257, -9261,
-9249, -9223, -9177, -9119, -9041, -8944, -8823, -8685, -8519, -8330, -8109, -7877, -7619, -7346, -7053, -6732, -6390, -6015, -5611, -5187,
-4735, -4261, -3771, -3257, -2737, -2195, -1650, -1108, -578, -48, 459, 963, 1452, 1927, 2391, 2840, 3262, 3662, 4035, 4384,
4702, 4996, 5259, 5486, 5676, 5839, 5967, 6064, 6144, 6199, 6245, 6265, 6265, 6253, 6223, 6178, 6109, 6036, 5941, 5841,
5716, 5587, 5438, 5280, 5125, 4960, 4795, 4637, 4473, 4296, 4126, 3942, 3764, 3575, 3391, 3203, 3010, 2808, 2609, 2404,
2202, 1996, 1799, 1600, 1411, 1213, 1020, 822, 630, 430, 232, 34, -158, -361, -559, -765, -964, -1162, -1356, -1546,
-1731, -1910, -2090, -2269, -2449, -2630, -2810, -2996, -3166, -3342, -3521, -3693, -3865, -4034, -4197, -4354, -4498, -4635, -4771, -4898,
-5025, -5147, -5269, -5383, -5492, -5582, -5678, -5752, -5823, -5880, -5922, -5954, -5960, -5945, -5919, -5873, -5806, -5729, -5641, -5535,
-5408, -5260, -5086, -4886, -4658, -4394, -4106, -3798, -3451, -3077, -2678, -2256, -1808, -1356, -879, -397, 105, 620, 1140, 1676,
2222, 2773, 3326, 3867, 4400, 4917, 5420, 5899, 6361, 6788, 7200, 7571, 7918, 8229, 8515, 8767, 8999, 9207, 9390, 9549,
9674, 9776, 9853, 9898, 9923, 9927, 9915, 9882, 9841, 9783, 9715, 9628, 9533, 9435, 9330, 9217, 9101, 8973, 8841, 8697,
8544, 8397, 8234, 8078, 7913, 7752, 7587, 7416, 7240, 7068, 6888, 6714, 6538, 6359, 6183, 6006, 5823, 5645, 5465, 5286,
5108, 4934, 4761, 4587, 4410, 4238, 4063, 3887, 3716, 3544, 3378, 3214, 3050, 2885, 2724, 2566, 2403, 2243, 2087, 1935,
1778, 1619, 1463, 1302, 1146, 992, 837, 684, 541, 393, 245, 99, -51, -196, -341, -487, -630, -778, -924, -1073,
-1220, -1373, -1516, -1656, -1788, -1931, -2067, -2203, -2340, -2479, -2622, -2758, -2900, -3041, -3185, -3328, -3473, -3625, -3772, -3917,
-4055, -4200, -4341, -4487, -4631, -4780, -4931, -5082, -5235, -5382, -5535, -5685, -5840, -5991, -6146, -6297, -6443, -6592, -6735, -6878,
-7021, -7169, -7318, -7459, -7605, -7742, -7882, -8013, -8141, -8270, -8397, -8522, -8641, -8751, -8857, -8960, -9054, -9147, -9236, -9313,
-9386, -9443, -9489, -9525, -9550, -9563, -9566, -9556, -9532, -9490, -9425, -9347, -9246, -9132, -8989, -8827, -8640, -8416, -8168, -7892,
-7582, -7263, -6910, -6545, -6157, -5738, -5299, -4843, -4356, -3856, -3342, -2810, -2271, -1720, -1153, -595, -34, 515, 1040, 1547,
2030, 2498, 2948, 3370, 3776, 4156, 4514, 4848, 5159, 5442, 5700, 5926, 6126, 6300, 6434, 6540, 6614, 6662, 6691, 6702,
6694, 6677, 6645, 6588, 6522, 6439, 6348, 6242, 6129, 5987, 5848, 5689, 5526, 5352, 5167, 4993, 4809, 4626, 4451, 4265,
4076, 3887, 3703, 3511, 3318, 3124, 2926, 2724, 2520, 2315, 2108, 1909, 1710, 1512, 1319, 1130, 942, 749, 559, 372,
184, -7, -195, -390, -582, -775, -969, -1153, -1338, -1519, -1690, -1864, -2036, -2205, -2374, -2542, -2713, -2882, -3051, -3222,
-3391, -3555, -3724, -3881, -4034, -4181, -4324, -4450, -4578, -4699, -4818, -4931, -5038, -5140, -5235, -5324, -5400, -5464, -5524, -5565,
-5584, -5588, -5570, -5531, -5469, -5389, -5287, -5171, -5037, -4884, -4713, -4514, -4293, -4039, -3766, -3458, -3121, -2756, -2367, -1948,
-1509, -1049, -575, -88, 413, 928, 1440, 1956, 2487, 3008, 3535, 4058, 4578, 5093, 5587, 6063, 6525, 6969, 7388, 7776,
8136, 8473, 8773, 9042, 9284, 9495, 9681, 9846, 9985, 10106, 10198, 10260, 10299, 10318, 10311, 10289, 10250, 10193, 10123, 10039,
9939, 9825, 9704, 9579, 9443, 9304, 9162, 9009, 8843, 8683, 8512, 8331, 8146, 7965, 7782, 7594, 7404, 7213, 7017, 6826,
6633, 6444, 6249, 6060, 5868, 5686, 5497, 5315, 5132, 4947, 4764, 4585, 4401, 4222, 4044, 3866, 3687, 3510, 3334, 3162,
2991, 2826, 2666, 2503, 2342, 2181, 2021, 1856, 1690, 1526, 1367, 1207, 1051, 896, 738, 582, 429, 276, 130, -18,
-164, 0, -72, -282, -535, -838, -1126, -1380, -1555, -1646, -1671, -1647, -1561, -1433, -1262, -1070, -847, -614, -384, -167,
57, 273, 505, 765, 1074, 1422, 1794, 2166, 2530, 2868, 3185, 3485, 3761, 4018, 4253, 4473, 4667, 4822, 4956, 5089,
5208, 5350, 5502, 5661, 5805, 5936, 6075, 6229, 6391, 6582, 6806, 7040, 7259, 7462, 7634, 7770, 7871, 7955, 8010, 8023,
7984, 7887, 7739, 7548, 7317, 7062, 6789, 6504, 6210, 5903, 5576, 5240, 4904, 4585, 4285, 3990, 3722, 3480, 3255, 3047,
2855, 2681, 2533, 2403, 2273, 2149, 2030, 1915, 1795, 1674, 1569, 1476, 1385, 1287, 1189, 1092, 994, 895, 812, 737,
667, 597, 521, 434, 343, 248, 153, 61, -25, -111, -184, -245, -298, -357, -410, -452, -489, -522, -562, -604,
-647, -704, -769, -826, -872, -919, -963, -1005, -1040, -1082, -1125, -1167, -1212, -1258, -1307, -1369, -1442, -1544, -1660, -1781,
-1894, -1999, -2098, -2196, -2290, -2386, -2499, -2610, -2725, -2833, -2937, -3038, -3133, -3247, -3383, -3527, -3678, -3826, -3970, -4105,
-4228, -4345, -4475, -4609, -4731, -4853, -4980, -5105, -5225, -5355, -5513, -5688, -5867, -6048, -6227, -6394, -6547, -6704, -6868, -7045,
-7230, -7428, -7614, -7783, -7945, -8110, -8282, -8464, -8653, -8855, -9042, -9196, -9308, -9379, -9415, -9427, -9417, -9366, -9258, -9087,
-8843, -8512, -8105, -7639, -7110, -6504, -5826, -5058, -4189, -3227, -2201, -1139, -54, 1035, 2105, 3130, 4098, 4987, 5774, 6466,
7063, 7575, 8001, 8343, 8610, 8800, 8907, 8945, 8928, 8882, 8812, 8708, 8575, 8413, 8211, 7985, 7748, 7514, 7284, 7059,
6846, 6614, 6355, 6082, 5810, 5539, 5277, 5034, 4803, 4573, 4335, 4096, 3849, 3605, 3383, 3184, 3002, 2828, 2659, 2484,
2308, 2134, 1973, 1826, 1689, 1568, 1447, 1319, 1176, 1032, 898, 775, 667, 576, 486, 385, 272, 159, 34, -91,
-208, -311, -418, -539, -663, -799, -946, -1087, -1220, -1332, -1441, -1544, -1652, -1769, -1901, -2027, -2153, -2270, -2382, -2489,
-2603, -2730, -2860, -2987, -3109, -3220, -3312, -3386, -3468, -3562, -3665, -3782, -3908, -4030, -4139, -4241, -4353, -4467, -4596, -4741,
-4894, -5037, -5164, -5287, -5397, -5504, -5626, -5773, -5934, -6100, -6265, -6426, -6572, -6716, -6867, -7023, -7170, -7304, -7411, -7480,
-7495, -7477, -7430, -7358, -7254, -7128, -6961, -6728, -6423, -6044, -5581, -5035, -4399, -3671, -2846, -1941, -966, 51, 1087, 2113,
3121, 4095, 5014, 5873, 6661, 7355, 7954, 8469, 8903, 9251, 9520, 9707, 9807, 9814, 9739, 9615, 9459, 9282, 9102, 8925,
8729, 8508, 8271, 8022, 7758, 7503, 7257, 7021, 6780, 6534, 6276, 6013, 5753, 5511, 5302, 5114, 4939, 4774, 4602, 4418,
4229, 4045, 3865, 3689, 3523, 3363, 3197, 3028, 2859, 2704, 2560, 2439, 2333, 2235, 2135, 2024, 1911, 1787, 1664, 1542,
1438, 1341, 1244, 1147, 1050, 951, 861, 787, 717, 662, 613, 560, 501, 433, 362, 289, 220, 164, 111, 54,
-6, -69, -130, -196, -252, -302, -348, -396, -444, -503, -567, -635, -704, -765, -818, -877, -930, -992, -1062, -1134,
-1212, -1283, -1352, -1420, -1485, -1555, -1631, -1717, -1806, -1891, -1970, -2047, -2119, -2195, -2282, -2378, -2483, -2589, -2693, -2790,
-2886, -2985, -3092, -3210, -3343, -3480, -3616, -3746, -3878, -4009, -4144, -4296, -4465, -4646, -4826, -5005, -5177, -5342, -5505, -5680,
-5866, -6056, -6252, -6435, -6608, -6768, -6918, -7078, -7241, -7414, -7587, -7749, -7879, -7985, -8067, -8129, -8179, -8239, -8292, -8325,
-8328, -8305, -8240, -8146, -8028, -7892, -7716, -7482, -7183, -6796, -6315, -5753, -5119, -4430, -3686, -2892, -2048, -1154, -218, 742,
1704, 2653, 3577, 4462, 5300, 6063, 6739, 7317, 7787, 8155, 8429, 8620, 8736, 8779, 8755, 8671, 8534, 8369, 8182, 7987,
7783, 7567, 7326, 7058, 6770, 6481, 6193, 5922, 5671, 5438, 5207, 4976, 4745, 4516, 4297, 4093, 3913, 3742, 3571, 3392,
3205, 3011, 2815, 2632, 2470, 2326, 2185, 2052, 1911, 1758, 1602, 1454, 1311, 1187, 1064, 945, 820, 682, 540, 406,
275, 163, 69, -18, -108, -206, -306, -416, -526, -616, -700, -781, -862, -951, -1046, -1152, -1257, -1352, -1432, -1509,
-1583, -1664, -1764, -1874, -1994, -2111, -2226, -2337, -2442, -2552, -2681, -2824, -2979, -3138, -3291, -3435, -3569, -3706, -3852, -4009,
-4180, -4360, -4537, -4703, -4869, -5030, -5194, -5371, -5567, -5776, -5974, -6163, -6343, -6499, -6651, -6804, -6966, -7132, -7291, -7440,
-7574, -7679, -7766, -7848, -7917, -7973, -8009, -7993, -7917, -7766, -7542, -7242, -6865, -6413, -5879, -5261, -4556, -3769, -2900, -1957,
-952, 104, 1205, 2326, 3436, 4509, 5521, 6447, 7284, 8026, 8672, 9215, 9651, 9979, 10195, 10312, 10351, 10340, 10287, 10205,
10096, 9951, 9760, 9532, 9282, 9007, 8738, 8479, 8225, 7968, 7706, 7433, 7157, 6879, 6614, 6370, 6145, 5919, 5699, 5469,
5234, 4989, 4756, 4539, 4340, 4152, 3972, 3793, 3610, 3429, 3251, 3089, 2940, 2806, 2677, 2549, 2414, 2279, 2139, 2008,
1892, 1785, 1688, 1593, 1496, 1397, 1293, 1195, 1104, 1025, 948, 876, 805, 724, 638, 551, 470, 399, 330, 262,
202, 131, 58, -21, -96, -168, -234, -295, -353, -413, -475, -547, -616, -682, -739, -795, -848, -904, -959, -1028,
-1097, -1163, -1223, -1284, -1338, -1391, -1452, -1522, -1596, -1672, -1747, -1819, -1892, -1960, -2035, -2120, -2213, -2306, -2407, -2502,
-2594, -2682, -2774, -2873, -2981, -3101, -3222, -3343, -3459, -3571, -3688, -3804, -3930, -4068, -4209, -4346, -4482, -4609, -4736, -4864,
-5007, -5163, -5324, -5489, -5654, -5810, -5958, -6104, -6257, -6420, -6590, -6766, -6937, -7096, -7242, -7388, -7535, -7689, -7855, -8024,
-8182, -8321, -8424, -8500, -8543, -8569, -8580, -8572, -8531, -8444, -8298, -8095, -7825, -7504, -7126, -6685, -6164, -5556, -4849, -4043,
-3159, -2214, -1234, -237, 763, 1742, 2698, 3602, 4443, 5210, 5904, 6523, 7073, 7543, 7933, 8236, 8456, 8591, 8659, 8673,
8642, 8570, 8458, 8313, 8131, 7921, 7694, 7469, 7250, 7039, 6826, 6611, 6383, 6138, 5890, 5650, 5421, 5208, 5002, 4803,
4596, 4387, 4173, 3961, 3764, 3588, 3424, 3272, 3116, 2958, 2797, 2631, 2478, 2338, 2209, 2090, 1972, 1847, 1714, 1573,
1439, 1312, 1197, 1096, 1001, 899, 790, 678, 567, 454, 352, 260, 169, 74, -28, -140, -259, -381, -489, -587,
-675, -765, -854, -953, -1059, -1168, -1272, -1373, -1468, -1563, -1662, -1773, -1898, -2022, -2149, -2268, -2376, -2478, -2578, -2689,
-2807, -2940, -3078, -3223, -3356, -3489, -3622, -3768, -3922, -4088, -4264, -4439, -4602, -4756, -4908, -5059, -5220, -5393, -5586, -5786,
-5982, -6170, -6350, -6520, -6697, -6875, -7055, -7229, -7389, -7524, -7634, -7722, -7797, -7865, -7927, -7973, -7994, -7963, -7875, -7726,
-7502, -7215, -6854, -6414, -5886, -5268, -4560, -3765, -2889, -1944, -929, 146, 1263, 2401, 3536, 4634, 5668, 6627, 7505, 8291,
8971, 9544, 10003, 10334, 10547, 10663, 10701, 10682, 10624, 10530, 10394, 10208, 9982, 9720, 9438, 9146, 8859, 8575, 8292, 8002,
7704, 7397, 7085, 6792, 6519, 6262, 6021, 5782, 5544, 5299, 5054, 4820, 4601, 4396, 4211, 4037, 3862, 3683, 3504, 3331,
3168, 3016, 2875, 2743, 2612, 2481, 2346, 2213, 2085, 1971, 1864, 1770, 1678, 1586, 1489, 1386, 1287, 1190, 1101, 1015,
936, 856, 775, 692, 608, 528, 456, 393, 332, 275, 210, 140, 69, -4, -74, -140, -201, -260, -318, -383,
-446, -510, -573, -630, -680, -732, -781, -838, -899, -967, -1036, -1100, -1159, -1217, -1273, -1327, -1389, -1453, -1516, -1584,
-1647, -1711, -1773, -1840, -1917, -1999, -2089, -2185, -2275, -2360, -2444, -2527, -2612, -2703, -2802, -2907, -3014, -3119, -3223, -3333,
-3449, -3575, -3712, -3857, -4005, -4149, -4288, -4419, -4547, -4686, -4837, -4995, -5163, -5331, -5501, -5668, -5837, -6013, -6197, -6392,
-6598, -6796, -6981, -7150, -7312, -7466, -7622, -7790, -7962, -8134, -8295, -8436, -8558, -8659, -8746, -8822, -8891, -8937, -8948, -8910,
-8820, -8672, -8483, -8245, -7960, -7614, -7191, -6673, -6049, -5322, -4495, -3590, -2618, -1596, -541, 544, 1625, 2677, 3682, 4625,
5490, 6272, 6974, 7585, 8098, 8508, 8815, 9027, 9154, 9203, 9191, 9117, 8985, 8801, 8576, 8323, 8061, 7799, 7546, 7300,
7054, 6800, 6533, 6262, 5995, 5738, 5497, 5269, 5044, 4819, 4587, 4355, 4129, 3911, 3714, 3536, 3369, 3203, 3032, 2857,
2680, 2511, 2350, 2204, 2065, 1934, 1797, 1658, 1513, 1371, 1235, 1114, 1007, 906, 803, 696, 582, 468, 352, 250,
154, 67, -21, -113, -212, -321, -430, -536, -628, -717, -804, -893, -986, -1091, -1201, -1308, -1411, -1507, -1598, -1693,
-1799, -1912, -2036, -2165, -2287, -2404, -2515, -2622, -2742, -2863, -2997, -3136, -3278, -3412, -3538, -3666, -3791, -3926, -4074, -4237,
-4392, -4550, -4690, -4832, -4968, -5112, -5267, -5435, -5607, -5779, -5945, -6099, -6248, -6394, -6550, -6712, -6880, -7033, -7177, -7295,
-7400, -7484, -7562, -7627, -7679, -7703, -7687, -7613, -7480, -7284, -7020, -6691, -6293, -5810, -5243, -4583, -3839, -3023, -2138, -1203,
-225, 793, 1830, 2861, 3869, 4825, 5721, 6547, 7298, 7965, 8551, 9036, 9417, 9694, 9875, 9977, 10019, 10014, 9977, 9902,
9779, 9619, 9426, 9209, 8983, 8757, 8540, 8317, 8089, 7847, 7589, 7318, 7052, 6792, 6549, 6312, 6081, 5841, 5601, 5358,
5125, 4901, 4697, 4511, 4336, 4166, 3993, 3816, 3643, 3469, 3314, 3167, 3029, 2895, 2760, 2623, 2492, 2359, 2247, 2140,
2051, 1964, 1875, 1785, 1687, 1584, 1487, 1393, 1304, 1220, 1135, 1049, 962, 874, 787, 709, 638, 573, 509, 441,
368, 289, 204, 123, 48, -25, -93, -162, -226, -297, -369, -435, -498, -554, -608, -661, -718, -784, -854, -928,
-996, -1066, -1129, -1191, -1255, -1317, -1387, -1460, -1533, -1604, -1675, -1744, -1820, -1902, -1991, -2091, -2195, -2300, -2400, -2496,
-2593, -2687, -2789, -2898, -3012, -3130, -3244, -3354, -3469, -3585, -3711, -3852, -3998, -4146, -4296, -4438, -4572, -4704, -4840, -4986,
-5140, -5301, -5466, -5627, -5785, -5939, -6100, -6270, -6449, -6639, -6826, -7005, -7167, -7320, -7458, -7602, -7749, -7903, -8052, -8188,
-8304, -8393, -8449, -8487, -8509, -8509, -8485, -8422, -8305, -8130, -7890, -7592, -7248, -6843, -6382, -5851, -5234, -4529, -3739, -2875,
-1959, -1004, -34, 937, 1894, 2816, 3690, 4500, 5237, 5904, 6500, 7024, 7475, 7847, 8143, 8359, 8503, 8582, 8609, 8591,
8531, 8425, 8275, 8089, 7880, 7655, 7430, 7209, 6993, 6776, 6549, 6315, 6072, 5827, 5589, 5366, 5157, 4957, 4752, 4546,
4338, 4127, 3926, 3738, 3565, 3405, 3245, 3088, 2921, 2751, 2586, 2433, 2291, 2160, 2037, 1911, 1782, 1644, 1505, 1370,
1240, 1122, 1008, 896, 777, 649, 518, 389, 262, 147, 45, -60, -161, -275, -397, -528, -650, -768, -880, -984,
-1092, -1202, -1323, -1446, -1571, -1687, -1799, -1901, -2004, -2110, -2233, -2367, -2505, -2644, -2779, -2907, -3033, -3162, -3300, -3449,
-3608, -3764, -3920, -4067, -4208, -4351, -4506, -4671, -4849, -5035, -5212, -5385, -5549, -5703, -5859, -6027, -6201, -6381, -6553, -6716,
-6862, -6992, -7110, -7229, -7344, -7451, -7542, -7609, -7638, -7631, -7591, -7522, -7428, -7296, -7118, -6878, -6563, -6169, -5687, -5125,
-4481, -3760, -2959, -2086, -1147, -157, 862, 1882, 2885, 3868, 4807, 5703, 6533, 7288, 7945, 8514, 8988, 9379, 9690, 9925,
10080, 10152, 10149, 10076, 9951, 9796, 9621, 9435, 9236, 9016, 8777, 8517, 8244, 7967, 7705, 7453, 7209, 6966, 6722, 6473,
6224, 5976, 5742, 5526, 5320, 5124, 4924, 4721, 4514, 4309, 4115, 3933, 3769, 3615, 3463, 3318, 3166, 3016, 2876, 2738,
2614, 2493, 2377, 2260, 2138, 2014, 1893, 1776, 1675, 1581, 1497, 1415, 1335, 1245, 1160, 1077, 997, 922, 851, 779,
710, 631, 553, 475, 400, 334, 275, 220, 164, 109, 43, -23, -91, -156, -219, -280, -343, -410, -478, -550,
-623, -687, -748, -804, -858, -912, -977, -1044, -1115, -1189, -1263, -1335, -1403, -1476, -1551, -1631, -1715, -1798, -1878, -1952,
-2023, -2096, -2174, -2262, -2358, -2462, -2566, -2676, -2777, -2880, -2986, -3100, -3218, -3341, -3469, -3596, -3717, -3836, -3959, -4091,
-4235, -4394, -4560, -4728, -4894, -5055, -5211, -5373, -5538, -5712, -5892, -6073, -6246, -6410, -6568, -6725, -6888, -7058, -7234, -7412,
-7581, -7732, -7864, -7976, -8082, -8181, -8279, -8367, -8436, -8476, -8480, -8442, -8374, -8269, -8130, -7954, -7720, -7425, -7045, -6589,
-6054, -5447, -4774, -4039, -3236, -2365, -1435, -457, 552, 1567, 2565, 3530, 4439, 5278, 6039, 6705, 7271, 7743, 8120, 8415,
8631, 8772, 8850, 8861, 8815, 8719, 8591, 8440, 8269, 8089, 7886, 7667, 7423, 7169, 6912, 6658, 6421, 6190, 5974, 5755,
5533, 5306, 5082, 4867, 4664, 4478, 4297, 4124, 3945, 3758, 3572, 3388, 3215, 3053, 2904, 2761, 2614, 2464, 2312, 2157,
2011, 1875, 1752, 1635, 1522, 1402, 1279, 1151, 1028, 908, 801, 698, 602, 499, 393, 283, 170, 57, -41, -136,
-223, -312, -410, -515, -625, -737, -843, -945, -1037, -1135, -1236, -1347, -1465, -1588, -1708, -1826, -1936, -2043, -2156, -2280,
-2412, -2553, -2694, -2836, -2968, -3095, -3227, -3364, -3509, -3666, -3827, -3987, -4139, -4285, -4433, -4588, -4748, -4924, -5105, -5290,
-5463, -5623, -5782, -5940, -6105, -6284, -6468, -6656, -6840, -7006, -7163, -7311, -7450, -7588, -7715, -7830, -7916, -7962, -7961, -7926,
-7849, -7736, -7581, -7378, -7100, -6743, -6292, -5745, -5103, -4369, -3548, -2640, -1648, -583, 524, 1647, 2750, 3819, 4832, 5785,
6665, 7464, 8166, 8764, 9253, 9643, 9944, 10160, 10309, 10389, 10398, 10338, 10217, 10055, 9859, 9655, 9442, 9221, 8989, 8740,
8468, 8185, 7896, 7618, 7349, 7084, 6832, 6574, 6314, 6050, 5795, 5551, 5320, 5103, 4898, 4696, 4486, 4277, 4069, 3861,
3672, 3497, 3337, 3186, 3038, 2888, 2745, 2604, 2469, 2348, 2235, 2129, 2018, 1905, 1791, 1673, 1565, 1461, 1371, 1286,
1207, 1125, 1047, 962, 881, 802, 726, 660, 591, 516, 439, 360, 278, 201, 130, 68, 13, -44, -101, -161,
-228, -291, -358, -416, -476, -537, -599, -665, -736, -803, -871, -930, -982, -1034, -1085, -1138, -1198, -1265, -1333, -1403,
-1470, -1536, -1607, -1677, -1758, -1841, -1924, -2008, -2084, -2157, -2233, -2309, -2392, -2485, -2587, -2693, -2797, -2903, -3009, -3113,
-3226, -3345, -3469, -3597, -3723, -3843, -3959, -4079, -4203, -4339, -4489, -4648, -4811, -4971, -5129, -5286, -5445, -5610, -5783, -5965,
-6149, -6332, -6505, -6677, -6844, -7019, -7204, -7399, -7599, -7792, -7969, -8133, -8276, -8410, -8539, -8664, -8783, -8885, -8960, -9005,
-9005, -8972, -8903, -8801, -8656, -8456, -8188, -7837, -7400, -6875, -6273, -5595, -4850, -4037, -3156, -2210, -1212, -169, 887, 1947,
2975, 3963, 4891, 5741, 6501, 7162, 7717, 8171, 8533, 8812, 9008, 9132, 9181, 9164, 9089, 8976, 8832, 8665, 8482, 8280,
8056, 7809, 7543, 7270, 6997, 6734, 6486, 6248, 6010, 5772, 5532, 5290, 5054, 4833, 4624, 4431, 4243, 4054, 3864, 3670,
3482, 3300, 3138, 2988, 2847, 2704, 2559, 2409, 2259, 2110, 1970, 1844, 1728, 1609, 1493, 1369, 1245, 1118, 996, 888,
785, 684, 582, 477, 361, 242, 127, 19, -81, -177, -271, -364, -465, -571, -680, -784, -879, -967, -1054, -1144,
-1244, -1349, -1461, -1569, -1672, -1771, -1865, -1959, -2063, -2177, -2298, -2422, -2543, -2661, -2780, -2894, -3014, -3148, -3290, -3441,
-3588, -3733, -3872, -4009, -4148, -4297, -4460, -4628, -4800, -4966, -5123, -5270, -5416, -5566, -5723, -5888, -6052, -6213, -6362, -6495,
-6616, -6735, -6849, -6959, -7061, -7138, -7190, -7202, -7174, -7113, -7021, -6899, -6738, -6524, -6249, -5902, -5476, -4972, -4387, -3723,
-2974, -2145, -1237, -266, 750, 1781, 2807, 3809, 4773, 5689, 6544, 7317, 8005, 8597, 9095, 9509, 9836, 10093, 10275, 10384,
10417, 10383, 10287, 10145, 9977, 9795, 9596, 9384, 9153, 8904, 8638, 8368, 8098, 7840, 7591, 7347, 7104, 6859, 6607, 6355,
6111, 5879, 5666, 5458, 5259, 5060, 4854, 4648, 4443, 4248, 4065, 3900, 3736, 3581, 3424, 3266, 3109, 2964, 2825, 2701,
2582, 2465, 2346, 2222, 2096, 1972, 1856, 1756, 1656, 1565, 1475, 1387, 1294, 1201, 1117, 1037, 963, 891, 820, 743,
659, 572, 487, 409, 335, 267, 204, 139, 70, -1, -74, -146, -212, -281, -344, -414, -484, -566, -647, -725,
-800, -870, -934, -996, -1062, -1130, -1204, -1277, -1354, -1425, -1497, -1569, -1643, -1724, -1816, -1906, -1994, -2083, -2168, -2243,
-2327, -2412, -2506, -2605, -2709, -2815, -2921, -3024, -3132, -3247, -3372, -3502, -3637, -3774, -3907, -4040, -4166, -4298, -4440, -4594,
-4753, -4919, -5088, -5253, -5414, -5576, -5743, -5921, -6104, -6292, -6478, -6656, -6826, -6988, -7151, -7323, -7502, -7680, -7859, -8023,
-8171, -8302, -8418, -8535, -8636, -8738, -8825, -8894, -8929, -8930, -8886, -8813, -8704, -8553, -8350, -8082, -7731, -7293, -6768, -6164,
-5481, -4727, -3911, -3034, -2099, -1120, -107, 921, 1935, 2924, 3869, 4755, 5566, 6294, 6918, 7439, 7863, 8193, 8437, 8604,
8696, 8718, 8676, 8582, 8445, 8284, 8106, 7920, 7717, 7503, 7270, 7021, 6761, 6499, 6249, 6008, 5779, 5555, 5330, 5103,
4869, 4643, 4424, 4221, 4032, 3849, 3668, 3482, 3292, 3101, 2918, 2748, 2588, 2441, 2295, 2146, 1995, 1838, 1687, 1543,
1410, 1287, 1171, 1055, 934, 805, 676, 555, 441, 334, 235, 133, 32, -86, -202, -315, -426, -534, -627, -722,
-818, -924, -1035, -1146, -1259, -1367, -1468, -1567, -1673, -1781, -1898, -2026, -2151, -2274, -2391, -2499, -2612, -2731, -2857, -2993,
-3135, -3275, -3410, -3541, -3671, -3801, -3940, -4088, -4240, -4395, -4544, -4687, -4827, -4965, -5115, -5273, -5446, -5616, -5785, -5943,
-6090, -6231, -6368, -6511, -6656, -6798, -6939, -7059, -7164, -7253, -7322, -7388, -7435, -7468, -7461, -7410, -7301, -7130, -6897, -6602,
-6249, -5829, -5343, -4777, -4132, -3412, -2625, -1776, -873, 77, 1057, 2057, 3054, 4026, 4953, 5814, 6602, 7317, 7950, 8499,
8959, 9324, 9600, 9792, 9913, 9979, 10007, 9989, 9939, 9838, 9697, 9521, 9321, 9110, 8900, 8687, 8472, 8250, 8016, 7767,
7512, 7266, 7024, 6794, 6571, 6352, 6126, 5898, 5668, 5446, 5237, 5046, 4864, 4692, 4521, 4351, 4173, 4001, 3833, 3678,
3531, 3393, 3258, 3125, 2988, 2859, 2735, 2621, 2515, 2421, 2328, 2235, 2135, 2032, 1930, 1829, 1732, 1648, 1567, 1487,
1404, 1321, 1238, 1161, 1086, 1020, 957, 894, 828, 753, 674, 596, 517, 444, 381, 316, 256, 188, 120, 54,
-13, -77, -135, -190, -249, -315, -384, -457, -532, -609, -675, -741, -803, -866, -938, -1010, -1083, -1161, -1234, -1307,
-1382, -1459, -1546, -1638, -1739, -1839, -1937, -2033, -2123, -2216, -2311, -2411, -2518, -2631, -2747, -2860, -2973, -3087, -3208, -3335,
-3471, -3613, -3757, -3899, -4035, -4169, -4304, -4446, -4596, -4758, -4928, -5097, -5265, -5426, -5591, -5757, -5930, -6113, -6300, -6484,
-6663, -6829, -6989, -7143, -7299, -7457, -7619, -7778, -7919, -8038, -8128, -8197, -8244, -8272, -8286, -8273, -8221, -8127, -7981, -7781,
-7526, -7214, -6843, -6409, -5892, -5289, -4595, -3821, -2973, -2069, -1129, -165, 811, 1778, 2725, 3627, 4480, 5274, 6000, 6661,
7246, 7758, 8184, 8511, 8754, 8914, 9003, 9031, 9009, 8938, 8825, 8669, 8481, 8267, 8045, 7820, 7596, 7372, 7147, 6909,
6661, 6405, 6146, 5899, 5661, 5439, 5222, 5006, 4789, 4568, 4354, 4148, 3956, 3776, 3606, 3441, 3269, 3096, 2922, 2750,
2589, 2441, 2298, 2164, 2028, 1887, 1745, 1602, 1460, 1330, 1206, 1092, 972, 853, 726, 595, 468, 345, 236, 126,
21, -92, -204, -324, -447, -568, -680, -784, -884, -988, -1091, -1206, -1322, -1438, -1549, -1657, -1762, -1866, -1977, -2095,
-2221, -2353, -2483, -2605, -2724, -2842, -2966, -3097, -3238, -3389, -3538, -3687, -3831, -3974, -4118, -4270, -4428, -4601, -4773, -4943,
-5109, -5267, -5426, -5589, -5757, -5939, -6124, -6307, -6478, -6641, -6791, -6938, -7078, -7225, -7367, -7498, -7616, -7706, -7779, -7832,
-7865, -7879, -7874, -7830, -7739, -7582, -7354, -7050, -6674, -6220, -5694, -5084, -4395, -3623, -2778, -1867, -899, 112, 1152, 2210,
3259, 4285, 5258, 6164, 6988, 7721, 8360, 8903, 9351, 9700, 9952, 10104, 10174, 10173, 10125, 10036, 9918, 9767, 9592, 9377,
9137, 8884, 8619, 8357, 8106, 7854, 7602, 7346, 7081, 6817, 6556, 6300, 6061, 5834, 5612, 5389, 5162, 4937, 4718, 4505,
4311, 4132, 3962, 3797, 3630, 3464, 3296, 3133, 2978, 2834, 2698, 2566, 2433, 2302, 2173, 2044, 1927, 1823, 1726, 1639,
1547, 1455, 1360, 1265, 1169, 1082, 999, 921, 845, 769, 689, 613, 536, 468, 404, 346, 288, 230, 167, 99,
27, -43, -111, -175, -236, -296, -359, -423, -490, -556, -616, -673, -730, -784, -843, -906, -975, -1046, -1115, -1183,
-1245, -1308, -1370, -1435, -1501, -1574, -1647, -1716, -1786, -1854, -1927, -2001, -2083, -2175, -2269, -2362, -2452, -2541, -2631, -2722,
-2817, -2920, -3029, -3142, -3256, -3368, -3482, -3601, -3726, -3860, -4005, -4152, -4300, -4444, -4586, -4728, -4873, -5027, -5193, -5361,
-5535, -5709, -5880, -6048, -6213, -6389, -6572, -6756, -6945, -7125, -7295, -7454, -7609, -7761, -7922, -8078, -8241, -8387, -8517, -8619,
-8699, -8755, -8795, -8815, -8811, -8773, -8688, -8555, -8359, -8106, -7795, -7418, -6971, -6440, -5812, -5084, -4256, -3342, -2360, -1329,
-263, 814, 1884, 2921, 3908, 4831, 5673, 6436, 7118, 7713, 8220, 8635, 8953, 9175, 9309, 9368, 9367, 9314, 9213, 9071,
8890, 8677, 8443, 8196, 7948, 7708, 7474, 7241, 7004, 6761, 6512, 6263, 6017, 5787, 5565, 5355, 5144, 4937, 4725, 4515,
4311, 4118, 3942, 3773, 3608, 3445, 3280, 3112, 2947, 2790, 2645, 2508, 2379, 2251, 2123, 1987, 1851, 1722, 1597, 1481,
1372, 1268, 1161, 1051, 935, 823, 713, 611, 515, 422, 324, 227, 119, 6, -105, -212, -312, -409, -503, -604,
-709, -819, -931, -1039, -1145, -1247, -1351, -1458, -1572, -1697, -1825, -1954, -2078, -2198, -2317, -2433, -2559, -2693, -2830, -2974,
-3114, -3255, -3391, -3528, -3668, -3822, -3980, -4145, -4309, -4470, -4622, -4771, -4923, -5083, -5252, -5430, -5609, -5783, -5951, -6108,
-6258, -6407, -6560, -6709, -6853, -6981, -7087, -7173, -7234, -7279, -7305, -7310, -7293, -7228, -7111, -6928, -6673, -6345, -5948, -5472,
-4922, -4290, -3580, -2793, -1942, -1034, -89, 887, 1876, 2871, 3845, 4790, 5684, 6512, 7263, 7933, 8522, 9025, 9434, 9746,
9968, 10106, 10168, 10176, 10137, 10067, 9964, 9828, 9657, 9458, 9230, 8989, 8745, 8501, 8259, 8016, 7764, 7510, 7245, 6980,
6726, 6483, 6249, 6022, 5797, 5569, 5338, 5111, 4890, 4684, 4490, 4312, 4141, 3971, 3804, 3633, 3470, 3315, 3169, 3029,
2897, 2763, 2631, 2493, 2363, 2239, 2123, 2016, 1915, 1822, 1727, 1628, 1527, 1430, 1333, 1246, 1157, 1076, 992, 908,
819, 735, 655, 579, 512, 448, 386, 319, 245, 172, 98, 25, -46, -112, -178, -244, -314, -381, -454, -520,
-584, -643, -704, -761, -828, -897, -969, -1044, -1119, -1189, -1260, -1326, -1400, -1477, -1554, -1634, -1713, -1791, -1865, -1941,
-2021, -2111, -2203, -2307, -2409, -2512, -2613, -2706, -2806, -2909, -3014, -3127, -3247, -3363, -3478, -3594, -3713, -3839, -3976, -4120,
-4270, -4426, -4576, -4727, -4871, -5022, -5173, -5335, -5508, -5685, -5862, -6035, -6205, -6378, -6557, -6742, -6932, -7130, -7322, -7501,
-7667, -7824, -7977, -8126, -8279, -8429, -8571, -8693, -8791, -8866, -8912, -8936, -8940, -8917, -8860, -8760, -8602, -8384, -8109, -7771,
-7376, -6916, -6382, -5766, -5059, -4266, -3393, -2457, -1478, -462, 560, 1573, 2561, 3501, 4373, 5175, 5894, 6533, 7095, 7576,
7977, 8291, 8518, 8662, 8738, 8751, 8712, 8631, 8504, 8344, 8144, 7915, 7669, 7418, 7170, 6927, 6691, 6455, 6212, 5962,
5714, 5470, 5235, 5012, 4799, 4590, 4384, 4174, 3963, 3757, 3562, 3379, 3205, 3044, 2885, 2721, 2557, 2392, 2233, 2080,
1940, 1807, 1678, 1545, 1410, 1272, 1132, 1002, 876, 761, 650, 538, 421, 302, 183, 65, -47, -153, -253, -350,
-455, -563, -677, -793, -902, -1006, -1102, -1197, -1297, -1398, -1505, -1617, -1724, -1832, -1934, -2033, -2136, -2246, -2365, -2492,
-2620, -2748, -2868, -2985, -3104, -3229, -3361, -3502, -3645, -3792, -3933, -4072, -4212, -4352, -4497, -4656, -4820, -4984, -5144, -5294,
-5436, -5580, -5724, -5878, -6037, -6201, -6355, -6501, -6633, -6756, -6872, -6981, -7084, -7181, -7257, -7302, -7321, -7311, -7270, -7199,
-7103, -6969, -6788, -6544, -6226, -5828, -5344, -4783, -4135, -3415, -2617, -1753, -825, 137, 1127, 2122, 3107, 4065, 4988, 5862,
6677, 7416, 8070, 8637, 9117, 9514, 9830, 10062, 10215, 10291, 10294, 10242, 10140, 10014, 9862, 9696, 9512, 9308, 9081, 8842,
8592, 8346, 8101, 7863, 7631, 7399, 7162, 6920, 6679, 6444, 6220, 6008, 5804, 5606, 5402, 5196, 4994, 4790, 4604, 4425,
4260, 4104, 3952, 3797, 3643, 3493, 3347, 3209, 3081, 2957, 2836, 2712, 2588, 2464, 2345, 2233, 2130, 2042, 1954, 1865,
1776, 1683, 1594, 1505, 1421, 1340, 1265, 1187, 1109, 1027, 945, 866, 793, 724, 663, 600, 536, 470, 394, 321,
247, 176, 107, 42, -29, -99, -173, -244, -319, -386, -447, -508, -570, -635, -704, -779, -856, -938, -1013, -1083,
-1158, -1232, -1309, -1394, -1478, -1560, -1641, -1720, -1800, -1880, -1968, -2066, -2166, -2275, -2382, -2491, -2592, -2697, -2807, -2918,
-3039, -3164, -3290, -3412, -3536, -3660, -3786, -3922, -4073, -4230, -4391, -4548, -4704, -4858, -5008, -5163, -5324, -5496, -5668, -5843,
-6008, -6173, -6333, -6496, -6664, -6840, -7016, -7189, -7350, -7496, -7624, -7742, -7856, -7971, -8076, -8168, -8240, -8287, -8294, -8269,
-8213, -8120, -7992, -7810, -7571, -7267, -6882, -6423, -5894, -5294, -4629, -3891, -3087, -2210, -1278, -300, 700, 1705, 2691, 3643,
4544, 5373, 6124, 6783, 7349, 7820, 8205, 8509, 8744, 8905, 8998, 9028, 8998, 8922, 8808, 8664, 8504, 8323, 8118, 7894,
7652, 7399, 7145, 6895, 6656, 6425, 6198, 5968, 5740, 5503, 5273, 5050, 4839, 4637, 4445, 4251, 4055, 3859, 3661, 3474,
3293, 3125, 2965, 2807, 2651, 2488, 2327, 2168, 2016, 1878, 1747, 1616, 1491, 1359, 1228, 1094, 959, 837, 723, 604,
491, 378, 255, 130, 8, -110, -221, -326, -430, -538, -652, -769, -889, -1011, -1125, -1235, -1346, -1453, -1571, -1693,
-1822, -1946, -2069, -2189, -2305, -2421, -2545, -2675, -2813, -2956, -3098, -3236, -3373, -3505, -3644, -3785, -3939, -4098, -4257, -4415,
-4567, -4719, -4874, -5031, -5199, -5377, -5555, -5732, -5904, -6066, -6225, -6383, -6547, -6718, -6890, -7058, -7213, -7356, -7484, -7599,
-7704, -7799, -7877, -7931, -7945, -7921, -7846, -7728, -7563, -7350, -7085, -6757, -6349, -5862, -5283, -4617, -3863, -3035, -2137, -1172,
-161, 889, 1941, 2980, 3977, 4924, 5806, 6620, 7354, 8002, 8558, 9019, 9387, 9668, 9874, 10014, 10087, 10101, 10053, 9953,
9804, 9628, 9427, 9218, 9003, 8778, 8542, 8293, 8030, 7764, 7493, 7233, 6986, 6742, 6500, 6256, 6015, 5770, 5533, 5307,
5094, 4892, 4697, 4503, 4308, 4112, 3921, 3736, 3565, 3406, 3255, 3111, 2966, 2824, 2682, 2548, 2419, 2300, 2189, 2079,
1969, 1855, 1741, 1628, 1523, 1426, 1335, 1250, 1171, 1087, 1002, 916, 833, 755, 681, 607, 536, 461, 383, 303,
226, 152, 84, 20, -39, -95, -156, -224, -291, -357, -421, -487, -549, -609, -678, -744, -814, -885, -948, -1007,
-1066, -1120, -1180, -1241, -1308, -1376, -1450, -1522, -1593, -1660, -1735, -1810, -1891, -1975, -2057, -2140, -2220, -2297, -2377, -2459,
-2546, -2645, -2749, -2851, -2957, -3062, -3164, -3274, -3387, -3506, -3629, -3752, -3877, -3999, -4119, -4244, -4376, -4518, -4672, -4827,
-4988, -5143, -5298, -5454, -5612, -5778, -5948, -6124, -6301, -6472, -6637, -6799, -6961, -7131, -7301, -7473, -7643, -7805, -7950, -8079,
-8193, -8296, -8391, -8479, -8548, -8598, -8616, -8597, -8539, -8443, -8304, -8125, -7892, -7597, -7226, -6776, -6244, -5637, -4961, -4214,
-3406, -2532, -1608, -635, 371, 1388, 2396, 3376, 4315, 5191, 5995, 6720, 7346, 7877, 8308, 8646, 8904, 9085, 9198, 9250,
9235, 9168, 9057, 8914, 8746, 8561, 8361, 8149, 7915, 7670, 7411, 7148, 6893, 6648, 6408, 6179, 5953, 5723, 5495, 5264,
5048, 4841, 4645, 4459, 4275, 4094, 3910, 3725, 3545, 3375, 3214, 3063, 2917, 2771, 2623, 2470, 2321, 2177, 2041, 1915,
1794, 1672, 1548, 1420, 1291, 1170, 1047, 933, 828, 718, 610, 494, 376, 260, 145, 35, -66, -163, -264, -367,
-478, -586, -695, -802, -905, -1001, -1102, -1210, -1322, -1439, -1557, -1674, -1788, -1898, -2007, -2124, -2247, -2378, -2510, -2650,
-2788, -2922, -3054, -3189, -3331, -3479, -3635, -3793, -3951, -4104, -4257, -4408, -4564, -4729, -4899, -5074, -5250, -5418, -5578, -5730,
-5886, -6041, -6199, -6361, -6520, -6674, -6809, -6934, -7048, -7154, -7246, -7325, -7382, -7413, -7399, -7341, -7236, -7087, -6887, -6636,
-6331, -5953, -5493, -4950, -4320, -3607, -2808, -1936, -996, -3, 1036, 2093, 3141, 4159, 5124, 6033, 6871, 7625, 8294, 8866,
9340, 9718, 10003, 10213, 10352, 10427, 10441, 10396, 10297, 10154, 9970, 9767, 9553, 9329, 9098, 8861, 8607, 8347, 8074, 7805,
7543, 7286, 7039, 6795, 6551, 6309, 6064, 5827, 5597, 5379, 5172, 4977, 4778, 4582, 4382, 4186, 3996, 3818, 3645, 3485,
3333, 3185, 3035, 2887, 2744, 2612, 2487, 2367, 2254, 2138, 2025, 1906, 1790, 1677, 1572, 1471, 1381, 1293, 1207, 1120,
1030, 947, 863, 784, 711, 637, 558, 479, 396, 314, 231, 156, 85, 17, -49, -113, -183, -256, -327, -396,
-464, -532, -599, -669, -741, -817, -893, -968, -1037, -1099, -1164, -1226, -1294, -1361, -1436, -1513, -1588, -1663, -1739, -1817,
-1899, -1986, -2072, -2166, -2257, -2344, -2428, -2515, -2604, -2697, -2800, -2905, -3020, -3132, -3246, -3359, -3477, -3598, -3727, -3860,
-3998, -4130, -4265, -4398, -4534, -4673, -4819, -4977, -5143, -5308, -5472, -5639, -5803, -5968, -6137, -6310, -6490, -6674, -6849, -7023,
-7190, -7356, -7522, -7695, -7870, -8043, -8208, -8360, -8496, -8614, -8720, -8816, -8906, -8977, -9028, -9049, -9035, -8982, -8888, -8748,
-8565, -8328, -8024, -7644, -7177, -6624, -5989, -5276, -4496, -3655, -2757, -1814, -831, 172, 1177, 2167, 3123, 4029, 4877, 5652,
6341, 6940, 7441, 7846, 8155, 8380, 8533, 8620, 8644, 8611, 8530, 8406, 8254, 8081, 7893, 7697, 7490, 7266, 7032, 6786,
6535, 6287, 6043, 5810, 5589, 5367, 5145, 4925, 4703, 4490, 4282, 4092, 3907, 3729, 3551, 3370, 3186, 3012, 2843, 2684,
2536, 2394, 2251, 2109, 1965, 1822, 1683, 1551, 1427, 1309, 1197, 1080, 961, 843, 721, 607, 499, 393, 293, 191,
82, -27, -143, -253, -361, -464, -560, -661, -762, -867, -975, -1084, -1191, -1296, -1396, -1497, -1604, -1712, -1829, -1950,
-2069, -2185, -2299, -2409, -2526, -2642, -2768, -2903, -3038, -3170, -3302, -3432, -3565, -3699, -3843, -3992, -4146, -4298, -4450, -4596,
-4745, -4894, -5052, -5216, -5388, -5555, -5720, -5876, -6031, -6175, -6318, -6463, -6611, -6751, -6884, -7001, -7104, -7186, -7255, -7306,
-7345, -7348, -7319, -7239, -7108, -6918, -6668, -6357, -5988, -5550, -5045, -4460, -3804, -3070, -2268, -1402, -484, 478, 1473, 2476,
3475, 4436, 5348, 6202, 6981, 7687, 8308, 8840, 9284, 9631, 9895, 10078, 10194, 10253, 10267, 10234, 10159, 10035, 9878, 9692,
9482, 9264, 9046, 8819, 8588, 8348, 8100, 7844, 7590, 7337, 7095, 6860, 6629, 6399, 6172, 5942, 5718, 5500, 5297, 5105,
4923, 4745, 4568, 4391, 4216, 4041, 3875, 3719, 3571, 3431, 3292, 3156, 3021, 2891, 2764, 2649, 2539, 2437, 2334, 2230,
2126, 2018, 1912, 1810, 1719, 1629, 1545, 1461, 1376, 1292, 1210, 1133, 1057, 988, 920, 850, 775, 701, 624, 545,
470, 400, 330, 266, 201, 136, 68, -1, -67, -132, -196, -261, -328, -399, -469, -547, -622, -696, -765, -833,
-901, -969, -1042, -1120, -1200, -1280, -1357, -1437, -1519, -1603, -1692, -1788, -1886, -1986, -2081, -2177, -2271, -2365, -2464, -2569,
-2680, -2792, -2911, -3028, -3145, -3267, -3392, -3526, -3664, -3804, -3948, -4091, -4232, -4370, -4515, -4664, -4825, -4989, -5161, -5330,
-5504, -5673, -5839, -6010, -6189, -6369, -6549, -6729, -6900, -7065, -7220, -7374, -7528, -7680, -7836, -7976, -8100, -8205, -8286, -8347,
-8390, -8414, -8417, -8393, -8331, -8229, -8074, -7871, -7614, -7306, -6931, -6487, -5959, -5352, -4658, -3889, -3054, -2175, -1254, -313,
642, 1597, 2526, 3422, 4270, 5060, 5783, 6438, 7022, 7517, 7932, 8255, 8491, 8646, 8732, 8759, 8730, 8658, 8542, 8389,
8207, 8005, 7792, 7574, 7354, 7131, 6901, 6663, 6420, 6173, 5927, 5692, 5463, 5246, 5029, 4818, 4605, 4392, 4184, 3987,
3802, 3622, 3448, 3279, 3106, 2934, 2761, 2598, 2439, 2292, 2146, 2008, 1866, 1722, 1577, 1437, 1301, 1172, 1048, 930,
808, 687, 560, 436, 317, 201, 92, -19, -126, -235, -353, -471, -587, -701, -808, -913, -1015, -1118, -1227, -1340,
-1453, -1567, -1678, -1786, -1894, -2006, -2122, -2245, -2375, -2504, -2633, -2759, -2883, -3006, -3136, -3276, -3416, -3565, -3714, -3863,
-4007, -4153, -4299, -4456, -4614, -4782, -4946, -5110, -5268, -5424, -5579, -5741, -5909, -6080, -6258, -6426, -6590, -6743, -6886, -7020,
-7159, -7291, -7417, -7531, -7629, -7702, -7757, -7790, -7799, -7781, -7729, -7631, -7476, -7250, -6952, -6578, -6128, -5597, -4990, -4303,
-3542, -2715, -1820, -871, 121, 1146, 2181, 3207, 4207, 5163, 6050, 6864, 7589, 8223, 8766, 9212, 9567, 9831, 10003, 10095,
10116, 10086, 10013, 9907, 9774, 9610, 9420, 9204, 8969, 8721, 8475, 8224, 7979, 7736, 7490, 7239, 6987, 6734, 6486, 6246,
6017, 5791, 5570, 5352, 5135, 4917, 4707, 4507, 4321, 4148, 3978, 3815, 3648, 3487, 3326, 3167, 3020, 2880, 2745, 2614,
2487, 2359, 2235, 2120, 2009, 1908, 1810, 1721, 1630, 1539, 1443, 1349, 1259, 1172, 1091, 1010, 936, 860, 782, 708,
634, 568, 503, 441, 379, 317, 248, 179, 109, 39, -28, -92, -158, -215, -280, -345, -409, -469, -532, -590,
-647, -706, -767, -833, -902, -973, -1044, -1109, -1172, -1237, -1302, -1369, -1439, -1513, -1583, -1657, -1733, -1804, -1880, -1970,
-2054, -2149, -2244, -2340, -2435, -2526, -2617, -2714, -2817, -2921, -3033, -3146, -3263, -3379, -3497, -3623, -3749, -3887, -4031, -4178,
-4325, -4466, -4607, -4748, -4897, -5051, -5213, -5380, -5547, -5718, -5883, -6048, -6215, -6387, -6564, -6740, -6915, -7084, -7243, -7390,
-7536, -7678, -7821, -7959, -8092, -8204, -8296, -8362, -8403, -8419, -8415, -8380, -8314, -8207, -8045, -7831, -7558, -7217, -6817, -6348,
-5804, -5179, -4463, -3663, -2793, -1861, -886, 107, 1110, 2096, 3055, 3968, 4822, 5603, 6311, 6942, 7495, 7969, 8361, 8672,
8901, 9047, 9125, 9139, 9103, 9020, 8899, 8745, 8563, 8354, 8136, 7904, 7674, 7445, 7218, 6991, 6758, 6521, 6282, 6044,
5808, 5588, 5369, 5161, 4954, 4743, 4538, 4336, 4141, 3953, 3777, 3606, 3444, 3278, 3112, 2946, 2785, 2632, 2485, 2347,
2215, 2078, 1943, 1806, 1669, 1536, 1409, 1292, 1174, 1059, 941, 823, 702, 582, 464, 357, 249, 146, 33, -78,
-196, -315, -430, -543, -652, -755, -862, -972, -1085, -1203, -1321, -1435, -1547, -1658, -1772, -1890, -2015, -2141, -2274, -2406,
-2535, -2661, -2786, -2918, -3050, -3197, -3344, -3493, -3641, -3789, -3934, -4084, -4238, -4402, -4569, -4737, -4904, -5069, -5228, -5390,
-5558, -5725, -5901, -6078, -6253, -6422, -6580, -6729, -6870, -7008, -7139, -7262, -7368, -7460, -7523, -7561, -7579, -7568, -7522, -7449,
-7323, -7144, -6894, -6570, -6166, -5680, -5120, -4473, -3751, -2957, -2099, -1186, -226, 766, 1772, 2779, 3769, 4726, 5636, 6479,
7245, 7928, 8526, 9030, 9445, 9771, 10009, 10167, 10234, 10242, 10196, 10108, 9989, 9842, 9670, 9474, 9257, 9017, 8769, 8513,
8257, 8005, 7752, 7502, 7248, 6992, 6735, 6483, 6240, 6003, 5776, 5556, 5334, 5115, 4896, 4683, 4484, 4292, 4113, 3938,
3774, 3608, 3448, 3287, 3130, 2980, 2836, 2701, 2567, 2434, 2304, 2176, 2051, 1935, 1824, 1723, 1626, 1529, 1433, 1337,
1240, 1142, 1048, 959, 874, 792, 706, 624, 545, 462, 385, 313, 247, 180, 111, 42, -32, -106, -182, -255,
-327, -396, -465, -534, -606, -677, -748, -815, -879, -943, -1006, -1075, -1144, -1218, -1294, -1373, -1448, -1523, -1595, -1670,
-1746, -1821, -1904, -1984, -2064, -2142, -2221, -2305, -2390, -2486, -2583, -2686, -2787, -2887, -2986, -3087, -3189, -3295, -3404, -3521,
-3639, -3758, -3879, -4002, -4125, -4259, -4398, -4545, -4699, -4850, -4997, -5148, -5297, -5449, -5604, -5771, -5942, -6114, -6282, -6455,
-6622, -6791, -6966, -7145, -7322, -7499, -7667, -7825, -7975, -8114, -8250, -8379, -8508, -8625, -8729, -8807, -8867, -8891, -8893, -8868,
-8816, -8726, -8595, -8410, -8170, -7864, -7499, -7074, -6576, -6010, -5363, -4638, -3829, -2949, -2009, -1031, -32, 975, 1963, 2920,
3821, 4661, 5426, 6112, 6716, 7238, 7683, 8050, 8337, 8544, 8674, 8736, 8740, 8689, 8599, 8478, 8315, 8127, 7917, 7689,
7455, 7218, 6983, 6754, 6524, 6296, 6066, 5833, 5604, 5376, 5160, 4952, 4751, 4552, 4356, 4156, 3963, 3774, 3595, 3426,
3261, 3102, 2945, 2785, 2629, 2472, 2321, 2181, 2048, 1914, 1786, 1655, 1523, 1392, 1259, 1137, 1019, 906, 795, 684,
568, 452, 336, 224, 118, 15, -85, -185, -292, -400, -511, -625, -731, -832, -933, -1032, -1136, -1243, -1356, -1468,
-1581, -1689, -1799, -1908, -2022, -2140, -2269, -2399, -2529, -2659, -2789, -2914, -3043, -3176, -3317, -3467, -3613, -3761, -3907, -4050,
-4195, -4347, -4503, -4666, -4830, -4992, -5151, -5305, -5456, -5610, -5762, -5925, -6090, -6244, -6398, -6545, -6675, -6800, -6917, -7025,
-7119, -7198, -7250, -7278, -7274, -7238, -7169, -7063, -6918, -6720, -6458, -6124, -5713, -5216, -4636, -3972, -3231, -2416, -1533, -602,
374, 1370, 2369, 3354, 4310, 5227, 6091, 6892, 7615, 8257, 8807, 9269, 9648, 9943, 10159, 10300, 10365, 10370, 10314, 10212,
10079, 9922, 9747, 9558, 9349, 9129, 8890, 8646, 8391, 8145, 7897, 7658, 7418, 7178, 6939, 6697, 6459, 6228, 6004, 5793,
5580, 5377, 5170, 4964, 4763, 4569, 4385, 4211, 4047, 3889, 3736, 3582, 3431, 3283, 3139, 3006, 2878, 2750, 2628, 2504,
2382, 2261, 2148, 2039, 1944, 1849, 1759, 1668, 1575, 1485, 1397, 1308, 1226, 1141, 1061, 978, 896, 812, 730, 654,
581, 513, 445, 376, 307, 234, 160, 85, 11, -61, -134, -205, -277, -349, -423, -500, -567, -634, -701, -764,
-830, -900, -975, -1051, -1128, -1207, -1286, -1363, -1440, -1520, -1602, -1688, -1777, -1861, -1946, -2029, -2114, -2205, -2303, -2407,
-2517, -2625, -2739, -2846, -2962, -3071, -3189, -3312, -3436, -3563, -3693, -3823, -3951, -4086, -4228, -4377, -4531, -4690, -4852, -5013,
-5171, -5328, -5490, -5654, -5824, -5995, -6172, -6347, -6517, -6687, -6857, -7029, -7207, -7379, -7553, -7720, -7874, -8014, -8143, -8264,
-8377, -8484, -8575, -8655, -8703, -8722, -8707, -8655, -8572, -8445, -8270, -8046, -7757, -7397, -6967, -6462, -5888, -5247, -4538, -3765,
-2925, -2023, -1077, -98, 889, 1867, 2815, 3715, 4555, 5325, 6010, 6613, 7122, 7550, 7898, 8168, 8368, 8502, 8574, 8584,
8543, 8460, 8341, 8199, 8029, 7840, 7631, 7406, 7169, 6923, 6681, 6442, 6212, 5983, 5758, 5532, 5306, 5080, 4858, 4646,
4444, 4244, 4055, 3862, 3674, 3481, 3299, 3121, 2953, 2793, 2638, 2484, 2331, 2175, 2026, 1880, 1739, 1606, 1479, 1354,
1227, 1100, 969, 842, 721, 599, 488, 376, 264, 147, 28, -89, -205, -318, -422, -528, -633, -739, -855, -967,
-1081, -1193, -1302, -1408, -1514, -1622, -1736, -1853, -1972, -2087, -2206, -2318, -2431, -2549, -2672, -2801, -2935, -3069, -3206, -3337,
-3472, -3604, -3742, -3887, -4035, -4185, -4341, -4492, -4643, -4794, -4948, -5112, -5279, -5445, -5617, -5782, -5941, -6097, -6252, -6408,
-6564, -6724, -6878, -7028, -7161, -7287, -7398, -7499, -7582, -7648, -7692, -7708, -7683, -7621, -7516, -7371, -7177, -6931, -6620, -6249,
-5798, -5265, -4649, -3953, -3179, -2332, -1425, -462, 542, 1564, 2575, 3566, 4510, 5404, 6237, 6999, 7685, 8288, 8798, 9219,
9551, 9804, 9985, 10100, 10150, 10141, 10079, 9968, 9819, 9642, 9453, 9248, 9035, 8811, 8574, 8329, 8076, 7819, 7563, 7317,
7075, 6839, 6603, 6367, 6132, 5902, 5679, 5467, 5262, 5066, 4871, 4678, 4486, 4295, 4115, 3943, 3776, 3622, 3472, 3329,
3186, 3044, 2911, 2780, 2655, 2536, 2423, 2308, 2195, 2079, 1968, 1862, 1759, 1665, 1576, 1492, 1407, 1322, 1239, 1159,
1077, 1000, 926, 848, 778, 698, 623, 547, 475, 403, 339, 274, 215, 150, 86, 19, -45, -115, -180, -247,
-313, -380, -451, -521, -590, -660, -726, -786, -849, -911, -978, -1047, -1119, -1195, -1269, -1345, -1422, -1499, -1581, -1663,
-1746, -1833, -1922, -2003, -2089, -2174, -2261, -2355, -2453, -2557, -2664, -2773, -2885, -2997, -3109, -3226, -3346, -3469, -3600, -3728,
-3856, -3988, -4119, -4258, -4404, -4559, -4717, -4880, -5041, -5205, -5365, -5531, -5694, -5864, -6036, -6214, -6387, -6557, -6726, -6892,
-7057, -7224, -7393, -7555, -7714, -7859, -7989, -8102, -8205, -8295, -8373, -8439, -8481, -8502, -8485, -8432, -8337, -8201, -8019, -7787,
-7493, -7131, -6692, -6178, -5584, -4920, -4188, -3396, -2545, -1642, -701, 277, 1262, 2245, 3200, 4109, 4963, 5747, 6451, 7069,
7591, 8022, 8365, 8626, 8810, 8928, 8986, 8983, 8927, 8830, 8700, 8544, 8363, 8172, 7962, 7739, 7498, 7257, 7007, 6758,
6513, 6279, 6049, 5825, 5602, 5378, 5157, 4943, 4735, 4537, 4345, 4157, 3974, 3788, 3603, 3427, 3251, 3085, 2927, 2773,
2626, 2475, 2322, 2175, 2026, 1886, 1754, 1625, 1500, 1374, 1247, 1121, 993, 872, 753, 639, 528, 415, 300, 183,
68, -50, -162, -268, -375, -481, -588, -695, -808, -924, -1033, -1143, -1254, -1361, -1472, -1583, -1705, -1825, -1950, -2067,
-2189, -2306, -2428, -2554, -2686, -2824, -2964, -3105, -3244, -3384, -3524, -3669, -3813, -3969, -4127, -4283, -4438, -4593, -4749, -4905,
-5066, -5234, -5405, -5576, -5744, -5907, -6063, -6217, -6372, -6524, -6679, -6831, -6972, -7107, -7229, -7336, -7429, -7505, -7566, -7598,
-7599, -7561, -7475, -7344, -7157, -6915, -6617, -6257, -5823, -5314, -4720, -4050, -3300, -2477, -1586, -642, 353, 1376, 2403, 3408,
4374, 5283, 6131, 6899, 7594, 8202, 8722, 9150, 9488, 9738, 9917, 10026, 10078, 10077, 10024, 9924, 9782, 9611, 9416, 9205,
8985, 8760, 8524, 8284, 8034, 7780, 7522, 7266, 7017, 6773, 6534, 6299, 6063, 5828, 5600, 5376, 5161, 4956, 4757, 4565,
4373, 4183, 3996, 3814, 3637, 3470, 3311, 3160, 3010, 2868, 2729, 2591, 2461, 2337, 2216, 2104, 1994, 1880, 1768, 1659,
1548, 1444, 1347, 1255, 1165, 1081, 994, 911, 827, 746, 669, 592, 519, 443, 364, 286, 207, 130, 57, -16,
-83, -150, -214, -280, -348, -419, -484, -553, -618, -686, -755, -826, -896, -970, -1039, -1109, -1174, -1238, -1306, -1371,
-1440, -1512, -1586, -1659, -1737, -1813, -1895, -1976, -2059, -2146, -2240, -2329, -2418, -2507, -2596, -2685, -2780, -2879, -2984, -3091,
-3203, -3317, -3434, -3550, -3671, -3794, -3924, -4053, -4190, -4320, -4455, -4589, -4726, -4869, -5025, -5180, -5343, -5505, -5669, -5834,
-5996, -6160, -6331, -6502, -6678, -6851, -7021, -7185, -7348, -7508, -7671, -7832, -7990, -8141, -8282, -8408, -8514, -8604, -8679, -8741,
-8785, -8806, -8796, -8756, -8672, -8546, -8372, -8144, -7861, -7513, -7093, -6593, -6015, -5353, -4622, -3827, -2976, -2080, -1147, -190,
779, 1744, 2686, 3591, 4444, 5236, 5957, 6598, 7150, 7615, 7989, 8277, 8486, 8624, 8698, 8714, 8676, 8597, 8480, 8334,
8167, 7984, 7788, 7583, 7365, 7138, 6904, 6663, 6420, 6183, 5951, 5730, 5509, 5295, 5080, 4868, 4658, 4458, 4265, 4081,
3902, 3726, 3550, 3376, 3202, 3036, 2878, 2725, 2579, 2436, 2292, 2152, 2008, 1867, 1733, 1605, 1481, 1359, 1241, 1124,
1000, 877, 759, 641, 531, 421, 311, 201, 88, -28, -140, -253, -361, -468, -571, -674, -780, -890, -1002, -1113,
-1223, -1332, -1439, -1546, -1659, -1779, -1898, -2021, -2142, -2262, -2381, -2502, -2621, -2756, -2888, -3028, -3168, -3308, -3449, -3589,
-3729, -3878, -4029, -4183, -4341, -4499, -4654, -4808, -4965, -5123, -5288, -5455, -5623, -5788, -5948, -6097, -6244, -6384, -6525, -6657,
-6789, -6909, -7017, -7107, -7180, -7234, -7265, -7275, -7251, -7188, -7078, -6915, -6692, -6403, -6052, -5636, -5151, -4592, -3961, -3256,
-2483, -1646, -756, 182, 1157, 2153, 3147, 4119, 5054, 5931, 6739, 7467, 8118, 8682, 9161, 9548, 9850, 10068, 10208, 10284,
10307, 10283, 10217, 10113, 9971, 9799, 9604, 9386, 9162, 8928, 8691, 8456, 8213, 7964, 7715, 7460, 7211, 6968, 6732, 6496,
6268, 6040, 5815, 5594, 5382, 5175, 4980, 4793, 4611, 4433, 4258, 4084, 3913, 3745, 3586, 3438, 3289, 3147, 3008, 2875,
2743, 2619, 2497, 2385, 2274, 2167, 2061, 1953, 1846, 1741, 1638, 1544, 1450, 1360, 1274, 1189, 1104, 1022, 940, 863,
789, 715, 640, 564, 486, 407, 330, 250, 177, 104, 37, -32, -103, -174, -242, -313, -382, -451, -520, -591,
-662, -738, -815, -892, -967, -1042, -1113, -1183, -1256, -1330, -1408, -1486, -1568, -1648, -1733, -1815, -1904, -1993, -2090, -2187,
-2285, -2384, -2481, -2579, -2676, -2779, -2882, -2996, -3112, -3226, -3348, -3471, -3594, -3723, -3859, -3996, -4138, -4284, -4430, -4574,
-4718, -4864, -5019, -5177, -5340, -5511, -5683, -5855, -6027, -6201, -6374, -6549, -6725, -6906, -7080, -7254, -7417, -7578, -7733, -7886,
-8040, -8185, -8324, -8452, -8558, -8644, -8710, -8754, -8778, -8780, -8754, -8693, -8595, -8442, -8248, -7991, -7677, -7298, -6846, -6319,
-5709, -5015, -4245, -3409, -2515, -1582, -626, 343, 1308, 2254, 3165, 4024, 4828, 5565, 6229, 6815, 7321, 7740, 8071, 8314,
8480, 8576, 8609, 8585, 8513, 8402, 8258, 8081, 7888, 7681, 7464, 7244, 7020, 6793, 6562, 6324, 6083, 5845, 5607, 5381,
5159, 4946, 4734, 4525, 4319, 4114, 3917, 3727, 3547, 3371, 3203, 3034, 2864, 2695, 2532, 2374, 2223, 2079, 1936, 1799,
1658, 1519, 1379, 1244, 1118, 990, 872, 753, 635, 517, 394, 278, 160, 49, -57, -164, -274, -385, -498, -610,
-722, -832, -936, -1040, -1142, -1251, -1358, -1468, -1581, -1693, -1802, -1910, -2020, -2136, -2254, -2378, -2505, -2633, -2757, -2882,
-3004, -3133, -3264, -3401, -3544, -3692, -3834, -3977, -4118, -4266, -4414, -4568, -4728, -4887, -5047, -5203, -5358, -5515, -5671, -5834,
-5998, -6167, -6329, -6489, -6635, -6780, -6916, -7044, -7168, -7287, -7392, -7482, -7551, -7597, -7622, -7619, -7590, -7525, -7412, -7249,
-7017, -6715, -6344, -5894, -5373, -4775, -4105, -3361, -2549, -1680, -759, 196, 1178, 2170, 3159, 4119, 5042, 5910, 6702, 7419,
8051, 8593, 9045, 9410, 9691, 9889, 10010, 10065, 10062, 10012, 9931, 9813, 9668, 9502, 9310, 9093, 8868, 8633, 8397, 8159,
7922, 7682, 7440, 7195, 6951, 6709, 6472, 6239, 6017, 5795, 5580, 5363, 5153, 4946, 4748, 4556, 4377, 4207, 4043, 3876,
3714, 3555, 3398, 3248, 3104, 2969, 2837, 2705, 2581, 2458, 2337, 2226, 2122, 2022, 1926, 1831, 1738, 1642, 1545, 1455,
1363, 1275, 1196, 1115, 1037, 959, 882, 808, 736, 665, 602, 538, 469, 397, 328, 257, 188, 117, 48, -14,
-82, -144, -209, -272, -338, -400, -466, -524, -586, -650, -718, -787, -859, -931, -998, -1068, -1136, -1204, -1274, -1345,
-1420, -1498, -1576, -1651, -1731, -1814, -1898, -1988, -2086, -2184, -2284, -2381, -2476, -2578, -2678, -2780, -2890, -3003, -3122, -3241,
-3360, -3487, -3614, -3746, -3884, -4031, -4177, -4326, -4472, -4620, -4766, -4916, -5074, -5239, -5408, -5580, -5750, -5921, -6092, -6261,
-6439, -6614, -6794, -6970, -7140, -7305, -7460, -7610, -7756, -7898, -8037, -8164, -8277, -8371, -8443, -8489, -8512, -8505, -8473, -8407,
-8300, -8150, -7944, -7681, -7355, -6966, -6505, -5973, -5362, -4664, -3892, -3045, -2139, -1188, -210, 779, 1760, 2719, 3632, 4494,
5287, 6013, 6663, 7236, 7732, 8148, 8480, 8731, 8903, 9002, 9036, 9015, 8946, 8839, 8695, 8521, 8325, 8108, 7881, 7650,
7420, 7188, 6957, 6721, 6483, 6243, 6005, 5769, 5540, 5320, 5107, 4895, 4686, 4481, 4277, 4083, 3891, 3709, 3537, 3368,
3199, 3034, 2867, 2705, 2548, 2397, 2255, 2117, 1976, 1840, 1702, 1566, 1428, 1298, 1174, 1054, 932, 812, 692, 572,
448, 326, 215, 101, -12, -120, -233, -352, -470, -590, -703, -809, -923, -1030, -1141, -1255, -1370, -1491, -1605, -1720,
-1836, -1949, -2067, -2191, -2321, -2454, -2584, -2716, -2846, -2977, -3108, -3245, -3387, -3535, -3683, -3834, -3984, -4134, -4282, -4439,
-4596, -4763, -4929, -5095, -5258, -5419, -5578, -5739, -5900, -6069, -6238, -6405, -6566, -6717, -6857, -6994, -7120, -7238, -7347, -7439,
-7513, -7567, -7594, -7595, -7568, -7510, -7414, -7273, -7074, -6809, -6473, -6062, -5572, -5007, -4364, -3649, -2863, -2020, -1125, -189,
770, 1742, 2708, 3656, 4571, 5440, 6249, 6988, 7644, 8215, 8699, 9097, 9411, 9647, 9802, 9879, 9898, 9862, 9782, 9672,
9532, 9370, 9186, 8982, 8757, 8525, 8282, 8037, 7795, 7554, 7311, 7070, 6828, 6584, 6343, 6108, 5879, 5657, 5443, 5228,
5018, 4810, 4607, 4408, 4221, 4043, 3872, 3711, 3549, 3393, 3237, 3081, 2933, 2793, 2657, 2523, 2395, 2269, 2143, 2022,
1905, 1800, 1697, 1598, 1503, 1410, 1316, 1220, 1125, 1035, 950, 862, 781, 701, 623, 542, 462, 387, 316, 250,
183, 117, 48, -24, -97, -170, -243, -313, -383, -451, -519, -589, -658, -724, -794, -860, -924, -988, -1053, -1121,
-1194, -1272, -1346, -1421, -1498, -1569, -1645, -1719, -1795, -1876, -1956, -2035, -2117, -2199, -2283, -2369, -2462, -2560, -2662, -2762,
-2865, -2967, -3066, -3173, -3278, -3392, -3508, -3627, -3746, -3870, -3995, -4125, -4258, -4400, -4545, -4697, -4845, -5000, -5149, -5301,
-5455, -5614, -5776, -5941, -6112, -6283, -6451, -6619, -6785, -6956, -7126, -7297, -7467, -7629, -7785, -7931, -8068, -8197, -8319, -8436,
-8541, -8634, -8707, -8754, -8773, -8763, -8724, -8654, -8544, -8390, -8189, -7928, -7607, -7219, -6766, -6243, -5650, -4978, -4236, -3414,
-2528, -1594, -623, 364, 1353, 2319, 3245, 4117, 4924, 5659, 6312, 6887, 7386, 7806, 8147, 8413, 8604, 8725, 8779, 8777,
8729, 8639, 8511, 8355, 8178, 7975, 7757, 7530, 7302, 7073, 6848, 6627, 6404, 6178, 5956, 5727, 5510, 5293, 5088, 4884,
4689, 4495, 4300, 4109, 3920, 3741, 3569, 3402, 3241, 3085, 2928, 2770, 2615, 2465, 2320, 2181, 2048, 1920, 1789, 1655,
1527, 1395, 1272, 1151, 1032, 919, 807, 690, 573, 456, 342, 229, 120, 18, -90, -198, -312, -424, -536, -651,
-762, -866, -973, -1082, -1193, -1310, -1427, -1543, -1661, -1780, -1894, -2012, -2136, -2268, -2400, -2535, -2672, -2804, -2937, -3070,
-3208, -3353, -3501, -3649, -3803, -3953, -4099, -4253, -4409, -4565, -4726, -4891, -5054, -5217, -5372, -5529, -5681, -5838, -5997, -6155,
-6309, -6465, -6604, -6734, -6848, -6953, -7048, -7127, -7186, -7221, -7224, -7196, -7129, -7025, -6878, -6686, -6436, -6128, -5740, -5274,
-4726, -4098, -3395, -2618, -1776, -881, 59, 1028, 2007, 2977, 3919, 4827, 5686, 6486, 7222, 7882, 8464, 8957, 9363, 9689,
9936, 10110, 10216, 10258, 10240, 10174, 10064, 9926, 9763, 9582, 9388, 9179, 8958, 8725, 8484, 8234, 7985, 7743, 7502, 7262,
7027, 6789, 6551, 6318, 6090, 5871, 5655, 5447, 5243, 5040, 4840, 4642, 4451, 4269, 4097, 3932, 3774, 3622, 3468, 3320,
3171, 3031, 2895, 2764, 2640, 2516, 2394, 2269, 2150, 2037, 1926, 1827, 1730, 1636, 1543, 1451, 1357, 1265, 1176, 1087,
1003, 920, 838, 754, 669, 587, 511, 432, 361, 291, 221, 151, 77, 3, -71, -147, -222, -296, -367, -440,
-513, -586, -660, -731, -804, -870, -938, -1006, -1077, -1151, -1228, -1309, -1389, -1468, -1548, -1630, -1712, -1797, -1883, -1970,
-2060, -2148, -2236, -2329, -2420, -2520, -2624, -2730, -2844, -2956, -3069, -3180, -3295, -3414, -3535, -3660, -3788, -3921, -4051, -4185,
-4318, -4458, -4608, -4760, -4919, -5080, -5240, -5400, -5560, -5724, -5885, -6056, -6229, -6403, -6576, -6750, -6918, -7085, -7259, -7428,
-7596, -7763, -7923, -8071, -8209, -8335, -8449, -8549, -8644, -8724, -8782, -8818, -8824, -8795, -8729, -8622, -8476, -8280, -8029, -7716,
-7339, -6887, -6369, -5776, -5117, -4394, -3604, -2753, -1854, -911, 54, 1026, 1988, 2917, 3799, 4619, 5366, 6038, 6621, 7120,
7535, 7870, 8130, 8325, 8451, 8516, 8522, 8481, 8397, 8277, 8129, 7961, 7769, 7562, 7339, 7103, 6863, 6625, 6387, 6153,
5928, 5703, 5478, 5256, 5035, 4818, 4606, 4400, 4204, 4012, 3823, 3634, 3447, 3267, 3091, 2918, 2758, 2601, 2450, 2297,
2145, 1993, 1848, 1706, 1571, 1440, 1313, 1183, 1058, 928, 802, 677, 558, 441, 327, 213, 96, -22, -137, -254,
-365, -474, -582, -691, -798, -910, -1021, -1135, -1248, -1357, -1466, -1572, -1681, -1792, -1908, -2028, -2145, -2262, -2379, -2495,
-2617, -2739, -2865, -2998, -3136, -3268, -3405, -3539, -3674, -3814, -3955, -4103, -4252, -4406, -4560, -4710, -4863, -5018, -5174, -5337,
-5500, -5665, -5827, -5984, -6136, -6286, -6433, -6581, -6730, -6875, -7013, -7140, -7256, -7356, -7442, -7508, -7555, -7578, -7572, -7527,
-7442, -7313, -7134, -6904, -6621, -6278, -5861, -5371, -4799, -4148, -3418, -2611, -1744, -819, 154, 1153, 2164, 3159, 4124, 5040,
5901, 6692, 7414, 8055, 8614, 9085, 9467, 9766, 9986, 10135, 10221, 10247, 10219, 10144, 10025, 9877, 9699, 9505, 9295, 9081,
8857, 8623, 8381, 8131, 7883, 7634, 7386, 7149, 6912, 6681, 6448, 6219, 5994, 5775, 5560, 5358, 5159, 4968, 4778, 4587,
4402, 4223, 4045, 3882, 3725, 3576, 3425, 3283, 3143, 3008, 2874, 2747, 2626, 2509, 2395, 2279, 2163, 2054, 1947, 1842,
1746, 1652, 1566, 1475, 1393, 1306, 1225, 1140, 1063, 984, 909, 829, 753, 674, 599, 522, 449, 383, 313, 247,
182, 116, 49, -24, -92, -160, -228, -300, -370, -437, -509, -582, -653, -721, -788, -853, -919, -986, -1057, -1128,
-1207, -1283, -1361, -1439, -1517, -1601, -1681, -1766, -1854, -1941, -2030, -2117, -2205, -2297, -2391, -2490, -2595, -2702, -2815, -2929,
-3044, -3159, -3278, -3399, -3528, -3657, -3786, -3920, -4054, -4194, -4334, -4479, -4634, -4793, -4955, -5121, -5288, -5452, -5619, -5785,
-5957, -6130, -6304, -6479, -6655, -6824, -6993, -7159, -7328, -7495, -7660, -7819, -7966, -8102, -8223, -8331, -8425, -8506, -8572, -8621,
-8641, -8636, -8591, -8507, -8379, -8203, -7975, -7691, -7334, -6911, -6408, -5826, -5172, -4448, -3656, -2807, -1904, -957, 18, 1007,
1996, 2958, 3880, 4749, 5547, 6270, 6906, 7451, 7904, 8268, 8548, 8754, 8888, 8960, 8972, 8935, 8851, 8728, 8576, 8401,
8213, 8007, 7784, 7550, 7308, 7061, 6811, 6568, 6328, 6096, 5867, 5640, 5417, 5194, 4977, 4764, 4559, 4363, 4169, 3980,
3793, 3608, 3428, 3248, 3076, 2912, 2754, 2599, 2446, 2295, 2144, 1996, 1852, 1715, 1581, 1450, 1323, 1194, 1065, 938,
813, 689, 572, 451, 337, 223, 103, -17, -132, -252, -362, -476, -583, -694, -805, -920, -1036, -1151, -1264, -1375,
-1489, -1601, -1719, -1838, -1961, -2085, -2205, -2331, -2454, -2574, -2700, -2832, -2969, -3107, -3250, -3390, -3532, -3673, -3814, -3958,
-4115, -4264, -4421, -4581, -4734, -4893, -5049, -5210, -5374, -5539, -5708, -5873, -6034, -6192, -6345, -6492, -6639, -6784, -6929, -7064,
-7191, -7303, -7402, -7483, -7549, -7590, -7607, -7594, -7541, -7446, -7299, -7096, -6843, -6533, -6159, -5718, -5205, -4617, -3951, -3209,
-2401, -1534, -614, 347, 1324, 2307, 3269, 4198, 5078, 5894, 6642, 7319, 7913, 8423, 8852, 9194, 9458, 9645, 9769, 9834,
9844, 9807, 9728, 9607, 9453, 9276, 9082, 8873, 8662, 8439, 8207, 7971, 7727, 7480, 7235, 6991, 6754, 6518, 6289, 6059,
5834, 5610, 5392, 5183, 4977, 4781, 4590, 4405, 4221, 4038, 3857, 3684, 3520, 3362, 3210, 3063, 2924, 2784, 2647, 2520,
2394, 2274, 2160, 2048, 1937, 1827, 1716, 1609, 1506, 1408, 1314, 1226, 1138, 1055, 970, 886, 807, 727, 651, 573,
501, 426, 349, 272, 194, 122, 50, -19, -83, -149, -213, -284, -350, -418, -486, -554, -622, -688, -758, -830,
-898, -970, -1040, -1108, -1174, -1238, -1306, -1374, -1445, -1520, -1598, -1674, -1753, -1832, -1914, -1999, -2086, -2173, -2263, -2357,
-2446, -2538, -2628, -2722, -2824, -2925, -3034, -3145, -3261, -3378, -3496, -3614, -3740, -3864, -3998, -4130, -4266, -4402, -4537, -4677,
-4822, -4969, -5127, -5287, -5452, -5616, -5780, -5941, -6107, -6274, -6443, -6613, -6783, -6953, -7118, -7277, -7437, -7593, -7748, -7900,
-8044, -8182, -8301, -8399, -8490, -8561, -8610, -8645, -8660, -8648, -8600, -8514, -8383, -8207, -7976, -7694, -7342, -6930, -6438, -5870,
-5227, -4514, -3735, -2902, -2028, -1115, -175, 773, 1722, 2646, 3540, 4381, 5163, 5879, 6519, 7077, 7550, 7935, 8234, 8456,
8606, 8691, 8722, 8700, 8635, 8529, 8390, 8231, 8051, 7860, 7657, 7442, 7219, 6989, 6751, 6512, 6275, 6046, 5820, 5599,
5384, 5166, 4956, 4748, 4546, 4352, 4164, 3978, 3802, 3623, 3450, 3277, 3107, 2944, 2785, 2635, 2489, 2344, 2199, 2054,
1912, 1773, 1641, 1511, 1386, 1261, 1138, 1014, 890, 765, 645, 528, 415, 302, 190, 70, -43, -161, -274, -391,
-499, -608, -715, -825, -936, -1049, -1164, -1276, -1391, -1501, -1614, -1728, -1849, -1971, -2096, -2221, -2346, -2470, -2594, -2722,
-2852, -2991, -3129, -3277, -3420, -3562, -3707, -3852, -4001, -4150, -4306, -4465, -4623, -4782, -4935, -5093, -5251, -5412, -5573, -5738,
-5901, -6056, -6204, -6348, -6484, -6612, -6739, -6859, -6968, -7064, -7142, -7203, -7242, -7253, -7237, -7190, -7101, -6967, -6775, -6518,
-6201, -5814, -5361, -4839, -4251, -3589, -2860, -2071, -1221, -325, 608, 1567, 2536, 3495, 4423, 5312, 6139, 6897, 7579, 8178,
8693, 9124, 9470, 9734, 9924, 10038, 10095, 10098, 10057, 9979, 9867, 9727, 9554, 9360, 9149, 8925, 8701, 8468, 8234, 7997,
7761, 7515, 7273, 7030, 6791, 6560, 6329, 6106, 5886, 5670, 5455, 5247, 5041, 4850, 4661, 4482, 4309, 4135, 3962, 3793,
3628, 3470, 3315, 3169, 3027, 2891, 2757, 2628, 2500, 2378, 2264, 2154, 2045, 1938, 1831, 1728, 1623, 1521, 1425, 1331,
1242, 1154, 1069, 987, 905, 824, 746, 669, 592, 521, 443, 368, 291, 214, 136, 61, -12, -82, -150, -220,
-287, -358, -430, -501, -571, -641, -711, -784, -854, -932, -1005, -1083, -1160, -1230, -1304, -1377, -1450, -1528, -1606, -1687,
-1771, -1853, -1937, -2026, -2113, -2206, -2306, -2402, -2503, -2603, -2699, -2800, -2901, -3008, -3117, -3233, -3352, -3474, -3597, -3724,
-3853, -3984, -4122, -4263, -4408, -4553, -4697, -4846, -4993, -5143, -5298, -5462, -5628, -5798, -5967, -6136, -6305, -6471, -6641, -6810,
-6982, -7153, -7313, -7475, -7630, -7775, -7918, -8056, -8186, -8309, -8420, -8512, -8583, -8630, -8652, -8652, -8627, -8570, -8479, -8345,
-8164, -7928, -7631, -7275, -6853, -6361, -5788, -5139, -4418, -3624, -2773, -1878, -948, -4, 942, 1878, 2783, 3644, 4454, 5203,
5881, 6491, 7023, 7480, 7855, 8147, 8362, 8501, 8573, 8588, 8554, 8478, 8368, 8220, 8050, 7864, 7660, 7450, 7232, 7015,
6796, 6568, 6343, 6110, 5879, 5649, 5425, 5207, 4998, 4791, 4585, 4384, 4185, 3991, 3805, 3621, 3449, 3279, 3110, 2944,
2779, 2619, 2462, 2309, 2164, 2024, 1883, 1745, 1608, 1471, 1337, 1207, 1080, 959, 840, 722, 602, 479, 360, 242,
127, 18, -96, -205, -317, -433, -549, -665, -777, -888, -993, -1101, -1211, -1322, -1434, -1549, -1667, -1779, -1893, -2010,
-2126, -2249, -2374, -2505, -2635, -2761, -2890, -3022, -3150, -3286, -3423, -3568, -3716, -3861, -4009, -4157, -4306, -4455, -4608, -4768,
-4928, -5089, -5250, -5408, -5567, -5723, -5883, -6045, -6208, -6371, -6525, -6674, -6812, -6942, -7063, -7174, -7279, -7370, -7440, -7492,
-7520, -7518, -7486, -7417, -7311, -7153, -6938, -6656, -6307, -5875, -5371, -4788, -4132, -3407, -2616, -1770, -872, 74, 1044, 2027,
3008, 3965, 4893, 5768, 6583, 7324, 7981, 8553, 9037, 9433, 9744, 9975, 10131, 10215, 10239, 10212, 10138, 10032, 9898, 9741,
9559, 9360, 9142, 8914, 8676, 8434, 8192, 7956, 7713, 7471, 7229, 6985, 6745, 6506, 6273, 6050, 5830, 5613, 5403, 5194,
4989, 4792, 4602, 4422, 4251, 4079, 3917, 3755, 3598, 3441, 3289, 3145, 3006, 2870, 2740, 2613, 2488, 2367, 2251, 2144,
2039, 1938, 1838, 1744, 1645, 1548, 1450, 1356, 1268, 1182, 1097, 1013, 936, 857, 775, 699, 628, 556, 484, 416,
342, 268, 194, 120, 46, -25, -95, -160, -229, -299, -369, -437, -506, -572, -640, -704, -774, -844, -917, -993,
-1068, -1142, -1219, -1288, -1364, -1438, -1516, -1595, -1677, -1757, -1843, -1926, -2011, -2105, -2198, -2295, -2396, -2499, -2602, -2705,
-2806, -2914, -3019, -3135, -3250, -3369, -3491, -3618, -3744, -3878, -4013, -4153, -4298, -4447, -4595, -4746, -4898, -5051, -5205, -5365,
-5528, -5696, -5867, -6043, -6216, -6387, -6562, -6735, -6912, -7087, -7261, -7431, -7594, -7750, -7900, -8043, -8181, -8313, -8434, -8542,
-8635, -8701, -8744, -8759, -8747, -8710, -8634, -8520, -8364, -8152, -7884, -7553, -7159, -6695, -6156, -5538, -4842, -4069, -3227, -2324,
-1379, -405, 580, 1559, 2513, 3428, 4291, 5088, 5816, 6469, 7046, 7545, 7963, 8303, 8559, 8740, 8846, 8887, 8871, 8810,
8708, 8567, 8399, 8207, 8000, 7776, 7547, 7318, 7086, 6856, 6623, 6388, 6154, 5920, 5687, 5459, 5239, 5024, 4815, 4608,
4406, 4207, 4012, 3819, 3642, 3466, 3296, 3128, 2964, 2801, 2640, 2482, 2331, 2186, 2046, 1905, 1769, 1632, 1495, 1358,
1231, 1102, 977, 858, 737, 618, 496, 374, 257, 143, 27, -81, -195, -304, -422, -536, -651, -764, -878, -986,
-1092, -1200, -1314, -1427, -1542, -1657, -1771, -1888, -2003, -2122, -2243, -2370, -2498, -2627, -2759, -2890, -3019, -3151, -3286, -3428,
-3572, -3718, -3866, -4016, -4164, -4312, -4465, -4620, -4781, -4939, -5099, -5260, -5419, -5572, -5731, -5889, -6045, -6204, -6361, -6518,
-6661, -6798, -6925, -7041, -7151, -7248, -7328, -7392, -7435, -7450, -7441, -7398, -7322, -7206, -7043, -6824, -6543, -6189, -5763, -5256,
-4680, -4024, -3298, -2510, -1664, -766, 158, 1110, 2068, 3017, 3946, 4840, 5681, 6468, 7186, 7823, 8376, 8845, 9232, 9537,
9761, 9911, 9992, 10016, 9983, 9910, 9802, 9671, 9509, 9335, 9139, 8925, 8703, 8467, 8228, 7991, 7754, 7516, 7282, 7045,
6808, 6571, 6338, 6111, 5889, 5675, 5464, 5253, 5050, 4843, 4650, 4462, 4281, 4108, 3945, 3782, 3626, 3468, 3315, 3164,
3021, 2880, 2751, 2618, 2490, 2366, 2244, 2130, 2018, 1913, 1811, 1716, 1618, 1523, 1427, 1334, 1240, 1150, 1063, 980,
896, 813, 732, 652, 576, 499, 428, 356, 288, 219, 144, 67, -6, -81, -157, -226, -299, -368, -438, -512,
-581, -651, -720, -784, -853, -921, -991, -1065, -1138, -1214, -1293, -1367, -1441, -1517, -1597, -1672, -1754, -1836, -1918, -2003,
-2085, -2172, -2262, -2356, -2454, -2552, -2657, -2761, -2866, -2975, -3079, -3191, -3305, -3419, -3540, -3665, -3790, -3919, -4049, -4185,
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-7556, -7714, -7860, -8000, -8133, -8255, -8372, -8478, -8569, -8648, -8695, -8720, -8716, -8681, -8613, -8511, -8367, -8174, -7922, -7615,
-7246, -6808, -6301, -5727, -5078, -4355, -3563, -2705, -1798, -851, 112, 1081, 2029, 2949, 3817, 4629, 5368, 6034, 6625, 7139,
7577, 7936, 8222, 8435, 8578, 8655, 8676, 8642, 8565, 8453, 8310, 8141, 7949, 7743, 7520, 7294, 7068, 6841, 6616, 6391,
6166, 5938, 5713, 5489, 5269, 5054, 4847, 4644, 4446, 4246, 4054, 3862, 3677, 3497, 3327, 3157, 2995, 2832, 2672, 2514,
2358, 2207, 2061, 1922, 1784, 1650, 1512, 1379, 1245, 1112, 986, 862, 744, 620, 500, 379, 260, 137, 20, -93,
-206, -321, -432, -549, -665, -782, -900, -1014, -1128, -1239, -1354, -1467, -1583, -1703, -1823, -1943, -2061, -2182, -2307, -2431,
-2561, -2694, -2829, -2966, -3099, -3235, -3371, -3511, -3653, -3796, -3950, -4100, -4252, -4402, -4555, -4709, -4864, -5022, -5181, -5341,
-5503, -5657, -5810, -5961, -6109, -6260, -6410, -6555, -6699, -6830, -6949, -7056, -7149, -7224, -7283, -7324, -7339, -7322, -7270, -7184,
-7053, -6878, -6653, -6376, -6031, -5619, -5130, -4566, -3924, -3208, -2426, -1591, -704, 220, 1164, 2112, 3048, 3953, 4824, 5642,
6407, 7106, 7734, 8284, 8751, 9137, 9445, 9680, 9841, 9939, 9979, 9963, 9902, 9801, 9668, 9512, 9336, 9150, 8948, 8738,
8514, 8279, 8043, 7806, 7565, 7332, 7098, 6871, 6641, 6409, 6185, 5963, 5746, 5535, 5331, 5131, 4934, 4736, 4546, 4364,
4182, 4014, 3848, 3692, 3538, 3389, 3242, 3103, 2959, 2823, 2697, 2568, 2446, 2322, 2203, 2086, 1976, 1866, 1765, 1666,
1574, 1479, 1388, 1299, 1207, 1117, 1032, 945, 861, 778, 694, 614, 536, 456, 379, 306, 234, 164, 93, 19,
-51, -124, -201, -275, -347, -420, -493, -566, -639, -713, -783, -853, -924, -990, -1061, -1133, -1205, -1282, -1360, -1440,
-1523, -1602, -1684, -1768, -1850, -1935, -2025, -2110, -2200, -2288, -2384, -2477, -2574, -2677, -2784, -2892, -3004, -3118, -3233, -3348,
-3466, -3585, -3708, -3834, -3965, -4096, -4231, -4367, -4506, -4650, -4802, -4957, -5112, -5272, -5429, -5589, -5749, -5910, -6071, -6239,
-6406, -6574, -6742, -6909, -7072, -7235, -7388, -7546, -7698, -7843, -7981, -8106, -8218, -8313, -8396, -8471, -8523, -8560, -8571, -8552,
-8501, -8405, -8271, -8090, -7862, -7578, -7234, -6823, -6346, -5800, -5183, -4505, -3765, -2968, -2117, -1224, -304, 633, 1577, 2492,
3376, 4205, 4976, 5682, 6306, 6851, 7318, 7700, 8009, 8247, 8416, 8529, 8580, 8583, 8537, 8450, 8331, 8187, 8022, 7838,
7637, 7425, 7202, 6974, 6741, 6513, 6287, 6065, 5848, 5629, 5415, 5204, 4992, 4789, 4588, 4397, 4205, 4017, 3835, 3655,
3478, 3305, 3136, 2974, 2819, 2662, 2513, 2361, 2213, 2068, 1926, 1787, 1655, 1523, 1394, 1267, 1140, 1010, 885, 761,
642, 523, 407, 290, 172, 52, -64, -181, -293, -404, -514, -626, -739, -851, -966, -1082, -1195, -1308, -1422, -1537,
-1650, -1770, -1888, -2012, -2136, -2257, -2384, -2509, -2638, -2768, -2906, -3043, -3186, -3327, -3470, -3610, -3753, -3902, -4051, -4206,
-4364, -4520, -4677, -4836, -4992, -5152, -5319, -5480, -5646, -5806, -5966, -6121, -6269, -6416, -6563, -6704, -6844, -6973, -7095, -7205,
-7294, -7366, -7418, -7446, -7446, -7412, -7340, -7225, -7061, -6841, -6566, -6231, -5829, -5359, -4808, -4185, -3485, -2712, -1872, -975,
-25, 957, 1956, 2947, 3913, 4835, 5706, 6508, 7245, 7900, 8480, 8971, 9379, 9704, 9947, 10115, 10222, 10264, 10254, 10199,
10101, 9966, 9805, 9620, 9414, 9202, 8980, 8753, 8515, 8276, 8029, 7782, 7534, 7290, 7048, 6815, 6582, 6350, 6128, 5901,
5682, 5472, 5263, 5067, 4870, 4682, 4494, 4313, 4129, 3958, 3790, 3630, 3477, 3330, 3186, 3047, 2909, 2776, 2650, 2523,
2403, 2285, 2172, 2059, 1946, 1837, 1732, 1632, 1538, 1445, 1358, 1271, 1183, 1096, 1010, 931, 846, 764, 686, 604,
526, 445, 368, 291, 219, 144, 76, 8, -62, -132, -203, -275, -348, -423, -497, -569, -643, -716, -788, -862,
-932, -1005, -1072, -1143, -1214, -1285, -1362, -1439, -1519, -1602, -1685, -1768, -1851, -1942, -2029, -2118, -2208, -2302, -2394, -2490,
-2584, -2684, -2789, -2894, -3005, -3122, -3239, -3359, -3480, -3604, -3729, -3856, -3987, -4125, -4261, -4401, -4538, -4684, -4836, -4988,
-5148, -5312, -5476, -5644, -5811, -5976, -6144, -6311, -6484, -6656, -6831, -7003, -7172, -7338, -7503, -7664, -7824, -7979, -8127, -8269,
-8394, -8502, -8601, -8681, -8743, -8795, -8817, -8818, -8784, -8709, -8594, -8433, -8219, -7953, -7622, -7223, -6751, -6204, -5582, -4892,
-4130, -3310, -2439, -1525, -578, 389, 1359, 2315, 3239, 4115, 4931, 5680, 6348, 6933, 7433, 7845, 8170, 8419, 8593, 8703,
8748, 8745, 8694, 8604, 8478, 8327, 8152, 7960, 7753, 7536, 7309, 7077, 6837, 6598, 6358, 6124, 5895, 5670, 5449, 5233,
5017, 4806, 4599, 4398, 4201, 4013, 3827, 3645, 3462, 3288, 3113, 2946, 2784, 2626, 2473, 2324, 2175, 2029, 1884, 1746,
1608, 1474, 1346, 1219, 1095, 968, 843, 720, 598, 479, 362, 248, 133, 17, -99, -217, -331, -445, -556, -665,
-771, -885, -995, -1107, -1223, -1337, -1450, -1562, -1675, -1792, -1908, -2030, -2151, -2273, -2397, -2522, -2645, -2770, -2901, -3035,
-3173, -3312, -3453, -3594, -3733, -3876, -4021, -4168, -4321, -4475, -4632, -4787, -4943, -5097, -5257, -5415, -5579, -5740, -5903, -6061,
-6212, -6361, -6506, -6644, -6782, -6915, -7042, -7158, -7262, -7346, -7418, -7463, -7490, -7484, -7450, -7373, -7255, -7082, -6860, -6576,
-6234, -5829, -5355, -4810, -4190, -3495, -2733, -1907, -1026, -97, 865, 1839, 2812, 3763, 4675, 5531, 6328, 7054, 7705, 8274,
8765, 9171, 9497, 9743, 9921, 10031, 10082, 10083, 10038, 9953, 9832, 9678, 9501, 9308, 9100, 8883, 8659, 8430, 8197, 7957,
7714, 7473, 7233, 6996, 6761, 6531, 6306, 6081, 5860, 5649, 5438, 5234, 5038, 4846, 4663, 4479, 4298, 4123, 3952, 3786,
3626, 3476, 3328, 3188, 3049, 2914, 2786, 2661, 2536, 2417, 2305, 2192, 2082, 1972, 1866, 1760, 1662, 1564, 1473, 1386,
1299, 1216, 1131, 1051, 968, 887, 811, 733, 656, 579, 499, 424, 349, 274, 204, 135, 66, 0, -70, -138,
-208, -282, -351, -419, -490, -563, -635, -709, -781, -852, -924, -992, -1060, -1130, -1202, -1277, -1352, -1431, -1514, -1592,
-1677, -1761, -1847, -1934, -2027, -2118, -2210, -2304, -2395, -2492, -2588, -2689, -2797, -2904, -3022, -3138, -3254, -3376, -3499, -3624,
-3754, -3885, -4023, -4160, -4298, -4439, -4584, -4729, -4881, -5041, -5203, -5367, -5534, -5703, -5870, -6036, -6204, -6373, -6546, -6719,
-6888, -7055, -7220, -7378, -7537, -7693, -7844, -7988, -8124, -8243, -8350, -8442, -8514, -8570, -8608, -8625, -8617, -8571, -8497, -8376,
-8209, -7996, -7721, -7390, -6988, -6516, -5970, -5349, -4657, -3902, -3088, -2229, -1331, -405, 541, 1483, 2411, 3307, 4158, 4952,
5682, 6336, 6915, 7403, 7816, 8140, 8382, 8553, 8658, 8706, 8698, 8647, 8555, 8428, 8275, 8104, 7913, 7712, 7500, 7275,
7047, 6812, 6575, 6338, 6101, 5873, 5647, 5428, 5211, 4997, 4784, 4579, 4377, 4181, 3993, 3806, 3624, 3445, 3269, 3093,
2923, 2758, 2600, 2445, 2291, 2145, 1993, 1848, 1701, 1561, 1427, 1293, 1163, 1030, 906, 777, 650, 525, 401, 282,
162, 43, -77, -197, -317, -437, -555, -671, -785, -897, -1012, -1128, -1244, -1361, -1479, -1596, -1714, -1832, -1954, -2073,
-2198, -2327, -2457, -2585, -2714, -2844, -2976, -3111, -3251, -3391, -3537, -3681, -3827, -3975, -4121, -4270, -4420, -4574, -4728, -4889,
-5043, -5199, -5356, -5513, -5669, -5827, -5989, -6143, -6293, -6439, -6578, -6707, -6832, -6948, -7057, -7158, -7243, -7309, -7363, -7385,
-7387, -7355, -7291, -7182, -7026, -6815, -6548, -6211, -5813, -5347, -4813, -4213, -3544, -2811, -2028, -1186, -303, 611, 1546, 2482,
3407, 4302, 5153, 5949, 6677, 7332, 7907, 8400, 8815, 9154, 9412, 9600, 9722, 9779, 9791, 9754, 9681, 9578, 9444, 9283,
9104, 8907, 8696, 8478, 8255, 8032, 7800, 7568, 7336, 7101, 6865, 6636, 6405, 6180, 5964, 5748, 5536, 5324, 5118, 4921,
4726, 4542, 4363, 4186, 4018, 3848, 3684, 3521, 3363, 3212, 3064, 2924, 2787, 2656, 2528, 2402, 2281, 2165, 2057, 1946,
1840, 1736, 1632, 1529, 1429, 1332, 1239, 1149, 1059, 976, 892, 811, 730, 649, 574, 497, 422, 348, 272, 194,
116, 37, -36, -109, -181, -250, -320, -390, -459, -530, -600, -668, -740, -810, -881, -954, -1029, -1105, -1176, -1250,
-1324, -1397, -1469, -1545, -1618, -1698, -1779, -1859, -1943, -2027, -2117, -2206, -2297, -2396, -2491, -2589, -2688, -2787, -2888, -2995,
-3094, -3207, -3320, -3438, -3559, -3684, -3810, -3937, -4070, -4205, -4342, -4486, -4627, -4772, -4918, -5066, -5214, -5368, -5526, -5685,
-5848, -6016, -6179, -6344, -6507, -6672, -6838, -7000, -7162, -7318, -7471, -7615, -7754, -7887, -8017, -8136, -8246, -8341, -8421, -8480,
-8508, -8522, -8507, -8465, -8389, -8278, -8128, -7928, -7676, -7367, -6994, -6559, -6055, -5475, -4827, -4109, -3327, -2493, -1616, -712,
207, 1124, 2025, 2899, 3732, 4514, 5236, 5893, 6479, 6998, 7441, 7804, 8096, 8311, 8459, 8539, 8565, 8539, 8473, 8374,
8245, 8088, 7913, 7725, 7523, 7317, 7109, 6894, 6680, 6459, 6234, 6010, 5789, 5570, 5359, 5149, 4945, 4746, 4547, 4352,
4160, 3976, 3794, 3621, 3450, 3287, 3120, 2958, 2798, 2640, 2486, 2340, 2195, 2055, 1916, 1780, 1640, 1506, 1375, 1247,
1120, 1000, 876, 756, 634, 512, 393, 274, 159, 45, -71, -185, -304, -422, -539, -654, -769, -880, -992, -1104,
-1217, -1337, -1453, -1571, -1691, -1810, -1929, -2054, -2178, -2310, -2438, -2572, -2705, -2839, -2973, -3109, -3248, -3391, -3538, -3687,
-3836, -3990, -4141, -4295, -4449, -4607, -4765, -4925, -5088, -5249, -5411, -5565, -5726, -5887, -6048, -6206, -6362, -6512, -6653, -6787,
-6909, -7019, -7120, -7206, -7276, -7327, -7357, -7356, -7327, -7262, -7155, -7004, -6797, -6532, -6200, -5795, -5311, -4755, -4122, -3422,
-2658, -1838, -964, -47, 900, 1865, 2826, 3769, 4684, 5555, 6368, 7118, 7791, 8380, 8887, 9303, 9639, 9896, 10075, 10185,
10235, 10232, 10177, 10083, 9960, 9811, 9640, 9451, 9248, 9029, 8801, 8563, 8323, 8083, 7838, 7604, 7365, 7125, 6888, 6652,
6418, 6193, 5970, 5752, 5540, 5330, 5126, 4925, 4732, 4545, 4369, 4193, 4031, 3866, 3706, 3549, 3393, 3246, 3100, 2960,
2823, 2694, 2568, 2443, 2323, 2208, 2098, 1991, 1888, 1788, 1689, 1591, 1494, 1397, 1303, 1213, 1122, 1037, 953, 875,
790, 711, 634, 560, 484, 410, 336, 263, 187, 113, 37, -40, -113, -188, -259, -330, -400, -474, -544, -614,
-687, -755, -827, -896, -970, -1049, -1123, -1201, -1279, -1357, -1436, -1512, -1591, -1672, -1754, -1837, -1924, -2009, -2100, -2193,
-2286, -2385, -2485, -2587, -2692, -2801, -2908, -3017, -3125, -3238, -3354, -3475, -3598, -3727, -3854, -3988, -4124, -4264, -4407, -4556,
-4705, -4861, -5015, -5169, -5325, -5485, -5645, -5809, -5978, -6149, -6324, -6495, -6670, -6838, -7013, -7181, -7348, -7516, -7677, -7833,
-7980, -8118, -8257, -8375, -8488, -8591, -8676, -8739, -8785, -8801, -8789, -8741, -8660, -8545, -8387, -8176, -7916, -7592, -7207, -6752,
-6225, -5626, -4957, -4212, -3400, -2532, -1615, -667, 297, 1259, 2197, 3103, 3959, 4754, 5482, 6138, 6720, 7228, 7655, 8008,
8285, 8490, 8622, 8689, 8698, 8659, 8577, 8459, 8310, 8138, 7948, 7737, 7521, 7299, 7074, 6849, 6625, 6396, 6172, 5945,
5720, 5497, 5279, 5064, 4855, 4654, 4454, 4258, 4063, 3876, 3694, 3515, 3344, 3177, 3011, 2852, 2692, 2536, 2381, 2233,
2089, 1951, 1811, 1677, 1541, 1405, 1277, 1144, 1020, 898, 779, 658, 536, 419, 301, 184, 69, -43, -157, -270,
-383, -497, -610, -723, -840, -949, -1062, -1171, -1281, -1397, -1508, -1625, -1742, -1860, -1978, -2095, -2216, -2344, -2469, -2599,
-2732, -2864, -2996, -3131, -3265, -3406, -3546, -3692, -3840, -3988, -4140, -4294, -4442, -4597, -4754, -4910, -5070, -5232, -5390, -5549,
-5705, -5863, -6020, -6177, -6334, -6489, -6636, -6777, -6909, -7031, -7143, -7243, -7327, -7398, -7447, -7474, -7472, -7440, -7375, -7272,
-7121, -6923, -6666, -6339, -5946, -5473, -4928, -4305, -3606, -2843, -2020, -1145, -230, 716, 1674, 2631, 3571, 4480, 5345, 6159,
6908, 7586, 8183, 8694, 9125, 9470, 9735, 9927, 10049, 10108, 10110, 10063, 9980, 9863, 9717, 9550, 9369, 9169, 8952, 8729,
8498, 8260, 8022, 7786, 7549, 7314, 7078, 6844, 6610, 6383, 6157, 5936, 5722, 5511, 5303, 5097, 4901, 4708, 4521, 4341,
4170, 4002, 3842, 3682, 3529, 3377, 3230, 3086, 2948, 2813, 2684, 2556, 2433, 2311, 2198, 2084, 1979, 1878, 1778, 1679,
1583, 1488, 1395, 1301, 1213, 1122, 1037, 953, 870, 788, 709, 629, 552, 480, 406, 332, 260, 186, 112, 34,
-40, -113, -187, -260, -334, -405, -476, -548, -619, -688, -758, -828, -898, -971, -1043, -1118, -1197, -1276, -1353, -1432,
-1510, -1590, -1671, -1752, -1836, -1921, -2007, -2094, -2186, -2279, -2371, -2470, -2575, -2681, -2786, -2895, -3005, -3115, -3227, -3340,
-3461, -3583, -3708, -3835, -3967, -4100, -4239, -4381, -4526, -4677, -4829, -4984, -5140, -5293, -5453, -5613, -5774, -5938, -6109, -6276,
-6446, -6618, -6788, -6958, -7125, -7293, -7458, -7619, -7773, -7919, -8058, -8187, -8305, -8418, -8517, -8601, -8668, -8712, -8732, -8721,
-8676, -8599, -8484, -8324, -8121, -7861, -7544, -7160, -6712, -6195, -5608, -4950, -4221, -3424, -2569, -1667, -731, 227, 1182, 2123,
3028, 3886, 4683, 5413, 6072, 6658, 7163, 7596, 7955, 8235, 8447, 8590, 8669, 8693, 8660, 8586, 8479, 8338, 8171, 7986,
7779, 7565, 7342, 7118, 6890, 6665, 6441, 6216, 5988, 5765, 5543, 5321, 5108, 4900, 4694, 4491, 4294, 4098, 3908, 3721,
3542, 3366, 3196, 3032, 2865, 2707, 2546, 2389, 2238, 2090, 1946, 1805, 1667, 1528, 1394, 1255, 1123, 994, 865, 742,
618, 495, 373, 249, 128, 9, -110, -226, -345, -460, -577, -695, -815, -931, -1051, -1166, -1283, -1396, -1513, -1629,
-1754, -1874, -1998, -2119, -2243, -2371, -2496, -2627, -2761, -2896, -3034, -3170, -3308, -3446, -3589, -3731, -3881, -4027, -4180, -4331,
-4484, -4639, -4794, -4946, -5105, -5262, -5422, -5576, -5730, -5884, -6033, -6181, -6327, -6468, -6607, -6742, -6866, -6980, -7081, -7165,
-7229, -7279, -7302, -7303, -7270, -7207, -7104, -6959, -6763, -6526, -6224, -5865, -5433, -4932, -4356, -3705, -2989, -2209, -1376, -497,
412, 1338, 2265, 3179, 4065, 4909, 5705, 6443, 7119, 7724, 8255, 8709, 9082, 9378, 9603, 9761, 9854, 9893, 9877, 9822,
9726, 9599, 9446, 9278, 9093, 8899, 8689, 8473, 8247, 8019, 7784, 7555, 7323, 7094, 6867, 6639, 6418, 6197, 5976, 5765,
5557, 5355, 5155, 4959, 4770, 4579, 4398, 4218, 4050, 3885, 3727, 3573, 3424, 3279, 3134, 2996, 2859, 2729, 2600, 2474,
2355, 2236, 2120, 2006, 1897, 1793, 1694, 1599, 1504, 1412, 1320, 1230, 1142, 1053, 968, 883, 798, 716, 636, 553,
476, 399, 326, 254, 182, 108, 39, -39, -112, -187, -261, -336, -411, -484, -556, -631, -704, -775, -847, -920,