#pragma once

#include <stdint.h>
#include <stddef.h>

const int16_t prompt_bt_connected[] = {
    0, 4, 16, 37, 66, 103, 147, 198, 256, 319, 388, 462,
    541, 622, 707, 793, 881, 969, 1056, 1143, 1228, 1311, 1390, 1466,
    1537, 1604, 1665, 1721, 1770, 1813, 1849, 1879, 1901, 1916, 1924, 1925,
    1919, 1906, 1887, 1861, 1829, 1791, 1747, 1698, 1645, 1586, 1524, 1457,
    1387, 1314, 1237, 1158, 1076, 992, 905, 816, 724, 631, 535, 436,
    335, 232, 125, 15, -97, -214, -335, -461, -591, -726, -866, -1011,
    -1162, -1319, -1482, -1651, -1825, -2005, -2192, -2383, -2580, -2781, -2986, -3195,
    -3407, -3621, -3836, -4051, -4265, -4477, -4685, -4889, -5087, -5277, -5459, -5629,
    -5788, -5933, -6064, -6177, -6273, -6349, -6404, -6437, -6447, -6433, -6393, -6327,
    -6233, -6113, -5964, -5788, -5583, -5350, -5089, -4801, -4486, -4145, -3780, -3391,
    -2979, -2547, -2096, -1628, -1145, -649, -142, 373, 894, 1420, 1946, 2471,
    2993, 3508, 4014, 4509, 4991, 5456, 5904, 6331, 6737, 7119, 7475, 7805,
    8106, 8378, 8620, 8832, 9012, 9161, 9278, 9363, 9417, 9440, 9434, 9397,
    9333, 9241, 9123, 8981, 8815, 8628, 8421, 8195, 7952, 7695, 7424, 7141,
    6848, 6547, 6238, 5924, 5605, 5283, 4959, 4633, 4307, 3981, 3656, 3332,
    3009, 2688, 2368, 2049, 1731, 1413, 1095, 777, 457, 135, -190, -518,
    -852, -1190, -1535, -1887, -2245, -2612, -2988, -3372, -3765, -4167, -4578, -4998,
    -5426, -5862, -6304, -6751, -7203, -7658, -8115, -8570, -9024, -9472, -9914, -10346,
    -10765, -11171, -11558, -11925, -12269, -12558, -12788, -12984, -13145, -13267, -13349, -13390,
    -13386, -13338, -13243, -13101, -12911, -12672, -12385, -12050, -11667, -11237, -10761, -10239,
    -9675, -9070, -8425, -7744, -7029, -6283, -5509, -4711, -3892, -3056, -2206, -1346,
    -481, 385, 1249, 2108, 2956, 3791, 4607, 5403, 6173, 6916, 7627, 8304,
    8944, 9545, 10104, 10621, 11093, 11518, 11897, 12227, 12510, 12744, 12930, 13069,
    13160, 13206, 13207, 13165, 13081, 12958, 12797, 12601, 12372, 12112, 11823, 11509,
    11172, 10814, 10438, 10047, 9643, 9227, 8804, 8373, 7939, 7502, 7064, 6627,
    6192, 5760, 5332, 4909, 4491, 4080, 3674, 3274, 2880, 2492, 2110, 1732,
    1358, 987, 620, 253, -111, -477, -843, -1211, -1582, -1957, -2335, -2718,
    -3106, -3500, -3899, -4304, -4714, -5129, -5550, -5973, -6400, -6829, -7259, -7688,
    -8115, -8537, -8954, -9363, -9761, -10147, -10518, -10872, -11207, -11519, -11806, -12067,
    -12298, -12497, -12661, -12790, -12880, -12931, -12939, -12904, -12825, -12701, -12530, -12313,
    -12049, -11738, -11381, -10977, -10529, -10038, -9504, -8930, -8317, -7669, -6987, -6274,
    -5533, -4769, -3982, -3179, -2361, -1532, -698, 139, 976, 1807, 2630, 3440,
    4234, 5009, 5760, 6486, 7181, 7845, 8474, 9065, 9617, 10128, 10596, 11019,
    11398, 11730, 12016, 12255, 12448, 12595, 12696, 12752, 12765, 12736, 12666, 12557,
    12412, 12231, 12018, 11775, 11504, 11207, 10887, 10547, 10188, 9814, 9427, 9028,
    8621, 8207, 7788, 7366, 6943, 6520, 6099, 5681, 5266, 4856, 4451, 4052,
    3658, 3270, 2888, 2512, 2141, 1774, 1412, 1053, 697, 343, -9, -362,
    -716, -1071, -1429, -1790, -2154, -2523, -2897, -3275, -3660, -4049, -4444, -4844,
    -5249, -5658, -6069, -6483, -6899, -7313, -7726, -8136, -8540, -8938, -9326, -9702,
    -10065, -10412, -10740, -11048, -11333, -11592, -11823, -12024, -12193, -12327, -12425, -12484,
    -12504, -12482, -12418, -12310, -12157, -11960, -11717, -11429, -11096, -10719, -10298, -9835,
    -9330, -8786, -8204, -7587, -6937, -6256, -5548, -4815, -4061, -3288, -2502, -1704,
    -898, -90, 718, 1524, 2321, 3108, 3880, 4634, 5367, 6075, 6755, 7405,
    8022, 8604, 9148, 9653, 10116, 10538, 10916, 11249, 11538, 11782, 11980, 12134,
    12244, 12310, 12334, 12317, 12261, 12166, 12035, 11870, 11673, 11446, 11191, 10911,
    10607, 10284, 9942, 9584, 9213, 8831, 8440, 8041, 7637, 7231, 6822, 6414,
    6006, 5601, 5199, 4802, 4409, 4021, 3640, 3263, 2893, 2528, 2168, 1812,
    1461, 1114, 769, 426, 85, -255, -597, -939, -1284, -1632, -1983, -2338,
    -2698, -3063, -3432, -3807, -4188, -4573, -4963, -5356, -5754, -6153, -6554, -6955,
    -7355, -7752, -8144, -8530, -8907, -9274, -9629, -9969, -10291, -10595, -10876, -11133,
    -11365, -11567, -11739, -11878, -11983, -12050, -12080, -12070, -12020, -11927, -11792, -11613,
    -11391, -11125, -10815, -10463, -10067, -9631, -9154, -8639, -8087, -7500, -6880, -6230,
    -5553, -4851, -4128, -3386, -2630, -1861, -1085, -304, 477, 1256, 2030, 2793,
    3543, 4277, 4991, 5682, 6347, 6984, 7589, 8161, 8697, 9195, 9654, 10073,
    10450, 10784, 11075, 11323, 11527, 11687, 11805, 11881, 11915, 11910, 11866, 11784,
    11667, 11517, 11334, 11123, 10884, 10620, 10333, 10025, 9700, 9358, 9003, 8636,
    8260, 7877, 7488, 7096, 6701, 6306, 5912, 5520, 5131, 4746, 4365, 3989,
    3619, 3253, 2894, 2540, 2190, 1846, 1506, 1169, 835, 504, 174, -155,
    -485, -816, -1148, -1483, -1821, -2163, -2510, -2861, -3217, -3578, -3944, -4314,
    -4690, -5069, -5452, -5838, -6225, -6613, -6999, -7384, -7764, -8139, -8506, -8864,
    -9210, -9542, -9859, -10157, -10435, -10691, -10921, -11125, -11299, -11443, -11553, -11629,
    -11668, -11669, -11631, -11553, -11434, -11273, -11070, -10825, -10537, -10208, -9838, -9427,
    -8977, -8489, -7965, -7407, -6817, -6197, -5550, -4878, -4185, -3473, -2745, -2006,
    -1257, -503, 251, 1005, 1754, 2495, 3224, 3937, 4633, 5307, 5957, 6580,
    7173, 7735, 8263, 8754, 9209, 9624, 10000, 10334, 10627, 10878, 11087, 11254,
    11379, 11463, 11508, 11513, 11480, 11411, 11308, 11171, 11003, 10807, 10583, 10334,
    10063, 9771, 9461, 9135, 8795, 8444, 8083, 7714, 7340, 6962, 6581, 6199,
    5818, 5439, 5062, 4688, 4319, 3955, 3595, 3241, 2892, 2548, 2210, 1876,
    1546, 1220, 896, 575, 256, -61, -380, -699, -1020, -1343, -1669, -1998,
    -2332, -2669, -3012, -3359, -3712, -4069, -4430, -4796, -5165, -5537, -5911, -6285,
    -6659, -7031, -7400, -7764, -8121, -8469, -8807, -9132, -9443, -9736, -10010, -10263,
    -10493, -10697, -10874, -11021, -11137, -11219, -11267, -11278, -11252, -11188, -11084, -10940,
    -10755, -10529, -10263, -9956, -9609, -9222, -8798, -8337, -7840, -7310, -6748, -6157,
    -5538, -4896, -4231, -3548, -2849, -2137, -1416, -689, 40, 769, 1495, 2213,
    2920, 3614, 4292, 4949, 5584, 6193, 6775, 7326, 7845, 8330, 8779, 9191,
    9565, 9899, 10193, 10447, 10660, 10833, 10965, 11057, 11111, 11126, 11105, 11048,
    10957, 10833, 10680, 10497, 10288, 10054, 9798, 9521, 9226, 8915, 8591, 8254,
    7908, 7553, 7193, 6828, 6461, 6092, 5724, 5357, 4992, 4630, 4272, 3918,
    3570, 3226, 2888, 2554, 2225, 1902, 1582, 1266, 953, 642, 333, 25,
    -281, -590, -899, -1210, -1525, -1842, -2163, -2488, -2818, -3152, -3491, -3835,
    -4183, -4535, -4891, -5250, -5611, -5972, -6334, -6694, -7052, -7405, -7752, -8091,
    -8420, -8738, -9042, -9330, -9600, -9851, -10079, -10284, -10462, -10612, -10733, -10821,
    -10877, -10898, -10883, -10831, -10741, -10613, -10445, -10238, -9991, -9706, -9381, -9018,
    -8618, -8182, -7712, -7208, -6674, -6110, -5520, -4905, -4269, -3613, -2942, -2257,
    -1563, -861, -156, 548, 1250, 1946, 2633, 3308, 3967, 4607, 5227, 5823,
    6392, 6934, 7444, 7922, 8366, 8774, 9145, 9479, 9774, 10030, 10247, 10424,
    10563, 10663, 10725, 10750, 10739, 10693, 10614, 10504, 10363, 10194, 9999, 9779,
    9538, 9275, 8995, 8699, 8389, 8067, 7734, 7394, 7047, 6696, 6342, 5986,
    5629, 5274, 4921, 4570, 4223, 3881, 3542, 3209, 2880, 2557, 2238, 1924,
    1614, 1307, 1004, 703, 405, 107, -189, -487, -785, -1086, -1388, -1694,
    -2003, -2316, -2634, -2955, -3282, -3613, -3948, -4287, -4630, -4976, -5324, -5673,
    -6023, -6372, -6718, -7060, -7397, -7727, -8048, -8359, -8656, -8939, -9205, -9453,
    -9680, -9884, -10063, -10216, -10341, -10435, -10498, -10528, -10523, -10483, -10406, -10293,
    -10141, -9952, -9724, -9458, -9155, -8815, -8438, -8027, -7581, -7103, -6595, -6058,
    -5494, -4907, -4297, -3669, -3024, -2366, -1697, -1021, -341, 340, 1020, 1694,
    2361, 3016, 3657, 4282, 4886, 5469, 6026, 6557, 7059, 7529, 7968, 8372,
    8740, 9073, 9368, 9626, 9846, 10028, 10173, 10280, 10350, 10384, 10383, 10348,
    10280, 10182, 10054, 9898, 9716, 9510, 9282, 9034, 8768, 8486, 8190, 7882,
    7563, 7236, 6903, 6564, 6223, 5879, 5535, 5191, 4849, 4510, 4173, 3841,
    3513, 3189, 2871, 2557, 2248, 1943, 1642, 1345, 1051, 760, 471, 183,
    -103, -390, -679, -968, -1260, -1554, -1852, -2154, -2459, -2769, -3083, -3401,
    -3724, -4051, -4381, -4715, -5051, -5388, -5726, -6063, -6398, -6730, -7058, -7378,
    -7691, -7994, -8285, -8563, -8825, -9069, -9294, -9498, -9678, -9833, -9961, -10060,
    -10130, -10167, -10172, -10143, -10079, -9979, -9843, -9670, -9460, -9214, -8931, -8612,
    -8258, -7869, -7448, -6995, -6511, -6000, -5462, -4901, -4318, -3715, -3096, -2464,
    -1820, -1168, -512, 146, 803, 1457, 2103, 2740, 3363, 3971, 4561, 5130,
    5676, 6196, 6688, 7152, 7584, 7984, 8350, 8681, 8976, 9236, 9458, 9644,
    9794, 9907, 9985, 10027, 10035, 10011, 9954, 9867, 9751, 9608, 9439, 9246,
    9032, 8798, 8545, 8277, 7994, 7699, 7394, 7080, 6760, 6434, 6104, 5773,
    5440, 5108, 4777, 4448, 4122, 3800, 3482, 3168, 2859, 2554, 2254, 1959,
    1667, 1379, 1094, 812, 533, 254, -23, -300, -578, -858, -1139, -1423,
    -1709, -2000, -2294, -2592, -2894, -3201, -3511, -3826, -4144, -4466, -4790, -5115,
    -5442, -5768, -6092, -6414, -6732, -7044, -7348, -7644, -7929, -8200, -8458, -8699,
    -8922, -9124, -9305, -9462, -9593, -9697, -9772, -9817, -9831, -9812, -9759, -9672,
    -9550, -9393, -9201, -8972, -8709, -8410, -8077, -7711, -7312, -6883, -6424, -5937,
    -5425, -4888, -4330, -3753, -3159, -2551, -1932, -1304, -671, -35, 600, 1233,
    1859, 2477, 3084, 3676, 4250, 4806, 5340, 5849, 6333, 6789, 7215, 7610,
    7973, 8302, 8597, 8858, 9083, 9272, 9427, 9546, 9630, 9680, 9697, 9682,
    9636, 9560, 9456, 9324, 9168, 8988, 8786, 8565, 8326, 8071, 7801, 7519,
    7227, 6926, 6618, 6304, 5987, 5667, 5346, 5025, 4704, 4386, 4070, 3758,
    3449, 3145, 2845, 2549, 2258, 1971, 1688, 1409, 1134, 860, 589, 320,
    52, -215, -484, -753, -1025, -1298, -1574, -1854, -2137, -2424, -2715, -3010,
    -3309, -3612, -3919, -4228, -4541, -4855, -5170, -5485, -5800, -6111, -6420, -6723,
    -7019, -7307, -7585, -7852, -8105, -8342, -8562, -8764, -8944, -9102, -9236, -9344,
    -9424, -9476, -9498, -9488, -9447, -9372, -9264, -9122, -8945, -8734, -8489, -8209,
    -7897, -7552, -7175, -6769, -6333, -5870, -5381, -4869, -4336, -3783, -3213, -2630,
    -2034, -1430, -819, -205, 409, 1022, 1629, 2229, 2818, 3394, 3954, 4497,
    5018, 5517, 5992, 6440, 6860, 7250, 7609, 7937, 8231, 8492, 8719, 8912,
    9070, 9195, 9285, 9343, 9369, 9362, 9326, 9260, 9167, 9047, 8902, 8735,
    8546, 8337, 8111, 7868, 7611, 7342, 7062, 6774, 6478, 6176, 5870, 5562,
    5251, 4941, 4631, 4323, 4017, 3714, 3415, 3120, 2829, 2542, 2260, 1981,
    1707, 1436, 1169, 904, 642, 382, 122, -136, -395, -656, -917, -1181,
    -1447, -1716, -1988, -2264, -2544, -2828, -3116, -3408, -3704, -4002, -4303, -4606,
    -4911, -5216, -5520, -5822, -6121, -6415, -6703, -6984, -7256, -7516, -7764, -7998,
    -8216, -8416, -8596, -8755, -8891, -9002, -9087, -9145, -9174, -9174, -9142, -9079,
    -8983, -8855, -8694, -8499, -8271, -8010, -7717, -7393, -7037, -6652, -6239, -5798,
    -5333, -4844, -4334, -3805, -3259, -2699, -2126, -1544, -956, -363, 230, 823,
    1412, 1993, 2566, 3126, 3672, 4201, 4711, 5199, 5665, 6105, 6518, 6903,
    7259, 7584, 7877, 8138, 8367, 8562, 8725, 8854, 8951, 9015, 9048, 9051,
    9024, 8968, 8885, 8776, 8643, 8487, 8310, 8113, 7899, 7669, 7424, 7167,
    6900, 6623, 6339, 6049, 5754, 5457, 5157, 4857, 4558, 4259, 3963, 3670,
    3380, 3093, 2811, 2533, 2259, 1989, 1723, 1460, 1201, 945, 691, 438,
    187, -62, -312, -563, -816, -1070, -1326, -1585, -1848, -2113, -2383, -2656,
    -2933, -3214, -3499, -3786, -4077, -4369, -4663, -4958, -5252, -5544, -5834, -6120,
    -6400, -6674, -6939, -7194, -7437, -7667, -7882, -8080, -8259, -8418, -8556, -8670,
    -8760, -8823, -8859, -8867, -8845, -8792, -8709, -8594, -8446, -8267, -8056, -7813,
    -7538, -7233, -6898, -6533, -6142, -5723, -5280, -4814, -4327, -3820, -3297, -2759,
    -2209, -1649, -1082, -510, 63, 636, 1206, 1771, 2326, 2871, 3403, 3919,
    4417, 4895, 5351, 5783, 6190, 6569, 6921, 7243, 7535, 7796, 8026, 8224,
    8389, 8523, 8625, 8696, 8737, 8747, 8729, 8683, 8610, 8511, 8389, 8244,
    8079, 7894, 7691, 7473, 7240, 6995, 6739, 6474, 6202, 5923, 5639, 5353,
    5064, 4774, 4484, 4195, 3909, 3624, 3343, 3065, 2791, 2521, 2256, 1994,
    1735, 1481, 1230, 981, 735, 491, 248, 6, -235, -477, -720, -965,
    -1212, -1462, -1714, -1970, -2230, -2493, -2760, -3030, -3304, -3581, -3861, -4143,
    -4427, -4711, -4995, -5279, -5559, -5837, -6109, -6375, -6634, -6883, -7122, -7347,
    -7559, -7755, -7934, -8093, -8232, -8349, -8442, -8511, -8553, -8568, -8555, -8512,
    -8440, -8337, -8204, -8039, -7844, -7617, -7360, -7074, -6758, -6413, -6042, -5645,
    -5223, -4779, -4313, -3829, -3328, -2812, -2283, -1744, -1198, -646, -92, 461,
    1013, 1560, 2100, 2629, 3147, 3650, 4136, 4603, 5050, 5474, 5874, 6248,
    6596, 6915, 7205, 7466, 7696, 7896, 8065, 8203, 8310, 8387, 8434, 8452,
    8442, 8404, 8341, 8253, 8141, 8007, 7852, 7678, 7487, 7281, 7060, 6826,
    6581, 6328, 6066, 5798, 5525, 5249, 4970, 4690, 4410, 4131, 3853, 3578,
    3305, 3036, 2770, 2508, 2250, 1996, 1746, 1499, 1255, 1015, 776, 540,
    305, 71, -162, -396, -630, -867, -1105, -1345, -1588, -1835, -2084, -2338,
    -2594, -2855, -3118, -3385, -3655, -3927, -4201, -4476, -4750, -5024, -5296, -5566,
    -5830, -6089, -6341, -6585, -6818, -7040, -7248, -7442, -7620, -7779, -7919, -8038,
    -8135, -8207, -8255, -8277, -8272, -8239, -8177, -8086, -7965, -7815, -7634, -7424,
    -7184, -6914, -6617, -6292, -5940, -5563, -5162, -4739, -4294, -3831, -3351, -2857,
    -2349, -1831, -1305, -773, -238, 297, 831, 1361, 1885, 2399, 2903, 3393,
    3867, 4324, 4761, 5177, 5571, 5939, 6282, 6599, 6887, 7147, 7377, 7579,
    7750, 7891, 8003, 8086, 8139, 8164, 8162, 8133, 8079, 8000, 7898, 7774,
    7630, 7467, 7287, 7092, 6882, 6659, 6426, 6183, 5932, 5675, 5412, 5146,
    4877, 4607, 4336, 4066, 3798, 3531, 3267, 3005, 2748, 2494, 2243, 1997,
    1754, 1514, 1278, 1045, 814, 585, 358, 131, -93, -319, -546, -774,
    -1003, -1235, -1469, -1706, -1947, -2190, -2437, -2688, -2942, -3199, -3459, -3721,
    -3985, -4251, -4516, -4781, -5045, -5306, -5563, -5815, -6060, -6298, -6526, -6744,
    -6949, -7140, -7316, -7475, -7616, -7737, -7836, -7913, -7966, -7994, -7997, -7972,
    -7920, -7840, -7732, -7594, -7428, -7232, -7008, -6756, -6476, -6169, -5836, -5479,
    -5098, -4694, -4271, -3828, -3369, -2894, -2407, -1909, -1403, -890, -374, 143,
    660, 1173, 1681, 2181, 2671, 3148, 3611, 4057, 4485, 4893, 5279, 5642,
    5981, 6293, 6580, 6838, 7069, 7271, 7445, 7590, 7706, 7793, 7853, 7884,
    7889, 7869, 7823, 7753, 7661, 7547, 7413, 7261, 7091, 6906, 6707, 6495,
    6272, 6040, 5800, 5553, 5300, 5044, 4785, 4524, 4263, 4001, 3741, 3483,
    3227, 2974, 2724, 2477, 2234, 1995, 1759, 1527, 1298, 1072, 848, 626,
    406, 188, -30, -248, -467, -686, -908, -1131, -1356, -1585, -1816, -2051,
    -2288, -2530, -2774, -3022, -3272, -3525, -3780, -4036, -4292, -4549, -4804, -5057,
    -5306, -5551, -5790, -6022, -6245, -6459, -6660, -6849, -7024, -7182, -7323, -7445,
    -7547, -7627, -7685, -7719, -7729, -7712, -7670, -7600, -7502, -7377, -7224, -7043,
    -6834, -6598, -6335, -6046, -5731, -5392, -5030, -4646, -4242, -3819, -3380, -2925,
    -2458, -1979, -1492, -998, -500, 0, 499, 996, 1489, 1974, 2450, 2915,
    3366, 3802, 4221, 4620, 4999, 5356, 5690, 5999, 6283, 6541, 6771, 6974,
    7150, 7297, 7417, 7509, 7574, 7612, 7624, 7611, 7573, 7512, 7429, 7324,
    7200, 7058, 6899, 6724, 6535, 6334, 6121, 5899, 5669, 5432, 5189, 4943,
    4693, 4441, 4189, 3936, 3685, 3434, 3186, 2941, 2698, 2459, 2224, 1991,
    1763, 1537, 1315, 1096, 879, 665, 452, 240, 29, -181, -392, -604,
    -817, -1032, -1250, -1470, -1692, -1918, -2147, -2379, -2614, -2853, -3094, -3338,
    -3583, -3831, -4078, -4326, -4573, -4818, -5060, -5298, -5531, -5757, -5975, -6184,
    -6383, -6569, -6741, -6898, -7039, -7163, -7267, -7350, -7412, -7452, -7467, -7459,
    -7425, -7364, -7278, -7164, -7024, -6857, -6662, -6441, -6194, -5922, -5624, -5303,
    -4959, -4594, -4209, -3805, -3385, -2950, -2501, -2042, -1573, -1097, -617, -134,
    348, 830, 1307, 1778, 2241, 2693, 3133, 3558, 3968, 4359, 4731, 5082,
    5411, 5716, 5997, 6253, 6483, 6687, 6864, 7014, 7137, 7233, 7303, 7347,
    7366, 7360, 7330, 7277, 7202, 7107, 6992, 6860, 6710, 6545, 6366, 6175,
    5972, 5760, 5540, 5313, 5080, 4842, 4602, 4359, 4115, 3871, 3628, 3385,
    3145, 2907, 2672, 2440, 2211, 1986, 1764, 1546, 1330, 1117, 907, 699,
    493, 289, 85, -118, -322, -527, -732, -940, -1149, -1361, -1575, -1792,
    -2013, -2236, -2463, -2692, -2925, -3159, -3396, -3635, -3874, -4114, -4353, -4590,
    -4825, -5056, -5282, -5503, -5716, -5920, -6115, -6298, -6468, -6625, -6765, -6889,
    -6995, -7082, -7147, -7192, -7213, -7212, -7185, -7134, -7058, -6955, -6827, -6673,
    -6492, -6286, -6054, -5797, -5516, -5212, -4886, -4539, -4172, -3787, -3385, -2968,
    -2538, -2097, -1646, -1189, -725, -259, 207, 673, 1135, 1592, 2042, 2482,
    2910, 3325, 3725, 4108, 4473, 4818, 5142, 5443, 5722, 5976, 6205, 6409,
    6587, 6739, 6866, 6966, 7040, 7090, 7115, 7115, 7092, 7047, 6981, 6894,
    6789, 6665, 6525, 6370, 6200, 6019, 5826, 5624, 5413, 5195, 4971, 4743,
    4511, 4277, 4042, 3806, 3570, 3336, 3103, 2873, 2645, 2420, 2198, 1979,
    1764, 1552, 1343, 1137, 933, 731, 532, 334, 136, -59, -256, -454,
    -652, -852, -1054, -1258, -1464, -1673, -1885, -2100, -2318, -2539, -2763, -2989,
    -3218, -3448, -3679, -3910, -4142, -4371, -4599, -4824, -5044, -5258, -5466, -5666,
    -5857, -6037, -6205, -6360, -6501, -6625, -6732, -6821, -6890, -6939, -6966, -6971,
    -6952, -6909, -6842, -6751, -6633, -6491, -6324, -6131, -5914, -5673, -5408, -5120,
    -4811, -4481, -4131, -3764, -3380, -2981, -2569, -2146, -1712, -1272, -826, -376,
    74, 525, 973, 1416, 1853, 2281, 2698, 3103, 3494, 3869, 4226, 4565,
    4883, 5181, 5456, 5708, 5936, 6140, 6319, 6473, 6602, 6706, 6785, 6840,
    6870, 6877, 6861, 6824, 6765, 6687, 6590, 6475, 6344, 6198, 6038, 5865,
    5682, 5489, 5287, 5078, 4864, 4644, 4421, 4196, 3968, 3741, 3513, 3286,
    3061, 2837, 2616, 2398, 2183, 1971, 1762, 1556, 1353, 1153, 956, 761,
    567, 375, 185, -5, -195, -385, -577, -769, -964, -1160, -1359, -1560,
    -1764, -1971, -2181, -2394, -2609, -2827, -3048, -3270, -3493, -3716, -3940, -4162,
    -4383, -4601, -4815, -5024, -5227, -5422, -5609, -5786, -5952, -6105, -6245, -6369,
    -6478, -6569, -6641, -6694, -6726, -6736, -6725, -6690, -6632, -6550, -6443, -6313,
    -6157, -5978, -5775, -5548, -5298, -5027, -4733, -4420, -4087, -3737, -3370, -2989,
    -2594, -2188, -1772, -1348, -918, -484, -48, 387, 820, 1250, 1674, 2090,
    2496, 2891, 3272, 3639, 3989, 4321, 4635, 4928, 5200, 5450, 5677, 5880,
    6060, 6216, 6347, 6454, 6537, 6596, 6632, 6645, 6636, 6605, 6554, 6484,
    6395, 6289, 6166, 6029, 5878, 5715, 5540, 5356, 5163, 4964, 4758, 4547,
    4332, 4115, 3895, 3675, 3455, 3236, 3017, 2801, 2587, 2375, 2166, 1961,
    1758, 1558, 1362, 1168, 976, 787, 600, 414, 230, 46, -137, -321,
    -506, -692, -879, -1068, -1259, -1453, -1650, -1849, -2051, -2256, -2463, -2673,
    -2885, -3099, -3315, -3531, -3747, -3962, -4176, -4387, -4595, -4798, -4996, -5187,
    -5370, -5544, -5707, -5859, -5998, -6122, -6232, -6324, -6399, -6455, -6492, -6508,
    -6503, -6475, -6426, -6353, -6256, -6137, -5993, -5827, -5637, -5424, -5189, -4932,
    -4654, -4357, -4040, -3707, -3357, -2992, -2614, -2224, -1824, -1417, -1003, -584,
    -164, 257, 676, 1093, 1504, 1908, 2304, 2688, 3061, 3419, 3762, 4088,
    4396, 4685, 4953, 5201, 5426, 5629, 5810, 5966, 6100, 6210, 6296, 6360,
    6401, 6419, 6416, 6392, 6348, 6285, 6204, 6106, 5992, 5863, 5721, 5567,
    5401, 5225, 5042, 4850, 4653, 4450, 4244, 4034, 3823, 3610, 3398, 3185,
    2974, 2764, 2557, 2352, 2149, 1949, 1753, 1559, 1368, 1180, 994, 811,
    630, 450, 271, 93, -83, -261, -439, -618, -799, -981, -1165, -1352,
    -1541, -1733, -1927, -2124, -2324, -2526, -2731, -2937, -3145, -3353, -3562, -3770,
    -3978, -4183, -4384, -4582, -4775, -4962, -5141, -5311, -5472, -5622, -5759, -5884,
    -5993, -6087, -6165, -6224, -6265, -6286, -6287, -6266, -6224, -6160, -6073, -5964,
    -5832, -5677, -5499, -5300, -5079, -4836, -4573, -4291, -3991, -3673, -3339, -2990,
    -2628, -2254, -1871, -1479, -1080, -677, -271, 135, 541, 945, 1344, 1736,
    2121, 2495, 2859, 3209, 3544, 3864, 4167, 4451, 4716, 4961, 5185, 5387,
    5567, 5725, 5860, 5973, 6063, 6130, 6176, 6199, 6202, 6185, 6148, 6092,
    6018, 5928, 5822, 5701, 5567, 5421, 5264, 5097, 4921, 4738, 4549, 4355,
    4156, 3954, 3751, 3545, 3340, 3134, 2930, 2727, 2526, 2327, 2130, 1937,
    1746, 1558, 1373, 1190, 1010, 833, 657, 483, 310, 138, -33, -204,
    -376, -549, -723, -899, -1076, -1256, -1438, -1622, -1809, -1999, -2192, -2386,
    -2583, -2782, -2983, -3184, -3386, -3587, -3788, -3986, -4182, -4375, -4563, -4745,
    -4920, -5087, -5245, -5393, -5529, -5653, -5763, -5858, -5937, -6000, -6044, -6070,
    -6076, -6062, -6027, -5971, -5894, -5794, -5672, -5529, -5363, -5177, -4968, -4740,
    -4491, -4224, -3938, -3635, -3317, -2984, -2638, -2280, -1911, -1535, -1151, -763,
    -371, 21, 414, 805, 1192, 1573, 1947, 2312, 2666, 3008, 3336, 3649,
    3946, 4226, 4488, 4730, 4952, 5153, 5333, 5491, 5628, 5743, 5836, 5907,
    5957, 5986, 5994, 5982, 5952, 5903, 5836, 5753, 5655, 5542, 5416, 5278,
    5129, 4970, 4803, 4628, 4447, 4260, 4069, 3875, 3679, 3481, 3282, 3084,
    2886, 2689, 2494, 2301, 2111, 1923, 1738, 1556, 1376, 1199, 1024, 852,
    682, 513, 346, 179, 13, -151, -317, -484, -652, -821, -992, -1165,
    -1340, -1518, -1698, -1881, -2066, -2253, -2443, -2635, -2828, -3022, -3217, -3412,
    -3606, -3799, -3989, -4176, -4359, -4536, -4707, -4871, -5026, -5172, -5307, -5430,
    -5540, -5636, -5717, -5782, -5830, -5860, -5871, -5863, -5835, -5787, -5717, -5627,
    -5516, -5383, -5229, -5054, -4859, -4643, -4408, -4155, -3884, -3596, -3292, -2974,
    -2643, -2300, -1947, -1585, -1216, -842, -464, -84, 295, 673, 1048, 1418,
    1781, 2137, 2482, 2816, 3137, 3444, 3735, 4010, 4268, 4507, 4727, 4927,
    5106, 5265, 5403, 5520, 5616, 5691, 5744, 5778, 5791, 5785, 5761, 5718,
    5659, 5583, 5492, 5387, 5268, 5138, 4997, 4846, 4686, 4519, 4346, 4167,
    3983, 3797, 3607, 3416, 3225, 3033, 2841, 2651, 2462, 2275, 2091, 1908,
    1729, 1552, 1377, 1206, 1036, 869, 704, 541, 379, 218, 57, -102,
    -262, -423, -585, -748, -912, -1079, -1248, -1419, -1592, -1768, -1946, -2127,
    -2309, -2494, -2680, -2868, -3056, -3245, -3432, -3619, -3803, -3985, -4163, -4336,
    -4503, -4663, -4816, -4959, -5092, -5215, -5325, -5421, -5504, -5571, -5622, -5656,
    -5672, -5669, -5647, -5606, -5545, -5463, -5361, -5239, -5096, -4932, -4749, -4546,
    -4324, -4084, -3827, -3553, -3264, -2960, -2643, -2315, -1976, -1629, -1275, -914,
    -550, -183, 183, 549, 912, 1271, 1625, 1970, 2306, 2632, 2946, 3246,
    3532, 3802, 4056, 4292, 4510, 4709, 4888, 5047, 5186, 5304, 5403, 5480,
    5538, 5576, 5594, 5593, 5575, 5538, 5485, 5416, 5332, 5234, 5123, 5001,
    4867, 4724, 4572, 4412, 4246, 4074, 3898, 3719, 3536, 3352, 3167, 2982,
    2797, 2612, 2429, 2248, 2069, 1892, 1718, 1546, 1377, 1211, 1047, 885,
    725, 566, 409, 254, 99, -55, -210, -365, -521, -679, -837, -998,
    -1160, -1324, -1491, -1661, -1832, -2006, -2182, -2360, -2540, -2721, -2902, -3084,
    -3266, -3447, -3626, -3802, -3975, -4143, -4307, -4463, -4613, -4754, -4886, -5007,
    -5117, -5214, -5297, -5366, -5420, -5457, -5477, -5480, -5464, -5430, -5376, -5303,
    -5210, -5097, -4964, -4811, -4640, -4449, -4239, -4012, -3768, -3508, -3232, -2943,
    -2640, -2326, -2002, -1668, -1327, -981, -630, -276, 78, 432, 784, 1133,
    1476, 1811, 2139, 2457, 2763, 3057, 3338, 3603, 3853, 4086, 4301, 4498,
    4676, 4836, 4975, 5095, 5196, 5276, 5337, 5379, 5402, 5406, 5393, 5363,
    5316, 5253, 5176, 5085, 4981, 4866, 4740, 4604, 4459, 4307, 4148, 3983,
    3814, 3642, 3466, 3289, 3110, 2931, 2752, 2573, 2396, 2221, 2047, 1876,
    1707, 1540, 1376, 1214, 1055, 898, 743, 589, 438, 287, 137, -12,
    -161, -311, -462, -613, -766, -921, -1077, -1235, -1396, -1559, -1724, -1891,
    -2061, -2232, -2406, -2580, -2756, -2931, -3107, -3282, -3455, -3626, -3795, -3959,
    -4118, -4271, -4418, -4556, -4686, -4806, -4915, -5013, -5097, -5168, -5224, -5264,
    -5289, -5296, -5286, -5257, -5211, -5145, -5060, -4957, -4834, -4692, -4531, -4351,
    -4154, -3939, -3708, -3461, -3199, -2922, -2633, -2333, -2022, -1702, -1375, -1041,
    -703, -362, -19, 323, 664, 1001, 1334, 1661, 1980, 2290, 2589, 2876,
    3151, 3412, 3657, 3887, 4100, 4295, 4472, 4631, 4772, 4893, 4995, 5078,
    5142, 5188, 5215, 5224, 5216, 5191, 5150, 5094, 5023, 4939, 4842, 4734,
    4614, 4485, 4348, 4203, 4051, 3893, 3731, 3565, 3396, 3225, 3053, 2880,
    2707, 2534, 2363, 2193, 2024, 1858, 1694, 1533, 1373, 1216, 1062, 910,
    759, 611, 463, 317, 172, 28, -116, -260, -406, -552, -699, -848,
    -998, -1151, -1305, -1462, -1621, -1782, -1946, -2111, -2278, -2446, -2615, -2785,
    -2955, -3124, -3292, -3458, -3622, -3778, -3928, -4071, -4207, -4336, -4457, -4567,
    -4668, -4757, -4833, -4897, -4946, -4981, -5001, -5005, -4992, -4962, -4915, -4851,
    -4769, -4670, -4552, -4418, -4266, -4097, -3912, -3711, -3495, -3265, -3021, -2765,
    -2498, -2221, -1935, -1641, -1341, -1035, -726, -415, -104, 206, 515, 821,
    1121, 1416, 1702, 1980, 2248, 2505, 2750, 2981, 3199, 3402, 3590, 3761,
    3917, 4055, 4177, 4282, 4369, 4439, 4493, 4530, 4550, 4555, 4544, 4519,
    4480, 4427, 4362, 4285, 4197, 4099, 3992, 3877, 3755, 3626, 3492, 3353,
    3211, 3065, 2917, 2768, 2618, 2468, 2318, 2169, 2021, 1875, 1730, 1588,
    1448, 1311, 1176, 1043, 913, 785, 660, 536, 414, 293, 174, 55,
    -62, -179, -296, -414, -532, -651, -771, -892, -1014, -1137, -1262, -1388,
    -1515, -1644, -1773, -1903, -2033, -2163, -2293, -2423, -2550, -2676, -2800, -2920,
    -3037, -3149, -3256, -3358, -3452, -3539, -3619, -3689, -3750, -3801, -3841, -3870,
    -3888, -3893, -3885, -3864, -3830, -3782, -3721, -3646, -3558, -3455, -3340, -3212,
    -3070, -2917, -2752, -2576, -2389, -2193, -1988, -1775, -1556, -1330, -1099, -864,
    -626, -387, -146, 92, 331, 566, 798, 1026, 1247, 1462, 1669, 1868,
    2058, 2237, 2406, 2564, 2710, 2843, 2964, 3073, 3168, 3250, 3319, 3375,
    3418, 3448, 3465, 3471, 3464, 3446, 3418, 3379, 3330, 3273, 3207, 3133,
    3053, 2965, 2873, 2775, 2673, 2568, 2459, 2349, 2236, 2123, 2009, 1894,
    1780, 1666, 1554, 1443, 1333, 1225, 1118, 1014, 911, 811, 712, 616,
    521, 427, 335, 244, 155, 66, -21, -109, -197, -285, -373, -461,
    -550, -639, -729, -821, -913, -1005, -1099, -1194, -1289, -1384, -1480, -1576,
    -1671, -1766, -1860, -1952, -2043, -2132, -2217, -2300, -2378, -2453, -2522, -2586,
    -2645, -2697, -2742, -2780, -2810, -2832, -2845, -2850, -2845, -2831, -2807, -2773,
    -2729, -2676, -2612, -2539, -2456, -2363, -2262, -2151, -2032, -1905, -1771, -1630,
    -1482, -1328, -1170, -1007, -840, -671, -499, -327, -153, 18, 190, 360,
    527, 691, 851, 1006, 1155, 1298, 1435, 1564, 1686, 1799, 1904, 2001,
    2088, 2166, 2235, 2294, 2344, 2384, 2415, 2437, 2450, 2455, 2450, 2438,
    2418, 2391, 2356, 2316, 2269, 2217, 2160, 2098, 2032, 1963, 1891, 1816,
    1740, 1661, 1582, 1502, 1421, 1340, 1259, 1179, 1100, 1022, 944, 868,
    794, 720, 649, 578, 509, 442, 376, 311, 247, 185, 123, 62,
    1, -58, -118, -177, -237, -297, -357, -417, -478, -539, -601, -663,
    -725, -788, -851, -915, -978, -1041, -1105, -1167, -1229, -1290, -1350, -1408,
    -1464, -1518, -1569, -1618, -1663, -1705, -1743, -1777, -1806, -1830, -1849, -1863,
    -1871, -1873, -1870, -1860, -1844, -1821, -1792, -1757, -1715, -1667, -1613, -1552,
    -1486, -1414, -1337, -1254, -1167, -1076, -980, -881, -779, -675, -568, -459,
    -349, -239, -128, -18, 90, 198, 304, 408, 509, 607, 701, 791,
    877, 958, 1034, 1105, 1170, 1230, 1284, 1332, 1374, 1410, 1440, 1464,
    1483, 1495, 1502, 1504, 1500, 1492, 1478, 1460, 1438, 1412, 1382, 1349,
    1313, 1274, 1233, 1190, 1145, 1098, 1051, 1003, 953, 904, 855, 805,
    756, 707, 659, 612, 565, 519, 474, 431, 388, 346, 305, 265,
    227, 189, 152, 115, 80, 45, 10, -23, -57, -90, -124, -157,
    -190, -223, -257, -290, -323, -357, -390, -424, -457, -491, -524, -557,
    -590, -622, -654, -685, -716, -745, -773, -800, -825, -849, -871, -891,
    -909, -924, -937, -948, -955, -960, -962, -961, -957, -949, -939, -925,
    -908, -888, -865, -839, -810, -778, -743, -706, -666, -624, -580, -534,
    -486, -437, -387, -335, -283, -231, -179, -126, -74, -22, 28, 77,
    126, 173, 218, 262, 303, 343, 380, 414, 446, 476, 503, 527,
    548, 566, 582, 594, 604, 612, 617, 619, 619, 616, 611, 604,
    596, 585, 573, 559, 544, 528, 510, 492, 473, 454, 433, 413,
    392, 372, 351, 330, 310, 290, 270, 250, 231, 213, 195, 178,
    161, 145, 130, 115, 100, 87, 74, 61, 49, 37, 26, 16,
    5, -4, -13, -22, -31, -40, -48, -56, -63, -71, -78, -85,
    -91, -98, -104, -109, -115, -120, -124, -128, -132, -135, -138, -140,
    -142, -143, -143, -143, -142, -141, -139, -137, -133, -130, -126, -121,
    -116, -110, -104, -97, -90, -83, -76, -69, -61, -54, -47, -39,
    -33, -26, -20, -14, -8, -4, 0, 5, 21, 47, 83, 128,
    182, 244, 313, 388, 468, 552, 638, 726, 814, 901, 986, 1068,
    1146, 1218, 1285, 1344, 1397, 1441, 1476, 1503, 1521, 1530, 1530, 1521,
    1504, 1479, 1446, 1405, 1358, 1304, 1245, 1180, 1111, 1037, 960, 879,
    795, 708, 618, 525, 429, 330, 228, 122, 12, -101, -220, -344,
    -474, -611, -754, -904, -1061, -1225, -1398, -1577, -1764, -1958, -2158, -2364,
    -2574, -2787, -3003, -3219, -3435, -3647, -3854, -4054, -4245, -4424, -4588, -4736,
    -4865, -4973, -5056, -5114, -5143, -5143, -5111, -5046, -4946, -4812, -4641, -4436,
    -4194, -3917, -3607, -3263, -2888, -2484, -2053, -1597, -1121, -626, -117, 402,
    929, 1460, 1989, 2513, 3029, 3532, 4018, 4484, 4926, 5342, 5727, 6081,
    6399, 6681, 6925, 7130, 7295, 7420, 7505, 7550, 7556, 7525, 7458, 7356,
    7222, 7059, 6867, 6651, 6412, 6154, 5878, 5589, 5287, 4976, 4658, 4335,
    4008, 3680, 3351, 3023, 2695, 2369, 2045, 1723, 1401, 1080, 759, 436,
    111, -217, -551, -891, -1239, -1596, -1962, -2339, -2727, -3127, -3538, -3960,
    -4393, -4836, -5286, -5743, -6204, -6666, -7126, -7582, -8029, -8463, -8880, -9276,
    -9646, -9986, -10290, -10555, -10775, -10947, -11066, -11129, -11131, -11071, -10946, -10753,
    -10492, -10162, -9762, -9293, -8758, -8156, -7493, -6769, -5991, -5162, -4288, -3373,
    -2426, -1451, -456, 550, 1563, 2574, 3576, 4560, 5521, 6450, 7342, 8190,
    8988, 9731, 10415, 11034, 11586, 12069, 12479, 12816, 13079, 13269, 13386, 13402,
    13318, 13170, 12961, 12695, 12378, 12014, 11609, 11168, 10695, 10196, 9676, 9140,
    8592, 8037, 7477, 6917, 6359, 5806, 5259, 4721, 4192, 3672, 3163, 2662,
    2170, 1686, 1209, 736, 266, -202, -671, -1142, -1618, -2099, -2587, -3083,
    -3588, -4102, -4625, -5156, -5695, -6241, -6791, -7343, -7894, -8441, -8981, -9508,
    -10020, -10511, -10976, -11411, -11810, -12168, -12481, -12743, -12950, -13097, -13181, -13198,
    -13145, -13020, -12820, -12545, -12194, -11767, -11266, -10691, -10046, -9334, -8558, -7723,
    -6835, -5899, -4921, -3908, -2868, -1808, -734, 343, 1417, 2481, 3527, 4546,
    5532, 6478, 7377, 8224, 9013, 9740, 10400, 10991, 11510, 11954, 12323, 12616,
    12834, 12978, 13049, 13050, 12984, 12854, 12663, 12417, 12119, 11775, 11390, 10968,
    10514, 10034, 9533, 9014, 8483, 7944, 7400, 6855, 6311, 5771, 5238, 4712,
    4195, 3688, 3189, 2700, 2220, 1747, 1281, 820, 362, -93, -549, -1007,
    -1469, -1935, -2409, -2890, -3379, -3877, -4384, -4899, -5422, -5952, -6486, -7023,
    -7560, -8093, -8620, -9137, -9639, -10121, -10580, -11011, -11407, -11765, -12080, -12347,
    -12561, -12718, -12814, -12845, -12809, -12704, -12526, -12275, -11950, -11551, -11080, -10537,
    -9924, -9246, -8505, -7705, -6852, -5951, -5008, -4030, -3023, -1995, -953, 95,
    1142, 2181, 3202, 4201, 5168, 6098, 6984, 7820, 8601, 9323, 9980, 10571,
    11092, 11540, 11916, 12218, 12447, 12603, 12689, 12705, 12655, 12542, 12370, 12142,
    11863, 11538, 11172, 10769, 10334, 9872, 9389, 8887, 8373, 7850, 7321, 6791,
    6261, 5735, 5214, 4701, 4196, 3700, 3213, 2735, 2266, 1804, 1349, 900,
    454, 10, -433, -878, -1327, -1780, -2239, -2705, -3179, -3662, -4153, -4653,
    -5160, -5674, -6193, -6715, -7238, -7758, -8273, -8778, -9270, -9744, -10196, -10622,
    -11016, -11373, -11690, -11960, -12180, -12346, -12453, -12498, -12479, -12391, -12234, -12006,
    -11707, -11335, -10892, -10379, -9799, -9153, -8445, -7679, -6861, -5994, -5085, -4140,
    -3166, -2170, -1158, -139, 880, 1893, 2892, 3869, 4818, 5732, 6604, 7429,
    8202, 8918, 9572, 10162, 10684, 11137, 11519, 11829, 12068, 12236, 12334, 12365,
    12331, 12235, 12080, 11870, 11610, 11303, 10956, 10571, 10155, 9711, 9245, 8760,
    8263, 7755, 7241, 6725, 6210, 5697, 5189, 4687, 4194, 3709, 3233, 2766,
    2308, 1857, 1413, 975, 540, 107, -323, -756, -1191, -1631, -2076, -2528,
    -2988, -3456, -3932, -4416, -4908, -5407, -5911, -6419, -6928, -7435, -7937, -8431,
    -8913, -9379, -9824, -10245, -10635, -10991, -11309, -11583, -11808, -11982, -12100, -12158,
    -12153, -12083, -11946, -11740, -11464, -11118, -10703, -10219, -9669, -9055, -8379, -7647,
    -6861, -6028, -5153, -4241, -3299, -2334, -1352, -361, 631, 1619, 2595, 3551,
    4481, 5379, 6237, 7051, 7815, 8524, 9175, 9764, 10287, 10743, 11130, 11448,
    11697, 11876, 11987, 12031, 12012, 11932, 11794, 11602, 11359, 11071, 10741, 10375,
    9976, 9550, 9101, 8633, 8151, 7659, 7160, 6659, 6156, 5656, 5161, 4672,
    4190, 3716, 3251, 2794, 2347, 1906, 1473, 1045, 621, 200, -219, -640,
    -1063, -1490, -1921, -2360, -2805, -3258, -3720, -4190, -4667, -5151, -5640, -6134,
    -6629, -7123, -7613, -8096, -8568, -9025, -9463, -9878, -10265, -10620, -10938, -11214,
    -11445, -11626, -11753, -11823, -11833, -11779, -11661, -11475, -11223, -10902, -10513, -10057,
    -9536, -8952, -8308, -7608, -6855, -6054, -5211, -4331, -3421, -2486, -1534, -571,
    395, 1358, 2311, 3246, 4158, 5039, 5883, 6685, 7440, 8143, 8790, 9376,
    9900, 10359, 10751, 11076, 11333, 11522, 11645, 11703, 11699, 11634, 11512, 11336,
    11111, 10840, 10528, 10179, 9798, 9389, 8957, 8506, 8040, 7563, 7078, 6591,
    6102, 5614, 5131, 4653, 4183, 3720, 3265, 2819, 2382, 1952, 1529, 1111,
    698, 288, -120, -529, -940, -1355, -1774, -2199, -2630, -3070, -3517, -3972,
    -4435, -4905, -5380, -5859, -6341, -6822, -7300, -7772, -8234, -8683, -9114, -9523,
    -9906, -10259, -10577, -10855, -11090, -11278, -11413, -11494, -11517, -11480, -11379, -11213,
    -10982, -10685, -10322, -9893, -9400, -8846, -8232, -7562, -6841, -6072, -5260, -4412,
    -3532, -2627, -1704, -769, 171, 1109, 2039, 2954, 3847, 4711, 5541, 6332,
    7077, 7773, 8415, 8999, 9523, 9984, 10381, 10712, 10977, 11176, 11310, 11381,
    11390, 11340, 11234, 11075, 10866, 10612, 10317, 9986, 9621, 9229, 8813, 8378,
    7927, 7465, 6996, 6521, 6046, 5571, 5100, 4633, 4174, 3721, 3277, 2842,
    2414, 1994, 1580, 1173, 770, 370, -27, -425, -824, -1226, -1633, -2045,
    -2464, -2889, -3323, -3764, -4213, -4668, -5130, -5596, -6064, -6532, -6998, -7459,
    -7911, -8351, -8775, -9178, -9557, -9908, -10225, -10505, -10744, -10937, -11081, -11172,
    -11208, -11184, -11100, -10954, -10744, -10469, -10130, -9727, -9262, -8735, -8151, -7512,
    -6821, -6082, -5302, -4484, -3634, -2759, -1864, -956, -41, 872, 1780, 2674,
    3548, 4396, 5212, 5990, 6726, 7415, 8051, 8633, 9157, 9619, 10020, 10356,
    10629, 10837, 10982, 11065, 11087, 11051, 10960, 10816, 10624, 10387, 10108, 9793,
    9446, 9070, 8670, 8250, 7815, 7367, 6912, 6451, 5988, 5526, 5066, 4611,
    4162, 3721, 3287, 2861, 2443, 2032, 1629, 1231, 838, 449, 61, -325,
    -713, -1104, -1499, -1898, -2304, -2717, -3137, -3565, -4000, -4441, -4889, -5342,
    -5797, -6253, -6707, -7157, -7599, -8030, -8447, -8844, -9219, -9566, -9883, -10164,
    -10406, -10604, -10755, -10856, -10903, -10894, -10826, -10697, -10507, -10254, -9938, -9560,
    -9121, -8622, -8066, -7455, -6794, -6086, -5335, -4547, -3727, -2880, -2013, -1132,
    -242, 647, 1532, 2405, 3261, 4093, 4894, 5661, 6386, 7067, 7699, 8277,
    8800, 9263, 9667, 10009, 10288, 10505, 10660, 10754, 10789, 10766, 10690, 10561,
    10385, 10163, 9901, 9602, 9271, 8911, 8527, 8123, 7702, 7269, 6827, 6380,
    5929, 5479, 5031, 4587, 4149, 3718, 3294, 2877, 2469, 2068, 1674, 1285,
    902, 523, 145, -231, -608, -988, -1371, -1758, -2152, -2552, -2959, -3373,
    -3795, -4224, -4658, -5098, -5540, -5984, -6427, -6866, -7298, -7720, -8129, -8520,
    -8890, -9235, -9550, -9832, -10076, -10279, -10437, -10546, -10604, -10608, -10555, -10443,
    -10271, -10039, -9746, -9392, -8978, -8505, -7977, -7394, -6762, -6083, -5361, -4602,
    -3810, -2992, -2152, -1297, -433, 433, 1296, 2149, 2986, 3801, 4588, 5342,
    6058, 6731, 7356, 7931, 8452, 8917, 9323, 9669, 9955, 10180, 10344, 10449,
    10496, 10486, 10423, 10310, 10148, 9942, 9696, 9413, 9097, 8753, 8384, 7995,
    7589, 7170, 6742, 6307, 5869, 5431, 4995, 4562, 4134, 3712, 3298, 2891,
    2492, 2100, 1715, 1336, 962, 592, 224, -141, -508, -877, -1249, -1625,
    -2006, -2394, -2789, -3190, -3599, -4015, -4436, -4863, -5293, -5725, -6156, -6584,
    -7007, -7420, -7821, -8206, -8571, -8912, -9226, -9508, -9754, -9961, -10125, -10242,
    -10310, -10326, -10287, -10192, -10038, -9825, -9554, -9222, -8833, -8386, -7884, -7329,
    -6724, -6073, -5380, -4649, -3885, -3094, -2281, -1452, -613, 230, 1071, 1904,
    2722, 3521, 4293, 5035, 5740, 6405, 7024, 7595, 8114, 8579, 8987, 9337,
    9629, 9861, 10034, 10149, 10208, 10211, 10161, 10062, 9915, 9724, 9493, 9225,
    8925, 8596, 8242, 7868, 7476, 7071, 6656, 6234, 5808, 5382, 4957, 4534,
    4117, 3705, 3300, 2903, 2513, 2130, 1754, 1384, 1019, 658, 300, -56,
    -413, -771, -1132, -1497, -1867, -2243, -2626, -3015, -3411, -3814, -4223, -4637,
    -5055, -5475, -5895, -6313, -6726, -7130, -7523, -7902, -8262, -8599, -8911, -9193,
    -9440, -9651, -9820, -9945, -10022, -10049, -10024, -9944, -9807, -9613, -9362, -9052,
    -8686, -8264, -7787, -7259, -6681, -6057, -5392, -4688, -3952, -3188, -2401, -1597,
    -782, 37, 856, 1669, 2469, 3251, 4009, 4738, 5433, 6089, 6702, 7269,
    7786, 8250, 8660, 9014, 9310, 9549, 9731, 9856, 9925, 9940, 9903, 9817,
    9684, 9508, 9292, 9039, 8754, 8440, 8101, 7740, 7363, 6971, 6569, 6160,
    5746, 5331, 4917, 4505, 4098, 3696, 3300, 2912, 2531, 2157, 1789, 1428,
    1072, 720, 371, 23, -323, -671, -1022, -1376, -1735, -2099, -2470, -2847,
    -3231, -3622, -4019, -4421, -4827, -5235, -5644, -6051, -6454, -6850, -7235, -7607,
    -7961, -8295, -8605, -8886, -9135, -9348, -9522, -9654, -9740, -9778, -9764, -9699,
    -9578, -9402, -9170, -8882, -8538, -8139, -7688, -7184, -6633, -6036, -5397, -4721,
    -4011, -3273, -2512, -1733, -942, -145, 652, 1445, 2227, 2993, 3736, 4452,
    5136, 5784, 6390, 6952, 7466, 7930, 8341, 8698, 8999, 9245, 9434, 9568,
    9647, 9674, 9649, 9576, 9457, 9295, 9093, 8855, 8584, 8284, 7960, 7613,
    7249, 6871, 6482, 6085, 5684, 5280, 4876, 4475, 4077, 3685, 3298, 2919,
    2546, 2181, 1822, 1469, 1121, 778, 438, 99, -237, -576, -916, -1260,
    -1608, -1962, -2321, -2687, -3059, -3438, -3822, -4212, -4607, -5004, -5402, -5798,
    -6192, -6579, -6956, -7321, -7670, -8000, -8307, -8587, -8837, -9053, -9231, -9369,
    -9463, -9510, -9509, -9457, -9352, -9193, -8980, -8712, -8389, -8013, -7585, -7107,
    -6580, -6009, -5397, -4746, -4063, -3351, -2615, -1860, -1093, -317, 459, 1232,
    1996, 2745, 3473, 4177, 4850, 5488, 6088, 6645, 7156, 7619, 8030, 8390,
    8695, 8946, 9143, 9286, 9375, 9412, 9399, 9339, 9233, 9084, 8896, 8672,
    8416, 8130, 7819, 7487, 7136, 6771, 6394, 6010, 5620, 5227, 4834, 4443,
    4055, 3672, 3295, 2924, 2560, 2202, 1851, 1507, 1167, 833, 501, 171,
    -156, -485, -816, -1150, -1488, -1830, -2178, -2533, -2894, -3261, -3634, -4012,
    -4395, -4781, -5168, -5555, -5939, -6317, -6686, -7045, -7388, -7714, -8018, -8297,
    -8547, -8764, -8947, -9090, -9191, -9248, -9258, -9218, -9128, -8985, -8790, -8541,
    -8240, -7885, -7480, -7025, -6524, -5977, -5390, -4765, -4107, -3420, -2709, -1978,
    -1234, -481, 274, 1028, 1774, 2507, 3221, 3911, 4573, 5202, 5795, 6347,
    6854, 7316, 7728, 8089, 8398, 8655, 8858, 9009, 9107, 9155, 9153, 9105,
    9011, 8876, 8702, 8491, 8248, 7977, 7680, 7360, 7023, 6671, 6306, 5934,
    5555, 5173, 4791, 4410, 4031, 3657, 3289, 2926, 2571, 2221, 1879, 1542,
    1211, 884, 560, 239, -79, -399, -721, -1045, -1373, -1705, -2042, -2386,
    -2735, -3091, -3453, -3820, -4192, -4567, -4944, -5320, -5694, -6064, -6426, -6777,
    -7115, -7436, -7737, -8014, -8264, -8483, -8669, -8817, -8925, -8991, -9011, -8983,
    -8907, -8780, -8601, -8371, -8089, -7756, -7373, -6941, -6463, -5941, -5378, -4778,
    -4145, -3482, -2795, -2088, -1366, -635, 100, 834, 1562, 2279, 2978, 3655,
    4306, 4926, 5511, 6057, 6562, 7021, 7433, 7796, 8108, 8370, 8579, 8738,
    8845, 8902, 8912, 8875, 8793, 8671, 8509, 8312, 8083, 7825, 7541, 7235,
    6910, 6570, 6218, 5857, 5490, 5119, 4747, 4375, 4006, 3641, 3281, 2927,
    2580, 2238, 1903, 1574, 1251, 932, 617, 304, -7, -318, -630, -945,
    -1263, -1585, -1912, -2245, -2584, -2929, -3280, -3636, -3997, -4361, -4727, -5094,
    -5459, -5819, -6173, -6518, -6850, -7167, -7464, -7739, -7989, -8209, -8398, -8550,
    -8665, -8738, -8768, -8752, -8688, -8576, -8414, -8201, -7938, -7625, -7263, -6854,
    -6399, -5900, -5361, -4786, -4176, -3537, -2874, -2190, -1490, -780, -65, 650,
    1360, 2060, 2745, 3409, 4049, 4660, 5237, 5777, 6277, 6734, 7146, 7510,
    7826, 8091, 8307, 8472, 8587, 8654, 8674, 8648, 8578, 8468, 8319, 8135,
    7919, 7673, 7403, 7109, 6797, 6470, 6130, 5780, 5424, 5063, 4701, 4339,
    3980, 3624, 3272, 2926, 2587, 2253, 1926, 1604, 1288, 977, 670, 365,
    61, -240, -544, -850, -1158, -1471, -1788, -2111, -2439, -2773, -3113, -3459,
    -3809, -4163, -4519, -4876, -5231, -5583, -5930, -6267, -6594, -6905, -7199, -7472,
    -7721, -7942, -8133, -8290, -8410, -8490, -8529, -8524, -8473, -8374, -8228, -8032,
    -7787, -7494, -7152, -6764, -6331, -5855, -5340, -4787, -4201, -3586, -2945, -2283,
    -1606, -917, -221, 474, 1167, 1851, 2521, 3173, 3801, 4402, 4971, 5505,
    6001, 6456, 6867, 7232, 7549, 7819, 8040, 8212, 8335, 8411, 8440, 8425,
    8366, 8268, 8131, 7960, 7756, 7524, 7265, 6985, 6685, 6369, 6041, 5702,
    5357, 5007, 4655, 4302, 3952, 3604, 3261, 2924, 2592, 2266, 1946, 1632,
    1323, 1019, 719, 422, 127, -167, -462, -759, -1058, -1362, -1669, -1982,
    -2300, -2624, -2954, -3289, -3629, -3972, -4318, -4666, -5012, -5356, -5694, -6025,
    -6345, -6652, -6942, -7213, -7460, -7682, -7875, -8035, -8160, -8248, -8295, -8300,
    -8260, -8175, -8043, -7863, -7636, -7361, -7039, -6672, -6260, -5806, -5313, -4783,
    -4220, -3628, -3009, -2370, -1714, -1045, -369, 308, 983, 1651, 2306, 2945,
    3562, 4153, 4714, 5242, 5734, 6185, 6595, 6960, 7280, 7553, 7779, 7957,
    8088, 8172, 8210, 8205, 8158, 8071, 7946, 7786, 7595, 7375, 7129, 6861,
    6573, 6269, 5952, 5624, 5290, 4950, 4607, 4265, 3923, 3584, 3249, 2919,
    2595, 2276, 1964, 1657, 1355, 1059, 766, 476, 189, -97, -384, -673,
    -963, -1258, -1556, -1859, -2167, -2481, -2801, -3126, -3456, -3789, -4126, -4463,
    -4801, -5136, -5467, -5791, -6105, -6406, -6693, -6961, -7207, -7429, -7623, -7786,
    -7916, -8010, -8065, -8079, -8050, -7978, -7860, -7695, -7485, -7228, -6925, -6577,
    -6186, -5754, -5283, -4775, -4234, -3664, -3067, -2449, -1814, -1166, -509, 149,
    808, 1460, 2101, 2726, 3332, 3913, 4466, 4988, 5474, 5922, 6331, 6696,
    7017, 7294, 7524, 7707, 7845, 7937, 7985, 7989, 7952, 7876, 7763, 7615,
    7436, 7227, 6994, 6737, 6461, 6169, 5863, 5546, 5222, 4892, 4559, 4226,
    3893, 3562, 3235, 2913, 2596, 2285, 1979, 1680, 1385, 1095, 810, 527,
    247, -31, -310, -591, -873, -1158, -1448, -1741, -2040, -2345, -2654, -2969,
    -3289, -3613, -3940, -4268, -4597, -4924, -5247, -5564, -5872, -6169, -6451, -6716,
    -6961, -7182, -7377, -7543, -7677, -7777, -7839, -7862, -7844, -7783, -7678, -7529,
    -7334, -7094, -6809, -6481, -6110, -5698, -5248, -4762, -4242, -3693, -3119, -2522,
    -1907, -1278, -641, 0, 641, 1277, 1904, 2516, 3110, 3681, 4226, 4741,
    5222, 5667, 6074, 6439, 6761, 7040, 7274, 7463, 7607, 7707, 7763, 7777,
    7750, 7684, 7582, 7445, 7278, 7081, 6859, 6614, 6350, 6069, 5774, 5468,
    5154, 4834, 4510, 4186, 3861, 3539, 3220, 2906, 2596, 2292, 1993, 1700,
    1413, 1130, 851, 575, 302, 30, -240, -513, -787, -1064, -1344, -1629,
    -1919, -2214, -2514, -2819, -3130, -3444, -3761, -4081, -4401, -4719, -5035, -5345,
    -5647, -5938, -6216, -6478, -6721, -6942, -7138, -7306, -7444, -7549, -7618, -7649,
    -7640, -7591, -7499, -7363, -7184, -6960, -6693, -6383, -6031, -5639, -5209, -4744,
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    7454, 7457, 7406, 7303, 7154, 6962, 6731, 6466, 6173, 5856, 5520, 5169,
    4808, 4441, 4071, 3700, 3333, 2970, 2614, 2265, 1923, 1589, 1262, 941,
    625, 312, 2, -308, -620, -935, -1255, -1580, -1912, -2251, -2598, -2951,
    -3310, -3673, -4039, -4405, -4767, -5123, -5468, -5798, -6109, -6396, -6655, -6880,
    -7067, -7211, -7309, -7356, -7350, -7288, -7168, -6988, -6748, -6449, -6091, -5677,
    -5209, -4692, -4128, -3523, -2884, -2215, -1525, -819, -105, 609, 1317, 2011,
    2684, 3330, 3941, 4513, 5040, 5518, 5943, 6312, 6623, 6875, 7067, 7200,
    7275, 7293, 7257, 7171, 7037, 6860, 6645, 6395, 6116, 5813, 5489, 5150,
    4799, 4442, 4080, 3718, 3358, 3002, 2652, 2308, 1972, 1644, 1322, 1007,
    697, 391, 87, -216, -520, -827, -1138, -1454, -1777, -2106, -2443, -2786,
    -3136, -3490, -3847, -4205, -4560, -4910, -5250, -5578, -5887, -6175, -6436, -6665,
    -6859, -7012, -7121, -7182, -7191, -7145, -7044, -6885, -6667, -6391, -6057, -5668,
    -5225, -4732, -4193, -3613, -2997, -2351, -1682, -995, -299, 399, 1094, 1777,
    2441, 3080, 3688, 4258, 4786, 5267, 5697, 6073, 6394, 6656, 6860, 7006,
    7095, 7128, 7108, 7037, 6919, 6757, 6557, 6322, 6057, 5766, 5455, 5127,
    4788, 4440, 4087, 3733, 3380, 3031, 2687, 2350, 2019, 1696, 1380, 1070,
    766, 466, 168, -127, -424, -723, -1026, -1334, -1647, -1967, -2295, -2628,
    -2968, -3313, -3662, -4011, -4359, -4703, -5039, -5363, -5671, -5958, -6221, -6455,
    -6654, -6815, -6934, -7007, -7030, -7001, -6918, -6778, -6581, -6327, -6017, -5651,
    -5233, -4765, -4250, -3694, -3102, -2478, -1829, -1162, -484, 198, 879, 1550,
    2205, 2838, 3441, 4009, 4537, 5020, 5455, 5838, 6166, 6439, 6654, 6813,
    6915, 6963, 6957, 6901, 6799, 6653, 6467, 6246, 5995, 5718, 5419, 5102,
    4773, 4435, 4091, 3745, 3400, 3058, 2720, 2388, 2063, 1745, 1435, 1130,
    831, 537, 246, -43, -333, -625, -919, -1218, -1523, -1834, -2152, -2476,
    -2807, -3143, -3483, -3824, -4165, -4503, -4833, -5154, -5459, -5747, -6011, -6247,
    -6452, -6621, -6749, -6833, -6870, -6856, -6789, -6668, -6492, -6259, -5971, -5629,
    -5234, -4790, -4300, -3767, -3197, -2596, -1968, -1321, -660, 6, 673, 1332,
    1978, 2602, 3200, 3766, 4293, 4779, 5217, 5606, 5942, 6224, 6450, 6621,
    6736, 6797, 6806, 6765, 6677, 6546, 6375, 6169, 5931, 5667, 5380, 5075,
    4756, 4428, 4093, 3756, 3418, 3082, 2751, 2425, 2105, 1792, 1487, 1188,
    894, 605, 320, 36, -246, -530, -817, -1108, -1404, -1707, -2015, -2331,
    -2652, -2979, -3310, -3644, -3977, -4308, -4634, -4950, -5253, -5540, -5804, -6044,
    -6253, -6428, -6565, -6659, -6709, -6709, -6659, -6556, -6399, -6187, -5920, -5601,
    -5229, -4808, -4341, -3832, -3285, -2705, -2098, -1470, -827, -176, 475, 1122,
    1757, 2374, 2967, 3529, 4055, 4541, 4983, 5377, 5720, 6011, 6247, 6429,
    6557, 6631, 6654, 6628, 6554, 6438, 6281, 6089, 5865, 5613, 5338, 5045,
    4737, 4419, 4093, 3763, 3433, 3104, 2779, 2459, 2144, 1837, 1536, 1242,
    954, 671, 391, 113, -162, -440, -719, -1003, -1291, -1584, -1884, -2191,
    -2503, -2821, -3144, -3469, -3796, -4120, -4440, -4752, -5053, -5337, -5602, -5844,
    -6057, -6238, -6382, -6487, -6548, -6562, -6527, -6441, -6302, -6110, -5865, -5567,
    -5217, -4819, -4375, -3889, -3364, -2806, -2219, -1611, -986, -351, 285, 920,
    1545, 2153, 2739, 3298, 3822, 4309, 4753, 5152, 5501, 5800, 6046, 6239,
    6378, 6466, 6502, 6489, 6430, 6328, 6185, 6007, 5796, 5557, 5295, 5013,
    4716, 4407, 4090, 3769, 3446, 3124, 2805, 2490, 2181, 1879, 1583, 1294,
    1011, 733, 458, 187, -83, -353, -626, -902, -1182, -1467, -1758, -2056,
    -2360, -2669, -2984, -3301, -3620, -3938, -4252, -4560, -4857, -5140, -5405, -5648,
    -5864, -6050, -6202, -6315, -6387, -6414, -6394, -6324, -6202, -6029, -5804, -5527,
    -5200, -4824, -4402, -3938, -3435, -2898, -2332, -1743, -1136, -518, 104, 725,
    1339, 1939, 2519, 3073, 3595, 4082, 4528, 4930, 5286, 5592, 5846, 6050,
    6201, 6300, 6350, 6350, 6305, 6217, 6088, 5923, 5725, 5499, 5249, 4978,
    4692, 4392, 4085, 3772, 3456, 3141, 2828, 2519, 2216, 1919, 1628, 1344,
    1065, 792, 523, 257, -7, -271, -537, -805, -1078, -1355, -1638, -1927,
    -2222, -2523, -2829, -3139, -3450, -3762, -4070, -4373, -4666, -4947, -5212, -5455,
    -5674, -5865, -6023, -6145, -6227, -6266, -6259, -6204, -6100, -5945, -5740, -5483,
    -5177, -4823, -4423, -3980, -3499, -2983, -2437, -1867, -1279, -677, -69, 539,
    1142, 1732, 2305, 2854, 3374, 3859, 4307, 4713, 5073, 5386, 5649, 5862,
    6024, 6135, 6197, 6211, 6179, 6104, 5989, 5837, 5653, 5439, 5201, 4942,
    4665, 4376, 4077, 3772, 3465, 3156, 2850, 2547, 2249, 1956, 1670, 1391,
    1117, 849, 585, 324, 65, -192, -451, -713, -978, -1248, -1523, -1803,
    -2090, -2383, -2681, -2982, -3287, -3591, -3894, -4191, -4481, -4759, -5023, -5267,
    -5488, -5683, -5847, -5976, -6067, -6117, -6124, -6084, -5995, -5858, -5671, -5434,
    -5148, -4815, -4436, -4015, -3555, -3060, -2535, -1984, -1413, -828, -235, 360,
    951, 1532, 2097, 2641, 3158, 3642, 4091, 4499, 4864, 5183, 5454, 5675,
    5848, 5970, 6044, 6071, 6052, 5990, 5889, 5750, 5578, 5377, 5151, 4903,
    4637, 4357, 4068, 3771, 3471, 3169, 2869, 2572, 2279, 1992, 1710, 1435,
    1166, 903, 643, 388, 135, -117, -370, -625, -883, -1145, -1412, -1685,
    -1964, -2248, -2538, -2832, -3128, -3426, -3723, -4015, -4301, -4576, -4838, -5083,
    -5306, -5503, -5672, -5808, -5908, -5969, -5987, -5961, -5888, -5768, -5599, -5381,
    -5115, -4802, -4444, -4044, -3605, -3130, -2624, -2092, -1539, -971, -393, 188,
    768, 1339, 1897, 2434, 2947, 3430, 3878, 4289, 4658, 4982, 5260, 5491,
    5673, 5806, 5892, 5931, 5924, 5876, 5787, 5661, 5502, 5313, 5098, 4861,
    4606, 4336, 4056, 3767, 3475, 3180, 2886, 2595, 2307, 2025, 1748, 1478,
    1213, 954, 700, 449, 201, -45, -292, -540, -791, -1046, -1306, -1571,
    -1842, -2118, -2400, -2686, -2976, -3267, -3557, -3844, -4126, -4398, -4658, -4902,
    -5126, -5327, -5500, -5643, -5751, -5821, -5851, -5838, -5780, -5675, -5523, -5323,
    -5077, -4784, -4446, -4066, -3647, -3193, -2706, -2193, -1658, -1106, -543, 24,
    592, 1153, 1702, 2234, 2742, 3223, 3671, 4083, 4455, 4785, 5069, 5308,
    5499, 5643, 5739, 5790, 5796, 5760, 5684, 5571, 5424, 5247, 5044, 4818,
    4573, 4313, 4042, 3762, 3477, 3189, 2901, 2615, 2333, 2056, 1784, 1518,
    1258, 1003, 753, 507, 264, 23, -217, -460, -704, -952, -1205, -1462,
    -1725, -1994, -2268, -2547, -2829, -3113, -3397, -3679, -3956, -4225, -4483, -4726,
    -4951, -5154, -5331, -5479, -5594, -5674, -5714, -5713, -5669, -5580, -5444, -5262,
    -5034, -4760, -4442, -4082, -3683, -3248, -2781, -2287, -1769, -1234, -686, -132,
    423, 974, 1514, 2039, 2543, 3021, 3468, 3881, 4256, 4590, 4881, 5127,
    5326, 5480, 5587, 5649, 5667, 5643, 5579, 5479, 5344, 5180, 4988, 4773,
    4539, 4288, 4026, 3754, 3476, 3196, 2914, 2634, 2357, 2085, 1817, 1556,
    1300, 1050, 804, 563, 325, 89, -146, -382, -621, -862, -1107, -1358,
    -1613, -1874, -2141, -2412, -2687, -2964, -3242, -3518, -3791, -4056, -4311, -4553,
    -4779, -4983, -5164, -5317, -5439, -5527, -5578, -5588, -5557, -5482, -5363, -5197,
    -4987, -4732, -4433, -4092, -3713, -3297, -2849, -2373, -1873, -1354, -822, -281,
    261, 801, 1333, 1851, 2349, 2824, 3270, 3683, 4060, 4398, 4695, 4947,
    5155, 5318, 5436, 5509, 5538, 5526, 5474, 5386, 5263, 5110, 4930, 4726,
    4502, 4261, 4007, 3744, 3474, 3200, 2925, 2651, 2380, 2112, 1849, 1592,
    1340, 1094, 853, 616, 383, 151, -78, -309, -541, -776, -1014, -1258,
    -1506, -1760, -2019, -2282, -2550, -2821, -3092, -3363, -3630, -3892, -4145, -4385,
    -4610, -4816, -5000, -5158, -5286, -5381, -5441, -5463, -5444, -5383, -5278, -5129,
    -4936, -4699, -4419, -4097, -3737, -3340, -2911, -2453, -1970, -1468, -950, -424,
    106, 635, 1158, 1668, 2161, 2632, 3076, 3490, 3869, 4210, 4511, 4770,
    4986, 5157, 5285, 5368, 5409, 5408, 5368, 5291, 5181, 5039, 4870, 4677,
    4463, 4232, 3987, 3732, 3470, 3203, 2935, 2666, 2400, 2137, 1879, 1626,
    1378, 1136, 899, 667, 438, 211, -13, -238, -465, -693, -926, -1162,
    -1403, -1650, -1901, -2158, -2418, -2682, -2948, -3213, -3475, -3733, -3982, -4221,
    -4446, -4653, -4839, -5000, -5134, -5236, -5305, -5337, -5330, -5282, -5192, -5058,
    -4882, -4662, -4400, -4096, -3755, -3377, -2966, -2525, -2060, -1574, -1072, -559,
    -41, 476, 989, 1492, 1979, 2446, 2888, 3300, 3680, 4025, 4330, 4595,
    4818, 4998, 5134, 5228, 5279, 5289, 5261, 5196, 5097, 4967, 4809, 4626,
    4422, 4201, 3965, 3719, 3464, 3204, 2942, 2679, 2418, 2160, 1907, 1658,
    1414, 1176, 943, 715, 490, 268, 48, -171, -392, -615, -840, -1070,
    -1305, -1544, -1789, -2038, -2292, -2549, -2808, -3067, -3325, -3578, -3825, -4061,
    -4285, -4492, -4680, -4845, -4984, -5093, -5169, -5211, -5215, -5179, -5103, -4985,
    -4824, -4621, -4376, -4091, -3767, -3407, -3014, -2592, -2143, -1673, -1187, -688,
    -183, 323, 827, 1321, 1802, 2264, 2703, 3115, 3496, 3842, 4152, 4422,
    4652, 4839, 4985, 5088, 5149, 5171, 5153, 5099, 5012, 4893, 4746, 4573,
    4380, 4168, 3941, 3703, 3456, 3203, 2947, 2690, 2435, 2182, 1933, 1688,
    1449, 1215, 986, 761, 541, 323, 107, -106, -320, -536, -753, -973,
    -1196, -1424, -1656, -1892, -2132, -2374, -2618, -2862, -3104, -3342, -3574, -3796,
    -4006, -4201, -4378, -4533, -4664, -4767, -4840, -4881, -4887, -4857, -4789, -4682,
    -4536, -4351, -4128, -3867, -3572, -3243, -2884, -2497, -2087, -1658, -1214, -758,
    -297, 165, 624, 1075, 1514, 1935, 2335, 2710, 3057, 3373, 3655, 3901,
    4111, 4282, 4415, 4510, 4568, 4589, 4576, 4529, 4452, 4348, 4217, 4065,
    3893, 3705, 3504, 3293, 3073, 2850, 2623, 2396, 2170, 1947, 1727, 1513,
    1303, 1098, 899, 705, 514, 327, 143, -39, -222, -405, -589, -775,
    -965, -1157, -1354, -1553, -1756, -1961, -2168, -2375, -2581, -2784, -2981, -3172,
    -3352, -3521, -3675, -3811, -3927, -4020, -4089, -4131, -4143, -4125, -4076, -3994,
    -3878, -3730, -3549, -3337, -3094, -2823, -2525, -2204, -1863, -1504, -1131, -749,
    -360, 30, 418, 801, 1174, 1533, 1875, 2197, 2496, 2768, 3013, 3229,
    3413, 3565, 3685, 3773, 3829, 3854, 3850, 3818, 3759, 3676, 3572, 3448,
    3307, 3152, 2986, 2810, 2627, 2440, 2250, 2059, 1869, 1681, 1496, 1315,
    1138, 965, 797, 634, 474, 317, 162, 9, -142, -294, -447, -602,
    -759, -918, -1080, -1245, -1413, -1583, -1754, -1925, -2096, -2265, -2430, -2589,
    -2741, -2883, -3013, -3129, -3229, -3311, -3373, -3412, -3429, -3420, -3385, -3324,
    -3235, -3119, -2976, -2807, -2612, -2394, -2154, -1894, -1616, -1324, -1019, -706,
    -387, -65, 254, 571, 880, 1178, 1463, 1732, 1982, 2211, 2417, 2600,
    2757, 2888, 2993, 3071, 3123, 3150, 3152, 3130, 3087, 3024, 2942, 2844,
    2732, 2607, 2473, 2331, 2182, 2030, 1875, 1719, 1563, 1409, 1257, 1109,
    964, 822, 685, 551, 420, 292, 166, 42, -80, -203, -327, -451,
    -577, -705, -835, -967, -1101, -1237, -1374, -1512, -1649, -1785, -1917, -2046,
    -2169, -2284, -2391, -2486, -2569, -2638, -2691, -2726, -2743, -2741, -2718, -2673,
    -2607, -2519, -2410, -2280, -2129, -1959, -1772, -1568, -1350, -1119, -879, -631,
    -378, -123, 131, 383, 629, 868, 1096, 1312, 1514, 1699, 1866, 2015,
    2144, 2252, 2339, 2405, 2451, 2476, 2481, 2468, 2437, 2390, 2329, 2254,
    2168, 2071, 1967, 1856, 1740, 1620, 1499, 1376, 1254, 1132, 1013, 896,
    782, 670, 562, 457, 354, 254, 156, 59, -35, -130, -226, -322,
    -418, -516, -616, -717, -819, -923, -1028, -1133, -1238, -1341, -1443, -1541,
    -1636, -1725, -1807, -1881, -1946, -2000, -2043, -2072, -2088, -2089, -2074, -2043,
    -1996, -1933, -1853, -1757, -1646, -1520, -1381, -1229, -1066, -894, -714, -528,
    -338, -147, 44, 234, 420, 601, 773, 937, 1090, 1231, 1359, 1472,
    1571, 1655, 1722, 1774, 1811, 1832, 1838, 1831, 1810, 1777, 1733, 1678,
    1615, 1545, 1468, 1386, 1301, 1213, 1123, 1032, 941, 852, 763, 676,
    592, 510, 430, 353, 277, 204, 133, 62, -6, -75, -143, -212,
    -281, -351, -421, -493, -565, -638, -712, -786, -860, -933, -1004, -1074,
    -1140, -1203, -1261, -1313, -1359, -1398, -1428, -1450, -1462, -1463, -1454, -1434,
    -1402, -1359, -1305, -1240, -1164, -1078, -983, -879, -767, -649, -526, -399,
    -269, -137, -6, 123, 251, 374, 493, 605, 709, 806, 893, 971,
    1039, 1096, 1143, 1178, 1204, 1218, 1223, 1219, 1205, 1183, 1154, 1118,
    1076, 1029, 977, 923, 866, 807, 747, 687, 626, 567, 508, 451,
    396, 342, 289, 239, 190, 143, 97, 52, 8, -35, -78, -121,
    -163, -206, -250, -293, -337, -382, -426, -470, -515, -558, -600, -641,
    -681, -717, -751, -782, -808, -830, -847, -859, -865, -865, -859, -846,
    -827, -801, -769, -730, -686, -635, -580, -520, -455, -388, -317, -245,
    -171, -97, -23, 48, 119, 187, 252, 314, 370, 423, 469, 511,
    546, 576, 599, 617, 629, 635, 636, 632, 623, 610, 593, 572,
    549, 523, 495, 466, 435, 404, 372, 341, 310, 279, 249, 221,
    193, 166, 141, 116, 93, 70, 49, 28, 9, -10, -28, -47,
    -65, -82, -100, -117, -134, -151, -168, -184, -200, -215, -229, -243,
    -255, -267, -276, -285, -291, -296, -299, -299, -298, -294, -288, -280,
    -270, -258, -245, -229, -212, -193, -174, -154, -133, -112, -90, -69,
    -49, -29, -10, 6, 23, 37, 50, 62, 71, 79, 85, 89,
    92, 93, 92, 90, 87, 82, 77, 71, 64, 57, 50, 43,
    36, 29, 22, 15, 10, 4,
};
const size_t prompt_bt_connected_len = 13230;

const int16_t prompt_bt_disconnected[] = {
    0, 6, 25, 55, 98, 150, 213, 283, 360, 443, 529, 617,
    705, 791, 875, 954, 1027, 1093, 1150, 1198, 1237, 1265, 1282, 1289,
    1285, 1271, 1247, 1214, 1172, 1122, 1065, 1002, 932, 858, 780, 697,
    610, 520, 427, 330, 230, 125, 15, -98, -219, -346, -480, -622,
    -772, -931, -1099, -1276, -1462, -1656, -1857, -2065, -2277, -2493, -2710, -2926,
    -3138, -3343, -3538, -3720, -3885, -4030, -4152, -4246, -4310, -4341, -4336, -4293,
    -4210, -4085, -3918, -3708, -3455, -3161, -2827, -2456, -2049, -1610, -1144, -654,
    -145, 376, 906, 1439, 1969, 2489, 2996, 3482, 3943, 4374, 4772, 5131,
    5449, 5723, 5951, 6132, 6264, 6349, 6387, 6379, 6326, 6232, 6099, 5931,
    5730, 5500, 5246, 4971, 4679, 4373, 4057, 3733, 3405, 3075, 2744, 2414,
    2086, 1760, 1435, 1112, 789, 465, 138, -192, -529, -873, -1228, -1594,
    -1972, -2364, -2769, -3189, -3621, -4065, -4519, -4980, -5446, -5911, -6371, -6822,
    -7257, -7671, -8057, -8409, -8720, -8983, -9191, -9340, -9423, -9435, -9372, -9231,
    -9008, -8703, -8314, -7843, -7291, -6662, -5959, -5189, -4356, -3469, -2536, -1566,
    -568, 446, 1467, 2486, 3489, 4468, 5412, 6312, 7158, 7942, 8657, 9298,
    9858, 10335, 10724, 11026, 11239, 11364, 11404, 11362, 11241, 11047, 10786, 10463,
    10085, 9660, 9193, 8693, 8166, 7618, 7056, 6484, 5909, 5332, 4758, 4190,
    3628, 3073, 2525, 1983, 1446, 911, 376, -160, -703, -1255, -1818, -2395,
    -2989, -3599, -4229, -4877, -5542, -6209, -6871, -7535, -8197, -8852, -9493, -10112,
    -10702, -11254, -11760, -12212, -12600, -12917, -13154, -13304, -13362, -13320, -13175, -12924,
    -12565, -12097, -11521, -10840, -10058, -9180, -8214, -7167, -6050, -4871, -3644, -2381,
    -1093, 204, 1499, 2778, 4028, 5236, 6390, 7479, 8494, 9424, 10263, 11004,
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    2684, 3330, 3941, 4513, 5040, 5518, 5943, 6312, 6623, 6875, 7067, 7200,
    7275, 7293, 7257, 7171, 7037, 6860, 6645, 6395, 6116, 5813, 5489, 5150,
    4799, 4442, 4080, 3718, 3358, 3002, 2652, 2308, 1972, 1644, 1322, 1007,
    697, 391, 87, -216, -520, -827, -1138, -1454, -1777, -2106, -2443, -2786,
    -3136, -3490, -3847, -4205, -4560, -4910, -5250, -5578, -5887, -6175, -6436, -6665,
    -6859, -7012, -7121, -7182, -7191, -7145, -7044, -6885, -6667, -6391, -6057, -5668,
    -5225, -4732, -4193, -3613, -2997, -2351, -1682, -995, -299, 399, 1094, 1777,
    2441, 3080, 3688, 4258, 4786, 5267, 5697, 6073, 6394, 6656, 6860, 7006,
    7095, 7128, 7108, 7037, 6919, 6757, 6557, 6322, 6057, 5766, 5455, 5127,
    4788, 4440, 4087, 3733, 3380, 3031, 2687, 2350, 2019, 1696, 1380, 1070,
    766, 466, 168, -127, -424, -723, -1026, -1334, -1647, -1967, -2295, -2628,
    -2968, -3313, -3662, -4011, -4359, -4703, -5039, -5363, -5671, -5958, -6221, -6455,
    -6654, -6815, -6934, -7007, -7030, -7001, -6918, -6778, -6581, -6327, -6017, -5651,
    -5233, -4765, -4250, -3694, -3102, -2478, -1829, -1162, -484, 198, 879, 1550,
    2205, 2838, 3441, 4009, 4537, 5020, 5455, 5838, 6166, 6439, 6654, 6813,
    6915, 6963, 6957, 6901, 6799, 6653, 6467, 6246, 5995, 5718, 5419, 5102,
    4773, 4435, 4091, 3745, 3400, 3058, 2720, 2388, 2063, 1745, 1435, 1130,
    831, 537, 246, -43, -333, -625, -919, -1218, -1523, -1834, -2152, -2476,
    -2807, -3143, -3483, -3824, -4165, -4503, -4833, -5154, -5459, -5747, -6011, -6247,
    -6452, -6621, -6749, -6833, -6870, -6856, -6789, -6668, -6492, -6259, -5971, -5629,
    -5234, -4790, -4300, -3767, -3197, -2596, -1968, -1321, -660, 6, 673, 1332,
    1978, 2602, 3200, 3766, 4293, 4779, 5217, 5606, 5942, 6224, 6450, 6621,
    6736, 6797, 6806, 6765, 6677, 6546, 6375, 6169, 5931, 5667, 5380, 5075,
    4756, 4428, 4093, 3756, 3418, 3082, 2751, 2425, 2105, 1792, 1487, 1188,
    894, 605, 320, 36, -246, -530, -817, -1108, -1404, -1707, -2015, -2331,
    -2652, -2979, -3310, -3644, -3977, -4308, -4634, -4950, -5253, -5540, -5804, -6044,
    -6253, -6428, -6565, -6659, -6709, -6709, -6659, -6556, -6399, -6187, -5920, -5601,
    -5229, -4808, -4341, -3832, -3285, -2705, -2098, -1470, -827, -176, 475, 1122,
    1757, 2374, 2967, 3529, 4055, 4541, 4983, 5377, 5720, 6011, 6247, 6429,
    6557, 6631, 6654, 6628, 6554, 6438, 6281, 6089, 5865, 5613, 5338, 5045,
    4737, 4419, 4093, 3763, 3433, 3104, 2779, 2459, 2144, 1837, 1536, 1242,
    954, 671, 391, 113, -162, -440, -719, -1003, -1291, -1584, -1884, -2191,
    -2503, -2821, -3144, -3469, -3796, -4120, -4440, -4752, -5053, -5337, -5602, -5844,
    -6057, -6238, -6382, -6487, -6548, -6562, -6527, -6441, -6302, -6110, -5865, -5567,
    -5217, -4819, -4375, -3889, -3364, -2806, -2219, -1611, -986, -351, 285, 920,
    1545, 2153, 2739, 3298, 3822, 4309, 4753, 5152, 5501, 5800, 6046, 6239,
    6378, 6466, 6502, 6489, 6430, 6328, 6185, 6007, 5796, 5557, 5295, 5013,
    4716, 4407, 4090, 3769, 3446, 3124, 2805, 2490, 2181, 1879, 1583, 1294,
    1011, 733, 458, 187, -83, -353, -626, -902, -1182, -1467, -1758, -2056,
    -2360, -2669, -2984, -3301, -3620, -3938, -4252, -4560, -4857, -5140, -5405, -5648,
    -5864, -6050, -6202, -6315, -6387, -6414, -6394, -6324, -6202, -6029, -5804, -5527,
    -5200, -4824, -4402, -3938, -3435, -2898, -2332, -1743, -1136, -518, 104, 725,
    1339, 1939, 2519, 3073, 3595, 4082, 4528, 4930, 5286, 5592, 5846, 6050,
    6201, 6300, 6350, 6350, 6305, 6217, 6088, 5923, 5725, 5499, 5249, 4978,
    4692, 4392, 4085, 3772, 3456, 3141, 2828, 2519, 2216, 1919, 1628, 1344,
    1065, 792, 523, 257, -7, -271, -537, -805, -1078, -1355, -1638, -1927,
    -2222, -2523, -2829, -3139, -3450, -3762, -4070, -4373, -4666, -4947, -5212, -5455,
    -5674, -5865, -6023, -6145, -6227, -6266, -6259, -6204, -6100, -5945, -5740, -5483,
    -5177, -4823, -4423, -3980, -3499, -2983, -2437, -1867, -1279, -677, -69, 539,
    1142, 1732, 2305, 2854, 3374, 3859, 4307, 4713, 5073, 5386, 5649, 5862,
    6024, 6135, 6197, 6211, 6179, 6104, 5989, 5837, 5653, 5439, 5201, 4942,
    4665, 4376, 4077, 3772, 3465, 3156, 2850, 2547, 2249, 1956, 1670, 1391,
    1117, 849, 585, 324, 65, -192, -451, -713, -978, -1248, -1523, -1803,
    -2090, -2383, -2681, -2982, -3287, -3591, -3894, -4191, -4481, -4759, -5023, -5267,
    -5488, -5683, -5847, -5976, -6067, -6117, -6124, -6084, -5995, -5858, -5671, -5434,
    -5148, -4815, -4436, -4015, -3555, -3060, -2535, -1984, -1413, -828, -235, 360,
    951, 1532, 2097, 2641, 3158, 3642, 4091, 4499, 4864, 5183, 5454, 5675,
    5848, 5970, 6044, 6071, 6052, 5990, 5889, 5750, 5578, 5377, 5151, 4903,
    4637, 4357, 4068, 3771, 3471, 3169, 2869, 2572, 2279, 1992, 1710, 1435,
    1166, 903, 643, 388, 135, -117, -370, -625, -883, -1145, -1412, -1685,
    -1964, -2248, -2538, -2832, -3128, -3426, -3723, -4015, -4301, -4576, -4838, -5083,
    -5306, -5503, -5672, -5808, -5908, -5969, -5987, -5961, -5888, -5768, -5599, -5381,
    -5115, -4802, -4444, -4044, -3605, -3130, -2624, -2092, -1539, -971, -393, 188,
    768, 1339, 1897, 2434, 2947, 3430, 3878, 4289, 4658, 4982, 5260, 5491,
    5673, 5806, 5892, 5931, 5924, 5876, 5787, 5661, 5502, 5313, 5098, 4861,
    4606, 4336, 4056, 3767, 3475, 3180, 2886, 2595, 2307, 2025, 1748, 1478,
    1213, 954, 700, 449, 201, -45, -292, -540, -791, -1046, -1306, -1571,
    -1842, -2118, -2400, -2686, -2976, -3267, -3557, -3844, -4126, -4398, -4658, -4902,
    -5126, -5327, -5500, -5643, -5751, -5821, -5851, -5838, -5780, -5675, -5523, -5323,
    -5077, -4784, -4446, -4066, -3647, -3193, -2706, -2193, -1658, -1106, -543, 24,
    592, 1153, 1702, 2234, 2742, 3223, 3671, 4083, 4455, 4785, 5069, 5308,
    5499, 5643, 5739, 5790, 5796, 5760, 5684, 5571, 5424, 5247, 5044, 4818,
    4573, 4313, 4042, 3762, 3477, 3189, 2901, 2615, 2333, 2056, 1784, 1518,
    1258, 1003, 753, 507, 264, 23, -217, -460, -704, -952, -1205, -1462,
    -1725, -1994, -2268, -2547, -2829, -3113, -3397, -3679, -3956, -4225, -4483, -4726,
    -4951, -5154, -5331, -5479, -5594, -5674, -5714, -5713, -5669, -5580, -5444, -5262,
    -5034, -4760, -4442, -4082, -3683, -3248, -2781, -2287, -1769, -1234, -686, -132,
    423, 974, 1514, 2039, 2543, 3021, 3468, 3881, 4256, 4590, 4881, 5127,
    5326, 5480, 5587, 5649, 5667, 5643, 5579, 5479, 5344, 5180, 4988, 4773,
    4539, 4288, 4026, 3754, 3476, 3196, 2914, 2634, 2357, 2085, 1817, 1556,
    1300, 1050, 804, 563, 325, 89, -146, -382, -621, -862, -1107, -1358,
    -1613, -1874, -2141, -2412, -2687, -2964, -3242, -3518, -3791, -4056, -4311, -4553,
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    -4987, -4732, -4433, -4092, -3713, -3297, -2849, -2373, -1873, -1354, -822, -281,
    261, 801, 1333, 1851, 2349, 2824, 3270, 3683, 4060, 4398, 4695, 4947,
    5155, 5318, 5436, 5509, 5538, 5526, 5474, 5386, 5263, 5110, 4930, 4726,
    4502, 4261, 4007, 3744, 3474, 3200, 2925, 2651, 2380, 2112, 1849, 1592,
    1340, 1094, 853, 616, 383, 151, -78, -309, -541, -776, -1014, -1258,
    -1506, -1760, -2019, -2282, -2550, -2821, -3092, -3363, -3630, -3892, -4145, -4385,
    -4610, -4816, -5000, -5158, -5286, -5381, -5441, -5463, -5444, -5383, -5278, -5129,
    -4936, -4699, -4419, -4097, -3737, -3340, -2911, -2453, -1970, -1468, -950, -424,
    106, 635, 1158, 1668, 2161, 2632, 3076, 3490, 3869, 4210, 4511, 4770,
    4986, 5157, 5285, 5368, 5409, 5408, 5368, 5291, 5181, 5039, 4870, 4677,
    4463, 4232, 3987, 3732, 3470, 3203, 2935, 2666, 2400, 2137, 1879, 1626,
    1378, 1136, 899, 667, 438, 211, -13, -238, -465, -693, -926, -1162,
    -1403, -1650, -1901, -2158, -2418, -2682, -2948, -3213, -3475, -3733, -3982, -4221,
    -4446, -4653, -4839, -5000, -5134, -5236, -5305, -5337, -5330, -5282, -5192, -5058,
    -4882, -4662, -4400, -4096, -3755, -3377, -2966, -2525, -2060, -1574, -1072, -559,
    -41, 476, 989, 1492, 1979, 2446, 2888, 3300, 3680, 4025, 4330, 4595,
    4818, 4998, 5134, 5228, 5279, 5289, 5261, 5196, 5097, 4967, 4809, 4626,
    4422, 4201, 3965, 3719, 3464, 3204, 2942, 2679, 2418, 2160, 1907, 1658,
    1414, 1176, 943, 715, 490, 268, 48, -171, -392, -615, -840, -1070,
    -1305, -1544, -1789, -2038, -2292, -2549, -2808, -3067, -3325, -3578, -3825, -4061,
    -4285, -4492, -4680, -4845, -4984, -5093, -5169, -5211, -5215, -5179, -5103, -4985,
    -4824, -4621, -4376, -4091, -3767, -3407, -3014, -2592, -2143, -1673, -1187, -688,
    -183, 323, 827, 1321, 1802, 2264, 2703, 3115, 3496, 3842, 4152, 4422,
    4652, 4839, 4985, 5088, 5149, 5171, 5153, 5099, 5012, 4893, 4746, 4573,
    4380, 4168, 3941, 3703, 3456, 3203, 2947, 2690, 2435, 2182, 1933, 1688,
    1449, 1215, 986, 761, 541, 323, 107, -106, -320, -536, -753, -973,
    -1196, -1424, -1656, -1892, -2132, -2374, -2618, -2862, -3104, -3342, -3574, -3796,
    -4006, -4201, -4378, -4533, -4664, -4767, -4840, -4881, -4887, -4857, -4789, -4682,
    -4536, -4351, -4128, -3867, -3572, -3243, -2884, -2497, -2087, -1658, -1214, -758,
    -297, 165, 624, 1075, 1514, 1935, 2335, 2710, 3057, 3373, 3655, 3901,
    4111, 4282, 4415, 4510, 4568, 4589, 4576, 4529, 4452, 4348, 4217, 4065,
    3893, 3705, 3504, 3293, 3073, 2850, 2623, 2396, 2170, 1947, 1727, 1513,
    1303, 1098, 899, 705, 514, 327, 143, -39, -222, -405, -589, -775,
    -965, -1157, -1354, -1553, -1756, -1961, -2168, -2375, -2581, -2784, -2981, -3172,
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    -3878, -3730, -3549, -3337, -3094, -2823, -2525, -2204, -1863, -1504, -1131, -749,
    -360, 30, 418, 801, 1174, 1533, 1875, 2197, 2496, 2768, 3013, 3229,
    3413, 3565, 3685, 3773, 3829, 3854, 3850, 3818, 3759, 3676, 3572, 3448,
    3307, 3152, 2986, 2810, 2627, 2440, 2250, 2059, 1869, 1681, 1496, 1315,
    1138, 965, 797, 634, 474, 317, 162, 9, -142, -294, -447, -602,
    -759, -918, -1080, -1245, -1413, -1583, -1754, -1925, -2096, -2265, -2430, -2589,
    -2741, -2883, -3013, -3129, -3229, -3311, -3373, -3412, -3429, -3420, -3385, -3324,
    -3235, -3119, -2976, -2807, -2612, -2394, -2154, -1894, -1616, -1324, -1019, -706,
    -387, -65, 254, 571, 880, 1178, 1463, 1732, 1982, 2211, 2417, 2600,
    2757, 2888, 2993, 3071, 3123, 3150, 3152, 3130, 3087, 3024, 2942, 2844,
    2732, 2607, 2473, 2331, 2182, 2030, 1875, 1719, 1563, 1409, 1257, 1109,
    964, 822, 685, 551, 420, 292, 166, 42, -80, -203, -327, -451,
    -577, -705, -835, -967, -1101, -1237, -1374, -1512, -1649, -1785, -1917, -2046,
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    -2607, -2519, -2410, -2280, -2129, -1959, -1772, -1568, -1350, -1119, -879, -631,
    -378, -123, 131, 383, 629, 868, 1096, 1312, 1514, 1699, 1866, 2015,
    2144, 2252, 2339, 2405, 2451, 2476, 2481, 2468, 2437, 2390, 2329, 2254,
    2168, 2071, 1967, 1856, 1740, 1620, 1499, 1376, 1254, 1132, 1013, 896,
    782, 670, 562, 457, 354, 254, 156, 59, -35, -130, -226, -322,
    -418, -516, -616, -717, -819, -923, -1028, -1133, -1238, -1341, -1443, -1541,
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    -338, -147, 44, 234, 420, 601, 773, 937, 1090, 1231, 1359, 1472,
    1571, 1655, 1722, 1774, 1811, 1832, 1838, 1831, 1810, 1777, 1733, 1678,
    1615, 1545, 1468, 1386, 1301, 1213, 1123, 1032, 941, 852, 763, 676,
    592, 510, 430, 353, 277, 204, 133, 62, -6, -75, -143, -212,
    -281, -351, -421, -493, -565, -638, -712, -786, -860, -933, -1004, -1074,
    -1140, -1203, -1261, -1313, -1359, -1398, -1428, -1450, -1462, -1463, -1454, -1434,
    -1402, -1359, -1305, -1240, -1164, -1078, -983, -879, -767, -649, -526, -399,
    -269, -137, -6, 123, 251, 374, 493, 605, 709, 806, 893, 971,
    1039, 1096, 1143, 1178, 1204, 1218, 1223, 1219, 1205, 1183, 1154, 1118,
    1076, 1029, 977, 923, 866, 807, 747, 687, 626, 567, 508, 451,
    396, 342, 289, 239, 190, 143, 97, 52, 8, -35, -78, -121,
    -163, -206, -250, -293, -337, -382, -426, -470, -515, -558, -600, -641,
    -681, -717, -751, -782, -808, -830, -847, -859, -865, -865, -859, -846,
    -827, -801, -769, -730, -686, -635, -580, -520, -455, -388, -317, -245,
    -171, -97, -23, 48, 119, 187, 252, 314, 370, 423, 469, 511,
    546, 576, 599, 617, 629, 635, 636, 632, 623, 610, 593, 572,
    549, 523, 495, 466, 435, 404, 372, 341, 310, 279, 249, 221,
    193, 166, 141, 116, 93, 70, 49, 28, 9, -10, -28, -47,
    -65, -82, -100, -117, -134, -151, -168, -184, -200, -215, -229, -243,
    -255, -267, -276, -285, -291, -296, -299, -299, -298, -294, -288, -280,
    -270, -258, -245, -229, -212, -193, -174, -154, -133, -112, -90, -69,
    -49, -29, -10, 6, 23, 37, 50, 62, 71, 79, 85, 89,
    92, 93, 92, 90, 87, 82, 77, 71, 64, 57, 50, 43,
    36, 29, 22, 15, 10, 4, 0, 5, 21, 47, 83, 128,
    182, 244, 313, 388, 468, 552, 638, 726, 814, 901, 986, 1068,
    1146, 1218, 1285, 1344, 1397, 1441, 1476, 1503, 1521, 1530, 1530, 1521,
    1504, 1479, 1446, 1405, 1358, 1304, 1245, 1180, 1111, 1037, 960, 879,
    795, 708, 618, 525, 429, 330, 228, 122, 12, -101, -220, -344,
    -474, -611, -754, -904, -1061, -1225, -1398, -1577, -1764, -1958, -2158, -2364,
    -2574, -2787, -3003, -3219, -3435, -3647, -3854, -4054, -4245, -4424, -4588, -4736,
    -4865, -4973, -5056, -5114, -5143, -5143, -5111, -5046, -4946, -4812, -4641, -4436,
    -4194, -3917, -3607, -3263, -2888, -2484, -2053, -1597, -1121, -626, -117, 402,
    929, 1460, 1989, 2513, 3029, 3532, 4018, 4484, 4926, 5342, 5727, 6081,
    6399, 6681, 6925, 7130, 7295, 7420, 7505, 7550, 7556, 7525, 7458, 7356,
    7222, 7059, 6867, 6651, 6412, 6154, 5878, 5589, 5287, 4976, 4658, 4335,
    4008, 3680, 3351, 3023, 2695, 2369, 2045, 1723, 1401, 1080, 759, 436,
    111, -217, -551, -891, -1239, -1596, -1962, -2339, -2727, -3127, -3538, -3960,
    -4393, -4836, -5286, -5743, -6204, -6666, -7126, -7582, -8029, -8463, -8880, -9276,
    -9646, -9986, -10290, -10555, -10775, -10947, -11066, -11129, -11131, -11071, -10946, -10753,
    -10492, -10162, -9762, -9293, -8758, -8156, -7493, -6769, -5991, -5162, -4288, -3373,
    -2426, -1451, -456, 550, 1563, 2574, 3576, 4560, 5521, 6450, 7342, 8190,
    8988, 9731, 10415, 11034, 11586, 12069, 12479, 12816, 13079, 13269, 13386, 13402,
    13318, 13170, 12961, 12695, 12378, 12014, 11609, 11168, 10695, 10196, 9676, 9140,
    8592, 8037, 7477, 6917, 6359, 5806, 5259, 4721, 4192, 3672, 3163, 2662,
    2170, 1686, 1209, 736, 266, -202, -671, -1142, -1618, -2099, -2587, -3083,
    -3588, -4102, -4625, -5156, -5695, -6241, -6791, -7343, -7894, -8441, -8981, -9508,
    -10020, -10511, -10976, -11411, -11810, -12168, -12481, -12743, -12950, -13097, -13181, -13198,
    -13145, -13020, -12820, -12545, -12194, -11767, -11266, -10691, -10046, -9334, -8558, -7723,
    -6835, -5899, -4921, -3908, -2868, -1808, -734, 343, 1417, 2481, 3527, 4546,
    5532, 6478, 7377, 8224, 9013, 9740, 10400, 10991, 11510, 11954, 12323, 12616,
    12834, 12978, 13049, 13050, 12984, 12854, 12663, 12417, 12119, 11775, 11390, 10968,
    10514, 10034, 9533, 9014, 8483, 7944, 7400, 6855, 6311, 5771, 5238, 4712,
    4195, 3688, 3189, 2700, 2220, 1747, 1281, 820, 362, -93, -549, -1007,
    -1469, -1935, -2409, -2890, -3379, -3877, -4384, -4899, -5422, -5952, -6486, -7023,
    -7560, -8093, -8620, -9137, -9639, -10121, -10580, -11011, -11407, -11765, -12080, -12347,
    -12561, -12718, -12814, -12845, -12809, -12704, -12526, -12275, -11950, -11551, -11080, -10537,
    -9924, -9246, -8505, -7705, -6852, -5951, -5008, -4030, -3023, -1995, -953, 95,
    1142, 2181, 3202, 4201, 5168, 6098, 6984, 7820, 8601, 9323, 9980, 10571,
    11092, 11540, 11916, 12218, 12447, 12603, 12689, 12705, 12655, 12542, 12370, 12142,
    11863, 11538, 11172, 10769, 10334, 9872, 9389, 8887, 8373, 7850, 7321, 6791,
    6261, 5735, 5214, 4701, 4196, 3700, 3213, 2735, 2266, 1804, 1349, 900,
    454, 10, -433, -878, -1327, -1780, -2239, -2705, -3179, -3662, -4153, -4653,
    -5160, -5674, -6193, -6715, -7238, -7758, -8273, -8778, -9270, -9744, -10196, -10622,
    -11016, -11373, -11690, -11960, -12180, -12346, -12453, -12498, -12479, -12391, -12234, -12006,
    -11707, -11335, -10892, -10379, -9799, -9153, -8445, -7679, -6861, -5994, -5085, -4140,
    -3166, -2170, -1158, -139, 880, 1893, 2892, 3869, 4818, 5732, 6604, 7429,
    8202, 8918, 9572, 10162, 10684, 11137, 11519, 11829, 12068, 12236, 12334, 12365,
    12331, 12235, 12080, 11870, 11610, 11303, 10956, 10571, 10155, 9711, 9245, 8760,
    8263, 7755, 7241, 6725, 6210, 5697, 5189, 4687, 4194, 3709, 3233, 2766,
    2308, 1857, 1413, 975, 540, 107, -323, -756, -1191, -1631, -2076, -2528,
    -2988, -3456, -3932, -4416, -4908, -5407, -5911, -6419, -6928, -7435, -7937, -8431,
    -8913, -9379, -9824, -10245, -10635, -10991, -11309, -11583, -11808, -11982, -12100, -12158,
    -12153, -12083, -11946, -11740, -11464, -11118, -10703, -10219, -9669, -9055, -8379, -7647,
    -6861, -6028, -5153, -4241, -3299, -2334, -1352, -361, 631, 1619, 2595, 3551,
    4481, 5379, 6237, 7051, 7815, 8524, 9175, 9764, 10287, 10743, 11130, 11448,
    11697, 11876, 11987, 12031, 12012, 11932, 11794, 11602, 11359, 11071, 10741, 10375,
    9976, 9550, 9101, 8633, 8151, 7659, 7160, 6659, 6156, 5656, 5161, 4672,
    4190, 3716, 3251, 2794, 2347, 1906, 1473, 1045, 621, 200, -219, -640,
    -1063, -1490, -1921, -2360, -2805, -3258, -3720, -4190, -4667, -5151, -5640, -6134,
    -6629, -7123, -7613, -8096, -8568, -9025, -9463, -9878, -10265, -10620, -10938, -11214,
    -11445, -11626, -11753, -11823, -11833, -11779, -11661, -11475, -11223, -10902, -10513, -10057,
    -9536, -8952, -8308, -7608, -6855, -6054, -5211, -4331, -3421, -2486, -1534, -571,
    395, 1358, 2311, 3246, 4158, 5039, 5883, 6685, 7440, 8143, 8790, 9376,
    9900, 10359, 10751, 11076, 11333, 11522, 11645, 11703, 11699, 11634, 11512, 11336,
    11111, 10840, 10528, 10179, 9798, 9389, 8957, 8506, 8040, 7563, 7078, 6591,
    6102, 5614, 5131, 4653, 4183, 3720, 3265, 2819, 2382, 1952, 1529, 1111,
    698, 288, -120, -529, -940, -1355, -1774, -2199, -2630, -3070, -3517, -3972,
    -4435, -4905, -5380, -5859, -6341, -6822, -7300, -7772, -8234, -8683, -9114, -9523,
    -9906, -10259, -10577, -10855, -11090, -11278, -11413, -11494, -11517, -11480, -11379, -11213,
    -10982, -10685, -10322, -9893, -9400, -8846, -8232, -7562, -6841, -6072, -5260, -4412,
    -3532, -2627, -1704, -769, 171, 1109, 2039, 2954, 3847, 4711, 5541, 6332,
    7077, 7773, 8415, 8999, 9523, 9984, 10381, 10712, 10977, 11176, 11310, 11381,
    11390, 11340, 11234, 11075, 10866, 10612, 10317, 9986, 9621, 9229, 8813, 8378,
    7927, 7465, 6996, 6521, 6046, 5571, 5100, 4633, 4174, 3721, 3277, 2842,
    2414, 1994, 1580, 1173, 770, 370, -27, -425, -824, -1226, -1633, -2045,
    -2464, -2889, -3323, -3764, -4213, -4668, -5130, -5596, -6064, -6532, -6998, -7459,
    -7911, -8351, -8775, -9178, -9557, -9908, -10225, -10505, -10744, -10937, -11081, -11172,
    -11208, -11184, -11100, -10954, -10744, -10469, -10130, -9727, -9262, -8735, -8151, -7512,
    -6821, -6082, -5302, -4484, -3634, -2759, -1864, -956, -41, 872, 1780, 2674,
    3548, 4396, 5212, 5990, 6726, 7415, 8051, 8633, 9157, 9619, 10020, 10356,
    10629, 10837, 10982, 11065, 11087, 11051, 10960, 10816, 10624, 10387, 10108, 9793,
    9446, 9070, 8670, 8250, 7815, 7367, 6912, 6451, 5988, 5526, 5066, 4611,
    4162, 3721, 3287, 2861, 2443, 2032, 1629, 1231, 838, 449, 61, -325,
    -713, -1104, -1499, -1898, -2304, -2717, -3137, -3565, -4000, -4441, -4889, -5342,
    -5797, -6253, -6707, -7157, -7599, -8030, -8447, -8844, -9219, -9566, -9883, -10164,
    -10406, -10604, -10755, -10856, -10903, -10894, -10826, -10697, -10507, -10254, -9938, -9560,
    -9121, -8622, -8066, -7455, -6794, -6086, -5335, -4547, -3727, -2880, -2013, -1132,
    -242, 647, 1532, 2405, 3261, 4093, 4894, 5661, 6386, 7067, 7699, 8277,
    8800, 9263, 9667, 10009, 10288, 10505, 10660, 10754, 10789, 10766, 10690, 10561,
    10385, 10163, 9901, 9602, 9271, 8911, 8527, 8123, 7702, 7269, 6827, 6380,
    5929, 5479, 5031, 4587, 4149, 3718, 3294, 2877, 2469, 2068, 1674, 1285,
    902, 523, 145, -231, -608, -988, -1371, -1758, -2152, -2552, -2959, -3373,
    -3795, -4224, -4658, -5098, -5540, -5984, -6427, -6866, -7298, -7720, -8129, -8520,
    -8890, -9235, -9550, -9832, -10076, -10279, -10437, -10546, -10604, -10608, -10555, -10443,
    -10271, -10039, -9746, -9392, -8978, -8505, -7977, -7394, -6762, -6083, -5361, -4602,
    -3810, -2992, -2152, -1297, -433, 433, 1296, 2149, 2986, 3801, 4588, 5342,
    6058, 6731, 7356, 7931, 8452, 8917, 9323, 9669, 9955, 10180, 10344, 10449,
    10496, 10486, 10423, 10310, 10148, 9942, 9696, 9413, 9097, 8753, 8384, 7995,
    7589, 7170, 6742, 6307, 5869, 5431, 4995, 4562, 4134, 3712, 3298, 2891,
    2492, 2100, 1715, 1336, 962, 592, 224, -141, -508, -877, -1249, -1625,
    -2006, -2394, -2789, -3190, -3599, -4015, -4436, -4863, -5293, -5725, -6156, -6584,
    -7007, -7420, -7821, -8206, -8571, -8912, -9226, -9508, -9754, -9961, -10125, -10242,
    -10310, -10326, -10287, -10192, -10038, -9825, -9554, -9222, -8833, -8386, -7884, -7329,
    -6724, -6073, -5380, -4649, -3885, -3094, -2281, -1452, -613, 230, 1071, 1904,
    2722, 3521, 4293, 5035, 5740, 6405, 7024, 7595, 8114, 8579, 8987, 9337,
    9629, 9861, 10034, 10149, 10208, 10211, 10161, 10062, 9915, 9724, 9493, 9225,
    8925, 8596, 8242, 7868, 7476, 7071, 6656, 6234, 5808, 5382, 4957, 4534,
    4117, 3705, 3300, 2903, 2513, 2130, 1754, 1384, 1019, 658, 300, -56,
    -413, -771, -1132, -1497, -1867, -2243, -2626, -3015, -3411, -3814, -4223, -4637,
    -5055, -5475, -5895, -6313, -6726, -7130, -7523, -7902, -8262, -8599, -8911, -9193,
    -9440, -9651, -9820, -9945, -10022, -10049, -10024, -9944, -9807, -9613, -9362, -9052,
    -8686, -8264, -7787, -7259, -6681, -6057, -5392, -4688, -3952, -3188, -2401, -1597,
    -782, 37, 856, 1669, 2469, 3251, 4009, 4738, 5433, 6089, 6702, 7269,
    7786, 8250, 8660, 9014, 9310, 9549, 9731, 9856, 9925, 9940, 9903, 9817,
    9684, 9508, 9292, 9039, 8754, 8440, 8101, 7740, 7363, 6971, 6569, 6160,
    5746, 5331, 4917, 4505, 4098, 3696, 3300, 2912, 2531, 2157, 1789, 1428,
    1072, 720, 371, 23, -323, -671, -1022, -1376, -1735, -2099, -2470, -2847,
    -3231, -3622, -4019, -4421, -4827, -5235, -5644, -6051, -6454, -6850, -7235, -7607,
    -7961, -8295, -8605, -8886, -9135, -9348, -9522, -9654, -9740, -9778, -9764, -9699,
    -9578, -9402, -9170, -8882, -8538, -8139, -7688, -7184, -6633, -6036, -5397, -4721,
    -4011, -3273, -2512, -1733, -942, -145, 652, 1445, 2227, 2993, 3736, 4452,
    5136, 5784, 6390, 6952, 7466, 7930, 8341, 8698, 8999, 9245, 9434, 9568,
    9647, 9674, 9649, 9576, 9457, 9295, 9093, 8855, 8584, 8284, 7960, 7613,
    7249, 6871, 6482, 6085, 5684, 5280, 4876, 4475, 4077, 3685, 3298, 2919,
    2546, 2181, 1822, 1469, 1121, 778, 438, 99, -237, -576, -916, -1260,
    -1608, -1962, -2321, -2687, -3059, -3438, -3822, -4212, -4607, -5004, -5402, -5798,
    -6192, -6579, -6956, -7321, -7670, -8000, -8307, -8587, -8837, -9053, -9231, -9369,
    -9463, -9510, -9509, -9457, -9352, -9193, -8980, -8712, -8389, -8013, -7585, -7107,
    -6580, -6009, -5397, -4746, -4063, -3351, -2615, -1860, -1093, -317, 459, 1232,
    1996, 2745, 3473, 4177, 4850, 5488, 6088, 6645, 7156, 7619, 8030, 8390,
    8695, 8946, 9143, 9286, 9375, 9412, 9399, 9339, 9233, 9084, 8896, 8672,
    8416, 8130, 7819, 7487, 7136, 6771, 6394, 6010, 5620, 5227, 4834, 4443,
    4055, 3672, 3295, 2924, 2560, 2202, 1851, 1507, 1167, 833, 501, 171,
    -156, -485, -816, -1150, -1488, -1830, -2178, -2533, -2894, -3261, -3634, -4012,
    -4395, -4781, -5168, -5555, -5939, -6317, -6686, -7045, -7388, -7714, -8018, -8297,
    -8547, -8764, -8947, -9090, -9191, -9248, -9258, -9218, -9128, -8985, -8790, -8541,
    -8240, -7885, -7480, -7025, -6524, -5977, -5390, -4765, -4107, -3420, -2709, -1978,
    -1234, -481, 274, 1028, 1774, 2507, 3221, 3911, 4573, 5202, 5795, 6347,
    6854, 7316, 7728, 8089, 8398, 8655, 8858, 9009, 9107, 9155, 9153, 9105,
    9011, 8876, 8702, 8491, 8248, 7977, 7680, 7360, 7023, 6671, 6306, 5934,
    5555, 5173, 4791, 4410, 4031, 3657, 3289, 2926, 2571, 2221, 1879, 1542,
    1211, 884, 560, 239, -79, -399, -721, -1045, -1373, -1705, -2042, -2386,
    -2735, -3091, -3453, -3820, -4192, -4567, -4944, -5320, -5694, -6064, -6426, -6777,
    -7115, -7436, -7737, -8014, -8264, -8483, -8669, -8817, -8925, -8991, -9011, -8983,
    -8907, -8780, -8601, -8371, -8089, -7756, -7373, -6941, -6463, -5941, -5378, -4778,
    -4145, -3482, -2795, -2088, -1366, -635, 100, 834, 1562, 2279, 2978, 3655,
    4306, 4926, 5511, 6057, 6562, 7021, 7433, 7796, 8108, 8370, 8579, 8738,
    8845, 8902, 8912, 8875, 8793, 8671, 8509, 8312, 8083, 7825, 7541, 7235,
    6910, 6570, 6218, 5857, 5490, 5119, 4747, 4375, 4006, 3641, 3281, 2927,
    2580, 2238, 1903, 1574, 1251, 932, 617, 304, -7, -318, -630, -945,
    -1263, -1585, -1912, -2245, -2584, -2929, -3280, -3636, -3997, -4361, -4727, -5094,
    -5459, -5819, -6173, -6518, -6850, -7167, -7464, -7739, -7989, -8209, -8398, -8550,
    -8665, -8738, -8768, -8752, -8688, -8576, -8414, -8201, -7938, -7625, -7263, -6854,
    -6399, -5900, -5361, -4786, -4176, -3537, -2874, -2190, -1490, -780, -65, 650,
    1360, 2060, 2745, 3409, 4049, 4660, 5237, 5777, 6277, 6734, 7146, 7510,
    7826, 8091, 8307, 8472, 8587, 8654, 8674, 8648, 8578, 8468, 8319, 8135,
    7919, 7673, 7403, 7109, 6797, 6470, 6130, 5780, 5424, 5063, 4701, 4339,
    3980, 3624, 3272, 2926, 2587, 2253, 1926, 1604, 1288, 977, 670, 365,
    61, -240, -544, -850, -1158, -1471, -1788, -2111, -2439, -2773, -3113, -3459,
    -3809, -4163, -4519, -4876, -5231, -5583, -5930, -6267, -6594, -6905, -7199, -7472,
    -7721, -7942, -8133, -8290, -8410, -8490, -8529, -8524, -8473, -8374, -8228, -8032,
    -7787, -7494, -7152, -6764, -6331, -5855, -5340, -4787, -4201, -3586, -2945, -2283,
    -1606, -917, -221, 474, 1167, 1851, 2521, 3173, 3801, 4402, 4971, 5505,
    6001, 6456, 6867, 7232, 7549, 7819, 8040, 8212, 8335, 8411, 8440, 8425,
    8366, 8268, 8131, 7960, 7756, 7524, 7265, 6985, 6685, 6369, 6041, 5702,
    5357, 5007, 4655, 4302, 3952, 3604, 3261, 2924, 2592, 2266, 1946, 1632,
    1323, 1019, 719, 422, 127, -167, -462, -759, -1058, -1362, -1669, -1982,
    -2300, -2624, -2954, -3289, -3629, -3972, -4318, -4666, -5012, -5356, -5694, -6025,
    -6345, -6652, -6942, -7213, -7460, -7682, -7875, -8035, -8160, -8248, -8295, -8300,
    -8260, -8175, -8043, -7863, -7636, -7361, -7039, -6672, -6260, -5806, -5313, -4783,
    -4220, -3628, -3009, -2370, -1714, -1045, -369, 308, 983, 1651, 2306, 2945,
    3562, 4153, 4714, 5242, 5734, 6185, 6595, 6960, 7280, 7553, 7779, 7957,
    8088, 8172, 8210, 8205, 8158, 8071, 7946, 7786, 7595, 7375, 7129, 6861,
    6573, 6269, 5952, 5624, 5290, 4950, 4607, 4265, 3923, 3584, 3249, 2919,
    2595, 2276, 1964, 1657, 1355, 1059, 766, 476, 189, -97, -384, -673,
    -963, -1258, -1556, -1859, -2167, -2481, -2801, -3126, -3456, -3789, -4126, -4463,
    -4801, -5136, -5467, -5791, -6105, -6406, -6693, -6961, -7207, -7429, -7623, -7786,
    -7916, -8010, -8065, -8079, -8050, -7978, -7860, -7695, -7485, -7228, -6925, -6577,
    -6186, -5754, -5283, -4775, -4234, -3664, -3067, -2449, -1814, -1166, -509, 149,
    808, 1460, 2101, 2726, 3332, 3913, 4466, 4988, 5474, 5922, 6331, 6696,
    7017, 7294, 7524, 7707, 7845, 7937, 7985, 7989, 7952, 7876, 7763, 7615,
    7436, 7227, 6994, 6737, 6461, 6169, 5863, 5546, 5222, 4892, 4559, 4226,
    3893, 3562, 3235, 2913, 2596, 2285, 1979, 1680, 1385, 1095, 810, 527,
    247, -31, -310, -591, -873, -1158, -1448, -1741, -2040, -2345, -2654, -2969,
    -3289, -3613, -3940, -4268, -4597, -4924, -5247, -5564, -5872, -6169, -6451, -6716,
    -6961, -7182, -7377, -7543, -7677, -7777, -7839, -7862, -7844, -7783, -7678, -7529,
    -7334, -7094, -6809, -6481, -6110, -5698, -5248, -4762, -4242, -3693, -3119, -2522,
    -1907, -1278, -641, 0, 641, 1277, 1904, 2516, 3110, 3681, 4226, 4741,
    5222, 5667, 6074, 6439, 6761, 7040, 7274, 7463, 7607, 7707, 7763, 7777,
    7750, 7684, 7582, 7445, 7278, 7081, 6859, 6614, 6350, 6069, 5774, 5468,
    5154, 4834, 4510, 4186, 3861, 3539, 3220, 2906, 2596, 2292, 1993, 1700,
    1413, 1130, 851, 575, 302, 30, -240, -513, -787, -1064, -1344, -1629,
    -1919, -2214, -2514, -2819, -3130, -3444, -3761, -4081, -4401, -4719, -5035, -5345,
    -5647, -5938, -6216, -6478, -6721, -6942, -7138, -7306, -7444, -7549, -7618, -7649,
    -7640, -7591, -7499, -7363, -7184, -6960, -6693, -6383, -6031, -5639, -5209, -4744,
    -4246, -3718, -3164, -2587, -1993, -1384, -765, -142, 482, 1103, 1715, 2314,
    2897, 3458, 3994, 4502, 4978, 5420, 5824, 6188, 6512, 6793, 7031, 7225,
    7375, 7481, 7546, 7568, 7551, 7495, 7404, 7278, 7122, 6936, 6726, 6492,
    6239, 5969, 5685, 5389, 5085, 4775, 4461, 4145, 3829, 3515, 3204, 2897,
    2594, 2297, 2005, 1719, 1438, 1161, 889, 621, 354, 90, -174, -438,
    -705, -974, -1246, -1522, -1803, -2089, -2380, -2676, -2976, -3281, -3590, -3900,
    -4212, -4522, -4830, -5133, -5429, -5715, -5989, -6247, -6488, -6708, -6905, -7075,
    -7216, -7325, -7401, -7439, -7440, -7401, -7321, -7199, -7034, -6826, -6576, -6283,
    -5950, -5578, -5168, -4722, -4244, -3737, -3203, -2647, -2072, -1482, -882, -276,
    331, 936, 1534, 2121, 2692, 3243, 3771, 4271, 4742, 5179, 5581, 5945,
    6269, 6552, 6793, 6991, 7147, 7260, 7332, 7363, 7355, 7309, 7228, 7113,
    6967, 6793, 6593, 6371, 6129, 5869, 5596, 5310, 5016, 4715, 4410, 4103,
    3796, 3490, 3186, 2886, 2591, 2300, 2015, 1735, 1461, 1191, 925, 663,
    403, 146, -111, -368, -627, -888, -1152, -1419, -1692, -1969, -2251, -2538,
    -2829, -3125, -3425, -3727, -4030, -4332, -4632, -4928, -5218, -5499, -5768, -6024,
    -6262, -6481, -6678, -6849, -6993, -7107, -7188, -7234, -7243, -7214, -7145, -7036,
    -6885, -6692, -6458, -6182, -5867, -5513, -5122, -4697, -4238, -3751, -3237, -2701,
    -2145, -1574, -992, -403, 188, 778, 1362, 1935, 2495, 3036, 3555, 4048,
    4513, 4946, 5345, 5708, 6032, 6316, 6560, 6763, 6924, 7043, 7122, 7161,
    7162, 7126, 7054, 6950, 6814, 6651, 6462, 6251, 6019, 5770, 5507, 5231,
    4947, 4655, 4359, 4061, 3762, 3463, 3167, 2874, 2586, 2302, 2024, 1750,
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    12412, 12231, 12018, 11775, 11504, 11207, 10887, 10547, 10188, 9814, 9427, 9028,
    8621, 8207, 7788, 7366, 6943, 6520, 6099, 5681, 5266, 4856, 4451, 4052,
    3658, 3270, 2888, 2512, 2141, 1774, 1412, 1053, 697, 343, -9, -362,
    -716, -1071, -1429, -1790, -2154, -2523, -2897, -3275, -3660, -4049, -4444, -4844,
    -5249, -5658, -6069, -6483, -6899, -7313, -7726, -8136, -8540, -8938, -9326, -9702,
    -10065, -10412, -10740, -11048, -11333, -11592, -11823, -12024, -12193, -12327, -12425, -12484,
    -12504, -12482, -12418, -12310, -12157, -11960, -11717, -11429, -11096, -10719, -10298, -9835,
    -9330, -8786, -8204, -7587, -6937, -6256, -5548, -4815, -4061, -3288, -2502, -1704,
    -898, -90, 718, 1524, 2321, 3108, 3880, 4634, 5367, 6075, 6755, 7405,
    8022, 8604, 9148, 9653, 10116, 10538, 10916, 11249, 11538, 11782, 11980, 12134,
    12244, 12310, 12334, 12317, 12261, 12166, 12035, 11870, 11673, 11446, 11191, 10911,
    10607, 10284, 9942, 9584, 9213, 8831, 8440, 8041, 7637, 7231, 6822, 6414,
    6006, 5601, 5199, 4802, 4409, 4021, 3640, 3263, 2893, 2528, 2168, 1812,
    1461, 1114, 769, 426, 85, -255, -597, -939, -1284, -1632, -1983, -2338,
    -2698, -3063, -3432, -3807, -4188, -4573, -4963, -5356, -5754, -6153, -6554, -6955,
    -7355, -7752, -8144, -8530, -8907, -9274, -9629, -9969, -10291, -10595, -10876, -11133,
    -11365, -11567, -11739, -11878, -11983, -12050, -12080, -12070, -12020, -11927, -11792, -11613,
    -11391, -11125, -10815, -10463, -10067, -9631, -9154, -8639, -8087, -7500, -6880, -6230,
    -5553, -4851, -4128, -3386, -2630, -1861, -1085, -304, 477, 1256, 2030, 2793,
    3543, 4277, 4991, 5682, 6347, 6984, 7589, 8161, 8697, 9195, 9654, 10073,
    10450, 10784, 11075, 11323, 11527, 11687, 11805, 11881, 11915, 11910, 11866, 11784,
    11667, 11517, 11334, 11123, 10884, 10620, 10333, 10025, 9700, 9358, 9003, 8636,
    8260, 7877, 7488, 7096, 6701, 6306, 5912, 5520, 5131, 4746, 4365, 3989,
    3619, 3253, 2894, 2540, 2190, 1846, 1506, 1169, 835, 504, 174, -155,
    -485, -816, -1148, -1483, -1821, -2163, -2510, -2861, -3217, -3578, -3944, -4314,
    -4690, -5069, -5452, -5838, -6225, -6613, -6999, -7384, -7764, -8139, -8506, -8864,
    -9210, -9542, -9859, -10157, -10435, -10691, -10921, -11125, -11299, -11443, -11553, -11629,
    -11668, -11669, -11631, -11553, -11434, -11273, -11070, -10825, -10537, -10208, -9838, -9427,
    -8977, -8489, -7965, -7407, -6817, -6197, -5550, -4878, -4185, -3473, -2745, -2006,
    -1257, -503, 251, 1005, 1754, 2495, 3224, 3937, 4633, 5307, 5957, 6580,
    7173, 7735, 8263, 8754, 9209, 9624, 10000, 10334, 10627, 10878, 11087, 11254,
    11379, 11463, 11508, 11513, 11480, 11411, 11308, 11171, 11003, 10807, 10583, 10334,
    10063, 9771, 9461, 9135, 8795, 8444, 8083, 7714, 7340, 6962, 6581, 6199,
    5818, 5439, 5062, 4688, 4319, 3955, 3595, 3241, 2892, 2548, 2210, 1876,
    1546, 1220, 896, 575, 256, -61, -380, -699, -1020, -1343, -1669, -1998,
    -2332, -2669, -3012, -3359, -3712, -4069, -4430, -4796, -5165, -5537, -5911, -6285,
    -6659, -7031, -7400, -7764, -8121, -8469, -8807, -9132, -9443, -9736, -10010, -10263,
    -10493, -10697, -10874, -11021, -11137, -11219, -11267, -11278, -11252, -11188, -11084, -10940,
    -10755, -10529, -10263, -9956, -9609, -9222, -8798, -8337, -7840, -7310, -6748, -6157,
    -5538, -4896, -4231, -3548, -2849, -2137, -1416, -689, 40, 769, 1495, 2213,
    2920, 3614, 4292, 4949, 5584, 6193, 6775, 7326, 7845, 8330, 8779, 9191,
    9565, 9899, 10193, 10447, 10660, 10833, 10965, 11057, 11111, 11126, 11105, 11048,
    10957, 10833, 10680, 10497, 10288, 10054, 9798, 9521, 9226, 8915, 8591, 8254,
    7908, 7553, 7193, 6828, 6461, 6092, 5724, 5357, 4992, 4630, 4272, 3918,
    3570, 3226, 2888, 2554, 2225, 1902, 1582, 1266, 953, 642, 333, 25,
    -281, -590, -899, -1210, -1525, -1842, -2163, -2488, -2818, -3152, -3491, -3835,
    -4183, -4535, -4891, -5250, -5611, -5972, -6334, -6694, -7052, -7405, -7752, -8091,
    -8420, -8738, -9042, -9330, -9600, -9851, -10079, -10284, -10462, -10612, -10733, -10821,
    -10877, -10898, -10883, -10831, -10741, -10613, -10445, -10238, -9991, -9706, -9381, -9018,
    -8618, -8182, -7712, -7208, -6674, -6110, -5520, -4905, -4269, -3613, -2942, -2257,
    -1563, -861, -156, 548, 1250, 1946, 2633, 3308, 3967, 4607, 5227, 5823,
    6392, 6934, 7444, 7922, 8366, 8774, 9145, 9479, 9774, 10030, 10247, 10424,
    10563, 10663, 10725, 10750, 10739, 10693, 10614, 10504, 10363, 10194, 9999, 9779,
    9538, 9275, 8995, 8699, 8389, 8067, 7734, 7394, 7047, 6696, 6342, 5986,
    5629, 5274, 4921, 4570, 4223, 3881, 3542, 3209, 2880, 2557, 2238, 1924,
    1614, 1307, 1004, 703, 405, 107, -189, -487, -785, -1086, -1388, -1694,
    -2003, -2316, -2634, -2955, -3282, -3613, -3948, -4287, -4630, -4976, -5324, -5673,
    -6023, -6372, -6718, -7060, -7397, -7727, -8048, -8359, -8656, -8939, -9205, -9453,
    -9680, -9884, -10063, -10216, -10341, -10435, -10498, -10528, -10523, -10483, -10406, -10293,
    -10141, -9952, -9724, -9458, -9155, -8815, -8438, -8027, -7581, -7103, -6595, -6058,
    -5494, -4907, -4297, -3669, -3024, -2366, -1697, -1021, -341, 340, 1020, 1694,
    2361, 3016, 3657, 4282, 4886, 5469, 6026, 6557, 7059, 7529, 7968, 8372,
    8740, 9073, 9368, 9626, 9846, 10028, 10173, 10280, 10350, 10384, 10383, 10348,
    10280, 10182, 10054, 9898, 9716, 9510, 9282, 9034, 8768, 8486, 8190, 7882,
    7563, 7236, 6903, 6564, 6223, 5879, 5535, 5191, 4849, 4510, 4173, 3841,
    3513, 3189, 2871, 2557, 2248, 1943, 1642, 1345, 1051, 760, 471, 183,
    -103, -390, -679, -968, -1260, -1554, -1852, -2154, -2459, -2769, -3083, -3401,
    -3724, -4051, -4381, -4715, -5051, -5388, -5726, -6063, -6398, -6730, -7058, -7378,
    -7691, -7994, -8285, -8563, -8825, -9069, -9294, -9498, -9678, -9833, -9961, -10060,
    -10130, -10167, -10172, -10143, -10079, -9979, -9843, -9670, -9460, -9214, -8931, -8612,
    -8258, -7869, -7448, -6995, -6511, -6000, -5462, -4901, -4318, -3715, -3096, -2464,
    -1820, -1168, -512, 146, 803, 1457, 2103, 2740, 3363, 3971, 4561, 5130,
    5676, 6196, 6688, 7152, 7584, 7984, 8350, 8681, 8976, 9236, 9458, 9644,
    9794, 9907, 9985, 10027, 10035, 10011, 9954, 9867, 9751, 9608, 9439, 9246,
    9032, 8798, 8545, 8277, 7994, 7699, 7394, 7080, 6760, 6434, 6104, 5773,
    5440, 5108, 4777, 4448, 4122, 3800, 3482, 3168, 2859, 2554, 2254, 1959,
    1667, 1379, 1094, 812, 533, 254, -23, -300, -578, -858, -1139, -1423,
    -1709, -2000, -2294, -2592, -2894, -3201, -3511, -3826, -4144, -4466, -4790, -5115,
    -5442, -5768, -6092, -6414, -6732, -7044, -7348, -7644, -7929, -8200, -8458, -8699,
    -8922, -9124, -9305, -9462, -9593, -9697, -9772, -9817, -9831, -9812, -9759, -9672,
    -9550, -9393, -9201, -8972, -8709, -8410, -8077, -7711, -7312, -6883, -6424, -5937,
    -5425, -4888, -4330, -3753, -3159, -2551, -1932, -1304, -671, -35, 600, 1233,
    1859, 2477, 3084, 3676, 4250, 4806, 5340, 5849, 6333, 6789, 7215, 7610,
    7973, 8302, 8597, 8858, 9083, 9272, 9427, 9546, 9630, 9680, 9697, 9682,
    9636, 9560, 9456, 9324, 9168, 8988, 8786, 8565, 8326, 8071, 7801, 7519,
    7227, 6926, 6618, 6304, 5987, 5667, 5346, 5025, 4704, 4386, 4070, 3758,
    3449, 3145, 2845, 2549, 2258, 1971, 1688, 1409, 1134, 860, 589, 320,
    52, -215, -484, -753, -1025, -1298, -1574, -1854, -2137, -2424, -2715, -3010,
    -3309, -3612, -3919, -4228, -4541, -4855, -5170, -5485, -5800, -6111, -6420, -6723,
    -7019, -7307, -7585, -7852, -8105, -8342, -8562, -8764, -8944, -9102, -9236, -9344,
    -9424, -9476, -9498, -9488, -9447, -9372, -9264, -9122, -8945, -8734, -8489, -8209,
    -7897, -7552, -7175, -6769, -6333, -5870, -5381, -4869, -4336, -3783, -3213, -2630,
    -2034, -1430, -819, -205, 409, 1022, 1629, 2229, 2818, 3394, 3954, 4497,
    5018, 5517, 5992, 6440, 6860, 7250, 7609, 7937, 8231, 8492, 8719, 8912,
    9070, 9195, 9285, 9343, 9369, 9362, 9326, 9260, 9167, 9047, 8902, 8735,
    8546, 8337, 8111, 7868, 7611, 7342, 7062, 6774, 6478, 6176, 5870, 5562,
    5251, 4941, 4631, 4323, 4017, 3714, 3415, 3120, 2829, 2542, 2260, 1981,
    1707, 1436, 1169, 904, 642, 382, 122, -136, -395, -656, -917, -1181,
    -1447, -1716, -1988, -2264, -2544, -2828, -3116, -3408, -3704, -4002, -4303, -4606,
    -4911, -5216, -5520, -5822, -6121, -6415, -6703, -6984, -7256, -7516, -7764, -7998,
    -8216, -8416, -8596, -8755, -8891, -9002, -9087, -9145, -9174, -9174, -9142, -9079,
    -8983, -8855, -8694, -8499, -8271, -8010, -7717, -7393, -7037, -6652, -6239, -5798,
    -5333, -4844, -4334, -3805, -3259, -2699, -2126, -1544, -956, -363, 230, 823,
    1412, 1993, 2566, 3126, 3672, 4201, 4711, 5199, 5665, 6105, 6518, 6903,
    7259, 7584, 7877, 8138, 8367, 8562, 8725, 8854, 8951, 9015, 9048, 9051,
    9024, 8968, 8885, 8776, 8643, 8487, 8310, 8113, 7899, 7669, 7424, 7167,
    6900, 6623, 6339, 6049, 5754, 5457, 5157, 4857, 4558, 4259, 3963, 3670,
    3380, 3093, 2811, 2533, 2259, 1989, 1723, 1460, 1201, 945, 691, 438,
    187, -62, -312, -563, -816, -1070, -1326, -1585, -1848, -2113, -2383, -2656,
    -2933, -3214, -3499, -3786, -4077, -4369, -4663, -4958, -5252, -5544, -5834, -6120,
    -6400, -6674, -6939, -7194, -7437, -7667, -7882, -8080, -8259, -8418, -8556, -8670,
    -8760, -8823, -8859, -8867, -8845, -8792, -8709, -8594, -8446, -8267, -8056, -7813,
    -7538, -7233, -6898, -6533, -6142, -5723, -5280, -4814, -4327, -3820, -3297, -2759,
    -2209, -1649, -1082, -510, 63, 636, 1206, 1771, 2326, 2871, 3403, 3919,
    4417, 4895, 5351, 5783, 6190, 6569, 6921, 7243, 7535, 7796, 8026, 8224,
    8389, 8523, 8625, 8696, 8737, 8747, 8729, 8683, 8610, 8511, 8389, 8244,
    8079, 7894, 7691, 7473, 7240, 6995, 6739, 6474, 6202, 5923, 5639, 5353,
    5064, 4774, 4484, 4195, 3909, 3624, 3343, 3065, 2791, 2521, 2256, 1994,
    1735, 1481, 1230, 981, 735, 491, 248, 6, -235, -477, -720, -965,
    -1212, -1462, -1714, -1970, -2230, -2493, -2760, -3030, -3304, -3581, -3861, -4143,
    -4427, -4711, -4995, -5279, -5559, -5837, -6109, -6375, -6634, -6883, -7122, -7347,
    -7559, -7755, -7934, -8093, -8232, -8349, -8442, -8511, -8553, -8568, -8555, -8512,
    -8440, -8337, -8204, -8039, -7844, -7617, -7360, -7074, -6758, -6413, -6042, -5645,
    -5223, -4779, -4313, -3829, -3328, -2812, -2283, -1744, -1198, -646, -92, 461,
    1013, 1560, 2100, 2629, 3147, 3650, 4136, 4603, 5050, 5474, 5874, 6248,
    6596, 6915, 7205, 7466, 7696, 7896, 8065, 8203, 8310, 8387, 8434, 8452,
    8442, 8404, 8341, 8253, 8141, 8007, 7852, 7678, 7487, 7281, 7060, 6826,
    6581, 6328, 6066, 5798, 5525, 5249, 4970, 4690, 4410, 4131, 3853, 3578,
    3305, 3036, 2770, 2508, 2250, 1996, 1746, 1499, 1255, 1015, 776, 540,
    305, 71, -162, -396, -630, -867, -1105, -1345, -1588, -1835, -2084, -2338,
    -2594, -2855, -3118, -3385, -3655, -3927, -4201, -4476, -4750, -5024, -5296, -5566,
    -5830, -6089, -6341, -6585, -6818, -7040, -7248, -7442, -7620, -7779, -7919, -8038,
    -8135, -8207, -8255, -8277, -8272, -8239, -8177, -8086, -7965, -7815, -7634, -7424,
    -7184, -6914, -6617, -6292, -5940, -5563, -5162, -4739, -4294, -3831, -3351, -2857,
    -2349, -1831, -1305, -773, -238, 297, 831, 1361, 1885, 2399, 2903, 3393,
    3867, 4324, 4761, 5177, 5571, 5939, 6282, 6599, 6887, 7147, 7377, 7579,
    7750, 7891, 8003, 8086, 8139, 8164, 8162, 8133, 8079, 8000, 7898, 7774,
    7630, 7467, 7287, 7092, 6882, 6659, 6426, 6183, 5932, 5675, 5412, 5146,
    4877, 4607, 4336, 4066, 3798, 3531, 3267, 3005, 2748, 2494, 2243, 1997,
    1754, 1514, 1278, 1045, 814, 585, 358, 131, -93, -319, -546, -774,
    -1003, -1235, -1469, -1706, -1947, -2190, -2437, -2688, -2942, -3199, -3459, -3721,
    -3985, -4251, -4516, -4781, -5045, -5306, -5563, -5815, -6060, -6298, -6526, -6744,
    -6949, -7140, -7316, -7475, -7616, -7737, -7836, -7913, -7966, -7994, -7997, -7972,
    -7920, -7840, -7732, -7594, -7428, -7232, -7008, -6756, -6476, -6169, -5836, -5479,
    -5098, -4694, -4271, -3828, -3369, -2894, -2407, -1909, -1403, -890, -374, 143,
    660, 1173, 1681, 2181, 2671, 3148, 3611, 4057, 4485, 4893, 5279, 5642,
    5981, 6293, 6580, 6838, 7069, 7271, 7445, 7590, 7706, 7793, 7853, 7884,
    7889, 7869, 7823, 7753, 7661, 7547, 7413, 7261, 7091, 6906, 6707, 6495,
    6272, 6040, 5800, 5553, 5300, 5044, 4785, 4524, 4263, 4001, 3741, 3483,
    3227, 2974, 2724, 2477, 2234, 1995, 1759, 1527, 1298, 1072, 848, 626,
    406, 188, -30, -248, -467, -686, -908, -1131, -1356, -1585, -1816, -2051,
    -2288, -2530, -2774, -3022, -3272, -3525, -3780, -4036, -4292, -4549, -4804, -5057,
    -5306, -5551, -5790, -6022, -6245, -6459, -6660, -6849, -7024, -7182, -7323, -7445,
    -7547, -7627, -7685, -7719, -7729, -7712, -7670, -7600, -7502, -7377, -7224, -7043,
    -6834, -6598, -6335, -6046, -5731, -5392, -5030, -4646, -4242, -3819, -3380, -2925,
    -2458, -1979, -1492, -998, -500, 0, 499, 996, 1489, 1974, 2450, 2915,
    3366, 3802, 4221, 4620, 4999, 5356, 5690, 5999, 6283, 6541, 6771, 6974,
    7150, 7297, 7417, 7509, 7574, 7612, 7624, 7611, 7573, 7512, 7429, 7324,
    7200, 7058, 6899, 6724, 6535, 6334, 6121, 5899, 5669, 5432, 5189, 4943,
    4693, 4441, 4189, 3936, 3685, 3434, 3186, 2941, 2698, 2459, 2224, 1991,
    1763, 1537, 1315, 1096, 879, 665, 452, 240, 29, -181, -392, -604,
    -817, -1032, -1250, -1470, -1692, -1918, -2147, -2379, -2614, -2853, -3094, -3338,
    -3583, -3831, -4078, -4326, -4573, -4818, -5060, -5298, -5531, -5757, -5975, -6184,
    -6383, -6569, -6741, -6898, -7039, -7163, -7267, -7350, -7412, -7452, -7467, -7459,
    -7425, -7364, -7278, -7164, -7024, -6857, -6662, -6441, -6194, -5922, -5624, -5303,
    -4959, -4594, -4209, -3805, -3385, -2950, -2501, -2042, -1573, -1097, -617, -134,
    348, 830, 1307, 1778, 2241, 2693, 3133, 3558, 3968, 4359, 4731, 5082,
    5411, 5716, 5997, 6253, 6483, 6687, 6864, 7014, 7137, 7233, 7303, 7347,
    7366, 7360, 7330, 7277, 7202, 7107, 6992, 6860, 6710, 6545, 6366, 6175,
    5972, 5760, 5540, 5313, 5080, 4842, 4602, 4359, 4115, 3871, 3628, 3385,
    3145, 2907, 2672, 2440, 2211, 1986, 1764, 1546, 1330, 1117, 907, 699,
    493, 289, 85, -118, -322, -527, -732, -940, -1149, -1361, -1575, -1792,
    -2013, -2236, -2463, -2692, -2925, -3159, -3396, -3635, -3874, -4114, -4353, -4590,
    -4825, -5056, -5282, -5503, -5716, -5920, -6115, -6298, -6468, -6625, -6765, -6889,
    -6995, -7082, -7147, -7192, -7213, -7212, -7185, -7134, -7058, -6955, -6827, -6673,
    -6492, -6286, -6054, -5797, -5516, -5212, -4886, -4539, -4172, -3787, -3385, -2968,
    -2538, -2097, -1646, -1189, -725, -259, 207, 673, 1135, 1592, 2042, 2482,
    2910, 3325, 3725, 4108, 4473, 4818, 5142, 5443, 5722, 5976, 6205, 6409,
    6587, 6739, 6866, 6966, 7040, 7090, 7115, 7115, 7092, 7047, 6981, 6894,
    6789, 6665, 6525, 6370, 6200, 6019, 5826, 5624, 5413, 5195, 4971, 4743,
    4511, 4277, 4042, 3806, 3570, 3336, 3103, 2873, 2645, 2420, 2198, 1979,
    1764, 1552, 1343, 1137, 933, 731, 532, 334, 136, -59, -256, -454,
    -652, -852, -1054, -1258, -1464, -1673, -1885, -2100, -2318, -2539, -2763, -2989,
    -3218, -3448, -3679, -3910, -4142, -4371, -4599, -4824, -5044, -5258, -5466, -5666,
    -5857, -6037, -6205, -6360, -6501, -6625, -6732, -6821, -6890, -6939, -6966, -6971,
    -6952, -6909, -6842, -6751, -6633, -6491, -6324, -6131, -5914, -5673, -5408, -5120,
    -4811, -4481, -4131, -3764, -3380, -2981, -2569, -2146, -1712, -1272, -826, -376,
    74, 525, 973, 1416, 1853, 2281, 2698, 3103, 3494, 3869, 4226, 4565,
    4883, 5181, 5456, 5708, 5936, 6140, 6319, 6473, 6602, 6706, 6785, 6840,
    6870, 6877, 6861, 6824, 6765, 6687, 6590, 6475, 6344, 6198, 6038, 5865,
    5682, 5489, 5287, 5078, 4864, 4644, 4421, 4196, 3968, 3741, 3513, 3286,
    3061, 2837, 2616, 2398, 2183, 1971, 1762, 1556, 1353, 1153, 956, 761,
    567, 375, 185, -5, -195, -385, -577, -769, -964, -1160, -1359, -1560,
    -1764, -1971, -2181, -2394, -2609, -2827, -3048, -3270, -3493, -3716, -3940, -4162,
    -4383, -4601, -4815, -5024, -5227, -5422, -5609, -5786, -5952, -6105, -6245, -6369,
    -6478, -6569, -6641, -6694, -6726, -6736, -6725, -6690, -6632, -6550, -6443, -6313,
    -6157, -5978, -5775, -5548, -5298, -5027, -4733, -4420, -4087, -3737, -3370, -2989,
    -2594, -2188, -1772, -1348, -918, -484, -48, 387, 820, 1250, 1674, 2090,
    2496, 2891, 3272, 3639, 3989, 4321, 4635, 4928, 5200, 5450, 5677, 5880,
    6060, 6216, 6347, 6454, 6537, 6596, 6632, 6645, 6636, 6605, 6554, 6484,
    6395, 6289, 6166, 6029, 5878, 5715, 5540, 5356, 5163, 4964, 4758, 4547,
    4332, 4115, 3895, 3675, 3455, 3236, 3017, 2801, 2587, 2375, 2166, 1961,
    1758, 1558, 1362, 1168, 976, 787, 600, 414, 230, 46, -137, -321,
    -506, -692, -879, -1068, -1259, -1453, -1650, -1849, -2051, -2256, -2463, -2673,
    -2885, -3099, -3315, -3531, -3747, -3962, -4176, -4387, -4595, -4798, -4996, -5187,
    -5370, -5544, -5707, -5859, -5998, -6122, -6232, -6324, -6399, -6455, -6492, -6508,
    -6503, -6475, -6426, -6353, -6256, -6137, -5993, -5827, -5637, -5424, -5189, -4932,
    -4654, -4357, -4040, -3707, -3357, -2992, -2614, -2224, -1824, -1417, -1003, -584,
    -164, 257, 676, 1093, 1504, 1908, 2304, 2688, 3061, 3419, 3762, 4088,
    4396, 4685, 4953, 5201, 5426, 5629, 5810, 5966, 6100, 6210, 6296, 6360,
    6401, 6419, 6416, 6392, 6348, 6285, 6204, 6106, 5992, 5863, 5721, 5567,
    5401, 5225, 5042, 4850, 4653, 4450, 4244, 4034, 3823, 3610, 3398, 3185,
    2974, 2764, 2557, 2352, 2149, 1949, 1753, 1559, 1368, 1180, 994, 811,
    630, 450, 271, 93, -83, -261, -439, -618, -799, -981, -1165, -1352,
    -1541, -1733, -1927, -2124, -2324, -2526, -2731, -2937, -3145, -3353, -3562, -3770,
    -3978, -4183, -4384, -4582, -4775, -4962, -5141, -5311, -5472, -5622, -5759, -5884,
    -5993, -6087, -6165, -6224, -6265, -6286, -6287, -6266, -6224, -6160, -6073, -5964,
    -5832, -5677, -5499, -5300, -5079, -4836, -4573, -4291, -3991, -3673, -3339, -2990,
    -2628, -2254, -1871, -1479, -1080, -677, -271, 135, 541, 945, 1344, 1736,
    2121, 2495, 2859, 3209, 3544, 3864, 4167, 4451, 4716, 4961, 5185, 5387,
    5567, 5725, 5860, 5973, 6063, 6130, 6176, 6199, 6202, 6185, 6148, 6092,
    6018, 5928, 5822, 5701, 5567, 5421, 5264, 5097, 4921, 4738, 4549, 4355,
    4156, 3954, 3751, 3545, 3340, 3134, 2930, 2727, 2526, 2327, 2130, 1937,
    1746, 1558, 1373, 1190, 1010, 833, 657, 483, 310, 138, -33, -204,
    -376, -549, -723, -899, -1076, -1256, -1438, -1622, -1809, -1999, -2192, -2386,
    -2583, -2782, -2983, -3184, -3386, -3587, -3788, -3986, -4182, -4375, -4563, -4745,
    -4920, -5087, -5245, -5393, -5529, -5653, -5763, -5858, -5937, -6000, -6044, -6070,
    -6076, -6062, -6027, -5971, -5894, -5794, -5672, -5529, -5363, -5177, -4968, -4740,
    -4491, -4224, -3938, -3635, -3317, -2984, -2638, -2280, -1911, -1535, -1151, -763,
    -371, 21, 414, 805, 1192, 1573, 1947, 2312, 2666, 3008, 3336, 3649,
    3946, 4226, 4488, 4730, 4952, 5153, 5333, 5491, 5628, 5743, 5836, 5907,
    5957, 5986, 5994, 5982, 5952, 5903, 5836, 5753, 5655, 5542, 5416, 5278,
    5129, 4970, 4803, 4628, 4447, 4260, 4069, 3875, 3679, 3481, 3282, 3084,
    2886, 2689, 2494, 2301, 2111, 1923, 1738, 1556, 1376, 1199, 1024, 852,
    682, 513, 346, 179, 13, -151, -317, -484, -652, -821, -992, -1165,
    -1340, -1518, -1698, -1881, -2066, -2253, -2443, -2635, -2828, -3022, -3217, -3412,
    -3606, -3799, -3989, -4176, -4359, -4536, -4707, -4871, -5026, -5172, -5307, -5430,
    -5540, -5636, -5717, -5782, -5830, -5860, -5871, -5863, -5835, -5787, -5717, -5627,
    -5516, -5383, -5229, -5054, -4859, -4643, -4408, -4155, -3884, -3596, -3292, -2974,
    -2643, -2300, -1947, -1585, -1216, -842, -464, -84, 295, 673, 1048, 1418,
    1781, 2137, 2482, 2816, 3137, 3444, 3735, 4010, 4268, 4507, 4727, 4927,
    5106, 5265, 5403, 5520, 5616, 5691, 5744, 5778, 5791, 5785, 5761, 5718,
    5659, 5583, 5492, 5387, 5268, 5138, 4997, 4846, 4686, 4519, 4346, 4167,
    3983, 3797, 3607, 3416, 3225, 3033, 2841, 2651, 2462, 2275, 2091, 1908,
    1729, 1552, 1377, 1206, 1036, 869, 704, 541, 379, 218, 57, -102,
    -262, -423, -585, -748, -912, -1079, -1248, -1419, -1592, -1768, -1946, -2127,
    -2309, -2494, -2680, -2868, -3056, -3245, -3432, -3619, -3803, -3985, -4163, -4336,
    -4503, -4663, -4816, -4959, -5092, -5215, -5325, -5421, -5504, -5571, -5622, -5656,
    -5672, -5669, -5647, -5606, -5545, -5463, -5361, -5239, -5096, -4932, -4749, -4546,
    -4324, -4084, -3827, -3553, -3264, -2960, -2643, -2315, -1976, -1629, -1275, -914,
    -550, -183, 183, 549, 912, 1271, 1625, 1970, 2306, 2632, 2946, 3246,
    3532, 3802, 4056, 4292, 4510, 4709, 4888, 5047, 5186, 5304, 5403, 5480,
    5538, 5576, 5594, 5593, 5575, 5538, 5485, 5416, 5332, 5234, 5123, 5001,
    4867, 4724, 4572, 4412, 4246, 4074, 3898, 3719, 3536, 3352, 3167, 2982,
    2797, 2612, 2429, 2248, 2069, 1892, 1718, 1546, 1377, 1211, 1047, 885,
    725, 566, 409, 254, 99, -55, -210, -365, -521, -679, -837, -998,
    -1160, -1324, -1491, -1661, -1832, -2006, -2182, -2360, -2540, -2721, -2902, -3084,
    -3266, -3447, -3626, -3802, -3975, -4143, -4307, -4463, -4613, -4754, -4886, -5007,
    -5117, -5214, -5297, -5366, -5420, -5457, -5477, -5480, -5464, -5430, -5376, -5303,
    -5210, -5097, -4964, -4811, -4640, -4449, -4239, -4012, -3768, -3508, -3232, -2943,
    -2640, -2326, -2002, -1668, -1327, -981, -630, -276, 78, 432, 784, 1133,
    1476, 1811, 2139, 2457, 2763, 3057, 3338, 3603, 3853, 4086, 4301, 4498,
    4676, 4836, 4975, 5095, 5196, 5276, 5337, 5379, 5402, 5406, 5393, 5363,
    5316, 5253, 5176, 5085, 4981, 4866, 4740, 4604, 4459, 4307, 4148, 3983,
    3814, 3642, 3466, 3289, 3110, 2931, 2752, 2573, 2396, 2221, 2047, 1876,
    1707, 1540, 1376, 1214, 1055, 898, 743, 589, 438, 287, 137, -12,
    -161, -311, -462, -613, -766, -921, -1077, -1235, -1396, -1559, -1724, -1891,
    -2061, -2232, -2406, -2580, -2756, -2931, -3107, -3282, -3455, -3626, -3795, -3959,
    -4118, -4271, -4418, -4556, -4686, -4806, -4915, -5013, -5097, -5168, -5224, -5264,
    -5289, -5296, -5286, -5257, -5211, -5145, -5060, -4957, -4834, -4692, -4531, -4351,
    -4154, -3939, -3708, -3461, -3199, -2922, -2633, -2333, -2022, -1702, -1375, -1041,
    -703, -362, -19, 323, 664, 1001, 1334, 1661, 1980, 2290, 2589, 2876,
    3151, 3412, 3657, 3887, 4100, 4295, 4472, 4631, 4772, 4893, 4995, 5078,
    5142, 5188, 5215, 5224, 5216, 5191, 5150, 5094, 5023, 4939, 4842, 4734,
    4614, 4485, 4348, 4203, 4051, 3893, 3731, 3565, 3396, 3225, 3053, 2880,
    2707, 2534, 2363, 2193, 2024, 1858, 1694, 1533, 1373, 1216, 1062, 910,
    759, 611, 463, 317, 172, 28, -116, -260, -406, -552, -699, -848,
    -998, -1151, -1305, -1462, -1621, -1782, -1946, -2111, -2278, -2446, -2615, -2785,
    -2955, -3124, -3292, -3458, -3622, -3778, -3928, -4071, -4207, -4336, -4457, -4567,
    -4668, -4757, -4833, -4897, -4946, -4981, -5001, -5005, -4992, -4962, -4915, -4851,
    -4769, -4670, -4552, -4418, -4266, -4097, -3912, -3711, -3495, -3265, -3021, -2765,
    -2498, -2221, -1935, -1641, -1341, -1035, -726, -415, -104, 206, 515, 821,
    1121, 1416, 1702, 1980, 2248, 2505, 2750, 2981, 3199, 3402, 3590, 3761,
    3917, 4055, 4177, 4282, 4369, 4439, 4493, 4530, 4550, 4555, 4544, 4519,
    4480, 4427, 4362, 4285, 4197, 4099, 3992, 3877, 3755, 3626, 3492, 3353,
    3211, 3065, 2917, 2768, 2618, 2468, 2318, 2169, 2021, 1875, 1730, 1588,
    1448, 1311, 1176, 1043, 913, 785, 660, 536, 414, 293, 174, 55,
    -62, -179, -296, -414, -532, -651, -771, -892, -1014, -1137, -1262, -1388,
    -1515, -1644, -1773, -1903, -2033, -2163, -2293, -2423, -2550, -2676, -2800, -2920,
    -3037, -3149, -3256, -3358, -3452, -3539, -3619, -3689, -3750, -3801, -3841, -3870,
    -3888, -3893, -3885, -3864, -3830, -3782, -3721, -3646, -3558, -3455, -3340, -3212,
    -3070, -2917, -2752, -2576, -2389, -2193, -1988, -1775, -1556, -1330, -1099, -864,
    -626, -387, -146, 92, 331, 566, 798, 1026, 1247, 1462, 1669, 1868,
    2058, 2237, 2406, 2564, 2710, 2843, 2964, 3073, 3168, 3250, 3319, 3375,
    3418, 3448, 3465, 3471, 3464, 3446, 3418, 3379, 3330, 3273, 3207, 3133,
    3053, 2965, 2873, 2775, 2673, 2568, 2459, 2349, 2236, 2123, 2009, 1894,
    1780, 1666, 1554, 1443, 1333, 1225, 1118, 1014, 911, 811, 712, 616,
    521, 427, 335, 244, 155, 66, -21, -109, -197, -285, -373, -461,
    -550, -639, -729, -821, -913, -1005, -1099, -1194, -1289, -1384, -1480, -1576,
    -1671, -1766, -1860, -1952, -2043, -2132, -2217, -2300, -2378, -2453, -2522, -2586,
    -2645, -2697, -2742, -2780, -2810, -2832, -2845, -2850, -2845, -2831, -2807, -2773,
    -2729, -2676, -2612, -2539, -2456, -2363, -2262, -2151, -2032, -1905, -1771, -1630,
    -1482, -1328, -1170, -1007, -840, -671, -499, -327, -153, 18, 190, 360,
    527, 691, 851, 1006, 1155, 1298, 1435, 1564, 1686, 1799, 1904, 2001,
    2088, 2166, 2235, 2294, 2344, 2384, 2415, 2437, 2450, 2455, 2450, 2438,
    2418, 2391, 2356, 2316, 2269, 2217, 2160, 2098, 2032, 1963, 1891, 1816,
    1740, 1661, 1582, 1502, 1421, 1340, 1259, 1179, 1100, 1022, 944, 868,
    794, 720, 649, 578, 509, 442, 376, 311, 247, 185, 123, 62,
    1, -58, -118, -177, -237, -297, -357, -417, -478, -539, -601, -663,
    -725, -788, -851, -915, -978, -1041, -1105, -1167, -1229, -1290, -1350, -1408,
    -1464, -1518, -1569, -1618, -1663, -1705, -1743, -1777, -1806, -1830, -1849, -1863,
    -1871, -1873, -1870, -1860, -1844, -1821, -1792, -1757, -1715, -1667, -1613, -1552,
    -1486, -1414, -1337, -1254, -1167, -1076, -980, -881, -779, -675, -568, -459,
    -349, -239, -128, -18, 90, 198, 304, 408, 509, 607, 701, 791,
    877, 958, 1034, 1105, 1170, 1230, 1284, 1332, 1374, 1410, 1440, 1464,
    1483, 1495, 1502, 1504, 1500, 1492, 1478, 1460, 1438, 1412, 1382, 1349,
    1313, 1274, 1233, 1190, 1145, 1098, 1051, 1003, 953, 904, 855, 805,
    756, 707, 659, 612, 565, 519, 474, 431, 388, 346, 305, 265,
    227, 189, 152, 115, 80, 45, 10, -23, -57, -90, -124, -157,
    -190, -223, -257, -290, -323, -357, -390, -424, -457, -491, -524, -557,
    -590, -622, -654, -685, -716, -745, -773, -800, -825, -849, -871, -891,
    -909, -924, -937, -948, -955, -960, -962, -961, -957, -949, -939, -925,
    -908, -888, -865, -839, -810, -778, -743, -706, -666, -624, -580, -534,
    -486, -437, -387, -335, -283, -231, -179, -126, -74, -22, 28, 77,
    126, 173, 218, 262, 303, 343, 380, 414, 446, 476, 503, 527,
    548, 566, 582, 594, 604, 612, 617, 619, 619, 616, 611, 604,
    596, 585, 573, 559, 544, 528, 510, 492, 473, 454, 433, 413,
    392, 372, 351, 330, 310, 290, 270, 250, 231, 213, 195, 178,
    161, 145, 130, 115, 100, 87, 74, 61, 49, 37, 26, 16,
    5, -4, -13, -22, -31, -40, -48, -56, -63, -71, -78, -85,
    -91, -98, -104, -109, -115, -120, -124, -128, -132, -135, -138, -140,
    -142, -143, -143, -143, -142, -141, -139, -137, -133, -130, -126, -121,
    -116, -110, -104, -97, -90, -83, -76, -69, -61, -54, -47, -39,
    -33, -26, -20, -14, -8, -4,
};
const size_t prompt_bt_disconnected_len = 13230;

const int16_t prompt_low_battery[] = {
    0, 3, 14, 31, 56, 87, 124, 168, 218, 273, 334, 400,
    470, 544, 621, 702, 785, 870, 956, 1044, 1132, 1220, 1307, 1393,
    1477, 1559, 1639, 1715, 1788, 1857, 1922, 1983, 2038, 2088, 2133, 2173,
    2206, 2234, 2256, 2272, 2282, 2286, 2284, 2276, 2263, 2244, 2219, 2189,
    2155, 2115, 2071, 2022, 1970, 1913, 1853, 1789, 1722, 1652, 1579, 1504,
    1426, 1346, 1263, 1179, 1092, 1004, 914, 822, 728, 632, 534, 434,
    331, 226, 119, 9, -103, -219, -338, -461, -587, -718, -852, -991,
    -1135, -1282, -1435, -1593, -1755, -1923, -2095, -2272, -2454, -2641, -2832, -3028,
    -3227, -3430, -3636, -3845, -4056, -4269, -4483, -4697, -4910, -5123, -5333, -5540,
    -5743, -5942, -6134, -6320, -6497, -6666, -6824, -6972, -7107, -7229, -7336, -7428,
    -7504, -7562, -7602, -7623, -7624, -7605, -7564, -7501, -7416, -7308, -7177, -7023,
    -6845, -6643, -6418, -6169, -5898, -5603, -5287, -4949, -4590, -4212, -3814, -3398,
    -2965, -2517, -2054, -1578, -1091, -594, -88, 424, 941, 1462, 1985, 2508,
    3029, 3546, 4058, 4563, 5059, 5544, 6018, 6477, 6922, 7350, 7759, 8150,
    8520, 8869, 9194, 9497, 9775, 10029, 10257, 10459, 10635, 10785, 10908, 11005,
    11075, 11120, 11139, 11133, 11102, 11048, 10970, 10870, 10749, 10607, 10446, 10266,
    10069, 9856, 9628, 9386, 9132, 8866, 8590, 8305, 8012, 7712, 7406, 7095,
    6781, 6463, 6142, 5821, 5498, 5175, 4851, 4529, 4207, 3886, 3566, 3247,
    2929, 2613, 2297, 1982, 1667, 1349, 1030, 713, 397, 82, -232, -547,
    -863, -1180, -1499, -1820, -2144, -2471, -2802, -3136, -3474, -3816, -4162, -4512,
    -4866, -5224, -5585, -5948, -6315, -6683, -7052, -7422, -7791, -8159, -8524, -8885,
    -9242, -9593, -9936, -10270, -10594, -10907, -11206, -11491, -11759, -12010, -12241, -12452,
    -12641, -12806, -12947, -13061, -13148, -13206, -13235, -13233, -13199, -13134, -13036, -12905,
    -12740, -12541, -12308, -12042, -11742, -11409, -11043, -10645, -10216, -9756, -9267, -8750,
    -8207, -7638, -7046, -6432, -5797, -5145, -4477, -3794, -3100, -2396, -1685, -969,
    -249, 469, 1187, 1900, 2607, 3305, 3992, 4665, 5324, 5965, 6587, 7187,
    7765, 8318, 8845, 9345, 9816, 10257, 10667, 11045, 11392, 11705, 11985, 12231,
    12444, 12623, 12769, 12881, 12961, 13009, 13025, 13010, 12966, 12893, 12792, 12665,
    12513, 12337, 12139, 11919, 11680, 11423, 11150, 10861, 10559, 10245, 9920, 9585,
    9243, 8895, 8541, 8184, 7824, 7461, 7099, 6736, 6374, 6014, 5657, 5302,
    4951, 4603, 4259, 3920, 3585, 3254, 2927, 2604, 2285, 1970, 1658, 1349,
    1042, 737, 433, 131, -170, -473, -776, -1080, -1386, -1694, -2004, -2318,
    -2634, -2954, -3278, -3606, -3937, -4273, -4612, -4955, -5300, -5649, -6001, -6354,
    -6708, -7063, -7418, -7771, -8122, -8470, -8813, -9151, -9481, -9804, -10117, -10419,
    -10708, -10984, -11245, -11488, -11714, -11920, -12105, -12268, -12407, -12521, -12609, -12669,
    -12702, -12705, -12679, -12621, -12533, -12412, -12259, -12074, -11857, -11607, -11324, -11010,
    -10664, -10287, -9880, -9444, -8980, -8488, -7971, -7429, -6864, -6278, -5672, -5049,
    -4410, -3757, -3092, -2418, -1736, -1049, -359, 330, 1020, 1705, 2385, 3057,
    3718, 4367, 5002, 5620, 6221, 6801, 7359, 7894, 8405, 8889, 9346, 9774,
    10173, 10542, 10880, 11186, 11461, 11703, 11913, 12090, 12235, 12349, 12431, 12482,
    12503, 12494, 12456, 12391, 12299, 12181, 12039, 11874, 11687, 11480, 11254, 11010,
    10750, 10475, 10187, 9887, 9577, 9258, 8931, 8597, 8259, 7916, 7571, 7223,
    6875, 6527, 6179, 5833, 5490, 5149, 4811, 4476, 4146, 3819, 3497, 3178,
    2864, 2554, 2247, 1944, 1643, 1346, 1051, 758, 467, 176, -113, -403,
    -694, -986, -1279, -1574, -1872, -2172, -2476, -2782, -3093, -3407, -3724, -4045,
    -4370, -4699, -5030, -5365, -5702, -6040, -6380, -6721, -7061, -7401, -7738, -8073,
    -8403, -8728, -9047, -9358, -9660, -9952, -10232, -10499, -10752, -10989, -11209, -11410,
    -11591, -11751, -11888, -12002, -12091, -12154, -12190, -12198, -12178, -12128, -12048, -11937,
    -11796, -11624, -11420, -11186, -10920, -10624, -10297, -9940, -9555, -9141, -8699, -8232,
    -7739, -7223, -6685, -6126, -5547, -4952, -4341, -3716, -3080, -2434, -1781, -1122,
    -460, 202, 864, 1523, 2177, 2823, 3460, 4085, 4697, 5294, 5873, 6433,
    6973, 7491, 7985, 8454, 8898, 9314, 9702, 10061, 10390, 10689, 10958, 11196,
    11403, 11579, 11724, 11838, 11922, 11976, 12001, 11997, 11966, 11907, 11823, 11715,
    11582, 11428, 11252, 11056, 10842, 10611, 10364, 10103, 9828, 9542, 9246, 8941,
    8628, 8309, 7985, 7656, 7325, 6992, 6658, 6323, 5990, 5657, 5327, 4999,
    4674, 4353, 4035, 3720, 3410, 3104, 2801, 2503, 2208, 1916, 1627, 1342,
    1058, 776, 496, 217, -60, -339, -618, -898, -1179, -1462, -1747, -2035,
    -2326, -2620, -2917, -3218, -3522, -3830, -4141, -4456, -4773, -5094, -5417, -5742,
    -6068, -6395, -6722, -7048, -7372, -7694, -8012, -8325, -8632, -8932, -9224, -9506,
    -9777, -10035, -10281, -10511, -10724, -10921, -11098, -11255, -11391, -11504, -11594, -11659,
    -11698, -11710, -11695, -11652, -11581, -11480, -11350, -11189, -10999, -10779, -10529, -10250,
    -9941, -9604, -9238, -8845, -8426, -7982, -7513, -7022, -6508, -5975, -5423, -4854,
    -4270, -3672, -3064, -2445, -1819, -1187, -552, 83, 719, 1353, 1981, 2603,
    3216, 3818, 4408, 4983, 5542, 6084, 6605, 7106, 7584, 8039, 8469, 8873,
    9250, 9600, 9921, 10214, 10477, 10710, 10914, 11088, 11232, 11347, 11432, 11489,
    11518, 11519, 11494, 11442, 11366, 11265, 11142, 10997, 10832, 10648, 10445, 10226,
    9991, 9743, 9481, 9209, 8926, 8634, 8335, 8030, 7719, 7405, 7087, 6768,
    6447, 6126, 5805, 5486, 5169, 4853, 4541, 4232, 3926, 3624, 3325, 3030,
    2739, 2452, 2168, 1888, 1610, 1335, 1063, 792, 523, 255, -11, -279,
    -547, -815, -1085, -1356, -1630, -1905, -2184, -2466, -2750, -3038, -3330, -3625,
    -3923, -4225, -4529, -4836, -5146, -5458, -5771, -6084, -6398, -6712, -7023, -7333,
    -7638, -7940, -8236, -8525, -8806, -9079, -9341, -9591, -9829, -10052, -10261, -10452,
    -10625, -10780, -10914, -11026, -11116, -11183, -11225, -11241, -11231, -11195, -11131, -11039,
    -10919, -10770, -10593, -10386, -10151, -9888, -9596, -9277, -8931, -8559, -8161, -7738,
    -7292, -6824, -6335, -5826, -5299, -4756, -4197, -3626, -3043, -2451, -1851, -1245,
    -636, -25, 585, 1193, 1797, 2396, 2986, 3566, 4134, 4689, 5228, 5751,
    6255, 6740, 7203, 7643, 8060, 8452, 8819, 9159, 9472, 9758, 10015, 10244,
    10445, 10617, 10760, 10875, 10962, 11022, 11054, 11059, 11039, 10994, 10925, 10833,
    10718, 10583, 10427, 10253, 10062, 9854, 9631, 9395, 9146, 8886, 8616, 8338,
    8052, 7760, 7462, 7161, 6857, 6550, 6242, 5934, 5626, 5319, 5014, 4711,
    4411, 4114, 3819, 3529, 3241, 2958, 2678, 2402, 2129, 1859, 1592, 1328,
    1066, 805, 547, 289, 33, -223, -480, -738, -996, -1256, -1519, -1783,
    -2050, -2320, -2592, -2868, -3148, -3430, -3716, -4005, -4297, -4591, -4888, -5187,
    -5487, -5789, -6090, -6391, -6690, -6988, -7282, -7572, -7857, -8136, -8407, -8671,
    -8924, -9166, -9397, -9614, -9816, -10003, -10172, -10324, -10456, -10568, -10658, -10725,
    -10770, -10790, -10785, -10755, -10698, -10614, -10504, -10366, -10200, -10007, -9786, -9538,
    -9263, -8961, -8633, -8280, -7902, -7500, -7076, -6630, -6164, -5679, -5176, -4657,
    -4123, -3577, -3019, -2452, -1877, -1297, -712, -126, 459, 1044, 1625, 2200,
    2768, 3327, 3875, 4410, 4930, 5435, 5922, 6390, 6839, 7265, 7670, 8050,
    8407, 8738, 9043, 9322, 9573, 9798, 9995, 10165, 10308, 10423, 10511, 10572,
    10608, 10617, 10602, 10563, 10501, 10416, 10310, 10183, 10037, 9873, 9692, 9495,
    9284, 9059, 8822, 8574, 8317, 8051, 7778, 7498, 7213, 6925, 6633, 6339,
    6044, 5748, 5452, 5157, 4864, 4573, 4284, 3998, 3715, 3436, 3159, 2886,
    2617, 2351, 2089, 1829, 1572, 1318, 1066, 816, 568, 321, 74, -171,
    -418, -665, -913, -1163, -1414, -1667, -1923, -2182, -2443, -2707, -2975, -3245,
    -3519, -3796, -4076, -4358, -4643, -4929, -5218, -5506, -5796, -6085, -6373, -6658,
    -6941, -7221, -7495, -7764, -8026, -8280, -8525, -8760, -8983, -9194, -9390, -9572,
    -9738, -9886, -10017, -10127, -10217, -10286, -10333, -10356, -10356, -10331, -10281, -10205,
    -10103, -9975, -9821, -9640, -9433, -9199, -8940, -8654, -8344, -8009, -7650, -7269,
    -6865, -6440, -5996, -5533, -5054, -4558, -4048, -3525, -2992, -2449, -1898, -1342,
    -781, -219, 343, 905, 1463, 2017, 2563, 3101, 3629, 4145, 4647, 5134,
    5605, 6058, 6491, 6905, 7297, 7666, 8012, 8334, 8632, 8904, 9150, 9370,
    9564, 9732, 9873, 9988, 10077, 10141, 10179, 10192, 10182, 10148, 10092, 10014,
    9916, 9798, 9661, 9506, 9335, 9149, 8948, 8735, 8509, 8273, 8027, 7773,
    7512, 7245, 6972, 6696, 6416, 6134, 5851, 5567, 5283, 5000, 4718, 4438,
    4161, 3886, 3613, 3344, 3079, 2816, 2557, 2301, 2049, 1799, 1552, 1308,
    1066, 825, 587, 349, 112, -123, -360, -597, -835, -1074, -1315, -1558,
    -1803, -2051, -2301, -2555, -2811, -3070, -3332, -3598, -3866, -4136, -4409, -4684,
    -4960, -5238, -5515, -5793, -6069, -6344, -6617, -6885, -7150, -7409, -7662, -7907,
    -8144, -8371, -8587, -8791, -8983, -9160, -9322, -9467, -9595, -9705, -9795, -9864,
    -9913, -9939, -9943, -9923, -9879, -9811, -9718, -9599, -9455, -9286, -9092, -8872,
    -8627, -8357, -8063, -7746, -7405, -7043, -6659, -6255, -5831, -5390, -4932, -4459,
    -3972, -3472, -2962, -2442, -1915, -1381, -844, -304, 236, 775, 1312, 1844,
    2370, 2888, 3396, 3894, 4378, 4848, 5303, 5741, 6161, 6561, 6941, 7299,
    7635, 7949, 8238, 8504, 8744, 8960, 9151, 9316, 9456, 9571, 9660, 9726,
    9767, 9784, 9778, 9749, 9699, 9628, 9537, 9426, 9298, 9152, 8991, 8814,
    8624, 8421, 8207, 7982, 7747, 7505, 7255, 7000, 6739, 6474, 6206, 5936,
    5664, 5391, 5119, 4847, 4576, 4307, 4040, 3776, 3514, 3255, 2999, 2747,
    2498, 2251, 2008, 1768, 1531, 1296, 1063, 832, 603, 375, 147, -79,
    -306, -534, -762, -991, -1222, -1455, -1690, -1927, -2167, -2410, -2655, -2904,
    -3155, -3409, -3666, -3926, -4187, -4451, -4716, -4982, -5248, -5515, -5780, -6045,
    -6306, -6565, -6820, -7069, -7313, -7550, -7779, -7998, -8208, -8406, -8592, -8764,
    -8922, -9065, -9191, -9299, -9389, -9459, -9509, -9538, -9546, -9531, -9493, -9431,
    -9346, -9236, -9102, -8944, -8762, -8555, -8324, -8069, -7791, -7490, -7167, -6823,
    -6458, -6073, -5670, -5249, -4812, -4360, -3895, -3417, -2929, -2431, -1926, -1415,
    -900, -382, 136, 654, 1170, 1682, 2188, 2687, 3176, 3656, 4123, 4577,
    5016, 5439, 5845, 6233, 6601, 6949, 7275, 7580, 7862, 8121, 8356, 8567,
    8754, 8917, 9056, 9170, 9260, 9327, 9370, 9391, 9389, 9365, 9320, 9256,
    9171, 9069, 8948, 8811, 8659, 8492, 8312, 8119, 7915, 7700, 7477, 7245,
    7007, 6762, 6513, 6259, 6002, 5743, 5482, 5221, 4959, 4698, 4438, 4179,
    3923, 3668, 3417, 3168, 2922, 2679, 2439, 2202, 1968, 1737, 1509, 1283,
    1059, 837, 617, 398, 179, -38, -256, -474, -693, -913, -1135, -1358,
    -1583, -1810, -2040, -2273, -2508, -2746, -2987, -3230, -3476, -3725, -3976, -4228,
    -4483, -4738, -4994, -5250, -5505, -5759, -6010, -6259, -6505, -6745, -6980, -7209,
    -7430, -7642, -7845, -8037, -8218, -8386, -8540, -8679, -8803, -8910, -8999, -9070,
    -9122, -9153, -9164, -9153, -9120, -9065, -8987, -8886, -8762, -8614, -8443, -8248,
    -8031, -7790, -7527, -7242, -6935, -6608, -6261, -5895, -5511, -5110, -4693, -4262,
    -3817, -3361, -2894, -2417, -1934, -1444, -950, -453, 44, 542, 1038, 1530,
    2016, 2497, 2968, 3430, 3881, 4319, 4743, 5152, 5545, 5920, 6277, 6614,
    6931, 7227, 7501, 7754, 7984, 8190, 8374, 8534, 8672, 8785, 8876, 8944,
    8989, 9013, 9015, 8996, 8956, 8897, 8819, 8724, 8611, 8482, 8339, 8181,
    8010, 7827, 7632, 7428, 7215, 6994, 6767, 6533, 6294, 6051, 5805, 5557,
    5306, 5055, 4804, 4553, 4304, 4055, 3808, 3564, 3322, 3082, 2845, 2612,
    2381, 2153, 1928, 1706, 1486, 1269, 1054, 841, 629, 418, 208, 0,
    -209, -419, -629, -840, -1052, -1266, -1482, -1700, -1920, -2143, -2368, -2596,
    -2827, -3060, -3296, -3534, -3775, -4017, -4261, -4506, -4751, -4997, -5242, -5486,
    -5728, -5967, -6203, -6435, -6662, -6882, -7096, -7301, -7498, -7684, -7859, -8023,
    -8173, -8310, -8431, -8537, -8625, -8696, -8749, -8783, -8797, -8790, -8762, -8713,
    -8642, -8549, -8433, -8296, -8135, -7952, -7747, -7520, -7271, -7001, -6710, -6400,
    -6070, -5721, -5356, -4974, -4576, -4164, -3740, -3303, -2856, -2401, -1937, -1468,
    -994, -518, -40, 437, 914, 1387, 1855, 2317, 2771, 3217, 3651, 4074,
    4484, 4879, 5258, 5622, 5967, 6294, 6602, 6890, 7157, 7403, 7627, 7830,
    8010, 8168, 8303, 8416, 8507, 8576, 8623, 8650, 8655, 8640, 8605, 8552,
    8481, 8392, 8286, 8165, 8030, 7880, 7718, 7544, 7360, 7166, 6963, 6752,
    6534, 6311, 6082, 5850, 5614, 5376, 5136, 4895, 4654, 4413, 4173, 3934,
    3697, 3462, 3229, 2998, 2771, 2546, 2324, 2105, 1888, 1675, 1463, 1254,
    1047, 842, 639, 436, 235, 34, -166, -367, -569, -771, -975, -1180,
    -1386, -1595, -1806, -2020, -2235, -2454, -2675, -2898, -3124, -3353, -3583, -3815,
    -4049, -4284, -4520, -4756, -4991, -5226, -5458, -5689, -5916, -6139, -6358, -6570,
    -6777, -6975, -7165, -7346, -7516, -7675, -7822, -7955, -8074, -8178, -8266, -8338,
    -8391, -8427, -8443, -8440, -8417, -8374, -8309, -8224, -8117, -7988, -7838, -7666,
    -7472, -7258, -7023, -6767, -6491, -6196, -5883, -5552, -5203, -4839, -4460, -4067,
    -3661, -3244, -2817, -2381, -1938, -1488, -1034, -577, -118, 340, 798, 1253,
    1703, 2148, 2585, 3014, 3433, 3841, 4237, 4619, 4986, 5337, 5672, 5989,
    6288, 6567, 6827, 7067, 7286, 7484, 7661, 7816, 7950, 8062, 8153, 8223,
    8272, 8300, 8309, 8298, 8268, 8220, 8154, 8072, 7973, 7860, 7732, 7591,
    7437, 7272, 7097, 6912, 6718, 6517, 6309, 6095, 5877, 5654, 5428, 5200,
    4970, 4739, 4508, 4276, 4046, 3816, 3588, 3362, 3138, 2917, 2698, 2481,
    2268, 2057, 1849, 1643, 1440, 1239, 1040, 843, 647, 453, 259, 66,
    -126, -319, -512, -706, -901, -1098, -1296, -1496, -1699, -1903, -2110, -2319,
    -2531, -2745, -2961, -3180, -3401, -3624, -3848, -4073, -4300, -4526, -4752, -4977,
    -5201, -5423, -5641, -5857, -6067, -6272, -6471, -6663, -6847, -7022, -7188, -7342,
    -7485, -7615, -7732, -7834, -7922, -7993, -8048, -8085, -8104, -8104, -8086, -8047,
    -7989, -7910, -7811, -7691, -7550, -7389, -7207, -7005, -6782, -6540, -6279, -5999,
    -5701, -5386, -5054, -4707, -4346, -3971, -3583, -3185, -2776, -2359, -1934, -1504,
    -1068, -630, -190, 250, 690, 1127, 1560, 1988, 2409, 2823, 3227, 3620,
    4002, 4371, 4726, 5066, 5390, 5697, 5987, 6259, 6512, 6745, 6959, 7153,
    7326, 7478, 7610, 7722, 7813, 7883, 7934, 7965, 7976, 7969, 7943, 7900,
    7840, 7763, 7671, 7565, 7444, 7311, 7166, 7009, 6842, 6666, 6482, 6290,
    6092, 5887, 5678, 5465, 5249, 5030, 4810, 4588, 4366, 4144, 3922, 3701,
    3482, 3265, 3050, 2837, 2626, 2418, 2212, 2009, 1809, 1611, 1416, 1222,
    1031, 842, 654, 467, 281, 95, -89, -274, -459, -646, -833, -1021,
    -1211, -1403, -1597, -1793, -1991, -2191, -2394, -2599, -2807, -3016, -3228, -3441,
    -3656, -3873, -4090, -4307, -4524, -4741, -4956, -5169, -5379, -5586, -5789, -5987,
    -6180, -6365, -6543, -6713, -6873, -7023, -7162, -7290, -7404, -7505, -7591, -7662,
    -7717, -7756, -7778, -7781, -7766, -7733, -7680, -7608, -7516, -7404, -7273, -7121,
    -6950, -6759, -6549, -6320, -6072, -5806, -5523, -5224, -4908, -4578, -4233, -3875,
    -3505, -3124, -2734, -2335, -1928, -1516, -1098, -678, -255, 167, 589, 1009,
    1426, 1837, 2243, 2641, 3031, 3410, 3779, 4135, 4478, 4807, 5121, 5419,
    5700, 5964, 6210, 6438, 6646, 6835, 7005, 7155, 7285, 7395, 7486, 7557,
    7609, 7642, 7656, 7652, 7631, 7592, 7537, 7466, 7381, 7281, 7167, 7041,
    6904, 6755, 6597, 6429, 6254, 6071, 5881, 5686, 5486, 5282, 5075, 4865,
    4654, 4441, 4228, 4015, 3802, 3590, 3379, 3170, 2963, 2758, 2556, 2355,
    2158, 1963, 1770, 1580, 1391, 1206, 1022, 839, 659, 479, 300, 122,
    -54, -232, -410, -589, -768, -949, -1131, -1315, -1500, -1688, -1878, -2070,
    -2264, -2461, -2659, -2860, -3063, -3268, -3474, -3681, -3890, -4098, -4307, -4515,
    -4721, -4926, -5129, -5328, -5524, -5715, -5900, -6080, -6252, -6416, -6572, -6718,
    -6853, -6977, -7089, -7188, -7274, -7345, -7400, -7440, -7464, -7470, -7459, -7430,
    -7383, -7317, -7232, -7128, -7005, -6863, -6702, -6522, -6323, -6106, -5872, -5619,
    -5351, -5066, -4765, -4450, -4122, -3780, -3427, -3063, -2690, -2308, -1919, -1524,
    -1124, -721, -316, 89, 495, 899, 1299, 1696, 2086, 2470, 2845, 3211,
    3567, 3911, 4243, 4561, 4865, 5154, 5427, 5683, 5922, 6143, 6347, 6531,
    6698, 6845, 6973, 7082, 7173, 7244, 7297, 7332, 7348, 7348, 7330, 7296,
    7245, 7180, 7100, 7007, 6900, 6781, 6651, 6510, 6360, 6200, 6033, 5859,
    5678, 5491, 5300, 5105, 4907, 4706, 4503, 4299, 4094, 3889, 3685, 3481,
    3279, 3078, 2879, 2682, 2487, 2294, 2104, 1916, 1731, 1548, 1367, 1188,
    1011, 836, 662, 490, 318, 147, -22, -193, -364, -535, -707, -881,
    -1055, -1231, -1409, -1589, -1771, -1955, -2141, -2329, -2520, -2712, -2907, -3103,
    -3301, -3499, -3699, -3899, -4100, -4299, -4498, -4695, -4890, -5082, -5271, -5455,
    -5634, -5807, -5973, -6133, -6283, -6425, -6557, -6678, -6788, -6885, -6969, -7040,
    -7096, -7137, -7162, -7171, -7163, -7139, -7096, -7036, -6958, -6861, -6746, -6613,
    -6462, -6292, -6104, -5899, -5677, -5438, -5182, -4911, -4626, -4326, -4012, -3687,
    -3350, -3002, -2645, -2280, -1908, -1529, -1146, -760, -371, 18, 408, 796,
    1181, 1562, 1938, 2307, 2669, 3022, 3366, 3698, 4019, 4326, 4621, 4900,
    5165, 5414, 5646, 5862, 6060, 6240, 6403, 6547, 6674, 6782, 6872, 6943,
    6997, 7034, 7053, 7055, 7040, 7010, 6965, 6905, 6830, 6743, 6642, 6530,
    6407, 6274, 6131, 5979, 5820, 5653, 5481, 5303, 5120, 4933, 4743, 4551,
    4356, 4161, 3964, 3768, 3571, 3376, 3181, 2988, 2797, 2607, 2420, 2234,
    2051, 1871, 1692, 1516, 1342, 1170, 1000, 832, 665, 499, 334, 170,
    6, -157, -321, -485, -650, -816, -984, -1152, -1323, -1495, -1669, -1846,
    -2024, -2204, -2387, -2571, -2758, -2946, -3135, -3326, -3518, -3710, -3902, -4094,
    -4285, -4474, -4662, -4847, -5028, -5206, -5379, -5546, -5707, -5861, -6007, -6145,
    -6273, -6391, -6498, -6594, -6677, -6747, -6803, -6845, -6872, -6884, -6879, -6858,
    -6820, -6766, -6693, -6604, -6497, -6372, -6229, -6069, -5892, -5698, -5488, -5261,
    -5018, -4761, -4489, -4203, -3905, -3594, -3272, -2940, -2599, -2250, -1894, -1531,
    -1164, -794, -421, -47, 326, 699, 1070, 1436, 1798, 2154, 2503, 2843,
    3174, 3495, 3805, 4103, 4387, 4658, 4915, 5156, 5382, 5592, 5785, 5962,
    6121, 6262, 6387, 6493, 6583, 6655, 6709, 6747, 6768, 6773, 6762, 6736,
    6694, 6639, 6570, 6488, 6394, 6288, 6172, 6045, 5910, 5766, 5614, 5455,
    5291, 5120, 4946, 4767, 4585, 4401, 4215, 4027, 3838, 3650, 3461, 3273,
    3086, 2901, 2717, 2534, 2354, 2176, 2000, 1826, 1654, 1485, 1317, 1152,
    988, 826, 666, 506, 348, 190, 33, -123, -280, -438, -597, -756,
    -916, -1078, -1241, -1406, -1573, -1742, -1913, -2086, -2261, -2437, -2616, -2796,
    -2978, -3161, -3345, -3529, -3714, -3898, -4082, -4264, -4444, -4622, -4797, -4968,
    -5135, -5296, -5452, -5601, -5743, -5876, -6001, -6116, -6221, -6315, -6397, -6466,
    -6523, -6565, -6594, -6607, -6606, -6588, -6555, -6505, -6439, -6356, -6255, -6139,
    -6005, -5854, -5687, -5504, -5304, -5089, -4859, -4614, -4356, -4084, -3799, -3503,
    -3196, -2879, -2553, -2219, -1878, -1531, -1179, -824, -466, -107, 251, 609,
    965, 1318, 1666, 2009, 2345, 2673, 2993, 3303, 3602, 3890, 4165, 4428,
    4676, 4911, 5130, 5334, 5523, 5695, 5850, 5989, 6111, 6217, 6305, 6377,
    6433, 6472, 6495, 6502, 6494, 6471, 6434, 6383, 6319, 6243, 6154, 6055,
    5945, 5825, 5696, 5559, 5415, 5264, 5107, 4944, 4777, 4606, 4432, 4255,
    4077, 3897, 3716, 3535, 3354, 3173, 2994, 2815, 2638, 2463, 2290, 2118,
    1949, 1781, 1616, 1453, 1292, 1133, 976, 820, 666, 513, 360, 209,
    58, -92, -243, -394, -546, -699, -853, -1008, -1164, -1322, -1482, -1644,
    -1808, -1973, -2141, -2310, -2481, -2654, -2828, -3004, -3180, -3357, -3534, -3711,
    -3888, -4063, -4236, -4408, -4576, -4741, -4902, -5058, -5208, -5352, -5490, -5619,
    -5741, -5853, -5955, -6047, -6128, -6197, -6253, -6296, -6326, -6341, -6342, -6328,
    -6299, -6254, -6193, -6116, -6023, -5913, -5788, -5646, -5488, -5315, -5126, -4922,
    -4704, -4471, -4225, -3966, -3695, -3413, -3120, -2817, -2505, -2186, -1860, -1528,
    -1191, -850, -507, -163, 181, 525, 867, 1207, 1542, 1872, 2195, 2512,
    2820, 3119, 3408, 3687, 3953, 4208, 4449, 4676, 4889, 5088, 5271, 5439,
    5591, 5727, 5848, 5952, 6039, 6111, 6167, 6207, 6232, 6242, 6236, 6217,
    6184, 6137, 6078, 6006, 5924, 5830, 5726, 5612, 5490, 5360, 5223, 5079,
    4929, 4774, 4614, 4450, 4284, 4115, 3944, 3771, 3598, 3424, 3250, 3076,
    2904, 2732, 2562, 2393, 2227, 2062, 1899, 1738, 1579, 1422, 1267, 1114,
    963, 813, 665, 518, 371, 226, 81, -63, -208, -353, -499, -645,
    -793, -941, -1091, -1243, -1396, -1551, -1708, -1867, -2027, -2189, -2353, -2519,
    -2686, -2854, -3023, -3193, -3363, -3533, -3703, -3871, -4038, -4203, -4365, -4524,
    -4679, -4830, -4975, -5115, -5248, -5373, -5491, -5600, -5700, -5790, -5870, -5938,
    -5994, -6038, -6069, -6086, -6089, -6078, -6053, -6012, -5956, -5885, -5798, -5696,
    -5578, -5445, -5296, -5132, -4953, -4760, -4553, -4332, -4098, -3851, -3593, -3324,
    -3044, -2755, -2458, -2152, -1840, -1522, -1200, -873, -544, -214, 116, 447,
    776, 1102, 1424, 1742, 2054, 2359, 2656, 2945, 3224, 3493, 3751, 3998,
    4231, 4452, 4659, 4852, 5031, 5194, 5343, 5476, 5594, 5697, 5784, 5856,
    5912, 5953, 5979, 5991, 5989, 5972, 5943, 5900, 5845, 5779, 5701, 5613,
    5515, 5407, 5291, 5168, 5037, 4900, 4757, 4609, 4456, 4300, 4140, 3978,
    3814, 3649, 3482, 3316, 3149, 2982, 2816, 2651, 2488, 2326, 2165, 2006,
    1850, 1695, 1542, 1391, 1242, 1095, 949, 805, 663, 521, 381, 241,
    102, -36, -176, -315, -455, -595, -736, -879, -1023, -1168, -1315, -1463,
    -1613, -1765, -1919, -2075, -2232, -2390, -2551, -2712, -2874, -3037, -3200, -3363,
    -3526, -3688, -3848, -4007, -4163, -4316, -4466, -4611, -4752, -4887, -5016, -5138,
    -5252, -5359, -5456, -5544, -5622, -5689, -5745, -5790, -5821, -5840, -5846, -5838,
    -5816, -5779, -5728, -5662, -5582, -5486, -5375, -5250, -5110, -4955, -4786, -4603,
    -4406, -4196, -3974, -3739, -3493, -3236, -2970, -2694, -2409, -2117, -1819, -1515,
    -1206, -893, -577, -260, 56, 374, 690, 1004, 1314, 1620, 1920, 2214,
    2501, 2780, 3049, 3309, 3559, 3797, 4024, 4238, 4439, 4627, 4800, 4960,
    5105, 5236, 5352, 5453, 5539, 5610, 5667, 5709, 5737, 5750, 5750, 5737,
    5710, 5672, 5621, 5559, 5486, 5403, 5311, 5209, 5099, 4982, 4858, 4727,
    4590, 4449, 4303, 4154, 4001, 3846, 3689, 3530, 3371, 3211, 3050, 2890,
    2731, 2573, 2415, 2259, 2105, 1952, 1802, 1653, 1506, 1360, 1217, 1076,
    936, 797, 660, 524, 389, 254, 121, -12, -145, -279, -413, -548,
    -683, -820, -958, -1097, -1237, -1380, -1523, -1669, -1816, -1965, -2116, -2268,
    -2422, -2576, -2732, -2888, -3045, -3201, -3358, -3513, -3668, -3820, -3971, -4118,
    -4263, -4403, -4539, -4669, -4794, -4912, -5023, -5127, -5222, -5308, -5385, -5451,
    -5507, -5551, -5584, -5604, -5612, -5606, -5587, -5555, -5508, -5448, -5373, -5283,
    -5180, -5062, -4930, -4783, -4623, -4450, -4263, -4064, -3853, -3629, -3395, -3150,
    -2896, -2632, -2361, -2082, -1796, -1505, -1209, -909, -607, -303, 1, 306,
    610, 911, 1210, 1504, 1794, 2077, 2354, 2623, 2883, 3134, 3376, 3606,
    3826, 4033, 4228, 4411, 4580, 4736, 4878, 5006, 5119, 5219, 5304, 5375,
    5431, 5474, 5503, 5519, 5521, 5510, 5487, 5452, 5405, 5348, 5280, 5201,
    5114, 5018, 4914, 4803, 4684, 4560, 4430, 4295, 4156, 4013, 3867, 3718,
    3568, 3415, 3262, 3109, 2955, 2801, 2648, 2496, 2345, 2195, 2046, 1900,
    1754, 1611, 1470, 1330, 1192, 1056, 921, 788, 656, 525, 396, 267,
    138, 10, -117, -245, -374, -503, -633, -764, -896, -1030, -1164, -1301,
    -1438, -1578, -1719, -1862, -2006, -2152, -2299, -2447, -2596, -2746, -2897, -3047,
    -3197, -3347, -3495, -3642, -3787, -3929, -4068, -4203, -4335, -4461, -4582, -4696,
    -4804, -4905, -4998, -5082, -5157, -5223, -5278, -5322, -5356, -5377, -5387, -5384,
    -5368, -5339, -5296, -5241, -5171, -5088, -4991, -4880, -4755, -4617, -4466, -4302,
    -4125, -3935, -3734, -3522, -3299, -3066, -2823, -2572, -2312, -2045, -1772, -1494,
    -1210, -923, -633, -341, -49, 243, 535, 825, 1112, 1395, 1674, 1947,
    2214, 2473, 2725, 2968, 3201, 3424, 3637, 3838, 4027, 4205, 4369, 4521,
    4660, 4785, 4896, 4994, 5078, 5149, 5205, 5249, 5279, 5296, 5300, 5292,
    5272, 5240, 5197, 5144, 5080, 5007, 4925, 4834, 4735, 4629, 4517, 4398,
    4274, 4146, 4013, 3876, 3736, 3594, 3450, 3304, 3157, 3010, 2862, 2715,
    2568, 2421, 2276, 2132, 1989, 1848, 1708, 1570, 1434, 1300, 1167, 1036,
    907, 779, 652, 526, 401, 277, 154, 31, -91, -214, -338, -462,
    -586, -712, -838, -966, -1095, -1226, -1358, -1491, -1626, -1763, -1902, -2041,
    -2182, -2324, -2468, -2611, -2756, -2900, -3044, -3188, -3331, -3472, -3611, -3748,
    -3882, -4013, -4139, -4261, -4378, -4489, -4594, -4692, -4783, -4865, -4939, -5003,
    -5058, -5103, -5136, -5159, -5170, -5169, -5156, -5131, -5092, -5041, -4976, -4899,
    -4808, -4704, -4586, -4456, -4313, -4158, -3990, -3810, -3619, -3417, -3205, -2982,
    -2751, -2511, -2263, -2008, -1747, -1481, -1209, -934, -656, -377, -96, 185,
    465, 744, 1020, 1292, 1561, 1824, 2081, 2331, 2574, 2809, 3035, 3251,
    3456, 3652, 3835, 4008, 4168, 4316, 4451, 4573, 4683, 4779, 4862, 4932,
    4988, 5032, 5063, 5082, 5088, 5082, 5065, 5037, 4997, 4948, 4888, 4819,
    4742, 4656, 4562, 4462, 4355, 4242, 4124, 4001, 3874, 3744, 3610, 3474,
    3336, 3196, 3055, 2914, 2772, 2631, 2489, 2349, 2209, 2070, 1933, 1797,
    1663, 1530, 1399, 1270, 1143, 1016, 892, 769, 647, 526, 406, 287,
    168, 50, -67, -185, -303, -422, -542, -662, -783, -906, -1030, -1155,
    -1281, -1409, -1539, -1670, -1802, -1936, -2071, -2208, -2345, -2483, -2621, -2760,
    -2898, -3036, -3174, -3309, -3443, -3575, -3705, -3831, -3953, -4071, -4184, -4292,
    -4393, -4489, -4577, -4657, -4729, -4793, -4847, -4892, -4926, -4949, -4962, -4963,
    -4953, -4930, -4896, -4849, -4789, -4716, -4631, -4534, -4423, -4300, -4165, -4018,
    -3859, -3688, -3507, -3315, -3112, -2901, -2680, -2451, -2214, -1971, -1721, -1466,
    -1206, -943, -677, -408, -139, 130, 400, 667, 933, 1195, 1454, 1707,
    1955, 2197, 2431, 2658, 2876, 3085, 3284, 3474, 3652, 3819, 3975, 4119,
    4251, 4371, 4478, 4572, 4654, 4723, 4780, 4824, 4856, 4876, 4884, 4881,
    4866, 4840, 4804, 4758, 4703, 4638, 4565, 4484, 4396, 4301, 4199, 4092,
    3979, 3862, 3741, 3616, 3488, 3358, 3225, 3092, 2957, 2821, 2685, 2549,
    2413, 2278, 2144, 2010, 1878, 1748, 1619, 1491, 1365, 1241, 1118, 997,
    877, 758, 641, 525, 410, 295, 181, 68, -45, -158, -272, -386,
    -500, -615, -732, -849, -968, -1087, -1209, -1331, -1455, -1581, -1708, -1836,
    -1966, -2096, -2228, -2360, -2493, -2626, -2759, -2892, -3024, -3154, -3283, -3410,
    -3535, -3656, -3774, -3888, -3998, -4102, -4201, -4293, -4379, -4458, -4528, -4591,
    -4645, -4689, -4724, -4748, -4762, -4765, -4757, -4738, -4706, -4663, -4608, -4541,
    -4461, -4369, -4265, -4149, -4022, -3882, -3732, -3570, -3397, -3215, -3022, -2820,
    -2610, -2392, -2166, -1933, -1694, -1450, -1202, -949, -694, -437, -178, 80,
    339, 596, 852, 1104, 1353, 1597, 1836, 2069, 2295, 2514, 2725, 2927,
    3120, 3304, 3477, 3639, 3791, 3931, 4060, 4177, 4281, 4374, 4455, 4524,
    4580, 4625, 4657, 4678, 4688, 4687, 4674, 4652, 4619, 4576, 4524, 4464,
    4395, 4319, 4235, 4145, 4048, 3946, 3839, 3727, 3611, 3492, 3370, 3245,
    3118, 2990, 2861, 2731, 2600, 2469, 2339, 2209, 2080, 1952, 1825, 1699,
    1575, 1453, 1331, 1212, 1094, 977, 862, 748, 635, 523, 412, 302,
    193, 84, -24, -133, -242, -351, -461, -572, -683, -795, -909, -1024,
    -1140, -1257, -1376, -1497, -1618, -1741, -1865, -1991, -2117, -2244, -2371, -2499,
    -2627, -2754, -2881, -3006, -3130, -3253, -3373, -3490, -3604, -3714, -3820, -3921,
    -4017, -4106, -4190, -4267, -4336, -4397, -4450, -4494, -4529, -4555, -4570, -4575,
    -4569, -4552, -4524, -4484, -4433, -4371, -4296, -4210, -4113, -4003, -3883, -3751,
    -3608, -3455, -3291, -3117, -2934, -2742, -2541, -2333, -2117, -1895, -1667, -1433,
    -1195, -954, -709, -462, -214, 34, 282, 529, 775, 1018, 1257, 1493,
    1723, 1948, 2166, 2378, 2581, 2777, 2964, 3141, 3309, 3467, 3614, 3751,
    3876, 3991, 4093, 4184, 4264, 4332, 4388, 4433, 4466, 4488, 4500, 4500,
    4490, 4470, 4440, 4401, 4352, 4296, 4231, 4159, 4080, 3994, 3903, 3805,
    3703, 3597, 3486, 3372, 3256, 3136, 3015, 2892, 2768, 2643, 2518, 2392,
    2267, 2142, 2018, 1895, 1773, 1652, 1533, 1415, 1298, 1183, 1069, 957,
    846, 737, 628, 521, 414, 309, 203, 99, -5, -109, -214, -319,
    -424, -530, -637, -745, -854, -964, -1075, -1187, -1301, -1416, -1533, -1651,
    -1770, -1890, -2011, -2133, -2255, -2377, -2500, -2622, -2744, -2865, -2985, -3102,
    -3218, -3331, -3441, -3547, -3650, -3747, -3840, -3927, -4009, -4083, -4151, -4211,
    -4264, -4308, -4343, -4369, -4385, -4391, -4388, -4373, -4348, -4312, -4265, -4207,
    -4138, -4057, -3965, -3862, -3748, -3623, -3488, -3343, -3187, -3022, -2848, -2665,
    -2473, -2275, -2069, -1856, -1638, -1415, -1187, -956, -722, -485, -247, -8,
    229, 467, 703, 937, 1167, 1394, 1616, 1833, 2043, 2248, 2445, 2634,
    2815, 2987, 3150, 3303, 3446, 3579, 3701, 3813, 3913, 4002, 4081, 4148,
    4204, 4249, 4283, 4306, 4318, 4320, 4312, 4295, 4268, 4232, 4187, 4134,
    4073, 4005, 3930, 3849, 3762, 3670, 3572, 3471, 3365, 3257, 3145, 3031,
    2914, 2797, 2678, 2558, 2438, 2317, 2197, 2077, 1958, 1840, 1722, 1606,
    1491, 1378, 1265, 1155, 1045, 937, 831, 725, 621, 518, 415, 314,
    213, 112, 12, -87, -188, -288, -389, -491, -594, -697, -801, -907,
    -1013, -1121, -1230, -1340, -1452, -1565, -1679, -1794, -1910, -2027, -2144, -2262,
    -2380, -2497, -2614, -2730, -2845, -2959, -3070, -3179, -3285, -3388, -3487, -3581,
    -3671, -3756, -3835, -3908, -3974, -4033, -4085, -4128, -4164, -4190, -4207, -4215,
    -4213, -4201, -4179, -4146, -4103, -4049, -3984, -3909, -3822, -3725, -3618, -3500,
    -3372, -3234, -3086, -2929, -2763, -2589, -2407, -2217, -2021, -1818, -1609, -1396,
    -1178, -956, -732, -505, -277, -48, 180, 409, 636, 861, 1082, 1301,
    1515, 1724, 1927, 2124, 2314, 2497, 2672, 2839, 2997, 3146, 3285, 3414,
    3533, 3642, 3740, 3828, 3905, 3971, 4027, 4072, 4106, 4130, 4144, 4148,
    4142, 4126, 4102, 4069, 4027, 3978, 3921, 3857, 3786, 3709, 3626, 3538,
    3446, 3349, 3248, 3144, 3038, 2928, 2817, 2704, 2590, 2476, 2360, 2245,
    2129, 2014, 1899, 1786, 1673, 1561, 1451, 1341, 1233, 1127, 1022, 918,
    815, 714, 613, 514, 416, 318, 221, 124, 28, -67, -163, -260,
    -357, -454, -553, -652, -752, -853, -955, -1058, -1162, -1268, -1375, -1483,
    -1593, -1703, -1814, -1926, -2039, -2152, -2265, -2378, -2490, -2602, -2712, -2821,
    -2929, -3034, -3136, -3235, -3331, -3422, -3510, -3592, -3669, -3740, -3804, -3862,
    -3913, -3956, -3992, -4018, -4037, -4046, -4046, -4036, -4016, -3986, -3947, -3897,
    -3836, -3766, -3684, -3593, -3492, -3380, -3259, -3128, -2988, -2839, -2681, -2515,
    -2341, -2160, -1973, -1779, -1580, -1376, -1167, -955, -740, -523, -304, -84,
    135, 354, 573, 789, 1002, 1212, 1419, 1620, 1816, 2007, 2190, 2367,
    2537, 2698, 2851, 2995, 3131, 3256, 3373, 3479, 3575, 3661, 3737, 3802,
    3857, 3902, 3937, 3962, 3976, 3982, 3978, 3964, 3942, 3912, 3873, 3827,
    3774, 3713, 3646, 3574, 3495, 3412, 3324, 3231, 3135, 3036, 2934, 2830,
    2723, 2615, 2506, 2396, 2285, 2174, 2063, 1952, 1842, 1733, 1625, 1517,
    1411, 1306, 1202, 1099, 998, 898, 799, 702, 605, 510, 415, 322,
    228, 136, 43, -48, -141, -233, -326, -420, -514, -609, -705, -801,
    -899, -998, -1098, -1200, -1302, -1406, -1511, -1616, -1723, -1830, -1938, -2047,
    -2155, -2263, -2372, -2479, -2585, -2690, -2794, -2895, -2993, -3089, -3182, -3270,
    -3355, -3435, -3509, -3579, -3642, -3699, -3749, -3791, -3826, -3854, -3873, -3883,
    -3884, -3876, -3859, -3832, -3796, -3750, -3693, -3627, -3551, -3465, -3369, -3264,
    -3149, -3025, -2892, -2750, -2600, -2442, -2277, -2105, -1926, -1741, -1550, -1355,
    -1156, -953, -747, -538, -328, -117, 93, 304, 513, 721, 927, 1129,
    1328, 1522, 1711, 1895, 2073, 2244, 2407, 2564, 2712, 2852, 2983, 3106,
    3219, 3322, 3416, 3501, 3575, 3640, 3694, 3739, 3774, 3799, 3815, 3822,
    3820, 3808, 3789, 3761, 3725, 3682, 3632, 3575, 3512, 3443, 3369, 3289,
    3205, 3118, 3026, 2931, 2834, 2734, 2632, 2528, 2424, 2318, 2212, 2105,
    1999, 1893, 1787, 1682, 1578, 1474, 1372, 1271, 1171, 1072, 975, 879,
    784, 690, 597, 505, 415, 324, 235, 146, 57, -31, -120, -209,
    -298, -387, -478, -569, -660, -753, -847, -942, -1038, -1135, -1233, -1332,
    -1433, -1534, -1636, -1739, -1843, -1947, -2051, -2155, -2259, -2362, -2464, -2565,
    -2665, -2762, -2857, -2950, -3039, -3125, -3207, -3284, -3357, -3424, -3486, -3541,
    -3591, -3633, -3668, -3695, -3715, -3726, -3729, -3723, -3708, -3684, -3651, -3608,
    -3556, -3494, -3422, -3341, -3251, -3152, -3043, -2925, -2799, -2664, -2522, -2371,
    -2214, -2050, -1879, -1702, -1520, -1334, -1143, -948, -751, -551, -350, -148,
    54, 256, 458, 658, 856, 1050, 1242, 1429, 1611, 1789, 1960, 2126,
    2284, 2436, 2579, 2715, 2843, 2962, 3072, 3173, 3265, 3347, 3420, 3484,
    3538, 3582, 3618, 3644, 3661, 3668, 3668, 3658, 3641, 3616, 3583, 3542,
    3495, 3442, 3382, 3317, 3246, 3171, 3091, 3008, 2920, 2830, 2737, 2641,
    2544, 2444, 2344, 2243, 2141, 2039, 1937, 1835, 1733, 1632, 1532, 1432,
    1334, 1237, 1141, 1046, 952, 859, 768, 678, 589, 500, 413, 326,
    240, 155, 69, -15, -100, -185, -271, -357, -443, -531, -619, -707,
    -797, -888, -980, -1073, -1167, -1262, -1358, -1455, -1553, -1652, -1752, -1851,
    -1951, -2051, -2151, -2250, -2348, -2446, -2541, -2635, -2727, -2816, -2903, -2986,
    -3065, -3140, -3211, -3276, -3336, -3391, -3439, -3481, -3516, -3543, -3563, -3576,
    -3580, -3576, -3563, -3541, -3511, -3471, -3423, -3365, -3298, -3222, -3137, -3043,
    -2940, -2828, -2709, -2581, -2445, -2302, -2152, -1995, -1832, -1664, -1490, -1312,
    -1129, -943, -754, -563, -370, -176, 18, 212, 406, 598, 789, 976,
    1160, 1341, 1517, 1688, 1854, 2013, 2167, 2313, 2453, 2584, 2708, 2824,
    2931, 3029, 3119, 3200, 3272, 3334, 3388, 3432, 3468, 3494, 3512, 3521,
    3522, 3514, 3499, 3476, 3445, 3408, 3364, 3313, 3257, 3195, 3129, 3057,
    2981, 2901, 2818, 2732, 2643, 2551, 2458, 2363, 2267, 2170, 2072, 1974,
    1876, 1778, 1680, 1583, 1487, 1391, 1297, 1203, 1111, 1020, 929, 840,
    753, 666, 580, 495, 411, 328, 245, 163, 81, 0, -82, -164,
    -246, -328, -411, -495, -579, -664, -750, -837, -925, -1014, -1105, -1196,
    -1288, -1381, -1475, -1570, -1665, -1760, -1856, -1952, -2048, -2143, -2238, -2332,
    -2424, -2514, -2603, -2689, -2772, -2853, -2929, -3002, -3071, -3134, -3193, -3246,
    -3294, -3335, -3370, -3397, -3418, -3431, -3436, -3434, -3423, -3404, -3376, -3339,
    -3294, -3240, -3178, -3106, -3026, -2937, -2840, -2734, -2621, -2499, -2370, -2234,
    -2091, -1942, -1787, -1626, -1460, -1289, -1115, -937, -756, -572, -387, -201,
    -14, 172, 358, 542, 725, 906, 1083, 1257, 1427, 1592, 1752, 1907,
    2055, 2197, 2332, 2459, 2580, 2692, 2796, 2892, 2980, 3059, 3129, 3191,
    3244, 3288, 3323, 3350, 3369, 3379, 3381, 3375, 3362, 3341, 3313, 3278,
    3237, 3189, 3136, 3078, 3015, 2947, 2875, 2799, 2719, 2637, 2552, 2465,
    2375, 2284, 2192, 2099, 2006, 1912, 1817, 1723, 1629, 1536, 1443, 1352,
    1261, 1171, 1082, 994, 907, 821, 737, 653, 571, 489, 408, 328,
    249, 170, 91, 12, -65, -144, -222, -301, -381, -461, -542, -623,
    -706, -789, -874, -959, -1045, -1133, -1221, -1310, -1400, -1491, -1582, -1674,
    -1766, -1858, -1950, -2042, -2133, -2223, -2311, -2399, -2484, -2567, -2648, -2725,
    -2799, -2870, -2937, -2999, -3056, -3108, -3154, -3195, -3229, -3257, -3278, -3292,
    -3298, -3297, -3288, -3271, -3246, -3212, -3170, -3120, -3061, -2994, -2919, -2835,
    -2743, -2643, -2535, -2420, -2297, -2168, -2032, -1889, -1741, -1588, -1429, -1266,
    -1099, -929, -756, -580, -403, -224, -45, 134, 312, 490, 666, 840,
    1011, 1178, 1342, 1501, 1656, 1805, 1948, 2086, 2216, 2340, 2457, 2566,
    2667, 2761, 2847, 2924, 2993, 3053, 3106, 3150, 3185, 3212, 3231, 3243,
    3246, 3241, 3230, 3211, 3185, 3153, 3114, 3070, 3020, 2965, 2905, 2840,
    2772, 2700, 2624, 2545, 2464, 2381, 2295, 2208, 2120, 2031, 1941, 1851,
    1760, 1670, 1580, 1490, 1401, 1313, 1225, 1139, 1053, 969, 885, 803,
    721, 641, 562, 483, 405, 328, 252, 176, 100, 25, -49, -125,
    -200, -276, -352, -429, -507, -585, -664, -744, -824, -906, -989, -1073,
    -1157, -1243, -1329, -1416, -1504, -1592, -1680, -1768, -1857, -1945, -2032, -2119,
    -2204, -2288, -2370, -2451, -2528, -2603, -2675, -2744, -2808, -2868, -2924, -2975,
    -3021, -3061, -3095, -3123, -3144, -3158, -3166, -3166, -3159, -3144, -3121, -3090,
    -3051, -3004, -2949, -2886, -2815, -2736, -2649, -2554, -2452, -2343, -2226, -2103,
    -1974, -1838, -1697, -1550, -1399, -1243, -1083, -920, -754, -586, -416, -245,
    -73, 98, 270, 441, 610, 777, 942, 1103, 1261, 1415, 1564, 1708,
    1847, 1980, 2106, 2226, 2339, 2446, 2544, 2635, 2719, 2794, 2862, 2922,
    2973, 3017, 3052, 3080, 3099, 3111, 3116, 3113, 3103, 3086, 3062, 3032,
    2997, 2955, 2908, 2856, 2799, 2738, 2673, 2604, 2532, 2457, 2379, 2299,
    2218, 2134, 2050, 1964, 1878, 1792, 1705, 1618, 1531, 1445, 1360, 1275,
    1191, 1107, 1025, 944, 864, 784, 706, 629, 552, 477, 402, 328,
    255, 182, 109, 37, -35, -107, -180, -252, -325, -399, -473, -548,
    -624, -700, -778, -856, -935, -1016, -1097, -1179, -1261, -1345, -1429, -1513,
    -1598, -1683, -1768, -1852, -1936, -2020, -2102, -2183, -2262, -2339, -2414, -2487,
    -2556, -2623, -2685, -2744, -2798, -2848, -2893, -2932, -2966, -2993, -3015, -3030,
    -3038, -3040, -3034, -3021, -3000, -2972, -2936, -2892, -2841, -2782, -2715, -2640,
    -2558, -2468, -2371, -2268, -2157, -2040, -1917, -1787, -1653, -1513, -1368, -1219,
    -1067, -911, -752, -591, -428, -264, -99, 66, 231, 395, 558, 718,
    877, 1032, 1185, 1333, 1477, 1616, 1750, 1879, 2001, 2118, 2227, 2330,
    2426, 2515, 2597, 2671, 2737, 2795, 2846, 2889, 2925, 2952, 2973, 2985,
    2991, 2989, 2981, 2966, 2944, 2916, 2883, 2844, 2800, 2750, 2697, 2639,
    2577, 2511, 2442, 2371, 2297, 2221, 2143, 2063, 1982, 1900, 1817, 1734,
    1651, 1568, 1485, 1402, 1319, 1238, 1157, 1077, 998, 919, 842, 766,
    691, 616, 543, 470, 398, 327, 257, 186, 117, 47, -21, -91,
    -160, -230, -300, -371, -442, -514, -586, -660, -734, -809, -885, -961,
    -1039, -1118, -1197, -1277, -1357, -1438, -1520, -1601, -1683, -1764, -1845, -1925,
    -2004, -2082, -2158, -2233, -2305, -2375, -2443, -2507, -2568, -2624, -2677, -2726,
    -2770, -2808, -2842, -2869, -2891, -2907, -2916, -2918, -2914, -2902, -2884, -2858,
    -2825, -2784, -2736, -2681, -2618, -2547, -2470, -2385, -2293, -2195, -2089, -1978,
    -1861, -1738, -1609, -1476, -1338, -1196, -1050, -901, -749, -594, -438, -281,
    -122, 35, 194, 352, 508, 663, 816, 965, 1112, 1255, 1394, 1528,
    1658, 1782, 1901, 2014, 2120, 2220, 2314, 2400, 2480, 2552, 2617, 2674,
    2724, 2767, 2802, 2830, 2851, 2864, 2871, 2870, 2863, 2850, 2830, 2805,
    2773, 2737, 2695, 2649, 2598, 2543, 2484, 2422, 2356, 2288, 2217, 2145,
    2070, 1994, 1916, 1838, 1758, 1679, 1599, 1519, 1439, 1359, 1280, 1202,
    1124, 1047, 971, 896, 821, 748, 676, 604, 533, 463, 394, 326,
    258, 191, 124, 57, -9, -75, -142, -209, -276, -344, -412, -481,
    -551, -621, -692, -764, -836, -910, -984, -1060, -1136, -1212, -1290, -1367,
    -1445, -1524, -1601, -1676, -1751, -1825, -1898, -1969, -2039, -2107, -2173, -2236,
    -2297, -2354, -2408, -2459, -2505, -2548, -2586, -2619, -2646, -2669, -2686, -2697,
    -2703, -2702, -2695, -2681, -2661, -2634, -2601, -2560, -2514, -2460, -2400, -2333,
    -2260, -2180, -2095, -2003, -1906, -1803, -1696, -1583, -1466, -1345, -1220, -1091,
    -960, -826, -690, -552, -412, -273, -132, 7, 147, 285, 422, 558,
    691, 821, 948, 1071, 1191, 1306, 1417, 1523, 1624, 1719, 1809, 1893,
    1971, 2043, 2108, 2167, 2220, 2266, 2306, 2339, 2366, 2386, 2401, 2409,
    2411, 2408, 2399, 2384, 2365, 2340, 2311, 2277, 2240, 2198, 2153, 2104,
    2052, 1998, 1941, 1883, 1822, 1759, 1696, 1631, 1565, 1499, 1432, 1366,
    1299, 1232, 1166, 1100, 1035, 970, 906, 843, 781, 720, 660, 600,
    542, 485, 428, 373, 318, 264, 210, 157, 105, 53, 1, -49,
    -101, -152, -203, -254, -306, -358, -410, -463, -516, -569, -623, -677,
    -732, -787, -842, -898, -954, -1010, -1066, -1122, -1178, -1233, -1288, -1342,
    -1396, -1448, -1500, -1550, -1598, -1644, -1689, -1731, -1770, -1807, -1841, -1872,
    -1900, -1924, -1944, -1960, -1973, -1981, -1984, -1984, -1978, -1968, -1953, -1933,
    -1909, -1879, -1845, -1806, -1762, -1713, -1659, -1601, -1539, -1472, -1401, -1326,
    -1248, -1166, -1081, -993, -902, -808, -713, -616, -517, -417, -316, -215,
    -113, -12, 88, 188, 288, 385, 481, 575, 667, 756, 842, 925,
    1005, 1081, 1153, 1222, 1286, 1346, 1402, 1453, 1500, 1542, 1580, 1612,
    1641, 1664, 1683, 1698, 1708, 1713, 1714, 1712, 1705, 1694, 1680, 1662,
    1641, 1617, 1589, 1559, 1527, 1492, 1455, 1416, 1375, 1333, 1290, 1245,
    1200, 1154, 1107, 1060, 1012, 965, 917, 870, 823, 777, 730, 685,
    640, 595, 551, 508, 466, 424, 383, 343, 304, 265, 226, 189,
    152, 115, 79, 43, 7, -28, -63, -98, -133, -169, -204, -239,
    -275, -310, -346, -383, -419, -456, -492, -530, -567, -604, -642, -679,
    -717, -754, -792, -829, -865, -901, -937, -972, -1006, -1038, -1070, -1101,
    -1130, -1158, -1183, -1208, -1230, -1250, -1267, -1283, -1296, -1306, -1313, -1318,
    -1320, -1319, -1314, -1307, -1296, -1283, -1266, -1246, -1222, -1196, -1166, -1133,
    -1098, -1059, -1017, -973, -926, -877, -825, -771, -715, -657, -598, -537,
    -474, -411, -346, -281, -216, -150, -84, -19, 45, 110, 174, 237,
    298, 358, 417, 474, 528, 581, 632, 680, 726, 769, 809, 847,
    882, 913, 942, 968, 991, 1011, 1028, 1042, 1054, 1062, 1067, 1070,
    1070, 1067, 1062, 1054, 1045, 1033, 1018, 1002, 985, 965, 944, 921,
    898, 873, 847, 820, 793, 764, 736, 707, 677, 648, 618, 589,
    559, 530, 501, 472, 443, 415, 387, 360, 333, 307, 281, 256,
    231, 207, 183, 160, 137, 115, 93, 71, 49, 28, 7, -12,
    -33, -53, -74, -94, -114, -134, -154, -175, -195, -215, -236, -256,
    -277, -297, -318, -338, -359, -379, -400, -420, -440, -460, -480, -499,
    -518, -536, -554, -571, -587, -603, -618, -632, -645, -657, -668, -677,
    -685, -692, -698, -702, -705, -706, -706, -704, -700, -695, -688, -679,
    -669, -657, -643, -628, -611, -593, -573, -552, -529, -505, -480, -454,
    -426, -398, -368, -338, -307, -276, -244, -211, -178, -146, -113, -80,
    -47, -15, 17, 48, 79, 109, 139, 168, 195, 222, 248, 272,
    296, 318, 338, 357, 375, 392, 407, 420, 432, 443, 452, 460,
    466, 471, 474, 476, 477, 476, 474, 471, 467, 462, 456, 449,
    441, 432, 423, 413, 402, 391, 379, 367, 354, 341, 328, 315,
    302, 289, 275, 262, 249, 236, 223, 210, 197, 185, 173, 161,
    149, 138, 127, 116, 106, 96, 86, 77, 68, 59, 50, 42,
    34, 26, 18, 11, 3, -3, -10, -16, -23, -29, -36, -42,
    -48, -54, -60, -66, -71, -77, -82, -87, -93, -98, -103, -107,
    -112, -116, -121, -125, -129, -132, -135, -139, -141, -144, -146, -148,
    -149, -151, -151, -152, -152, -152, -151, -150, -149, -147, -145, -142,
    -139, -136, -133, -129, -125, -120, -116, -111, -106, -100, -95, -90,
    -84, -78, -73, -67, -61, -56, -50, -45, -40, -35, -30, -26,
    -21, -17, -14, -10, -7, -5, -2, -1, 0, 1, 2, 2,
    2, 2, 1, 0, 3, 14, 31, 56, 87, 124, 168, 218,
    273, 334, 400, 470, 544, 621, 702, 785, 870, 956, 1044, 1132,
    1220, 1307, 1393, 1477, 1559, 1639, 1715, 1788, 1857, 1922, 1983, 2038,
    2088, 2133, 2173, 2206, 2234, 2256, 2272, 2282, 2286, 2284, 2276, 2263,
    2244, 2219, 2189, 2155, 2115, 2071, 2022, 1970, 1913, 1853, 1789, 1722,
    1652, 1579, 1504, 1426, 1346, 1263, 1179, 1092, 1004, 914, 822, 728,
    632, 534, 434, 331, 226, 119, 9, -103, -219, -338, -461, -587,
    -718, -852, -991, -1135, -1282, -1435, -1593, -1755, -1923, -2095, -2272, -2454,
    -2641, -2832, -3028, -3227, -3430, -3636, -3845, -4056, -4269, -4483, -4697, -4910,
    -5123, -5333, -5540, -5743, -5942, -6134, -6320, -6497, -6666, -6824, -6972, -7107,
    -7229, -7336, -7428, -7504, -7562, -7602, -7623, -7624, -7605, -7564, -7501, -7416,
    -7308, -7177, -7023, -6845, -6643, -6418, -6169, -5898, -5603, -5287, -4949, -4590,
    -4212, -3814, -3398, -2965, -2517, -2054, -1578, -1091, -594, -88, 424, 941,
    1462, 1985, 2508, 3029, 3546, 4058, 4563, 5059, 5544, 6018, 6477, 6922,
    7350, 7759, 8150, 8520, 8869, 9194, 9497, 9775, 10029, 10257, 10459, 10635,
    10785, 10908, 11005, 11075, 11120, 11139, 11133, 11102, 11048, 10970, 10870, 10749,
    10607, 10446, 10266, 10069, 9856, 9628, 9386, 9132, 8866, 8590, 8305, 8012,
    7712, 7406, 7095, 6781, 6463, 6142, 5821, 5498, 5175, 4851, 4529, 4207,
    3886, 3566, 3247, 2929, 2613, 2297, 1982, 1667, 1349, 1030, 713, 397,
    82, -232, -547, -863, -1180, -1499, -1820, -2144, -2471, -2802, -3136, -3474,
    -3816, -4162, -4512, -4866, -5224, -5585, -5948, -6315, -6683, -7052, -7422, -7791,
    -8159, -8524, -8885, -9242, -9593, -9936, -10270, -10594, -10907, -11206, -11491, -11759,
    -12010, -12241, -12452, -12641, -12806, -12947, -13061, -13148, -13206, -13235, -13233, -13199,
    -13134, -13036, -12905, -12740, -12541, -12308, -12042, -11742, -11409, -11043, -10645, -10216,
    -9756, -9267, -8750, -8207, -7638, -7046, -6432, -5797, -5145, -4477, -3794, -3100,
    -2396, -1685, -969, -249, 469, 1187, 1900, 2607, 3305, 3992, 4665, 5324,
    5965, 6587, 7187, 7765, 8318, 8845, 9345, 9816, 10257, 10667, 11045, 11392,
    11705, 11985, 12231, 12444, 12623, 12769, 12881, 12961, 13009, 13025, 13010, 12966,
    12893, 12792, 12665, 12513, 12337, 12139, 11919, 11680, 11423, 11150, 10861, 10559,
    10245, 9920, 9585, 9243, 8895, 8541, 8184, 7824, 7461, 7099, 6736, 6374,
    6014, 5657, 5302, 4951, 4603, 4259, 3920, 3585, 3254, 2927, 2604, 2285,
    1970, 1658, 1349, 1042, 737, 433, 131, -170, -473, -776, -1080, -1386,
    -1694, -2004, -2318, -2634, -2954, -3278, -3606, -3937, -4273, -4612, -4955, -5300,
    -5649, -6001, -6354, -6708, -7063, -7418, -7771, -8122, -8470, -8813, -9151, -9481,
    -9804, -10117, -10419, -10708, -10984, -11245, -11488, -11714, -11920, -12105, -12268, -12407,
    -12521, -12609, -12669, -12702, -12705, -12679, -12621, -12533, -12412, -12259, -12074, -11857,
    -11607, -11324, -11010, -10664, -10287, -9880, -9444, -8980, -8488, -7971, -7429, -6864,
    -6278, -5672, -5049, -4410, -3757, -3092, -2418, -1736, -1049, -359, 330, 1020,
    1705, 2385, 3057, 3718, 4367, 5002, 5620, 6221, 6801, 7359, 7894, 8405,
    8889, 9346, 9774, 10173, 10542, 10880, 11186, 11461, 11703, 11913, 12090, 12235,
    12349, 12431, 12482, 12503, 12494, 12456, 12391, 12299, 12181, 12039, 11874, 11687,
    11480, 11254, 11010, 10750, 10475, 10187, 9887, 9577, 9258, 8931, 8597, 8259,
    7916, 7571, 7223, 6875, 6527, 6179, 5833, 5490, 5149, 4811, 4476, 4146,
    3819, 3497, 3178, 2864, 2554, 2247, 1944, 1643, 1346, 1051, 758, 467,
    176, -113, -403, -694, -986, -1279, -1574, -1872, -2172, -2476, -2782, -3093,
    -3407, -3724, -4045, -4370, -4699, -5030, -5365, -5702, -6040, -6380, -6721, -7061,
    -7401, -7738, -8073, -8403, -8728, -9047, -9358, -9660, -9952, -10232, -10499, -10752,
    -10989, -11209, -11410, -11591, -11751, -11888, -12002, -12091, -12154, -12190, -12198, -12178,
    -12128, -12048, -11937, -11796, -11624, -11420, -11186, -10920, -10624, -10297, -9940, -9555,
    -9141, -8699, -8232, -7739, -7223, -6685, -6126, -5547, -4952, -4341, -3716, -3080,
    -2434, -1781, -1122, -460, 202, 864, 1523, 2177, 2823, 3460, 4085, 4697,
    5294, 5873, 6433, 6973, 7491, 7985, 8454, 8898, 9314, 9702, 10061, 10390,
    10689, 10958, 11196, 11403, 11579, 11724, 11838, 11922, 11976, 12001, 11997, 11966,
    11907, 11823, 11715, 11582, 11428, 11252, 11056, 10842, 10611, 10364, 10103, 9828,
    9542, 9246, 8941, 8628, 8309, 7985, 7656, 7325, 6992, 6658, 6323, 5990,
    5657, 5327, 4999, 4674, 4353, 4035, 3720, 3410, 3104, 2801, 2503, 2208,
    1916, 1627, 1342, 1058, 776, 496, 217, -60, -339, -618, -898, -1179,
    -1462, -1747, -2035, -2326, -2620, -2917, -3218, -3522, -3830, -4141, -4456, -4773,
    -5094, -5417, -5742, -6068, -6395, -6722, -7048, -7372, -7694, -8012, -8325, -8632,
    -8932, -9224, -9506, -9777, -10035, -10281, -10511, -10724, -10921, -11098, -11255, -11391,
    -11504, -11594, -11659, -11698, -11710, -11695, -11652, -11581, -11480, -11350, -11189, -10999,
    -10779, -10529, -10250, -9941, -9604, -9238, -8845, -8426, -7982, -7513, -7022, -6508,
    -5975, -5423, -4854, -4270, -3672, -3064, -2445, -1819, -1187, -552, 83, 719,
    1353, 1981, 2603, 3216, 3818, 4408, 4983, 5542, 6084, 6605, 7106, 7584,
    8039, 8469, 8873, 9250, 9600, 9921, 10214, 10477, 10710, 10914, 11088, 11232,
    11347, 11432, 11489, 11518, 11519, 11494, 11442, 11366, 11265, 11142, 10997, 10832,
    10648, 10445, 10226, 9991, 9743, 9481, 9209, 8926, 8634, 8335, 8030, 7719,
    7405, 7087, 6768, 6447, 6126, 5805, 5486, 5169, 4853, 4541, 4232, 3926,
    3624, 3325, 3030, 2739, 2452, 2168, 1888, 1610, 1335, 1063, 792, 523,
    255, -11, -279, -547, -815, -1085, -1356, -1630, -1905, -2184, -2466, -2750,
    -3038, -3330, -3625, -3923, -4225, -4529, -4836, -5146, -5458, -5771, -6084, -6398,
    -6712, -7023, -7333, -7638, -7940, -8236, -8525, -8806, -9079, -9341, -9591, -9829,
    -10052, -10261, -10452, -10625, -10780, -10914, -11026, -11116, -11183, -11225, -11241, -11231,
    -11195, -11131, -11039, -10919, -10770, -10593, -10386, -10151, -9888, -9596, -9277, -8931,
    -8559, -8161, -7738, -7292, -6824, -6335, -5826, -5299, -4756, -4197, -3626, -3043,
    -2451, -1851, -1245, -636, -25, 585, 1193, 1797, 2396, 2986, 3566, 4134,
    4689, 5228, 5751, 6255, 6740, 7203, 7643, 8060, 8452, 8819, 9159, 9472,
    9758, 10015, 10244, 10445, 10617, 10760, 10875, 10962, 11022, 11054, 11059, 11039,
    10994, 10925, 10833, 10718, 10583, 10427, 10253, 10062, 9854, 9631, 9395, 9146,
    8886, 8616, 8338, 8052, 7760, 7462, 7161, 6857, 6550, 6242, 5934, 5626,
    5319, 5014, 4711, 4411, 4114, 3819, 3529, 3241, 2958, 2678, 2402, 2129,
    1859, 1592, 1328, 1066, 805, 547, 289, 33, -223, -480, -738, -996,
    -1256, -1519, -1783, -2050, -2320, -2592, -2868, -3148, -3430, -3716, -4005, -4297,
    -4591, -4888, -5187, -5487, -5789, -6090, -6391, -6690, -6988, -7282, -7572, -7857,
    -8136, -8407, -8671, -8924, -9166, -9397, -9614, -9816, -10003, -10172, -10324, -10456,
    -10568, -10658, -10725, -10770, -10790, -10785, -10755, -10698, -10614, -10504, -10366, -10200,
    -10007, -9786, -9538, -9263, -8961, -8633, -8280, -7902, -7500, -7076, -6630, -6164,
    -5679, -5176, -4657, -4123, -3577, -3019, -2452, -1877, -1297, -712, -126, 459,
    1044, 1625, 2200, 2768, 3327, 3875, 4410, 4930, 5435, 5922, 6390, 6839,
    7265, 7670, 8050, 8407, 8738, 9043, 9322, 9573, 9798, 9995, 10165, 10308,
    10423, 10511, 10572, 10608, 10617, 10602, 10563, 10501, 10416, 10310, 10183, 10037,
    9873, 9692, 9495, 9284, 9059, 8822, 8574, 8317, 8051, 7778, 7498, 7213,
    6925, 6633, 6339, 6044, 5748, 5452, 5157, 4864, 4573, 4284, 3998, 3715,
    3436, 3159, 2886, 2617, 2351, 2089, 1829, 1572, 1318, 1066, 816, 568,
    321, 74, -171, -418, -665, -913, -1163, -1414, -1667, -1923, -2182, -2443,
    -2707, -2975, -3245, -3519, -3796, -4076, -4358, -4643, -4929, -5218, -5506, -5796,
    -6085, -6373, -6658, -6941, -7221, -7495, -7764, -8026, -8280, -8525, -8760, -8983,
    -9194, -9390, -9572, -9738, -9886, -10017, -10127, -10217, -10286, -10333, -10356, -10356,
    -10331, -10281, -10205, -10103, -9975, -9821, -9640, -9433, -9199, -8940, -8654, -8344,
    -8009, -7650, -7269, -6865, -6440, -5996, -5533, -5054, -4558, -4048, -3525, -2992,
    -2449, -1898, -1342, -781, -219, 343, 905, 1463, 2017, 2563, 3101, 3629,
    4145, 4647, 5134, 5605, 6058, 6491, 6905, 7297, 7666, 8012, 8334, 8632,
    8904, 9150, 9370, 9564, 9732, 9873, 9988, 10077, 10141, 10179, 10192, 10182,
    10148, 10092, 10014, 9916, 9798, 9661, 9506, 9335, 9149, 8948, 8735, 8509,
    8273, 8027, 7773, 7512, 7245, 6972, 6696, 6416, 6134, 5851, 5567, 5283,
    5000, 4718, 4438, 4161, 3886, 3613, 3344, 3079, 2816, 2557, 2301, 2049,
    1799, 1552, 1308, 1066, 825, 587, 349, 112, -123, -360, -597, -835,
    -1074, -1315, -1558, -1803, -2051, -2301, -2555, -2811, -3070, -3332, -3598, -3866,
    -4136, -4409, -4684, -4960, -5238, -5515, -5793, -6069, -6344, -6617, -6885, -7150,
    -7409, -7662, -7907, -8144, -8371, -8587, -8791, -8983, -9160, -9322, -9467, -9595,
    -9705, -9795, -9864, -9913, -9939, -9943, -9923, -9879, -9811, -9718, -9599, -9455,
    -9286, -9092, -8872, -8627, -8357, -8063, -7746, -7405, -7043, -6659, -6255, -5831,
    -5390, -4932, -4459, -3972, -3472, -2962, -2442, -1915, -1381, -844, -304, 236,
    775, 1312, 1844, 2370, 2888, 3396, 3894, 4378, 4848, 5303, 5741, 6161,
    6561, 6941, 7299, 7635, 7949, 8238, 8504, 8744, 8960, 9151, 9316, 9456,
    9571, 9660, 9726, 9767, 9784, 9778, 9749, 9699, 9628, 9537, 9426, 9298,
    9152, 8991, 8814, 8624, 8421, 8207, 7982, 7747, 7505, 7255, 7000, 6739,
    6474, 6206, 5936, 5664, 5391, 5119, 4847, 4576, 4307, 4040, 3776, 3514,
    3255, 2999, 2747, 2498, 2251, 2008, 1768, 1531, 1296, 1063, 832, 603,
    375, 147, -79, -306, -534, -762, -991, -1222, -1455, -1690, -1927, -2167,
    -2410, -2655, -2904, -3155, -3409, -3666, -3926, -4187, -4451, -4716, -4982, -5248,
    -5515, -5780, -6045, -6306, -6565, -6820, -7069, -7313, -7550, -7779, -7998, -8208,
    -8406, -8592, -8764, -8922, -9065, -9191, -9299, -9389, -9459, -9509, -9538, -9546,
    -9531, -9493, -9431, -9346, -9236, -9102, -8944, -8762, -8555, -8324, -8069, -7791,
    -7490, -7167, -6823, -6458, -6073, -5670, -5249, -4812, -4360, -3895, -3417, -2929,
    -2431, -1926, -1415, -900, -382, 136, 654, 1170, 1682, 2188, 2687, 3176,
    3656, 4123, 4577, 5016, 5439, 5845, 6233, 6601, 6949, 7275, 7580, 7862,
    8121, 8356, 8567, 8754, 8917, 9056, 9170, 9260, 9327, 9370, 9391, 9389,
    9365, 9320, 9256, 9171, 9069, 8948, 8811, 8659, 8492, 8312, 8119, 7915,
    7700, 7477, 7245, 7007, 6762, 6513, 6259, 6002, 5743, 5482, 5221, 4959,
    4698, 4438, 4179, 3923, 3668, 3417, 3168, 2922, 2679, 2439, 2202, 1968,
    1737, 1509, 1283, 1059, 837, 617, 398, 179, -38, -256, -474, -693,
    -913, -1135, -1358, -1583, -1810, -2040, -2273, -2508, -2746, -2987, -3230, -3476,
    -3725, -3976, -4228, -4483, -4738, -4994, -5250, -5505, -5759, -6010, -6259, -6505,
    -6745, -6980, -7209, -7430, -7642, -7845, -8037, -8218, -8386, -8540, -8679, -8803,
    -8910, -8999, -9070, -9122, -9153, -9164, -9153, -9120, -9065, -8987, -8886, -8762,
    -8614, -8443, -8248, -8031, -7790, -7527, -7242, -6935, -6608, -6261, -5895, -5511,
    -5110, -4693, -4262, -3817, -3361, -2894, -2417, -1934, -1444, -950, -453, 44,
    542, 1038, 1530, 2016, 2497, 2968, 3430, 3881, 4319, 4743, 5152, 5545,
    5920, 6277, 6614, 6931, 7227, 7501, 7754, 7984, 8190, 8374, 8534, 8672,
    8785, 8876, 8944, 8989, 9013, 9015, 8996, 8956, 8897, 8819, 8724, 8611,
    8482, 8339, 8181, 8010, 7827, 7632, 7428, 7215, 6994, 6767, 6533, 6294,
    6051, 5805, 5557, 5306, 5055, 4804, 4553, 4304, 4055, 3808, 3564, 3322,
    3082, 2845, 2612, 2381, 2153, 1928, 1706, 1486, 1269, 1054, 841, 629,
    418, 208, 0, -209, -419, -629, -840, -1052, -1266, -1482, -1700, -1920,
    -2143, -2368, -2596, -2827, -3060, -3296, -3534, -3775, -4017, -4261, -4506, -4751,
    -4997, -5242, -5486, -5728, -5967, -6203, -6435, -6662, -6882, -7096, -7301, -7498,
    -7684, -7859, -8023, -8173, -8310, -8431, -8537, -8625, -8696, -8749, -8783, -8797,
    -8790, -8762, -8713, -8642, -8549, -8433, -8296, -8135, -7952, -7747, -7520, -7271,
    -7001, -6710, -6400, -6070, -5721, -5356, -4974, -4576, -4164, -3740, -3303, -2856,
    -2401, -1937, -1468, -994, -518, -40, 437, 914, 1387, 1855, 2317, 2771,
    3217, 3651, 4074, 4484, 4879, 5258, 5622, 5967, 6294, 6602, 6890, 7157,
    7403, 7627, 7830, 8010, 8168, 8303, 8416, 8507, 8576, 8623, 8650, 8655,
    8640, 8605, 8552, 8481, 8392, 8286, 8165, 8030, 7880, 7718, 7544, 7360,
    7166, 6963, 6752, 6534, 6311, 6082, 5850, 5614, 5376, 5136, 4895, 4654,
    4413, 4173, 3934, 3697, 3462, 3229, 2998, 2771, 2546, 2324, 2105, 1888,
    1675, 1463, 1254, 1047, 842, 639, 436, 235, 34, -166, -367, -569,
    -771, -975, -1180, -1386, -1595, -1806, -2020, -2235, -2454, -2675, -2898, -3124,
    -3353, -3583, -3815, -4049, -4284, -4520, -4756, -4991, -5226, -5458, -5689, -5916,
    -6139, -6358, -6570, -6777, -6975, -7165, -7346, -7516, -7675, -7822, -7955, -8074,
    -8178, -8266, -8338, -8391, -8427, -8443, -8440, -8417, -8374, -8309, -8224, -8117,
    -7988, -7838, -7666, -7472, -7258, -7023, -6767, -6491, -6196, -5883, -5552, -5203,
    -4839, -4460, -4067, -3661, -3244, -2817, -2381, -1938, -1488, -1034, -577, -118,
    340, 798, 1253, 1703, 2148, 2585, 3014, 3433, 3841, 4237, 4619, 4986,
    5337, 5672, 5989, 6288, 6567, 6827, 7067, 7286, 7484, 7661, 7816, 7950,
    8062, 8153, 8223, 8272, 8300, 8309, 8298, 8268, 8220, 8154, 8072, 7973,
    7860, 7732, 7591, 7437, 7272, 7097, 6912, 6718, 6517, 6309, 6095, 5877,
    5654, 5428, 5200, 4970, 4739, 4508, 4276, 4046, 3816, 3588, 3362, 3138,
    2917, 2698, 2481, 2268, 2057, 1849, 1643, 1440, 1239, 1040, 843, 647,
    453, 259, 66, -126, -319, -512, -706, -901, -1098, -1296, -1496, -1699,
    -1903, -2110, -2319, -2531, -2745, -2961, -3180, -3401, -3624, -3848, -4073, -4300,
    -4526, -4752, -4977, -5201, -5423, -5641, -5857, -6067, -6272, -6471, -6663, -6847,
    -7022, -7188, -7342, -7485, -7615, -7732, -7834, -7922, -7993, -8048, -8085, -8104,
    -8104, -8086, -8047, -7989, -7910, -7811, -7691, -7550, -7389, -7207, -7005, -6782,
    -6540, -6279, -5999, -5701, -5386, -5054, -4707, -4346, -3971, -3583, -3185, -2776,
    -2359, -1934, -1504, -1068, -630, -190, 250, 690, 1127, 1560, 1988, 2409,
    2823, 3227, 3620, 4002, 4371, 4726, 5066, 5390, 5697, 5987, 6259, 6512,
    6745, 6959, 7153, 7326, 7478, 7610, 7722, 7813, 7883, 7934, 7965, 7976,
    7969, 7943, 7900, 7840, 7763, 7671, 7565, 7444, 7311, 7166, 7009, 6842,
    6666, 6482, 6290, 6092, 5887, 5678, 5465, 5249, 5030, 4810, 4588, 4366,
    4144, 3922, 3701, 3482, 3265, 3050, 2837, 2626, 2418, 2212, 2009, 1809,
    1611, 1416, 1222, 1031, 842, 654, 467, 281, 95, -89, -274, -459,
    -646, -833, -1021, -1211, -1403, -1597, -1793, -1991, -2191, -2394, -2599, -2807,
    -3016, -3228, -3441, -3656, -3873, -4090, -4307, -4524, -4741, -4956, -5169, -5379,
    -5586, -5789, -5987, -6180, -6365, -6543, -6713, -6873, -7023, -7162, -7290, -7404,
    -7505, -7591, -7662, -7717, -7756, -7778, -7781, -7766, -7733, -7680, -7608, -7516,
    -7404, -7273, -7121, -6950, -6759, -6549, -6320, -6072, -5806, -5523, -5224, -4908,
    -4578, -4233, -3875, -3505, -3124, -2734, -2335, -1928, -1516, -1098, -678, -255,
    167, 589, 1009, 1426, 1837, 2243, 2641, 3031, 3410, 3779, 4135, 4478,
    4807, 5121, 5419, 5700, 5964, 6210, 6438, 6646, 6835, 7005, 7155, 7285,
    7395, 7486, 7557, 7609, 7642, 7656, 7652, 7631, 7592, 7537, 7466, 7381,
    7281, 7167, 7041, 6904, 6755, 6597, 6429, 6254, 6071, 5881, 5686, 5486,
    5282, 5075, 4865, 4654, 4441, 4228, 4015, 3802, 3590, 3379, 3170, 2963,
    2758, 2556, 2355, 2158, 1963, 1770, 1580, 1391, 1206, 1022, 839, 659,
    479, 300, 122, -54, -232, -410, -589, -768, -949, -1131, -1315, -1500,
    -1688, -1878, -2070, -2264, -2461, -2659, -2860, -3063, -3268, -3474, -3681, -3890,
    -4098, -4307, -4515, -4721, -4926, -5129, -5328, -5524, -5715, -5900, -6080, -6252,
    -6416, -6572, -6718, -6853, -6977, -7089, -7188, -7274, -7345, -7400, -7440, -7464,
    -7470, -7459, -7430, -7383, -7317, -7232, -7128, -7005, -6863, -6702, -6522, -6323,
    -6106, -5872, -5619, -5351, -5066, -4765, -4450, -4122, -3780, -3427, -3063, -2690,
    -2308, -1919, -1524, -1124, -721, -316, 89, 495, 899, 1299, 1696, 2086,
    2470, 2845, 3211, 3567, 3911, 4243, 4561, 4865, 5154, 5427, 5683, 5922,
    6143, 6347, 6531, 6698, 6845, 6973, 7082, 7173, 7244, 7297, 7332, 7348,
    7348, 7330, 7296, 7245, 7180, 7100, 7007, 6900, 6781, 6651, 6510, 6360,
    6200, 6033, 5859, 5678, 5491, 5300, 5105, 4907, 4706, 4503, 4299, 4094,
    3889, 3685, 3481, 3279, 3078, 2879, 2682, 2487, 2294, 2104, 1916, 1731,
    1548, 1367, 1188, 1011, 836, 662, 490, 318, 147, -22, -193, -364,
    -535, -707, -881, -1055, -1231, -1409, -1589, -1771, -1955, -2141, -2329, -2520,
    -2712, -2907, -3103, -3301, -3499, -3699, -3899, -4100, -4299, -4498, -4695, -4890,
    -5082, -5271, -5455, -5634, -5807, -5973, -6133, -6283, -6425, -6557, -6678, -6788,
    -6885, -6969, -7040, -7096, -7137, -7162, -7171, -7163, -7139, -7096, -7036, -6958,
    -6861, -6746, -6613, -6462, -6292, -6104, -5899, -5677, -5438, -5182, -4911, -4626,
    -4326, -4012, -3687, -3350, -3002, -2645, -2280, -1908, -1529, -1146, -760, -371,
    18, 408, 796, 1181, 1562, 1938, 2307, 2669, 3022, 3366, 3698, 4019,
    4326, 4621, 4900, 5165, 5414, 5646, 5862, 6060, 6240, 6403, 6547, 6674,
    6782, 6872, 6943, 6997, 7034, 7053, 7055, 7040, 7010, 6965, 6905, 6830,
    6743, 6642, 6530, 6407, 6274, 6131, 5979, 5820, 5653, 5481, 5303, 5120,
    4933, 4743, 4551, 4356, 4161, 3964, 3768, 3571, 3376, 3181, 2988, 2797,
    2607, 2420, 2234, 2051, 1871, 1692, 1516, 1342, 1170, 1000, 832, 665,
    499, 334, 170, 6, -157, -321, -485, -650, -816, -984, -1152, -1323,
    -1495, -1669, -1846, -2024, -2204, -2387, -2571, -2758, -2946, -3135, -3326, -3518,
    -3710, -3902, -4094, -4285, -4474, -4662, -4847, -5028, -5206, -5379, -5546, -5707,
    -5861, -6007, -6145, -6273, -6391, -6498, -6594, -6677, -6747, -6803, -6845, -6872,
    -6884, -6879, -6858, -6820, -6766, -6693, -6604, -6497, -6372, -6229, -6069, -5892,
    -5698, -5488, -5261, -5018, -4761, -4489, -4203, -3905, -3594, -3272, -2940, -2599,
    -2250, -1894, -1531, -1164, -794, -421, -47, 326, 699, 1070, 1436, 1798,
    2154, 2503, 2843, 3174, 3495, 3805, 4103, 4387, 4658, 4915, 5156, 5382,
    5592, 5785, 5962, 6121, 6262, 6387, 6493, 6583, 6655, 6709, 6747, 6768,
    6773, 6762, 6736, 6694, 6639, 6570, 6488, 6394, 6288, 6172, 6045, 5910,
    5766, 5614, 5455, 5291, 5120, 4946, 4767, 4585, 4401, 4215, 4027, 3838,
    3650, 3461, 3273, 3086, 2901, 2717, 2534, 2354, 2176, 2000, 1826, 1654,
    1485, 1317, 1152, 988, 826, 666, 506, 348, 190, 33, -123, -280,
    -438, -597, -756, -916, -1078, -1241, -1406, -1573, -1742, -1913, -2086, -2261,
    -2437, -2616, -2796, -2978, -3161, -3345, -3529, -3714, -3898, -4082, -4264, -4444,
    -4622, -4797, -4968, -5135, -5296, -5452, -5601, -5743, -5876, -6001, -6116, -6221,
    -6315, -6397, -6466, -6523, -6565, -6594, -6607, -6606, -6588, -6555, -6505, -6439,
    -6356, -6255, -6139, -6005, -5854, -5687, -5504, -5304, -5089, -4859, -4614, -4356,
    -4084, -3799, -3503, -3196, -2879, -2553, -2219, -1878, -1531, -1179, -824, -466,
    -107, 251, 609, 965, 1318, 1666, 2009, 2345, 2673, 2993, 3303, 3602,
    3890, 4165, 4428, 4676, 4911, 5130, 5334, 5523, 5695, 5850, 5989, 6111,
    6217, 6305, 6377, 6433, 6472, 6495, 6502, 6494, 6471, 6434, 6383, 6319,
    6243, 6154, 6055, 5945, 5825, 5696, 5559, 5415, 5264, 5107, 4944, 4777,
    4606, 4432, 4255, 4077, 3897, 3716, 3535, 3354, 3173, 2994, 2815, 2638,
    2463, 2290, 2118, 1949, 1781, 1616, 1453, 1292, 1133, 976, 820, 666,
    513, 360, 209, 58, -92, -243, -394, -546, -699, -853, -1008, -1164,
    -1322, -1482, -1644, -1808, -1973, -2141, -2310, -2481, -2654, -2828, -3004, -3180,
    -3357, -3534, -3711, -3888, -4063, -4236, -4408, -4576, -4741, -4902, -5058, -5208,
    -5352, -5490, -5619, -5741, -5853, -5955, -6047, -6128, -6197, -6253, -6296, -6326,
    -6341, -6342, -6328, -6299, -6254, -6193, -6116, -6023, -5913, -5788, -5646, -5488,
    -5315, -5126, -4922, -4704, -4471, -4225, -3966, -3695, -3413, -3120, -2817, -2505,
    -2186, -1860, -1528, -1191, -850, -507, -163, 181, 525, 867, 1207, 1542,
    1872, 2195, 2512, 2820, 3119, 3408, 3687, 3953, 4208, 4449, 4676, 4889,
    5088, 5271, 5439, 5591, 5727, 5848, 5952, 6039, 6111, 6167, 6207, 6232,
    6242, 6236, 6217, 6184, 6137, 6078, 6006, 5924, 5830, 5726, 5612, 5490,
    5360, 5223, 5079, 4929, 4774, 4614, 4450, 4284, 4115, 3944, 3771, 3598,
    3424, 3250, 3076, 2904, 2732, 2562, 2393, 2227, 2062, 1899, 1738, 1579,
    1422, 1267, 1114, 963, 813, 665, 518, 371, 226, 81, -63, -208,
    -353, -499, -645, -793, -941, -1091, -1243, -1396, -1551, -1708, -1867, -2027,
    -2189, -2353, -2519, -2686, -2854, -3023, -3193, -3363, -3533, -3703, -3871, -4038,
    -4203, -4365, -4524, -4679, -4830, -4975, -5115, -5248, -5373, -5491, -5600, -5700,
    -5790, -5870, -5938, -5994, -6038, -6069, -6086, -6089, -6078, -6053, -6012, -5956,
    -5885, -5798, -5696, -5578, -5445, -5296, -5132, -4953, -4760, -4553, -4332, -4098,
    -3851, -3593, -3324, -3044, -2755, -2458, -2152, -1840, -1522, -1200, -873, -544,
    -214, 116, 447, 776, 1102, 1424, 1742, 2054, 2359, 2656, 2945, 3224,
    3493, 3751, 3998, 4231, 4452, 4659, 4852, 5031, 5194, 5343, 5476, 5594,
    5697, 5784, 5856, 5912, 5953, 5979, 5991, 5989, 5972, 5943, 5900, 5845,
    5779, 5701, 5613, 5515, 5407, 5291, 5168, 5037, 4900, 4757, 4609, 4456,
    4300, 4140, 3978, 3814, 3649, 3482, 3316, 3149, 2982, 2816, 2651, 2488,
    2326, 2165, 2006, 1850, 1695, 1542, 1391, 1242, 1095, 949, 805, 663,
    521, 381, 241, 102, -36, -176, -315, -455, -595, -736, -879, -1023,
    -1168, -1315, -1463, -1613, -1765, -1919, -2075, -2232, -2390, -2551, -2712, -2874,
    -3037, -3200, -3363, -3526, -3688, -3848, -4007, -4163, -4316, -4466, -4611, -4752,
    -4887, -5016, -5138, -5252, -5359, -5456, -5544, -5622, -5689, -5745, -5790, -5821,
    -5840, -5846, -5838, -5816, -5779, -5728, -5662, -5582, -5486, -5375, -5250, -5110,
    -4955, -4786, -4603, -4406, -4196, -3974, -3739, -3493, -3236, -2970, -2694, -2409,
    -2117, -1819, -1515, -1206, -893, -577, -260, 56, 374, 690, 1004, 1314,
    1620, 1920, 2214, 2501, 2780, 3049, 3309, 3559, 3797, 4024, 4238, 4439,
    4627, 4800, 4960, 5105, 5236, 5352, 5453, 5539, 5610, 5667, 5709, 5737,
    5750, 5750, 5737, 5710, 5672, 5621, 5559, 5486, 5403, 5311, 5209, 5099,
    4982, 4858, 4727, 4590, 4449, 4303, 4154, 4001, 3846, 3689, 3530, 3371,
    3211, 3050, 2890, 2731, 2573, 2415, 2259, 2105, 1952, 1802, 1653, 1506,
    1360, 1217, 1076, 936, 797, 660, 524, 389, 254, 121, -12, -145,
    -279, -413, -548, -683, -820, -958, -1097, -1237, -1380, -1523, -1669, -1816,
    -1965, -2116, -2268, -2422, -2576, -2732, -2888, -3045, -3201, -3358, -3513, -3668,
    -3820, -3971, -4118, -4263, -4403, -4539, -4669, -4794, -4912, -5023, -5127, -5222,
    -5308, -5385, -5451, -5507, -5551, -5584, -5604, -5612, -5606, -5587, -5555, -5508,
    -5448, -5373, -5283, -5180, -5062, -4930, -4783, -4623, -4450, -4263, -4064, -3853,
    -3629, -3395, -3150, -2896, -2632, -2361, -2082, -1796, -1505, -1209, -909, -607,
    -303, 1, 306, 610, 911, 1210, 1504, 1794, 2077, 2354, 2623, 2883,
    3134, 3376, 3606, 3826, 4033, 4228, 4411, 4580, 4736, 4878, 5006, 5119,
    5219, 5304, 5375, 5431, 5474, 5503, 5519, 5521, 5510, 5487, 5452, 5405,
    5348, 5280, 5201, 5114, 5018, 4914, 4803, 4684, 4560, 4430, 4295, 4156,
    4013, 3867, 3718, 3568, 3415, 3262, 3109, 2955, 2801, 2648, 2496, 2345,
    2195, 2046, 1900, 1754, 1611, 1470, 1330, 1192, 1056, 921, 788, 656,
    525, 396, 267, 138, 10, -117, -245, -374, -503, -633, -764, -896,
    -1030, -1164, -1301, -1438, -1578, -1719, -1862, -2006, -2152, -2299, -2447, -2596,
    -2746, -2897, -3047, -3197, -3347, -3495, -3642, -3787, -3929, -4068, -4203, -4335,
    -4461, -4582, -4696, -4804, -4905, -4998, -5082, -5157, -5223, -5278, -5322, -5356,
    -5377, -5387, -5384, -5368, -5339, -5296, -5241, -5171, -5088, -4991, -4880, -4755,
    -4617, -4466, -4302, -4125, -3935, -3734, -3522, -3299, -3066, -2823, -2572, -2312,
    -2045, -1772, -1494, -1210, -923, -633, -341, -49, 243, 535, 825, 1112,
    1395, 1674, 1947, 2214, 2473, 2725, 2968, 3201, 3424, 3637, 3838, 4027,
    4205, 4369, 4521, 4660, 4785, 4896, 4994, 5078, 5149, 5205, 5249, 5279,
    5296, 5300, 5292, 5272, 5240, 5197, 5144, 5080, 5007, 4925, 4834, 4735,
    4629, 4517, 4398, 4274, 4146, 4013, 3876, 3736, 3594, 3450, 3304, 3157,
    3010, 2862, 2715, 2568, 2421, 2276, 2132, 1989, 1848, 1708, 1570, 1434,
    1300, 1167, 1036, 907, 779, 652, 526, 401, 277, 154, 31, -91,
    -214, -338, -462, -586, -712, -838, -966, -1095, -1226, -1358, -1491, -1626,
    -1763, -1902, -2041, -2182, -2324, -2468, -2611, -2756, -2900, -3044, -3188, -3331,
    -3472, -3611, -3748, -3882, -4013, -4139, -4261, -4378, -4489, -4594, -4692, -4783,
    -4865, -4939, -5003, -5058, -5103, -5136, -5159, -5170, -5169, -5156, -5131, -5092,
    -5041, -4976, -4899, -4808, -4704, -4586, -4456, -4313, -4158, -3990, -3810, -3619,
    -3417, -3205, -2982, -2751, -2511, -2263, -2008, -1747, -1481, -1209, -934, -656,
    -377, -96, 185, 465, 744, 1020, 1292, 1561, 1824, 2081, 2331, 2574,
    2809, 3035, 3251, 3456, 3652, 3835, 4008, 4168, 4316, 4451, 4573, 4683,
    4779, 4862, 4932, 4988, 5032, 5063, 5082, 5088, 5082, 5065, 5037, 4997,
    4948, 4888, 4819, 4742, 4656, 4562, 4462, 4355, 4242, 4124, 4001, 3874,
    3744, 3610, 3474, 3336, 3196, 3055, 2914, 2772, 2631, 2489, 2349, 2209,
    2070, 1933, 1797, 1663, 1530, 1399, 1270, 1143, 1016, 892, 769, 647,
    526, 406, 287, 168, 50, -67, -185, -303, -422, -542, -662, -783,
    -906, -1030, -1155, -1281, -1409, -1539, -1670, -1802, -1936, -2071, -2208, -2345,
    -2483, -2621, -2760, -2898, -3036, -3174, -3309, -3443, -3575, -3705, -3831, -3953,
    -4071, -4184, -4292, -4393, -4489, -4577, -4657, -4729, -4793, -4847, -4892, -4926,
    -4949, -4962, -4963, -4953, -4930, -4896, -4849, -4789, -4716, -4631, -4534, -4423,
    -4300, -4165, -4018, -3859, -3688, -3507, -3315, -3112, -2901, -2680, -2451, -2214,
    -1971, -1721, -1466, -1206, -943, -677, -408, -139, 130, 400, 667, 933,
    1195, 1454, 1707, 1955, 2197, 2431, 2658, 2876, 3085, 3284, 3474, 3652,
    3819, 3975, 4119, 4251, 4371, 4478, 4572, 4654, 4723, 4780, 4824, 4856,
    4876, 4884, 4881, 4866, 4840, 4804, 4758, 4703, 4638, 4565, 4484, 4396,
    4301, 4199, 4092, 3979, 3862, 3741, 3616, 3488, 3358, 3225, 3092, 2957,
    2821, 2685, 2549, 2413, 2278, 2144, 2010, 1878, 1748, 1619, 1491, 1365,
    1241, 1118, 997, 877, 758, 641, 525, 410, 295, 181, 68, -45,
    -158, -272, -386, -500, -615, -732, -849, -968, -1087, -1209, -1331, -1455,
    -1581, -1708, -1836, -1966, -2096, -2228, -2360, -2493, -2626, -2759, -2892, -3024,
    -3154, -3283, -3410, -3535, -3656, -3774, -3888, -3998, -4102, -4201, -4293, -4379,
    -4458, -4528, -4591, -4645, -4689, -4724, -4748, -4762, -4765, -4757, -4738, -4706,
    -4663, -4608, -4541, -4461, -4369, -4265, -4149, -4022, -3882, -3732, -3570, -3397,
    -3215, -3022, -2820, -2610, -2392, -2166, -1933, -1694, -1450, -1202, -949, -694,
    -437, -178, 80, 339, 596, 852, 1104, 1353, 1597, 1836, 2069, 2295,
    2514, 2725, 2927, 3120, 3304, 3477, 3639, 3791, 3931, 4060, 4177, 4281,
    4374, 4455, 4524, 4580, 4625, 4657, 4678, 4688, 4687, 4674, 4652, 4619,
    4576, 4524, 4464, 4395, 4319, 4235, 4145, 4048, 3946, 3839, 3727, 3611,
    3492, 3370, 3245, 3118, 2990, 2861, 2731, 2600, 2469, 2339, 2209, 2080,
    1952, 1825, 1699, 1575, 1453, 1331, 1212, 1094, 977, 862, 748, 635,
    523, 412, 302, 193, 84, -24, -133, -242, -351, -461, -572, -683,
    -795, -909, -1024, -1140, -1257, -1376, -1497, -1618, -1741, -1865, -1991, -2117,
    -2244, -2371, -2499, -2627, -2754, -2881, -3006, -3130, -3253, -3373, -3490, -3604,
    -3714, -3820, -3921, -4017, -4106, -4190, -4267, -4336, -4397, -4450, -4494, -4529,
    -4555, -4570, -4575, -4569, -4552, -4524, -4484, -4433, -4371, -4296, -4210, -4113,
    -4003, -3883, -3751, -3608, -3455, -3291, -3117, -2934, -2742, -2541, -2333, -2117,
    -1895, -1667, -1433, -1195, -954, -709, -462, -214, 34, 282, 529, 775,
    1018, 1257, 1493, 1723, 1948, 2166, 2378, 2581, 2777, 2964, 3141, 3309,
    3467, 3614, 3751, 3876, 3991, 4093, 4184, 4264, 4332, 4388, 4433, 4466,
    4488, 4500, 4500, 4490, 4470, 4440, 4401, 4352, 4296, 4231, 4159, 4080,
    3994, 3903, 3805, 3703, 3597, 3486, 3372, 3256, 3136, 3015, 2892, 2768,
    2643, 2518, 2392, 2267, 2142, 2018, 1895, 1773, 1652, 1533, 1415, 1298,
    1183, 1069, 957, 846, 737, 628, 521, 414, 309, 203, 99, -5,
    -109, -214, -319, -424, -530, -637, -745, -854, -964, -1075, -1187, -1301,
    -1416, -1533, -1651, -1770, -1890, -2011, -2133, -2255, -2377, -2500, -2622, -2744,
    -2865, -2985, -3102, -3218, -3331, -3441, -3547, -3650, -3747, -3840, -3927, -4009,
    -4083, -4151, -4211, -4264, -4308, -4343, -4369, -4385, -4391, -4388, -4373, -4348,
    -4312, -4265, -4207, -4138, -4057, -3965, -3862, -3748, -3623, -3488, -3343, -3187,
    -3022, -2848, -2665, -2473, -2275, -2069, -1856, -1638, -1415, -1187, -956, -722,
    -485, -247, -8, 229, 467, 703, 937, 1167, 1394, 1616, 1833, 2043,
    2248, 2445, 2634, 2815, 2987, 3150, 3303, 3446, 3579, 3701, 3813, 3913,
    4002, 4081, 4148, 4204, 4249, 4283, 4306, 4318, 4320, 4312, 4295, 4268,
    4232, 4187, 4134, 4073, 4005, 3930, 3849, 3762, 3670, 3572, 3471, 3365,
    3257, 3145, 3031, 2914, 2797, 2678, 2558, 2438, 2317, 2197, 2077, 1958,
    1840, 1722, 1606, 1491, 1378, 1265, 1155, 1045, 937, 831, 725, 621,
    518, 415, 314, 213, 112, 12, -87, -188, -288, -389, -491, -594,
    -697, -801, -907, -1013, -1121, -1230, -1340, -1452, -1565, -1679, -1794, -1910,
    -2027, -2144, -2262, -2380, -2497, -2614, -2730, -2845, -2959, -3070, -3179, -3285,
    -3388, -3487, -3581, -3671, -3756, -3835, -3908, -3974, -4033, -4085, -4128, -4164,
    -4190, -4207, -4215, -4213, -4201, -4179, -4146, -4103, -4049, -3984, -3909, -3822,
    -3725, -3618, -3500, -3372, -3234, -3086, -2929, -2763, -2589, -2407, -2217, -2021,
    -1818, -1609, -1396, -1178, -956, -732, -505, -277, -48, 180, 409, 636,
    861, 1082, 1301, 1515, 1724, 1927, 2124, 2314, 2497, 2672, 2839, 2997,
    3146, 3285, 3414, 3533, 3642, 3740, 3828, 3905, 3971, 4027, 4072, 4106,
    4130, 4144, 4148, 4142, 4126, 4102, 4069, 4027, 3978, 3921, 3857, 3786,
    3709, 3626, 3538, 3446, 3349, 3248, 3144, 3038, 2928, 2817, 2704, 2590,
    2476, 2360, 2245, 2129, 2014, 1899, 1786, 1673, 1561, 1451, 1341, 1233,
    1127, 1022, 918, 815, 714, 613, 514, 416, 318, 221, 124, 28,
    -67, -163, -260, -357, -454, -553, -652, -752, -853, -955, -1058, -1162,
    -1268, -1375, -1483, -1593, -1703, -1814, -1926, -2039, -2152, -2265, -2378, -2490,
    -2602, -2712, -2821, -2929, -3034, -3136, -3235, -3331, -3422, -3510, -3592, -3669,
    -3740, -3804, -3862, -3913, -3956, -3992, -4018, -4037, -4046, -4046, -4036, -4016,
    -3986, -3947, -3897, -3836, -3766, -3684, -3593, -3492, -3380, -3259, -3128, -2988,
    -2839, -2681, -2515, -2341, -2160, -1973, -1779, -1580, -1376, -1167, -955, -740,
    -523, -304, -84, 135, 354, 573, 789, 1002, 1212, 1419, 1620, 1816,
    2007, 2190, 2367, 2537, 2698, 2851, 2995, 3131, 3256, 3373, 3479, 3575,
    3661, 3737, 3802, 3857, 3902, 3937, 3962, 3976, 3982, 3978, 3964, 3942,
    3912, 3873, 3827, 3774, 3713, 3646, 3574, 3495, 3412, 3324, 3231, 3135,
    3036, 2934, 2830, 2723, 2615, 2506, 2396, 2285, 2174, 2063, 1952, 1842,
    1733, 1625, 1517, 1411, 1306, 1202, 1099, 998, 898, 799, 702, 605,
    510, 415, 322, 228, 136, 43, -48, -141, -233, -326, -420, -514,
    -609, -705, -801, -899, -998, -1098, -1200, -1302, -1406, -1511, -1616, -1723,
    -1830, -1938, -2047, -2155, -2263, -2372, -2479, -2585, -2690, -2794, -2895, -2993,
    -3089, -3182, -3270, -3355, -3435, -3509, -3579, -3642, -3699, -3749, -3791, -3826,
    -3854, -3873, -3883, -3884, -3876, -3859, -3832, -3796, -3750, -3693, -3627, -3551,
    -3465, -3369, -3264, -3149, -3025, -2892, -2750, -2600, -2442, -2277, -2105, -1926,
    -1741, -1550, -1355, -1156, -953, -747, -538, -328, -117, 93, 304, 513,
    721, 927, 1129, 1328, 1522, 1711, 1895, 2073, 2244, 2407, 2564, 2712,
    2852, 2983, 3106, 3219, 3322, 3416, 3501, 3575, 3640, 3694, 3739, 3774,
    3799, 3815, 3822, 3820, 3808, 3789, 3761, 3725, 3682, 3632, 3575, 3512,
    3443, 3369, 3289, 3205, 3118, 3026, 2931, 2834, 2734, 2632, 2528, 2424,
    2318, 2212, 2105, 1999, 1893, 1787, 1682, 1578, 1474, 1372, 1271, 1171,
    1072, 975, 879, 784, 690, 597, 505, 415, 324, 235, 146, 57,
    -31, -120, -209, -298, -387, -478, -569, -660, -753, -847, -942, -1038,
    -1135, -1233, -1332, -1433, -1534, -1636, -1739, -1843, -1947, -2051, -2155, -2259,
    -2362, -2464, -2565, -2665, -2762, -2857, -2950, -3039, -3125, -3207, -3284, -3357,
    -3424, -3486, -3541, -3591, -3633, -3668, -3695, -3715, -3726, -3729, -3723, -3708,
    -3684, -3651, -3608, -3556, -3494, -3422, -3341, -3251, -3152, -3043, -2925, -2799,
    -2664, -2522, -2371, -2214, -2050, -1879, -1702, -1520, -1334, -1143, -948, -751,
    -551, -350, -148, 54, 256, 458, 658, 856, 1050, 1242, 1429, 1611,
    1789, 1960, 2126, 2284, 2436, 2579, 2715, 2843, 2962, 3072, 3173, 3265,
    3347, 3420, 3484, 3538, 3582, 3618, 3644, 3661, 3668, 3668, 3658, 3641,
    3616, 3583, 3542, 3495, 3442, 3382, 3317, 3246, 3171, 3091, 3008, 2920,
    2830, 2737, 2641, 2544, 2444, 2344, 2243, 2141, 2039, 1937, 1835, 1733,
    1632, 1532, 1432, 1334, 1237, 1141, 1046, 952, 859, 768, 678, 589,
    500, 413, 326, 240, 155, 69, -15, -100, -185, -271, -357, -443,
    -531, -619, -707, -797, -888, -980, -1073, -1167, -1262, -1358, -1455, -1553,
    -1652, -1752, -1851, -1951, -2051, -2151, -2250, -2348, -2446, -2541, -2635, -2727,
    -2816, -2903, -2986, -3065, -3140, -3211, -3276, -3336, -3391, -3439, -3481, -3516,
    -3543, -3563, -3576, -3580, -3576, -3563, -3541, -3511, -3471, -3423, -3365, -3298,
    -3222, -3137, -3043, -2940, -2828, -2709, -2581, -2445, -2302, -2152, -1995, -1832,
    -1664, -1490, -1312, -1129, -943, -754, -563, -370, -176, 18, 212, 406,
    598, 789, 976, 1160, 1341, 1517, 1688, 1854, 2013, 2167, 2313, 2453,
    2584, 2708, 2824, 2931, 3029, 3119, 3200, 3272, 3334, 3388, 3432, 3468,
    3494, 3512, 3521, 3522, 3514, 3499, 3476, 3445, 3408, 3364, 3313, 3257,
    3195, 3129, 3057, 2981, 2901, 2818, 2732, 2643, 2551, 2458, 2363, 2267,
    2170, 2072, 1974, 1876, 1778, 1680, 1583, 1487, 1391, 1297, 1203, 1111,
    1020, 929, 840, 753, 666, 580, 495, 411, 328, 245, 163, 81,
    0, -82, -164, -246, -328, -411, -495, -579, -664, -750, -837, -925,
    -1014, -1105, -1196, -1288, -1381, -1475, -1570, -1665, -1760, -1856, -1952, -2048,
    -2143, -2238, -2332, -2424, -2514, -2603, -2689, -2772, -2853, -2929, -3002, -3071,
    -3134, -3193, -3246, -3294, -3335, -3370, -3397, -3418, -3431, -3436, -3434, -3423,
    -3404, -3376, -3339, -3294, -3240, -3178, -3106, -3026, -2937, -2840, -2734, -2621,
    -2499, -2370, -2234, -2091, -1942, -1787, -1626, -1460, -1289, -1115, -937, -756,
    -572, -387, -201, -14, 172, 358, 542, 725, 906, 1083, 1257, 1427,
    1592, 1752, 1907, 2055, 2197, 2332, 2459, 2580, 2692, 2796, 2892, 2980,
    3059, 3129, 3191, 3244, 3288, 3323, 3350, 3369, 3379, 3381, 3375, 3362,
    3341, 3313, 3278, 3237, 3189, 3136, 3078, 3015, 2947, 2875, 2799, 2719,
    2637, 2552, 2465, 2375, 2284, 2192, 2099, 2006, 1912, 1817, 1723, 1629,
    1536, 1443, 1352, 1261, 1171, 1082, 994, 907, 821, 737, 653, 571,
    489, 408, 328, 249, 170, 91, 12, -65, -144, -222, -301, -381,
    -461, -542, -623, -706, -789, -874, -959, -1045, -1133, -1221, -1310, -1400,
    -1491, -1582, -1674, -1766, -1858, -1950, -2042, -2133, -2223, -2311, -2399, -2484,
    -2567, -2648, -2725, -2799, -2870, -2937, -2999, -3056, -3108, -3154, -3195, -3229,
    -3257, -3278, -3292, -3298, -3297, -3288, -3271, -3246, -3212, -3170, -3120, -3061,
    -2994, -2919, -2835, -2743, -2643, -2535, -2420, -2297, -2168, -2032, -1889, -1741,
    -1588, -1429, -1266, -1099, -929, -756, -580, -403, -224, -45, 134, 312,
    490, 666, 840, 1011, 1178, 1342, 1501, 1656, 1805, 1948, 2086, 2216,
    2340, 2457, 2566, 2667, 2761, 2847, 2924, 2993, 3053, 3106, 3150, 3185,
    3212, 3231, 3243, 3246, 3241, 3230, 3211, 3185, 3153, 3114, 3070, 3020,
    2965, 2905, 2840, 2772, 2700, 2624, 2545, 2464, 2381, 2295, 2208, 2120,
    2031, 1941, 1851, 1760, 1670, 1580, 1490, 1401, 1313, 1225, 1139, 1053,
    969, 885, 803, 721, 641, 562, 483, 405, 328, 252, 176, 100,
    25, -49, -125, -200, -276, -352, -429, -507, -585, -664, -744, -824,
    -906, -989, -1073, -1157, -1243, -1329, -1416, -1504, -1592, -1680, -1768, -1857,
    -1945, -2032, -2119, -2204, -2288, -2370, -2451, -2528, -2603, -2675, -2744, -2808,
    -2868, -2924, -2975, -3021, -3061, -3095, -3123, -3144, -3158, -3166, -3166, -3159,
    -3144, -3121, -3090, -3051, -3004, -2949, -2886, -2815, -2736, -2649, -2554, -2452,
    -2343, -2226, -2103, -1974, -1838, -1697, -1550, -1399, -1243, -1083, -920, -754,
    -586, -416, -245, -73, 98, 270, 441, 610, 777, 942, 1103, 1261,
    1415, 1564, 1708, 1847, 1980, 2106, 2226, 2339, 2446, 2544, 2635, 2719,
    2794, 2862, 2922, 2973, 3017, 3052, 3080, 3099, 3111, 3116, 3113, 3103,
    3086, 3062, 3032, 2997, 2955, 2908, 2856, 2799, 2738, 2673, 2604, 2532,
    2457, 2379, 2299, 2218, 2134, 2050, 1964, 1878, 1792, 1705, 1618, 1531,
    1445, 1360, 1275, 1191, 1107, 1025, 944, 864, 784, 706, 629, 552,
    477, 402, 328, 255, 182, 109, 37, -35, -107, -180, -252, -325,
    -399, -473, -548, -624, -700, -778, -856, -935, -1016, -1097, -1179, -1261,
    -1345, -1429, -1513, -1598, -1683, -1768, -1852, -1936, -2020, -2102, -2183, -2262,
    -2339, -2414, -2487, -2556, -2623, -2685, -2744, -2798, -2848, -2893, -2932, -2966,
    -2993, -3015, -3030, -3038, -3040, -3034, -3021, -3000, -2972, -2936, -2892, -2841,
    -2782, -2715, -2640, -2558, -2468, -2371, -2268, -2157, -2040, -1917, -1787, -1653,
    -1513, -1368, -1219, -1067, -911, -752, -591, -428, -264, -99, 66, 231,
    395, 558, 718, 877, 1032, 1185, 1333, 1477, 1616, 1750, 1879, 2001,
    2118, 2227, 2330, 2426, 2515, 2597, 2671, 2737, 2795, 2846, 2889, 2925,
    2952, 2973, 2985, 2991, 2989, 2981, 2966, 2944, 2916, 2883, 2844, 2800,
    2750, 2697, 2639, 2577, 2511, 2442, 2371, 2297, 2221, 2143, 2063, 1982,
    1900, 1817, 1734, 1651, 1568, 1485, 1402, 1319, 1238, 1157, 1077, 998,
    919, 842, 766, 691, 616, 543, 470, 398, 327, 257, 186, 117,
    47, -21, -91, -160, -230, -300, -371, -442, -514, -586, -660, -734,
    -809, -885, -961, -1039, -1118, -1197, -1277, -1357, -1438, -1520, -1601, -1683,
    -1764, -1845, -1925, -2004, -2082, -2158, -2233, -2305, -2375, -2443, -2507, -2568,
    -2624, -2677, -2726, -2770, -2808, -2842, -2869, -2891, -2907, -2916, -2918, -2914,
    -2902, -2884, -2858, -2825, -2784, -2736, -2681, -2618, -2547, -2470, -2385, -2293,
    -2195, -2089, -1978, -1861, -1738, -1609, -1476, -1338, -1196, -1050, -901, -749,
    -594, -438, -281, -122, 35, 194, 352, 508, 663, 816, 965, 1112,
    1255, 1394, 1528, 1658, 1782, 1901, 2014, 2120, 2220, 2314, 2400, 2480,
    2552, 2617, 2674, 2724, 2767, 2802, 2830, 2851, 2864, 2871, 2870, 2863,
    2850, 2830, 2805, 2773, 2737, 2695, 2649, 2598, 2543, 2484, 2422, 2356,
    2288, 2217, 2145, 2070, 1994, 1916, 1838, 1758, 1679, 1599, 1519, 1439,
    1359, 1280, 1202, 1124, 1047, 971, 896, 821, 748, 676, 604, 533,
    463, 394, 326, 258, 191, 124, 57, -9, -75, -142, -209, -276,
    -344, -412, -481, -551, -621, -692, -764, -836, -910, -984, -1060, -1136,
    -1212, -1290, -1367, -1445, -1524, -1601, -1676, -1751, -1825, -1898, -1969, -2039,
    -2107, -2173, -2236, -2297, -2354, -2408, -2459, -2505, -2548, -2586, -2619, -2646,
    -2669, -2686, -2697, -2703, -2702, -2695, -2681, -2661, -2634, -2601, -2560, -2514,
    -2460, -2400, -2333, -2260, -2180, -2095, -2003, -1906, -1803, -1696, -1583, -1466,
    -1345, -1220, -1091, -960, -826, -690, -552, -412, -273, -132, 7, 147,
    285, 422, 558, 691, 821, 948, 1071, 1191, 1306, 1417, 1523, 1624,
    1719, 1809, 1893, 1971, 2043, 2108, 2167, 2220, 2266, 2306, 2339, 2366,
    2386, 2401, 2409, 2411, 2408, 2399, 2384, 2365, 2340, 2311, 2277, 2240,
    2198, 2153, 2104, 2052, 1998, 1941, 1883, 1822, 1759, 1696, 1631, 1565,
    1499, 1432, 1366, 1299, 1232, 1166, 1100, 1035, 970, 906, 843, 781,
    720, 660, 600, 542, 485, 428, 373, 318, 264, 210, 157, 105,
    53, 1, -49, -101, -152, -203, -254, -306, -358, -410, -463, -516,
    -569, -623, -677, -732, -787, -842, -898, -954, -1010, -1066, -1122, -1178,
    -1233, -1288, -1342, -1396, -1448, -1500, -1550, -1598, -1644, -1689, -1731, -1770,
    -1807, -1841, -1872, -1900, -1924, -1944, -1960, -1973, -1981, -1984, -1984, -1978,
    -1968, -1953, -1933, -1909, -1879, -1845, -1806, -1762, -1713, -1659, -1601, -1539,
    -1472, -1401, -1326, -1248, -1166, -1081, -993, -902, -808, -713, -616, -517,
    -417, -316, -215, -113, -12, 88, 188, 288, 385, 481, 575, 667,
    756, 842, 925, 1005, 1081, 1153, 1222, 1286, 1346, 1402, 1453, 1500,
    1542, 1580, 1612, 1641, 1664, 1683, 1698, 1708, 1713, 1714, 1712, 1705,
    1694, 1680, 1662, 1641, 1617, 1589, 1559, 1527, 1492, 1455, 1416, 1375,
    1333, 1290, 1245, 1200, 1154, 1107, 1060, 1012, 965, 917, 870, 823,
    777, 730, 685, 640, 595, 551, 508, 466, 424, 383, 343, 304,
    265, 226, 189, 152, 115, 79, 43, 7, -28, -63, -98, -133,
    -169, -204, -239, -275, -310, -346, -383, -419, -456, -492, -530, -567,
    -604, -642, -679, -717, -754, -792, -829, -865, -901, -937, -972, -1006,
    -1038, -1070, -1101, -1130, -1158, -1183, -1208, -1230, -1250, -1267, -1283, -1296,
    -1306, -1313, -1318, -1320, -1319, -1314, -1307, -1296, -1283, -1266, -1246, -1222,
    -1196, -1166, -1133, -1098, -1059, -1017, -973, -926, -877, -825, -771, -715,
    -657, -598, -537, -474, -411, -346, -281, -216, -150, -84, -19, 45,
    110, 174, 237, 298, 358, 417, 474, 528, 581, 632, 680, 726,
    769, 809, 847, 882, 913, 942, 968, 991, 1011, 1028, 1042, 1054,
    1062, 1067, 1070, 1070, 1067, 1062, 1054, 1045, 1033, 1018, 1002, 985,
    965, 944, 921, 898, 873, 847, 820, 793, 764, 736, 707, 677,
    648, 618, 589, 559, 530, 501, 472, 443, 415, 387, 360, 333,
    307, 281, 256, 231, 207, 183, 160, 137, 115, 93, 71, 49,
    28, 7, -12, -33, -53, -74, -94, -114, -134, -154, -175, -195,
    -215, -236, -256, -277, -297, -318, -338, -359, -379, -400, -420, -440,
    -460, -480, -499, -518, -536, -554, -571, -587, -603, -618, -632, -645,
    -657, -668, -677, -685, -692, -698, -702, -705, -706, -706, -704, -700,
    -695, -688, -679, -669, -657, -643, -628, -611, -593, -573, -552, -529,
    -505, -480, -454, -426, -398, -368, -338, -307, -276, -244, -211, -178,
    -146, -113, -80, -47, -15, 17, 48, 79, 109, 139, 168, 195,
    222, 248, 272, 296, 318, 338, 357, 375, 392, 407, 420, 432,
    443, 452, 460, 466, 471, 474, 476, 477, 476, 474, 471, 467,
    462, 456, 449, 441, 432, 423, 413, 402, 391, 379, 367, 354,
    341, 328, 315, 302, 289, 275, 262, 249, 236, 223, 210, 197,
    185, 173, 161, 149, 138, 127, 116, 106, 96, 86, 77, 68,
    59, 50, 42, 34, 26, 18, 11, 3, -3, -10, -16, -23,
    -29, -36, -42, -48, -54, -60, -66, -71, -77, -82, -87, -93,
    -98, -103, -107, -112, -116, -121, -125, -129, -132, -135, -139, -141,
    -144, -146, -148, -149, -151, -151, -152, -152, -152, -151, -150, -149,
    -147, -145, -142, -139, -136, -133, -129, -125, -120, -116, -111, -106,
    -100, -95, -90, -84, -78, -73, -67, -61, -56, -50, -45, -40,
    -35, -30, -26, -21, -17, -14, -10, -7, -5, -2, -1, 0,
    1, 2, 2, 2, 2, 1,
};
const size_t prompt_low_battery_len = 13230;