// Copyright 2022 The Fuchsia Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

// Raw data of a short .wav file. Audio of a person saying "test" with
// duration less than 1s. Input PCM data used for CVSD codec testing.
pub const INPUT_TEST_S16LE64000MONO: [i16; 31949] = [
    144, 167, 141, 153, 167, 148, 145, 136, 128, 133, 153, 157, 166, 158, 154, 155, 163, 150, 153,
    157, 158, 146, 160, 167, 165, 155, 150, 150, 153, 152, 142, 140, 137, 145, 136, 134, 130, 143,
    150, 169, 179, 182, 173, 176, 168, 166, 178, 167, 156, 131, 130, 127, 126, 136, 138, 147, 151,
    156, 165, 161, 179, 181, 185, 191, 195, 204, 191, 200, 196, 207, 206, 212, 217, 222, 219, 207,
    211, 216, 210, 215, 214, 223, 216, 222, 225, 220, 230, 226, 229, 225, 223, 215, 193, 191, 180,
    162, 153, 151, 148, 144, 153, 145, 152, 136, 135, 123, 135, 122, 114, 107, 118, 132, 135, 135,
    129, 119, 128, 126, 122, 126, 125, 114, 109, 105, 107, 104, 115, 107, 102, 108, 118, 105, 96,
    99, 98, 99, 101, 104, 101, 103, 111, 106, 102, 105, 105, 94, 98, 87, 88, 77, 79, 72, 76, 88,
    98, 107, 113, 113, 103, 106, 117, 126, 122, 133, 137, 123, 110, 102, 102, 93, 81, 78, 67, 68,
    59, 69, 77, 86, 92, 102, 116, 121, 128, 115, 109, 111, 118, 117, 101, 96, 89, 78, 76, 80, 80,
    69, 57, 65, 70, 81, 68, 56, 60, 57, 63, 46, 54, 37, 31, 10, -6, -17, -22, -10, -16, -31, -29,
    -20, -10, -32, -43, -41, -30, -35, -46, -48, -48, -52, -66, -77, -93, -104, -125, -138, -139,
    -142, -141, -158, -166, -187, -192, -210, -221, -237, -240, -239, -253, -269, -271, -265, -283,
    -313, -332, -335, -330, -345, -355, -350, -340, -335, -337, -317, -308, -307, -311, -309, -312,
    -318, -313, -313, -316, -305, -292, -289, -296, -279, -281, -269, -276, -255, -248, -240, -254,
    -259, -251, -250, -251, -264, -265, -283, -290, -286, -298, -331, -356, -367, -359, -360, -349,
    -356, -369, -378, -380, -369, -360, -352, -355, -358, -369, -368, -379, -376, -381, -383, -385,
    -399, -408, -421, -431, -437, -441, -445, -424, -409, -391, -397, -393, -392, -381, -379, -372,
    -364, -341, -338, -344, -353, -338, -341, -346, -343, -341, -354, -371, -370, -371, -372, -365,
    -357, -354, -354, -356, -359, -358, -364, -369, -368, -375, -384, -399, -408, -423, -434, -439,
    -440, -457, -471, -496, -500, -500, -486, -477, -474, -470, -464, -462, -449, -435, -426, -410,
    -407, -401, -391, -372, -366, -371, -381, -377, -375, -357, -344, -326, -312, -307, -299, -296,
    -277, -271, -255, -253, -240, -238, -231, -226, -225, -221, -216, -193, -189, -197, -196, -201,
    -207, -223, -222, -210, -201, -201, -214, -203, -196, -182, -182, -173, -159, -155, -153, -148,
    -159, -180, -190, -193, -186, -188, -188, -193, -201, -208, -206, -199, -193, -193, -213, -220,
    -217, -209, -209, -197, -180, -166, -171, -169, -175, -154, -144, -133, -130, -133, -128, -139,
    -148, -157, -149, -141, -133, -151, -160, -152, -133, -130, -126, -125, -131, -138, -130, -124,
    -135, -133, -145, -144, -151, -142, -146, -153, -159, -174, -191, -201, -195, -204, -217, -223,
    -226, -223, -207, -204, -212, -215, -209, -209, -213, -201, -196, -196, -205, -199, -189, -178,
    -162, -162, -165, -159, -165, -164, -182, -176, -165, -142, -129, -124, -115, -103, -96, -89,
    -75, -55, -43, -46, -53, -50, -52, -43, -47, -26, -25, -22, -21, -14, -18, -31, -36, -35, -32,
    -25, -27, -28, -43, -45, -50, -42, -43, -38, -29, -35, -55, -80, -88, -88, -98, -105, -107,
    -105, -106, -110, -109, -99, -92, -103, -113, -102, -92, -79, -69, -53, -61, -61, -62, -43,
    -38, -18, -13, 6, -10, -11, -9, 12, 29, 28, 22, 37, 47, 62, 61, 52, 47, 40, 48, 42, 52, 54, 38,
    22, 23, 30, 28, 23, 34, 27, 21, 21, 24, 18, 4, 13, 17, 17, 15, 32, 44, 51, 56, 65, 74, 71, 77,
    87, 97, 87, 75, 74, 83, 76, 61, 50, 54, 68, 67, 77, 86, 100, 97, 99, 121, 138, 141, 134, 133,
    138, 147, 157, 173, 167, 167, 162, 176, 166, 153, 144, 158, 155, 144, 132, 143, 149, 160, 153,
    144, 126, 114, 118, 120, 112, 117, 110, 107, 91, 69, 66, 61, 65, 60, 55, 51, 48, 31, 27, 17,
    27, 30, 27, 21, 20, 23, 6, 12, 15, 31, 30, 22, 11, -6, -11, -21, -33, -33, -36, -28, -30, -34,
    -28, -37, -38, -46, -30, -27, -26, -31, -25, -19, -14, -19, -28, -11, 5, 17, 4, 16, 15, 26, 22,
    24, 28, 44, 54, 48, 58, 57, 59, 54, 62, 81, 89, 91, 91, 92, 92, 88, 67, 62, 55, 54, 37, 38, 35,
    39, 40, 34, 18, 6, 8, 12, -5, 8, -1, 9, 12, 11, 25, 25, 45, 30, 39, 40, 46, 32, 29, 35, 31, 23,
    20, 31, 39, 49, 46, 42, 47, 52, 53, 51, 53, 45, 39, 32, 31, 36, 46, 42, 26, 18, 23, 14, -1,
    -10, -14, -31, -47, -50, -63, -70, -76, -70, -83, -81, -93, -90, -107, -108, -116, -124, -149,
    -160, -178, -161, -161, -163, -168, -166, -170, -172, -170, -163, -157, -160, -154, -150, -137,
    -119, -110, -100, -92, -74, -60, -47, -39, -37, -41, -54, -56, -52, -44, -37, -36, -33, -33,
    -25, -21, -17, -19, -18, -18, -23, -26, -20, -8, -8, -13, -21, -22, -35, -57, -70, -81, -95,
    -121, -131, -119, -113, -110, -112, -102, -98, -86, -85, -68, -75, -68, -84, -83, -83, -83,
    -89, -91, -94, -93, -82, -68, -74, -83, -74, -56, -49, -47, -42, -33, -34, -44, -44, -38, -38,
    -51, -55, -62, -61, -62, -56, -57, -67, -69, -76, -74, -79, -92, -101, -107, -118, -120, -129,
    -129, -143, -143, -140, -132, -131, -141, -142, -155, -157, -167, -181, -174, -172, -176, -193,
    -203, -220, -227, -231, -226, -230, -236, -227, -210, -200, -203, -205, -202, -186, -173, -154,
    -152, -154, -159, -145, -122, -115, -112, -115, -113, -113, -112, -108, -118, -115, -118, -123,
    -120, -116, -106, -102, -108, -113, -119, -113, -114, -125, -133, -138, -139, -139, -149, -160,
    -158, -157, -148, -152, -143, -136, -133, -123, -119, -115, -122, -121, -122, -112, -120, -109,
    -109, -108, -112, -123, -115, -111, -104, -90, -86, -89, -102, -108, -109, -125, -130, -129,
    -122, -123, -119, -118, -127, -134, -134, -131, -133, -115, -100, -93, -98, -105, -91, -91,
    -87, -84, -75, -77, -93, -97, -105, -111, -129, -121, -121, -102, -108, -99, -99, -87, -82,
    -75, -58, -49, -45, -59, -60, -65, -59, -63, -61, -55, -41, -41, -61, -75, -70, -51, -40, -39,
    -49, -51, -37, -28, -26, -21, -6, 15, 20, 20, 28, 21, 10, -5, -17, -18, -15, -23, -21, -30,
    -22, -14, -21, -26, -13, -3, -6, -23, -18, -16, -25, -15, -5, -13, -26, -25, -3, 6, 7, 8, 24,
    34, 37, 32, 30, 38, 30, 23, 21, 24, 34, 41, 52, 57, 57, 61, 68, 77, 74, 62, 58, 56, 55, 34, 28,
    27, 13, 4, 1, 25, 19, 17, 23, 28, 29, 20, 26, 18, 11, 10, 6, 1, -8, -20, -30, -49, -68, -102,
    -107, -88, -81, -93, -97, -107, -106, -115, -106, -117, -120, -133, -127, -126, -120, -107,
    -99, -83, -89, -80, -65, -29, -8, 6, 8, 15, 25, 40, 52, 58, 51, 40, 45, 65, 84, 90, 84, 88,
    101, 104, 121, 124, 123, 116, 123, 139, 133, 119, 101, 101, 94, 82, 77, 74, 62, 37, 21, 22, 31,
    27, 15, 1, -5, -9, -7, 7, 30, 35, 32, 20, 25, 30, 41, 48, 52, 35, 39, 29, 39, 23, 40, 45, 59,
    60, 74, 87, 102, 116, 125, 140, 124, 123, 97, 107, 105, 112, 98, 96, 96, 102, 101, 84, 78, 71,
    72, 69, 63, 68, 71, 69, 53, 33, 22, 15, 5, -11, -27, -50, -60, -77, -68, -79, -87, -104, -113,
    -108, -98, -79, -74, -73, -83, -80, -80, -67, -67, -50, -25, 4, 20, 23, 28, 32, 29, 36, 65, 94,
    108, 103, 106, 125, 146, 151, 155, 165, 168, 164, 169, 180, 192, 199, 205, 206, 194, 181, 178,
    174, 177, 164, 150, 132, 132, 134, 134, 126, 122, 123, 132, 139, 144, 149, 144, 140, 125, 125,
    126, 149, 148, 141, 115, 113, 105, 109, 96, 96, 92, 103, 94, 84, 87, 102, 108, 96, 106, 125,
    137, 151, 164, 178, 172, 169, 174, 179, 175, 167, 160, 150, 152, 148, 142, 145, 135, 126, 122,
    129, 141, 140, 128, 118, 109, 109, 125, 130, 128, 106, 115, 114, 114, 101, 91, 83, 83, 72, 59,
    28, 25, 32, 30, 34, 38, 53, 69, 79, 101, 100, 106, 100, 95, 94, 106, 112, 113, 121, 119, 107,
    103, 111, 119, 114, 115, 127, 141, 153, 162, 171, 181, 198, 207, 219, 228, 231, 229, 235, 243,
    241, 212, 196, 193, 203, 215, 210, 206, 196, 204, 199, 202, 206, 218, 226, 216, 226, 227, 234,
    231, 233, 231, 223, 221, 218, 226, 219, 213, 196, 188, 180, 166, 154, 144, 131, 125, 118, 121,
    122, 140, 146, 141, 133, 139, 143, 139, 134, 139, 136, 144, 138, 153, 161, 166, 166, 167, 181,
    187, 187, 195, 198, 188, 188, 186, 211, 204, 212, 205, 219, 228, 227, 236, 250, 262, 248, 224,
    224, 220, 230, 224, 215, 213, 220, 236, 240, 233, 222, 225, 219, 223, 234, 251, 263, 257, 244,
    250, 256, 263, 250, 230, 220, 212, 220, 220, 231, 237, 233, 225, 227, 221, 223, 223, 232, 239,
    240, 217, 206, 203, 218, 221, 225, 225, 222, 223, 247, 258, 256, 251, 255, 252, 249, 250, 252,
    266, 272, 284, 273, 273, 262, 251, 247, 255, 258, 249, 248, 252, 255, 236, 229, 222, 230, 219,
    203, 188, 184, 180, 176, 154, 144, 132, 124, 124, 118, 126, 122, 135, 124, 121, 126, 124, 133,
    126, 134, 117, 102, 81, 71, 63, 60, 60, 72, 77, 81, 65, 65, 58, 61, 61, 75, 84, 80, 87, 93,
    107, 113, 127, 120, 125, 133, 152, 174, 188, 191, 170, 167, 176, 200, 209, 210, 205, 196, 200,
    205, 210, 214, 203, 189, 191, 198, 199, 194, 190, 195, 187, 182, 167, 164, 166, 171, 170, 152,
    147, 128, 125, 126, 127, 136, 134, 140, 141, 146, 135, 124, 119, 129, 125, 127, 133, 145, 133,
    122, 124, 146, 157, 165, 155, 156, 157, 153, 155, 149, 153, 150, 150, 147, 142, 140, 139, 129,
    122, 120, 117, 112, 92, 88, 85, 73, 58, 41, 42, 37, 30, 24, 28, 25, 29, 17, 4, -11, -24, -31,
    -44, -56, -69, -90, -103, -111, -125, -130, -137, -133, -137, -143, -152, -162, -166, -163,
    -156, -157, -153, -142, -121, -119, -118, -117, -100, -90, -65, -56, -59, -60, -38, -20, -12,
    -21, -12, -8, -9, -11, -7, -16, -23, -28, -22, -20, -37, -42, -50, -40, -36, -32, -35, -50,
    -63, -62, -76, -84, -100, -100, -106, -101, -103, -126, -137, -151, -149, -157, -145, -137,
    -132, -153, -166, -169, -148, -125, -112, -126, -150, -150, -132, -115, -108, -116, -127, -147,
    -147, -130, -109, -104, -113, -108, -94, -78, -81, -93, -94, -83, -62, -65, -72, -81, -91, -94,
    -108, -120, -130, -124, -120, -130, -144, -163, -172, -181, -193, -195, -207, -212, -231, -238,
    -247, -251, -271, -277, -286, -284, -298, -300, -297, -301, -312, -322, -320, -310, -304, -305,
    -300, -288, -291, -284, -280, -266, -260, -253, -238, -229, -224, -215, -207, -183, -173, -164,
    -159, -153, -150, -139, -135, -136, -140, -136, -131, -128, -139, -135, -144, -134, -134, -117,
    -117, -120, -138, -140, -137, -127, -123, -124, -128, -143, -148, -157, -147, -148, -155, -148,
    -144, -139, -149, -133, -122, -113, -113, -96, -102, -111, -119, -113, -120, -134, -133, -128,
    -117, -119, -132, -145, -142, -138, -129, -135, -125, -138, -132, -138, -130, -142, -137, -126,
    -131, -133, -136, -129, -132, -127, -125, -121, -128, -116, -119, -124, -130, -131, -129, -132,
    -133, -119, -118, -128, -135, -130, -125, -131, -143, -145, -140, -135, -134, -123, -110, -92,
    -67, -64, -63, -91, -82, -74, -47, -46, -34, -41, -45, -41, -23, -11, -7, -13, -4, -1, 15, 19,
    21, 14, 14, 13, 6, 15, 8, 16, 12, 22, 12, 8, 1, -8, -2, 20, 29, 25, 9, 18, 33, 63, 77, 76, 71,
    76, 88, 86, 100, 108, 110, 99, 93, 91, 94, 103, 105, 98, 102, 109, 109, 110, 118, 121, 121,
    125, 135, 140, 140, 137, 148, 144, 154, 161, 166, 155, 143, 137, 125, 108, 95, 107, 102, 108,
    97, 83, 65, 66, 91, 101, 99, 87, 81, 76, 72, 84, 82, 83, 76, 66, 60, 62, 70, 72, 64, 55, 46,
    49, 54, 57, 67, 67, 67, 59, 70, 79, 92, 94, 113, 124, 146, 158, 164, 156, 140, 137, 139, 156,
    181, 186, 191, 189, 200, 213, 212, 211, 208, 222, 234, 247, 250, 245, 244, 241, 252, 250, 252,
    242, 232, 222, 223, 219, 227, 242, 256, 258, 247, 253, 255, 257, 246, 249, 261, 280, 286, 283,
    281, 285, 294, 288, 294, 295, 302, 313, 317, 311, 309, 315, 334, 326, 324, 311, 328, 339, 351,
    346, 345, 341, 342, 344, 350, 347, 338, 319, 322, 309, 304, 286, 280, 284, 291, 294, 281, 274,
    274, 284, 282, 285, 281, 282, 275, 269, 263, 260, 261, 255, 239, 227, 227, 219, 213, 195, 191,
    182, 176, 167, 170, 170, 175, 171, 171, 173, 199, 212, 209, 195, 203, 207, 218, 218, 226, 223,
    224, 221, 236, 257, 282, 292, 288, 288, 290, 298, 290, 281, 282, 292, 298, 293, 286, 282, 283,
    282, 279, 265, 259, 268, 261, 255, 254, 259, 266, 254, 245, 241, 244, 250, 240, 242, 245, 264,
    260, 252, 231, 232, 223, 222, 222, 232, 251, 240, 229, 212, 199, 196, 186, 190, 197, 199, 194,
    173, 172, 182, 182, 187, 187, 198, 200, 209, 212, 215, 209, 223, 217, 198, 172, 163, 157, 146,
    130, 105, 98, 90, 87, 69, 58, 45, 45, 37, 45, 40, 40, 36, 22, 20, 16, 25, 14, 5, -7, -24, -34,
    -24, -22, -26, -43, -50, -56, -57, -59, -58, -64, -78, -94, -92, -79, -77, -83, -71, -66, -68,
    -62, -59, -55, -69, -59, -58, -57, -72, -78, -72, -56, -52, -43, -43, -35, -44, -48, -54, -57,
    -52, -39, -33, -45, -58, -62, -62, -64, -59, -62, -65, -72, -84, -80, -89, -89, -95, -87, -87,
    -83, -77, -69, -58, -50, -47, -47, -58, -65, -74, -83, -83, -93, -91, -107, -110, -112, -111,
    -103, -109, -124, -119, -110, -108, -118, -124, -122, -128, -126, -123, -123, -127, -126, -125,
    -130, -142, -146, -137, -137, -142, -167, -160, -161, -162, -180, -189, -201, -203, -202, -194,
    -189, -199, -211, -215, -210, -198, -206, -202, -211, -206, -199, -192, -201, -208, -199, -191,
    -191, -203, -203, -202, -193, -188, -192, -192, -191, -186, -193, -203, -203, -206, -202, -211,
    -212, -224, -213, -205, -190, -200, -212, -216, -215, -209, -215, -218, -216, -216, -221, -222,
    -209, -201, -198, -198, -194, -191, -186, -170, -172, -172, -177, -168, -153, -156, -167, -178,
    -178, -168, -164, -163, -174, -177, -186, -168, -168, -163, -168, -168, -159, -151, -164, -176,
    -176, -168, -168, -174, -171, -170, -190, -201, -214, -211, -209, -213, -210, -210, -197, -200,
    -213, -220, -219, -222, -224, -220, -210, -209, -213, -212, -202, -196, -187, -186, -180, -193,
    -197, -208, -203, -186, -179, -165, -171, -180, -174, -162, -154, -163, -164, -150, -136, -133,
    -141, -141, -137, -129, -129, -132, -129, -115, -116, -114, -108, -105, -104, -100, -95, -83,
    -82, -74, -81, -56, -43, -44, -51, -54, -36, -29, -21, -19, -20, -12, -17, -26, -40, -38, -15,
    -5, 3, -11, 7, 22, 30, 21, 38, 58, 78, 80, 74, 65, 67, 76, 83, 86, 89, 80, 74, 60, 62, 62, 62,
    71, 56, 48, 42, 56, 62, 50, 45, 37, 38, 38, 31, 12, 19, 7, 18, 9, 18, 4, -9, -6, -8, -8, -22,
    -27, -37, -32, -35, -40, -44, -40, -36, -34, -47, -44, -64, -61, -54, -38, -41, -45, -52, -53,
    -65, -62, -64, -69, -80, -76, -72, -70, -80, -90, -94, -93, -88, -91, -77, -83, -78, -87, -80,
    -61, -51, -50, -66, -62, -55, -30, -42, -46, -49, -34, -29, -25, -16, -8, 1, 0, -6, -6, -6, 0,
    6, 14, 18, 23, 24, 27, 16, 22, 32, 35, 31, 34, 42, 39, 42, 48, 54, 52, 42, 42, 35, 33, 25, 17,
    13, 17, 24, 15, 9, 7, 10, 9, 4, 4, 0, 0, -6, -18, -25, -34, -30, -42, -62, -82, -82, -69, -73,
    -82, -82, -78, -72, -54, -30, -16, -29, -37, -42, -50, -43, -43, -39, -54, -62, -59, -68, -77,
    -97, -103, -104, -109, -93, -89, -89, -117, -128, -120, -112, -112, -120, -139, -158, -167,
    -165, -173, -183, -181, -186, -191, -191, -189, -180, -185, -185, -189, -191, -194, -195, -205,
    -203, -203, -195, -198, -197, -195, -181, -183, -182, -184, -185, -195, -196, -180, -178, -181,
    -175, -172, -167, -168, -153, -138, -143, -140, -144, -131, -134, -142, -148, -149, -155, -155,
    -153, -143, -152, -163, -159, -161, -160, -168, -170, -182, -192, -188, -180, -172, -175, -184,
    -192, -194, -190, -200, -203, -211, -207, -215, -216, -216, -232, -243, -252, -246, -239, -238,
    -230, -229, -226, -215, -205, -202, -209, -212, -213, -209, -210, -217, -227, -224, -210, -204,
    -211, -225, -231, -233, -227, -232, -236, -234, -235, -233, -240, -235, -230, -233, -228, -230,
    -226, -231, -224, -223, -226, -250, -255, -251, -239, -243, -246, -248, -247, -248, -244, -242,
    -239, -240, -243, -247, -242, -236, -240, -243, -243, -244, -246, -242, -234, -238, -255, -261,
    -259, -252, -246, -244, -233, -225, -224, -225, -224, -215, -192, -173, -162, -160, -161, -146,
    -146, -139, -144, -141, -149, -141, -143, -149, -168, -172, -167, -156, -158, -169, -174, -180,
    -161, -164, -163, -175, -173, -169, -168, -176, -177, -177, -181, -191, -194, -183, -185, -198,
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    25, 42, 51, 65, 84, 93, 93, 85, 85, 89, 111, 122, 137, 138, 127, 123, 128, 120, 99, 88, 88, 89,
    84, 68, 59, 60, 67, 70, 66, 62, 63, 68, 65, 58, 39, 36, 34, 25, 32, 15, 25, 13, 9, -1, -1, 8,
    16, 14, 3, 2, 9, 16, 29, 29, 39, 48, 64, 71, 68, 70, 67, 62, 46, 43, 53, 66, 66, 63, 57, 61,
    52, 53, 54, 79, 74, 67, 54, 68, 77, 82, 77, 66, 57, 54, 56, 57, 54, 60, 53, 48, 34, 52, 69, 89,
    88, 91, 99, 119, 132, 139, 140, 156, 151, 157, 158, 177, 185, 191, 202, 201, 209, 220, 233,
    227, 231, 242, 253, 242, 253, 255, 261, 258, 266, 269, 266, 279, 292, 295, 288, 284, 281, 277,
    277, 281, 287, 283, 277, 267, 260, 253, 250, 241, 231, 233, 225, 227, 218, 216, 205, 201, 193,
    214, 221, 226, 217, 212, 210, 211, 219, 219, 218, 211, 215, 221, 228, 233, 234, 244, 242, 236,
    227, 224, 218, 208, 182, 184, 170, 176, 170, 164, 155, 146, 142, 138, 143, 136, 130, 122, 110,
    108, 103, 103, 106, 104, 117, 105, 102, 90, 87, 88, 80, 82, 83, 99, 93, 72, 62, 62, 80, 67, 67,
    50, 57, 66, 76, 60, 52, 61, 80, 89, 88, 99, 110, 126, 135, 151, 155, 154, 144, 142, 140, 143,
    146, 143, 133, 123, 124, 114, 107, 89, 93, 100, 89, 75, 65, 78, 69, 63, 53, 65, 64, 61, 59, 52,
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    13, 7, 12, 21, 29, 26, 34, 39, 59, 68, 77, 87, 99, 115, 134, 135, 158, 168, 182, 189, 182, 181,
    181, 185, 192, 193, 201, 201, 188, 182, 180, 195, 195, 192, 192, 194, 186, 177, 166, 167, 164,
    161, 158, 156, 152, 146, 130, 126, 131, 128, 118, 115, 111, 107, 100, 103, 111, 103, 106, 104,
    106, 108, 115, 114, 108, 102, 105, 112, 118, 126, 127, 124, 125, 140, 150, 157, 154, 151, 152,
    165, 173, 183, 175, 176, 178, 185, 185, 187, 196, 203, 208, 204, 200, 190, 197, 190, 190, 179,
    182, 190, 200, 193, 187, 179, 191, 187, 179, 176, 167, 174, 155, 164, 164, 177, 182, 192, 199,
    213, 215, 225, 225, 236, 245, 270, 278, 280, 280, 290, 305, 327, 339, 354, 365, 378, 378, 371,
    371, 377, 385, 381, 368, 378, 385, 388, 382, 382, 393, 396, 397, 392, 385, 373, 379, 371, 368,
    357, 371, 368, 368, 368, 371, 363, 351, 337, 339, 336, 329, 307, 305, 301, 300, 289, 281, 274,
    267, 263, 247, 245, 247, 254, 245, 225, 215, 211, 218, 224, 218, 203, 200, 207, 212, 205, 204,
    213, 210, 216, 210, 223, 222, 223, 210, 202, 189, 184, 185, 184, 184, 186, 181, 188, 189, 182,
    176, 183, 186, 183, 187, 186, 184, 173, 174, 175, 171, 158, 165, 166, 168, 162, 157, 167, 175,
    177, 162, 169, 166, 173, 161, 163, 159, 157, 149, 158, 168, 179, 180, 190, 196, 193, 195, 204,
    220, 214, 218, 210, 219, 210, 223, 212, 210, 206, 201, 198, 190, 186, 173, 153, 149, 141, 149,
    144, 159, 161, 167, 149, 152, 151, 159, 157, 152, 160, 142, 140, 130, 128, 115, 114, 113, 119,
    113, 111, 104, 94, 83, 69, 50, 46, 40, 25, 13, 8, 12, 2, -6, -10, -21, -24, -28, -33, -36, -47,
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    51, 60, 62, 59, 50, 46, 37, 41, 44, 36, 29, 31, 24, 18, 9, 7, 14, 11, 5, -2, -8, -7, -9, -8, 0,
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    30, 38, 37, 43, 51, 58, 65, 61, 60, 64, 62, 72, 73, 81, 92, 92, 87, 90, 92, 102, 100, 110, 113,
    106, 96, 101, 111, 113, 112, 97, 100, 104, 108, 99, 90, 84, 85, 77, 79, 80, 86, 78, 84, 81, 88,
    87, 86, 88, 88, 97, 101, 103, 105, 109, 109, 109, 115, 131, 139, 147, 155, 162, 173, 184, 198,
    205, 216, 220, 226, 230, 234, 248, 247, 253, 243, 241, 235, 236, 230, 222, 225, 211, 213, 196,
    189, 189, 184, 173, 161, 156, 157, 153, 161, 158, 165, 163, 154, 147, 122, 116, 108, 100, 94,
    84, 78, 74, 64, 59, 57, 61, 63, 58, 52, 44, 40, 41, 42, 36, 34, 34, 43, 45, 52, 47, 56, 60, 62,
    66, 75, 82, 82, 84, 83, 92, 102, 107, 108, 108, 113, 123, 113, 113, 99, 96, 82, 86, 79, 76, 69,
    60, 52, 36, 35, 48, 52, 51, 38, 33, 36, 33, 29, 26, 25, 30, 36, 38, 46, 50, 54, 51, 39, 39, 45,
    61, 68, 75, 84, 92, 94, 91, 98, 98, 113, 123, 128, 124, 123, 138, 134, 126, 126, 129, 136, 137,
    143, 140, 149, 153, 159, 158, 161, 163, 158, 154, 156, 156, 150, 135, 129, 115, 105, 89, 70,
    66, 67, 66, 68, 59, 60, 48, 42, 29, 22, 13, 7, -4, -22, -19, -29, -29, -53, -57, -70, -68, -62,
    -55, -46, -50, -44, -46, -22, -10, 8, 7, 12, 11, 21, 24, 37, 37, 41, 32, 27, 14, -1, 4, -3, 6,
    4, 10, 9, 6, 0, -7, 1, 9, 17, 13, -8, -12, -22, -20, -24, -36, -36, -40, -34, -25, -27, -23,
    -18, -14, -6, 0, 21, 31, 31, 39, 40, 56, 58, 73, 86, 91, 93, 78, 83, 71, 73, 66, 74, 78, 75,
    62, 52, 36, 39, 31, 42, 31, 30, 27, 19, 20, 5, 17, 7, 21, 12, 16, 22, 28, 30, 23, 25, 19, 14,
    6, -8, -11, -17, -9, -11, -23, -30, -45, -43, -43, -52, -51, -66, -67, -70, -65, -65, -60, -69,
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    132, 131, 143, 158, 166, 172, 169, 177, 167, 159, 160, 151, 155, 150, 149, 148, 139, 128, 130,
    130, 129, 123, 121, 113, 111, 95, 103, 99, 102, 103, 110, 103, 108, 105, 116, 115, 114, 114,
    111, 117, 116, 118, 113, 122, 119, 128, 111, 116, 103, 104, 93, 93, 100, 100, 102, 97, 96, 95,
    96, 98, 96, 96, 99, 104, 110, 100, 96, 95, 94, 95, 90, 100, 101, 106, 98, 100, 93, 100, 107,
    103, 108, 107, 112, 117, 122, 111, 114, 96, 107, 96, 105, 104, 106, 98, 106, 112, 126, 136,
    152, 162, 162, 172, 176, 187, 186, 182, 176, 178, 179, 174, 175, 171, 173, 160, 155, 152, 162,
    164, 170, 161, 167, 167, 174, 184, 195, 191, 183, 178, 173, 174, 162, 164, 148, 149, 140, 138,
    133, 123, 118, 107, 112, 108, 121, 123, 124, 123, 115, 123, 119, 126, 123, 123, 122, 117, 117,
    115, 122, 127, 118, 111, 113, 105, 106, 99, 103, 98, 94, 95, 88, 86, 82, 81, 81, 85, 99, 98,
    102, 89, 97, 83, 86, 82, 89, 97, 99, 99, 105, 100, 116, 118, 131, 137, 148, 147, 147, 139, 141,
    139, 144, 139, 146, 145, 144, 136, 127, 131, 140, 140, 147, 139, 152, 150, 156, 147, 143, 141,
    153, 157, 163, 160, 162, 161, 159, 162, 163, 159, 162, 162, 163, 157, 160, 155, 160, 161, 172,
    176, 167, 168, 157, 160, 159, 159, 160, 157, 150, 148, 143, 149, 137, 138, 134, 136, 130, 132,
    134, 123, 118, 111, 115, 110, 106, 109, 92, 86, 73, 80, 85, 77, 71, 51, 45, 37, 37, 27, 27, 19,
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    5, 15, 13, 14, 8, 22, 22, 28, 33, 33, 29, 29, 27, 28, 18, 12, 1, -5, -14, -14, -18, -22, -36,
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    147, 147, 141, 136, 123, 128, 116, 122, 118, 128, 127, 121, 124, 136, 140, 133, 123, 113, 121,
    119, 130, 117, 112, 114, 117, 118, 117, 112, 113, 115, 126, 132, 137, 144, 153, 149, 149, 161,
    176, 195, 200, 206, 205, 206, 208, 210, 222, 223, 231, 225, 235, 225, 231, 229, 239, 240, 239,
    242, 239, 234, 236, 230, 216, 207, 200, 198, 186, 176, 172, 167, 156, 145, 135, 130, 103, 93,
    87, 88, 86, 77, 70, 74, 73, 90, 90, 93, 97, 101, 108, 105, 114, 122, 130, 139, 139, 142, 144,
    149, 163, 171, 179, 178, 194, 206, 220, 231, 244, 251, 260, 266, 270, 277, 280, 281, 283, 277,
    272, 261, 259, 260, 263, 272, 279, 276, 272, 271, 268, 270, 268, 267, 258, 252, 245, 250, 241,
    243, 249, 244, 248, 235, 238, 231, 237, 248, 250, 245, 233, 233, 235, 244, 250, 249, 250, 246,
    240, 232, 224, 215, 211, 218, 211, 207, 186, 183, 179, 183, 179, 173, 160, 152, 151, 159, 161,
    168, 166, 165, 163, 168, 171, 170, 170, 168, 161, 142, 135, 122, 119, 108, 107, 89, 84, 82, 79,
    78, 67, 62, 55, 40, 26, 13, 8, 18, 17, 21, 19, 24, 28, 26, 33, 44, 61, 60, 58, 47, 46, 43, 42,
    39, 38, 32, 35, 25, 19, 8, 0, 1, -15, -18, -32, -32, -45, -41, -38, -25, -26, -16, -7, 13, 30,
    34, 45, 46, 69, 70, 80, 79, 86, 94, 102, 92, 79, 88, 95, 103, 108, 107, 106, 93, 97, 95, 102,
    91, 87, 86, 82, 88, 66, 51, 34, 29, 30, 19, 4, -10, -14, -12, -20, -24, -30, -22, -19, -8, -10,
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    56, 51, 37, 50, 54, 62, 68, 70, 61, 71, 112, 144, 140, 138, 152, 166, 144, 111, 89, 69, 56, 39,
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    167, 153, 145, 140, 120, 100, 87, 95, 100, 105, 123, 136, 160, 160, 161, 136, 127, 132, 143,
    153, 141, 143, 152, 163, 172, 172, 178, 174, 179, 172, 171, 173, 179, 174, 161, 155, 150, 127,
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    115, 172, 273, 370, 449, 451, 336, 109, -107, -249, -281, -241, -129, 20, 124, 158, 162, 175,
    259, 398, 484, 446, 341, 278, 205, 114, 74, 148, 234, 270, 224, 180, 204, 290, 347, 322, 275,
    243, 259, 294, 358, 420, 483, 484, 379, 251, 195, 219, 276, 376, 446, 428, 315, 205, 157, 191,
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    388, 439, 441, 431, 408, 385, 475, 660, 825, 863, 740, 499, 245, 65, 17, 3, -25, -78, -112,
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    -174, -260, -226, -81, 164, 303, 240, 86, 10, 16, 104, 270, 375, 335, 241, 152, 42, -21, 58,
    196, 287, 310, 269, 165, 18, -104, -155, -101, 17, 46, -19, -110, -151, -125, -29, 100, 199,
    228, 172, 82, 38, 50, 99, 202, 400, 581, 624, 486, 205, -73, -275, -365, -400, -339, -228, -86,
    53, 184, 214, 164, 84, 4, -100, -167, -142, -66, 34, 149, 221, 223, 174, 82, -84, -239, -269,
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    298, 53, -90, -121, -118, -96, -45, -59, -156, -266, -360, -411, -340, -158, -1, 69, 158, 234,
    268, 296, 345, 362, 316, 213, 62, -47, -83, -117, -136, -106, -69, -120, -222, -291, -306,
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    -574, -513, -388, -233, -79, 16, 89, 144, 119, 13, -64, -82, -91, -45, 51, 81, 64, 93, 186,
    264, 334, 427, 500, 527, 477, 328, 151, 28, -19, -31, -29, -45, -78, -45, 74, 201, 274, 343,
    421, 444, 395, 288, 201, 187, 217, 193, 95, -41, -155, -252, -336, -384, -403, -367, -316,
    -284, -286, -344, -424, -452, -375, -273, -228, -211, -165, -91, 31, 187, 308, 344, 367, 370,
    297, 121, -66, -211, -291, -299, -279, -223, -89, 108, 279, 377, 440, 504, 552, 596, 630, 633,
    586, 475, 335, 197, 97, 91, 190, 357, 421, 330, 154, -11, -129, -170, -99, 32, 161, 220, 209,
    117, -8, -88, -91, -42, -9, 10, 28, 28, -14, -57, -31, 75, 177, 218, 168, 55, -89, -241, -376,
    -454, -461, -389, -322, -292, -293, -243, -127, 26, 162, 314, 505, 704, 792, 696, 486, 321,
    243, 214, 209, 193, 123, -10, -74, -12, 182, 406, 641, 786, 823, 727, 579, 436, 332, 262, 220,
    195, 138, 47, -79, -239, -365, -362, -257, -172, -144, -121, -70, -52, -6, 90, 202, 224, 184,
    102, -15, -190, -332, -376, -374, -338, -271, -180, -123, -66, 35, 176, 264, 272, 214, 110, -8,
    -140, -226, -228, -149, -35, 55, 121, 162, 200, 223, 205, 141, 80, 31, 3, -51, -123, -217,
    -301, -347, -339, -249, -126, -8, 151, 368, 544, 568, 469, 319, 145, -73, -326, -541, -667,
    -683, -619, -518, -380, -276, -231, -249, -296, -370, -457, -506, -464, -355, -178, 19, 180,
    191, 110, -3, -88, -188, -273, -324, -344, -351, -333, -309, -287, -292, -265, -185, -94, -29,
    23, 136, 285, 410, 531, 615, 604, 495, 387, 271, 135, -19, -116, -174, -192, -155, -100, -59,
    10, 113, 199, 248, 260, 225, 133, 49, 14, -3, -13, -42, -69, -110, -173, -270, -355, -368,
    -324, -239, -83, 155, 390, 571, 687, 741, 691, 516, 249, -77, -369, -590, -743, -826, -808,
    -658, -429, -164, 115, 340, 473, 500, 479, 422, 378, 330, 280, 172, 46, -29, -19, 77, 176, 268,
    311, 356, 397, 412, 381, 331, 289, 278, 322, 396, 442, 394, 280, 125, -29, -181, -289, -324,
    -238, -103, 16, 46, 22, -38, -86, -79, -45, -37, -94, -145, -155, -82, 26, 105, 131, 120, 68,
    -111, -372, -595, -663, -626, -514, -372, -186, 30, 331, 648, 913, 1069, 1101, 1001, 747, 403,
    86, -112, -135, -89, -49, -68, -122, -223, -323, -335, -224, -64, 88, 220, 300, 347, 399, 472,
    513, 517, 461, 294, 30, -211, -378, -484, -494, -378, -166, 69, 237, 253, 181, 112, 114, 83,
    30, -26, -71, -155, -307, -486, -680, -784, -766, -633, -478, -341, -204, -55, 114, 252, 298,
    247, 129, -18, -194, -366, -517, -647, -677, -544, -327, -142, 39, 272, 481, 563, 505, 321, 60,
    -182, -331, -363, -320, -242, -222, -224, -209, -174, -113, 58, 319, 580, 712, 704, 620, 525,
    467, 401, 289, 151, 35, -28, -67, -111, -139, -98, 51, 235, 388, 444, 459, 472, 488, 510, 566,
    637, 658, 570, 430, 235, 11, -172, -211, -105, 8, 58, 73, 104, 189, 261, 336, 399, 451, 442,
    377, 252, 69, -105, -167, -44, 130, 265, 346, 402, 395, 366, 343, 347, 320, 329, 352, 387, 370,
    318, 196, 71, -10, -39, -56, 11, 147, 273, 361, 473, 647, 812, 894, 819, 608, 370, 182, 33,
    -87, -163, -182, -104, 64, 273, 435, 535, 588, 594, 541, 461, 324, 117, -78, -195, -269, -336,
    -323, -193, -47, 106, 291, 509, 656, 738, 747, 636, 479, 384, 376, 370, 332, 220, 57, -79, -81,
    5, 104, 183, 288, 407, 498, 508, 454, 416, 467, 561, 607, 530, 366, 215, 120, 118, 195, 349,
    508, 613, 580, 425, 230, 102, 71, 126, 255, 352, 342, 222, 25, -211, -440, -558, -596, -578,
    -524, -435, -321, -185, -1, 185, 329, 413, 374, 218, 70, -12, -83, -187, -306, -420, -534,
    -629, -713, -771, -789, -732, -641, -496, -320, -71, 231, 550, 758, 816, 786, 691, 492, 192,
    -110, -293, -358, -349, -325, -305, -267, -190, -53, 109, 254, 380, 500, 619, 688, 689, 604,
    488, 375, 268, 136, -21, -151, -236, -238, -118, 114, 392, 597, 713, 764, 805, 806, 751, 659,
    538, 402, 234, 36, -222, -452, -532, -434, -219, 10, 224, 411, 583, 743, 847, 890, 914, 989,
    1120, 1239, 1255, 1153, 1022, 924, 840, 741, 614, 475, 353, 295, 361, 554, 882, 1251, 1595,
    1823, 1884, 1762, 1536, 1330, 1192, 1100, 1026, 938, 832, 733, 580, 378, 176, 66, 22, 18, 35,
    51, 83, 191, 336, 439, 473, 489, 522, 501, 452, 390, 356, 396, 469, 511, 489, 410, 301, 147,
    -30, -175, -267, -316, -329, -316, -302, -268, -167, 61, 347, 610, 784, 825, 744, 615, 476,
    331, 147, -22, -187, -335, -480, -644, -776, -777, -631, -463, -360, -298, -328, -424, -557,
    -650, -686, -671, -638, -694, -867, -1108, -1348, -1568, -1673, -1653, -1576, -1490, -1379,
    -1260, -1194, -1175, -1135, -1095, -1051, -980, -891, -846, -882, -976, -1078, -1154, -1182,
    -1178, -1158, -1145, -1119, -1037, -902, -773, -708, -645, -589, -507, -426, -315, -274, -271,
    -273, -202, -108, -26, 54, 114, 150, 121, 40, -101, -288, -421, -427, -292, -139, 25, 151, 224,
    219, 153, 65, -29, -103, -218, -355, -459, -448, -316, -72, 186, 331, 373, 393, 365, 229, 12,
    -181, -256, -163, 22, 167, 261, 386, 525, 585, 532, 413, 274, 197, 219, 316, 457, 663, 892,
    1097, 1211, 1229, 1160, 1031, 918, 854, 858, 898, 947, 979, 983, 949, 925, 908, 900, 856, 815,
    771, 769, 817, 935, 1094, 1290, 1487, 1613, 1643, 1559, 1393, 1156, 895, 650, 403, 198, 46,
    -88, -186, -160, -25, 152, 378, 655, 838, 851, 778, 668, 534, 392, 241, 49, -145, -256, -356,
    -487, -585, -602, -550, -439, -343, -290, -238, -122, 28, 152, 241, 274, 260, 242, 236, 157,
    45, -78, -183, -278, -317, -315, -263, -183, -98, -78, -118, -231, -362, -472, -482, -491,
    -528, -659, -817, -996, -1102, -1132, -1127, -1094, -1037, -980, -1020, -1154, -1318, -1410,
    -1417, -1378, -1343, -1375, -1456, -1534, -1555, -1534, -1504, -1470, -1467, -1553, -1738,
    -2005, -2284, -2471, -2479, -2332, -2120, -1893, -1671, -1532, -1438, -1309, -1158, -1030,
    -953, -868, -786, -679, -627, -648, -702, -692, -613, -513, -412, -364, -387, -469, -583, -683,
    -713, -596, -375, -108, 121, 303, 502, 740, 947, 1050, 1066, 1015, 902, 748, 520, 265, 95, 113,
    278, 462, 574, 542, 481, 447, 432, 389, 380, 442, 485, 487, 449, 372, 284, 242, 261, 316, 360,
    310, 137, -36, -109, -150, -193, -237, -233, -157, -1, 154, 262, 350, 466, 581, 672, 676, 544,
    309, 90, -63, -148, -91, 118, 425, 744, 1007, 1139, 1136, 1088, 1035, 990, 928, 893, 917, 1037,
    1212, 1362, 1484, 1644, 1785, 1874, 1828, 1703, 1473, 1213, 936, 685, 504, 421, 431, 489, 556,
    568, 531, 482, 426, 369, 374, 470, 581, 606, 529, 369, 172, -33, -221, -392, -486, -537, -554,
    -564, -575, -590, -584, -530, -459, -400, -332, -294, -285, -261, -208, -167, -131, -136, -203,
    -354, -533, -696, -781, -755, -636, -478, -306, -141, -47, -46, -113, -237, -399, -621, -889,
    -1197, -1465, -1692, -1841, -1891, -1848, -1777, -1687, -1574, -1476, -1380, -1283, -1190,
    -1160, -1191, -1270, -1366, -1497, -1679, -1891, -2111, -2292, -2398, -2387, -2193, -1813,
    -1291, -762, -371, -180, -99, -57, -31, -77, -229, -466, -702, -934, -1126, -1211, -1101, -763,
    -274, 233, 582, 702, 683, 624, 582, 625, 739, 875, 994, 1061, 1022, 839, 617, 472, 420, 440,
    422, 272, 9, -253, -414, -389, -147, 246, 662, 986, 1170, 1099, 812, 432, 112, -41, -45, 11,
    -8, -114, -247, -328, -343, -299, -172, 54, 293, 431, 444, 368, 284, 276, 381, 566, 798, 1026,
    1134, 1082, 926, 774, 610, 533, 533, 532, 511, 528, 563, 595, 681, 828, 1009, 1215, 1380, 1377,
    1222, 1018, 805, 645, 596, 618, 611, 626, 647, 610, 585, 600, 633, 657, 727, 775, 797, 860,
    979, 1072, 1175, 1333, 1474, 1547, 1474, 1225, 838, 491, 209, -4, -130, -169, -155, -89, 25,
    145, 251, 372, 475, 538, 575, 548, 453, 324, 215, 117, 39, -24, -102, -171, -201, -218, -231,
    -238, -205, -169, -119, -105, -124, -189, -261, -371, -477, -580, -659, -725, -786, -855, -930,
    -990, -1033, -1064, -1107, -1132, -1133, -1089, -1035, -1030, -1114, -1278, -1475, -1657,
    -1796, -1930, -2082, -2228, -2302, -2303, -2290, -2293, -2315, -2299, -2241, -2198, -2197,
    -2251, -2312, -2358, -2361, -2364, -2361, -2291, -2039, -1629, -1200, -876, -727, -728, -785,
    -842, -892, -1013, -1155, -1258, -1247, -1123, -961, -749, -469, -101, 290, 629, 849, 949, 972,
    960, 921, 929, 1023, 1200, 1331, 1355, 1283, 1184, 1127, 1058, 907, 656, 424, 370, 519, 746,
    914, 1002, 1060, 1114, 1075, 879, 528, 145, -114, -209, -179, -91, -4, 71, 102, 75, -50, -225,
    -329, -319, -261, -226, -244, -286, -296, -282, -317, -390, -443, -494, -608, -767, -901, -933,
    -728, -264, 293, 766, 1128, 1351, 1414, 1349, 1202, 1014, 826, 737, 736, 750, 739, 717, 739,
    821, 940, 1061, 1151, 1191, 1214, 1219, 1208, 1192, 1245, 1357, 1430, 1364, 1190, 925, 691,
    550, 525, 547, 623, 759, 937, 1136, 1308, 1396, 1391, 1322, 1223, 1105, 985, 856, 692, 526,
    376, 242, 128, 69, 64, 71, 71, 85, 91, 116, 192, 310, 432, 527, 615, 652, 617, 498, 382, 289,
    233, 174, 99, -7, -115, -188, -208, -231, -239, -238, -196, -181, -193, -246, -317, -386, -451,
    -519, -599, -674, -728, -798, -889, -982, -1021, -971, -861, -806, -850, -996, -1216, -1485,
    -1807, -2136, -2457, -2679, -2780, -2816, -2879, -2917, -2886, -2753, -2571, -2369, -2208,
    -2094, -2040, -2049, -2081, -2163, -2276, -2354, -2288, -2043, -1708, -1423, -1271, -1243,
    -1235, -1176, -1107, -1040, -988, -928, -875, -859, -869, -764, -425, 97, 676, 1203, 1592,
    1758, 1702, 1455, 1096, 788, 666, 669, 705, 718, 720, 732, 830, 958, 1057, 1140, 1262, 1339,
    1305, 1133, 889, 664, 596, 663, 745, 793, 778, 656, 451, 234, 44, -69, -59, -40, -120, -221,
    -274, -275, -231, -156, -125, -129, -112, -147, -265, -375, -395, -342, -238, -163, -171, -230,
    -221, -139, -19, 150, 299, 400, 508, 613, 623, 573, 565, 617, 755, 924, 1052, 1053, 1054, 1074,
    1096, 1118, 1157, 1179, 1156, 1119, 1033, 922, 891, 987, 1169, 1393, 1599, 1698, 1694, 1639,
    1582, 1471, 1327, 1153, 996, 890, 804, 711, 603, 534, 507, 518, 521, 476, 404, 366, 395, 470,
    595, 742, 908, 1092, 1287, 1418, 1431, 1328, 1161, 960, 757, 540, 315, 92, -60, -151, -168,
    -116, -7, 111, 235, 346, 438, 503, 563, 593, 572, 493, 360, 176, -27, -236, -437, -647, -833,
    -971, -1025, -1016, -945, -843, -738, -679, -656, -670, -703, -810, -927, -1041, -1138, -1273,
    -1429, -1605, -1768, -1900, -2019, -2182, -2358, -2471, -2481, -2449, -2471, -2575, -2673,
    -2709, -2674, -2668, -2706, -2812, -2948, -3086, -3124, -3006, -2678, -2132, -1481, -875, -458,
    -255, -228, -274, -325, -384, -434, -465, -481, -460, -359, -116, 241, 677, 1079, 1403, 1591,
    1630, 1498, 1286, 1118, 1110, 1322, 1685, 1968, 2089, 2091, 2054, 1972, 1854, 1688, 1469, 1288,
    1259, 1321, 1393, 1435, 1440, 1360, 1250, 1090, 857, 543, 230, -94, -370, -563, -691, -773,
    -772, -664, -534, -422, -365, -411, -529, -666, -826, -964, -971, -889, -797, -748, -741, -808,
    -883, -888, -863, -783, -624, -420, -269, -125, -3, 73, 154, 285, 418, 495, 537, 556, 519, 554,
    685, 865, 1009, 1129, 1166, 1125, 1021, 954, 941, 1000, 1094, 1179, 1184, 1123, 1020, 943, 936,
    974, 1056, 1123, 1160, 1151, 1130, 1083, 995, 862, 706, 515, 326, 135, -43, -191, -246, -211,
    -98, 56, 231, 332, 363, 333, 278, 201, 135, 76, -3, -105, -175, -204, -179, -101, 32, 184, 348,
    504, 614, 650, 592, 489, 350, 218, 53, -109, -237, -330, -416, -508, -600, -651, -665, -672,
    -720, -802, -887, -960, -1054, -1139, -1218, -1269, -1303, -1327, -1391, -1486, -1611, -1758,
    -1940, -2132, -2282, -2370, -2390, -2352, -2294, -2227, -2177, -2163, -2201, -2320, -2515,
    -2732, -2910, -3032, -3156, -3295, -3420, -3472, -3448, -3393, -3390, -3420, -3357, -3030,
    -2411, -1637, -892, -329, -4, 113, 100, 6, -164, -386, -582, -749, -885, -974, -886, -574, -4,
    744, 1514, 2129, 2560, 2802, 2845, 2737, 2636, 2597, 2620, 2661, 2604, 2351, 1966, 1605, 1373,
    1253, 1222, 1186, 1168, 1232, 1386, 1535, 1652, 1739, 1781, 1775, 1636, 1243, 657, 115, -255,
    -436, -458, -385, -359, -404, -536, -793, -1104, -1326, -1406, -1386, -1315, -1277, -1293,
    -1315, -1291, -1280, -1253, -1227, -1262, -1377, -1483, -1570, -1589, -1452, -1143, -746, -307,
    138, 454, 609, 644, 624, 580, 604, 626, 587, 500, 494, 561, 679, 819, 951, 1105, 1298, 1471,
    1546, 1514, 1455, 1371, 1274, 1168, 1070, 1050, 1067, 1088, 1054, 1022, 1013, 1063, 1139, 1195,
    1197, 1185, 1193, 1230, 1237, 1193, 1064, 889, 696, 508, 300, 49, -227, -449, -572, -630, -637,
    -621, -520, -394, -234, -63, 137, 386, 615, 775, 849, 871, 864, 828, 763, 672, 632, 621, 599,
    487, 325, 141, -17, -113, -143, -165, -183, -195, -206, -233, -229, -180, -126, -109, -145,
    -267, -424, -616, -797, -962, -1114, -1286, -1484, -1658, -1805, -1972, -2194, -2413, -2555,
    -2514, -2351, -2192, -2201, -2388, -2694, -3049, -3395, -3728, -4030, -4302, -4522, -4701,
    -4811, -4828, -4780, -4641, -4431, -4073, -3489, -2613, -1580, -698, -164, 7, -66, -209, -303,
    -370, -425, -425, -318, -154, 13, 194, 522, 1130, 1985, 2881, 3551, 3915, 3996, 3925, 3851,
    3829, 3871, 3971, 4084, 4136, 4050, 3812, 3457, 3057, 2748, 2545, 2409, 2319, 2240, 2170, 2114,
    2081, 2064, 2046, 2009, 1826, 1454, 934, 358, -215, -707, -1067, -1316, -1457, -1516, -1526,
    -1544, -1536, -1490, -1414, -1355, -1321, -1326, -1311, -1326, -1378, -1523, -1688, -1844,
    -1913, -1923, -1886, -1818, -1661, -1429, -1154, -871, -571, -267, 71, 361, 613, 789, 955,
    1095, 1193, 1270, 1300, 1333, 1396, 1457, 1512, 1547, 1619, 1746, 1952, 2212, 2429, 2576, 2664,
    2695, 2697, 2733, 2833, 2977, 3153, 3283, 3273, 3039, 2626, 2091, 1534, 1010, 527, 123, -154,
    -247, -215, -66, 211, 549, 884, 1100, 1150, 1000, 719, 389, 46, -270, -535, -711, -820, -878,
    -858, -755, -581, -405, -262, -183, -150, -123, -127, -120, -82, 26, 185, 386, 619, 831, 963,
    1014, 1045, 1063, 1108, 1174, 1218, 1188, 1068, 893, 716, 559, 450, 388, 362, 354, 324, 253,
    108, -100, -341, -529, -650, -752, -911, -1144, -1418, -1682, -1910, -2093, -2233, -2288,
    -2271, -2202, -2193, -2316, -2598, -2980, -3368, -3745, -4071, -4328, -4546, -4752, -4941,
    -5069, -5159, -5219, -5254, -5117, -4647, -3663, -2262, -832, 270, 967, 1408, 1745, 2002, 2053,
    1891, 1590, 1293, 979, 637, 312, 172, 407, 1063, 1973, 2858, 3560, 4022, 4300, 4449, 4501,
    4481, 4467, 4484, 4498, 4431, 4267, 3988, 3603, 3249, 2952, 2686, 2436, 2243, 2064, 1909, 1800,
    1738, 1668, 1557, 1383, 1119, 796, 450, 49, -378, -800, -1223, -1644, -1981, -2192, -2312,
    -2335, -2275, -2178, -2054, -1894, -1711, -1531, -1349, -1245, -1281, -1445, -1679, -1916,
    -2104, -2229, -2301, -2277, -2113, -1836, -1537, -1217, -912, -616, -293, 47, 368, 650, 938,
    1212, 1465, 1707, 1902, 2042, 2179, 2309, 2408, 2483, 2568, 2643, 2669, 2707, 2754, 2795, 2776,
    2691, 2507, 2281, 1992, 1664, 1299, 1007, 792, 689, 699, 796, 915, 1024, 1068, 1045, 987, 916,
    840, 731, 582, 344, 30, -307, -604, -844, -994, -1089, -1180, -1260, -1282, -1262, -1183,
    -1024, -748, -391, -39, 192, 259, 206, 154, 102, 27, -64, -102, -48, 89, 282, 512, 813, 1192,
    1602, 1942, 2119, 2121, 1995, 1728, 1336, 877, 434, 62, -207, -333, -368, -343, -252, -59, 166,
    358, 460, 477, 455, 391, 231, -86, -508, -945, -1339, -1673, -1988, -2310, -2578, -2745, -2831,
    -2882, -2969, -3128, -3410, -3704, -3963, -4192, -4439, -4720, -5023, -5269, -5401, -5463,
    -5567, -5698, -5686, -5292, -4248, -2627, -800, 736, 1759, 2343, 2719, 2970, 2976, 2649, 2149,
    1707, 1356, 958, 494, 195, 403, 1225, 2336, 3333, 4050, 4515, 4813, 5014, 5107, 5085, 5027,
    5066, 5106, 5031, 4779, 4390, 3936, 3551, 3266, 2950, 2581, 2265, 2042, 1931, 1906, 1912, 1828,
    1672, 1474, 1181, 769, 274, -329, -1016, -1673, -2212, -2601, -2831, -2923, -2968, -2914,
    -2718, -2434, -2181, -2005, -1891, -1816, -1721, -1674, -1769, -2036, -2353, -2650, -2846,
    -2956, -3002, -3020, -2912, -2650, -2260, -1803, -1311, -826, -333, 184, 636, 978, 1241, 1473,
    1660, 1806, 1937, 2034, 2098, 2126, 2133, 2086, 2060, 2083, 2166, 2293, 2448, 2604, 2736, 2806,
    2767, 2619, 2395, 2157, 1890, 1617, 1340, 1060, 803, 664, 653, 749, 897, 1045, 1161, 1229,
    1251, 1168, 995, 754, 503, 255, 24, -193, -462, -765, -1053, -1247, -1336, -1314, -1251, -1138,
    -974, -778, -637, -559, -514, -458, -357, -236, -155, -151, -173, -201, -182, -112, 1, 116,
    273, 499, 740, 925, 1008, 1011, 963, 970, 1012, 1052, 1082, 1097, 1105, 1064, 967, 798, 592,
    423, 314, 237, 162, 54, -84, -193, -271, -353, -496, -687, -932, -1223, -1543, -1863, -2173,
    -2458, -2735, -3035, -3411, -3826, -4262, -4696, -5118, -5537, -5896, -6149, -6255, -6309,
    -6389, -6435, -6253, -5638, -4430, -2568, -335, 1662, 2972, 3599, 3869, 3962, 3890, 3443, 2627,
    1720, 1023, 494, -5, -305, -65, 835, 2170, 3527, 4600, 5279, 5676, 5852, 5839, 5703, 5598,
    5581, 5583, 5456, 5132, 4671, 4181, 3771, 3417, 3088, 2753, 2448, 2173, 1937, 1822, 1850, 1947,
    2074, 2153, 2056, 1675, 1040, 217, -750, -1721, -2557, -3178, -3570, -3761, -3801, -3681,
    -3371, -2939, -2528, -2163, -1821, -1593, -1548, -1678, -1939, -2337, -2785, -3183, -3433,
    -3531, -3536, -3510, -3404, -3135, -2714, -2241, -1746, -1201, -627, -57, 432, 803, 1050, 1252,
    1441, 1566, 1600, 1588, 1565, 1490, 1374, 1265, 1223, 1283, 1411, 1602, 1832, 2108, 2373, 2597,
    2779, 2891, 2924, 2953, 3034, 3135, 3195, 3220, 3208, 3090, 2808, 2374, 1794, 1158, 581, 127,
    -206, -423, -520, -471, -284, 9, 310, 524, 608, 540, 343, 72, -279, -689, -1124, -1484, -1787,
    -2025, -2163, -2152, -2027, -1864, -1716, -1584, -1374, -1062, -702, -411, -212, -78, 54, 203,
    305, 256, 95, -76, -227, -364, -444, -460, -389, -254, -68, 144, 382, 627, 820, 923, 966, 930,
    819, 628, 404, 173, -51, -258, -479, -701, -920, -1094, -1212, -1280, -1399, -1564, -1749,
    -1885, -2043, -2278, -2643, -3105, -3589, -4025, -4440, -4944, -5534, -6164, -6735, -7248,
    -7643, -7891, -7829, -7215, -5841, -3669, -1008, 1655, 3797, 5190, 5912, 6098, 5808, 5025,
    3775, 2200, 587, -844, -1957, -2630, -2627, -1802, -307, 1484, 3102, 4280, 4990, 5327, 5391,
    5328, 5217, 5073, 4913, 4748, 4541, 4205, 3819, 3432, 3071, 2693, 2303, 1895, 1535, 1310, 1245,
    1371, 1660, 2034, 2341, 2471, 2289, 1709, 788, -342, -1579, -2746, -3709, -4377, -4769, -4821,
    -4547, -3993, -3273, -2495, -1791, -1237, -896, -813, -986, -1379, -1953, -2617, -3214, -3661,
    -3960, -4141, -4157, -4019, -3732, -3302, -2790, -2243, -1714, -1171, -634, -118, 288, 596,
    871, 1173, 1437, 1595, 1662, 1691, 1724, 1755, 1811, 1936, 2116, 2366, 2643, 2952, 3217, 3411,
    3470, 3399, 3167, 2818, 2372, 1888, 1393, 1030, 886, 975, 1158, 1342, 1458, 1568, 1705, 1860,
    1922, 1845, 1644, 1346, 997, 666, 378, 92, -216, -534, -864, -1227, -1592, -1954, -2284, -2541,
    -2663, -2666, -2573, -2410, -2169, -1900, -1661, -1432, -1162, -814, -430, -74, 198, 368, 407,
    368, 256, 64, -176, -437, -663, -834, -913, -903, -763, -490, -91, 319, 719, 1095, 1437, 1740,
    1950, 2005, 1897, 1699, 1479, 1204, 943, 764, 725, 740, 749, 677, 564, 448, 369, 271, 112,
    -127, -381, -620, -847, -1140, -1490, -1845, -2169, -2470, -2811, -3233, -3717, -4190, -4660,
    -5164, -5704, -6242, -6726, -7086, -7281, -7326, -7140, -6467, -5090, -3019, -553, 1844, 3751,
    5031, 5732, 5891, 5492, 4555, 3206, 1645, 114, -1222, -2243, -2733, -2495, -1486, 94, 1934,
    3663, 5026, 5934, 6401, 6498, 6347, 6069, 5699, 5301, 4929, 4598, 4248, 3866, 3478, 3131, 2854,
    2525, 2131, 1762, 1567, 1585, 1779, 2094, 2440, 2697, 2757, 2507, 1891, 964, -184, -1467,
    -2736, -3831, -4644, -5084, -5129, -4773, -4146, -3316, -2441, -1652, -1078, -738, -675, -887,
    -1349, -1999, -2769, -3501, -4061, -4417, -4629, -4718, -4635, -4348, -3877, -3325, -2748,
    -2181, -1600, -1033, -477, 43, 491, 834, 1094, 1288, 1367, 1303, 1148, 983, 879, 892, 1029,
    1283, 1635, 2076, 2576, 3101, 3608, 4082, 4498, 4824, 4979, 4850, 4428, 3734, 2896, 2070, 1387,
    872, 555, 420, 472, 677, 997, 1411, 1827, 2172, 2391, 2408, 2207, 1774, 1151, 422, -304, -972,
    -1576, -2117, -2580, -2939, -3159, -3254, -3271, -3203, -2968, -2553, -1996, -1376, -804, -364,
    -91, 20, -31, -223, -500, -835, -1178, -1455, -1640, -1770, -1874, -1891, -1737, -1381, -896,
    -432, -44, 258, 532, 806, 1127, 1469, 1807, 2059, 2173, 2100, 1877, 1568, 1247, 966, 755, 629,
    614, 707, 821, 941, 1103, 1310, 1462, 1486, 1323, 998, 550, 55, -476, -1008, -1481, -1858,
    -2201, -2575, -3011, -3476, -3949, -4430, -4914, -5378, -5805, -6202, -6584, -6934, -7267,
    -7494, -7463, -6969, -5855, -4115, -1927, 386, 2523, 4253, 5356, 5805, 5652, 4996, 3859, 2352,
    658, -973, -2251, -2984, -3038, -2359, -1008, 758, 2558, 4082, 5127, 5642, 5728, 5546, 5211,
    4838, 4470, 4136, 3853, 3622, 3415, 3206, 2983, 2751, 2506, 2241, 1939, 1622, 1415, 1380, 1500,
    1738, 2007, 2157, 2033, 1559, 736, -395, -1713, -3073, -4323, -5304, -5899, -6071, -5853,
    -5305, -4555, -3694, -2868, -2172, -1709, -1502, -1590, -1982, -2615, -3360, -4096, -4702,
    -5125, -5343, -5366, -5201, -4883, -4470, -3980, -3450, -2915, -2376, -1816, -1243, -703, -214,
    181, 490, 773, 1028, 1219, 1293, 1287, 1270, 1250, 1247, 1316, 1471, 1766, 2154, 2631, 3154,
    3669, 4104, 4377, 4468, 4403, 4187, 3827, 3321, 2712, 2051, 1452, 987, 709, 638, 769, 1021,
    1336, 1623, 1853, 1929, 1815, 1518, 1098, 606, 60, -539, -1143, -1709, -2171, -2545, -2827,
    -3042, -3196, -3279, -3343, -3343, -3269, -3074, -2767, -2326, -1786, -1210, -697, -322, -150,
    -210, -455, -867, -1366, -1875, -2338, -2689, -2851, -2779, -2475, -1972, -1303, -579, 93, 662,
    1044, 1232, 1240, 1158, 1064, 1059, 1184, 1415, 1696, 1970, 2206, 2375, 2520, 2628, 2650, 2559,
    2381, 2162, 1915, 1646, 1359, 1105, 929, 824, 721, 575, 331, -4, -394, -776, -1126, -1418,
    -1637, -1831, -2011, -2138, -2249, -2372, -2573, -2845, -3238, -3748, -4358, -5053, -5757,
    -6375, -6869, -7290, -7563, -7531, -7058, -6093, -4688, -2982, -1095, 882, 2773, 4286, 5214,
    5484, 5179, 4429, 3356, 2058, 611, -702, -1646, -2052, -1908, -1265, -238, 1030, 2388, 3672,
    4646, 5234, 5462, 5448, 5283, 5031, 4705, 4342, 4028, 3773, 3522, 3229, 2911, 2583, 2257, 1946,
    1640, 1395, 1275, 1310, 1440, 1620, 1746, 1721, 1494, 1014, 252, -788, -1970, -3161, -4221,
    -5032, -5521, -5682, -5488, -4974, -4229, -3377, -2568, -1918, -1536, -1422, -1579, -1962,
    -2517, -3156, -3831, -4414, -4819, -4974, -4899, -4596, -4137, -3594, -3011, -2406, -1771,
    -1110, -435, 170, 683, 1111, 1493, 1833, 2087, 2245, 2254, 2129, 1903, 1694, 1571, 1574, 1685,
    1892, 2230, 2674, 3196, 3754, 4312, 4805, 5130, 5281, 5234, 4971, 4458, 3730, 2879, 2046, 1380,
    904, 610, 496, 521, 669, 872, 1121, 1314, 1464, 1498, 1413, 1127, 691, 128, -497, -1066, -1555,
    -1968, -2329, -2647, -2913, -3138, -3280, -3333, -3286, -3110, -2805, -2398, -1916, -1432,
    -1016, -704, -469, -333, -339, -469, -712, -996, -1243, -1436, -1588, -1637, -1477, -1139,
    -686, -208, 212, 527, 751, 933, 1055, 1141, 1255, 1398, 1619, 1935, 2318, 2638, 2880, 3030,
    3102, 3058, 2933, 2697, 2429, 2166, 1945, 1749, 1607, 1552, 1559, 1599, 1642, 1616, 1499, 1306,
    1059, 759, 456, 173, -103, -373, -606, -778, -903, -1042, -1244, -1493, -1716, -1933, -2186,
    -2505, -2886, -3312, -3771, -4223, -4641, -5035, -5333, -5498, -5433, -5119, -4599, -3940,
    -3139, -2102, -799, 697, 2181, 3439, 4292, 4666, 4606, 4152, 3376, 2358, 1278, 330, -366, -784,
    -930, -780, -268, 626, 1757, 2885, 3796, 4429, 4776, 4864, 4758, 4530, 4267, 4029, 3843, 3698,
    3517, 3283, 3019, 2747, 2494, 2264, 2038, 1820, 1606, 1440, 1307, 1239, 1207, 1146, 978, 678,
    208, -455, -1264, -2150, -2986, -3683, -4124, -4299, -4205, -3916, -3477, -2959, -2362, -1786,
    -1352, -1129, -1092, -1166, -1338, -1624, -1996, -2347, -2540, -2616, -2642, -2636, -2543,
    -2356, -2115, -1862, -1615, -1352, -1024, -619, -190, 264, 702, 1112, 1426, 1666, 1843, 1965,
    2028, 1992, 1926, 1874, 1859, 1849, 1913, 2141, 2519, 2885, 3219, 3557, 3824, 3945, 3849, 3554,
    3063, 2438, 1789, 1181, 694, 395, 255, 184, 231, 410, 667, 896, 1080, 1170, 1105, 910, 601,
    204, -246, -688, -1100, -1459, -1712, -1890, -2171, -2529, -2858, -3068, -3186, -3271, -3286,
    -3174, -2877, -2440, -1968, -1515, -1115, -803, -614, -548, -602, -740, -885, -1042, -1179,
    -1205, -1068, -832, -565, -318, -88, 113, 302, 436, 475, 463, 417, 375, 329, 346, 441, 671,
    1026, 1469, 1946, 2403, 2722, 2814, 2738, 2652, 2626, 2611, 2518, 2361, 2182, 2009, 1754, 1415,
    1059, 804, 680, 640, 569, 401, 183, -4, -99, -119, -79, -89, -199, -448, -816, -1292, -1799,
    -2301, -2753, -3140, -3476, -3825, -4190, -4556, -4930, -5312, -5647, -5924, -6193, -6500,
    -6777, -6899, -6755, -6291, -5517, -4431, -3035, -1418, 288, 1892, 3215, 4055, 4272, 3870,
    3002, 1831, 502, -814, -1937, -2734, -3102, -2981, -2367, -1343, 39, 1512, 2773, 3590, 4023,
    4175, 4089, 3823, 3454, 3086, 2839, 2791, 2868, 2889, 2740, 2524, 2354, 2215, 2002, 1726, 1423,
    1160, 986, 971, 1105, 1269, 1295, 1120, 687, 40, -841, -1816, -2774, -3570, -4161, -4462,
    -4398, -4021, -3445, -2751, -2002, -1299, -774, -501, -489, -734, -1177, -1773, -2419, -3013,
    -3505, -3848, -4031, -4049, -3919, -3676, -3365, -3062, -2755, -2376, -1948, -1521, -1144,
    -747, -347, 27, 310, 479, 584, 674, 759, 810, 838, 912, 1008, 1130, 1287, 1511, 1809, 2164,
    2543, 2874, 3081, 3135, 2996, 2671, 2231, 1742, 1272, 844, 521, 298, 195, 215, 337, 542, 795,
    1054, 1273, 1405, 1413, 1279, 1051, 798, 492, 107, -283, -630, -937, -1257, -1588, -1917,
    -2232, -2453, -2564, -2584, -2518, -2372, -2168, -1918, -1554, -1090, -658, -405, -336, -334,
    -321, -352, -494, -688, -767, -745, -770, -860, -867, -687, -485, -454, -523, -452, -193, 5,
    -57, -248, -343, -289, -108, 176, 448, 630, 731, 877, 1061, 1341, 1744, 2161, 2371, 2406, 2412,
    2418, 2332, 2172, 2000, 1818, 1586, 1309, 994, 635, 232, -140, -396, -497, -497, -464, -418,
    -365, -350, -373, -414, -458, -531, -649, -827, -1088, -1477, -1970, -2447, -2786, -3041,
    -3317, -3632, -3892, -4139, -4464, -4849, -5201, -5507, -5832, -6122, -6323, -6431, -6394,
    -6120, -5565, -4809, -3905, -2841, -1553, -30, 1581, 2958, 3809, 4071, 3900, 3477, 2817, 1881,
    764, -244, -902, -1238, -1387, -1343, -905, 25, 1234, 2416, 3422, 4157, 4545, 4591, 4486, 4340,
    4205, 4089, 3997, 3829, 3547, 3226, 2932, 2675, 2436, 2207, 1978, 1780, 1657, 1627, 1666, 1684,
    1652, 1566, 1404, 1068, 506, -265, -1141, -2057, -2875, -3485, -3829, -3880, -3667, -3188,
    -2568, -1925, -1385, -976, -748, -719, -858, -1173, -1619, -2137, -2652, -3125, -3460, -3612,
    -3630, -3595, -3470, -3247, -2944, -2660, -2369, -2037, -1595, -1074, -543, -87, 351, 763,
    1107, 1329, 1460, 1576, 1672, 1718, 1730, 1796, 1947, 2143, 2374, 2687, 3028, 3348, 3564, 3606,
    3463, 3189, 2878, 2529, 2224, 2049, 1997, 1922, 1800, 1754, 1851, 2041, 2204, 2293, 2323, 2311,
    2226, 2081, 1931, 1786, 1625, 1450, 1300, 1114, 827, 429, 0, -392, -699, -972, -1236, -1488,
    -1594, -1556, -1419, -1227, -964, -629, -346, -209, -222, -246, -279, -402, -604, -698, -655,
    -595, -570, -481, -296, -72, 131, 279, 294, 186, 5, -199, -363, -417, -342, -211, -79, 87, 326,
    639, 952, 1294, 1678, 2043, 2272, 2301, 2269, 2247, 2272, 2235, 2165, 2096, 2051, 1982, 1840,
    1630, 1391, 1170, 1025, 893, 703, 474, 305, 247, 232, 202, 138, 59, -5, -119, -279, -449, -563,
    -667, -825, -1002, -1172, -1352, -1552, -1724, -1909, -2182, -2567, -3003, -3472, -3970, -4528,
    -5105, -5629, -5944, -5969, -5711, -5184, -4475, -3650, -2767, -1796, -655, 649, 1979, 3059,
    3704, 3899, 3628, 2970, 2075, 1186, 476, -10, -258, -335, -207, 156, 773, 1590, 2488, 3336,
    4031, 4527, 4764, 4727, 4506, 4221, 3902, 3623, 3472, 3395, 3239, 3018, 2848, 2740, 2633, 2527,
    2486, 2484, 2455, 2367, 2238, 2134, 2021, 1826, 1492, 1003, 311, -568, -1517, -2329, -2925,
    -3277, -3371, -3221, -2898, -2492, -1997, -1475, -1034, -715, -561, -629, -918, -1281, -1724,
    -2297, -2892, -3242, -3322, -3299, -3280, -3226, -3045, -2721, -2280, -1801, -1380, -1049,
    -756, -386, 66, 473, 814, 1089, 1272, 1343, 1380, 1420, 1405, 1391, 1473, 1664, 1931, 2270,
    2618, 2969, 3345, 3738, 3948, 3976, 3866, 3677, 3382, 3067, 2749, 2458, 2249, 2108, 1977, 1933,
    2094, 2335, 2500, 2557, 2576, 2509, 2359, 2173, 1949, 1667, 1391, 1129, 847, 520, 171, -212,
    -547, -798, -955, -1059, -1070, -955, -773, -544, -237, 120, 372, 470, 473, 427, 255, -46,
    -453, -885, -1240, -1380, -1299, -1142, -985, -816, -573, -324, -85, 80, 192, 314, 438, 424,
    139, -294, -585, -600, -466, -379, -406, -367, -138, 165, 345, 533, 994, 1586, 1910, 1896,
    1833, 1885, 1958, 1972, 1797, 1436, 1043, 752, 498, 233, 40, -10, -8, 14, 88, 280, 553, 798,
    888, 854, 699, 431, 147, -30, -100, -215, -384, -564, -754, -998, -1247, -1486, -1709, -1962,
    -2201, -2422, -2632, -2869, -3172, -3552, -3987, -4367, -4655, -4928, -5280, -5655, -5943,
    -6058, -5891, -5317, -4308, -3048, -1698, -304, 1262, 2948, 4381, 5174, 5289, 4941, 4215, 3095,
    1630, 65, -1291, -2133, -2438, -2387, -2054, -1366, -263, 1075, 2378, 3398, 4005, 4238, 4205,
    4069, 3915, 3735, 3554, 3390, 3256, 3042, 2749, 2456, 2159, 1825, 1494, 1281, 1222, 1290, 1391,
    1503, 1653, 1843, 1950, 1835, 1438, 728, -253, -1323, -2231, -2868, -3270, -3499, -3524, -3233,
    -2568, -1686, -850, -238, 127, 297, 286, 78, -336, -894, -1511, -2060, -2485, -2767, -2967,
    -3061, -2993, -2770, -2451, -2077, -1670, -1280, -957, -679, -372, 3, 416, 781, 982, 1049,
    1052, 1080, 1069, 976, 888, 892, 997, 1138, 1389, 1781, 2242, 2604, 2862, 3051, 3170, 3126,
    2892, 2532, 2162, 1828, 1524, 1208, 1029, 1045, 1204, 1395, 1629, 1908, 2143, 2261, 2284, 2255,
    2146, 1996, 1842, 1671, 1410, 1059, 674, 327, 79, -81, -231, -433, -630, -745, -799, -810,
    -795, -712, -590, -495, -441, -374, -296, -296, -343, -363, -309, -218, -118, -30, 52, 198,
    454, 677, 811, 818, 694, 486, 268, 126, -58, -268, -495, -643, -690, -599, -418, -188, 104,
    422, 709, 1001, 1310, 1536, 1662, 1790, 1958, 2014, 1852, 1556, 1241, 917, 630, 444, 358, 292,
    223, 169, 131, 67, 59, 108, 171, 176, 125, 54, 2, -19, -3, 11, 7, -25, -69, -126, -248, -438,
    -677, -898, -1141, -1393, -1601, -1767, -1988, -2329, -2712, -3050, -3413, -3884, -4443, -4949,
    -5323, -5548, -5652, -5670, -5540, -5125, -4411, -3472, -2348, -1044, 414, 1938, 3397, 4488,
    4971, 4847, 4290, 3420, 2309, 1024, -302, -1441, -2122, -2339, -2201, -1724, -874, 303, 1597,
    2730, 3499, 3863, 3975, 3932, 3824, 3671, 3482, 3272, 3146, 3093, 3034, 2878, 2698, 2526, 2408,
    2342, 2254, 2143, 2099, 2199, 2298, 2302, 2172, 1929, 1506, 876, 19, -977, -1953, -2725, -3311,
    -3655, -3671, -3279, -2626, -1830, -1015, -307, 195, 520, 652, 516, 72, -563, -1270, -1926,
    -2458, -2874, -3189, -3364, -3346, -3240, -3097, -2875, -2592, -2311, -2036, -1687, -1337,
    -1038, -785, -545, -358, -191, -1, 159, 222, 170, 137, 183, 338, 532, 787, 1117, 1496, 1836,
    2106, 2266, 2332, 2344, 2356, 2329, 2201, 1997, 1753, 1539, 1388, 1295, 1246, 1270, 1399, 1525,
    1600, 1636, 1704, 1775, 1858, 1934, 1977, 1945, 1855, 1628, 1250, 848, 560, 398, 266, 153, -2,
    -174, -333, -401, -472, -516, -423, -160, 78, 120, -48, -294, -501, -552, -495, -411, -395,
    -454, -535, -561, -421, -143, 106, 229, 266, 285, 220, 55, -163, -336, -440, -473, -459, -452,
    -437, -417, -376, -290, -157, -26, 26, 22, 32, 107, 245, 360, 437, 527, 673, 745, 672, 550,
    472, 429, 402, 393, 374, 308, 248, 193, 143, 125, 114, 29, -179, -395, -487, -496, -511, -599,
    -688, -733, -774, -868, -1020, -1243, -1517, -1793, -2042, -2296, -2531, -2733, -2907, -3100,
    -3231, -3348, -3544, -3867, -4203, -4512, -4803, -5074, -5353, -5679, -5990, -6131, -6037,
    -5665, -4907, -3702, -2147, -385, 1428, 3053, 4162, 4582, 4329, 3563, 2472, 1181, -267, -1731,
    -2913, -3509, -3407, -2719, -1601, -237, 1189, 2427, 3278, 3681, 3701, 3541, 3367, 3266, 3244,
    3242, 3243, 3215, 3203, 3159, 3021, 2784, 2494, 2123, 1702, 1392, 1322, 1454, 1721, 2041, 2302,
    2388, 2200, 1652, 719, -462, -1720, -2880, -3757, -4265, -4374, -4106, -3467, -2603, -1665,
    -746, -5, 386, 385, 85, -448, -1157, -1920, -2639, -3287, -3762, -4010, -4081, -4070, -3992,
    -3825, -3629, -3484, -3325, -3066, -2702, -2369, -2081, -1756, -1400, -1076, -808, -538, -291,
    -144, -113, -130, -144, -75, 103, 414, 803, 1227, 1632, 1972, 2193, 2319, 2367, 2342, 2168,
    1825, 1407, 1047, 781, 644, 662, 874, 1211, 1600, 1972, 2291, 2580, 2790, 2871, 2832, 2735,
    2587, 2333, 2012, 1694, 1466, 1258, 986, 657, 456, 447, 425, 229, -1, -75, -92, -157, -240,
    -253, -227, -229, -326, -495, -674, -781, -820, -858, -896, -885, -746, -521, -291, -95, 146,
    367, 447, 336, 166, -52, -360, -651, -830, -954, -1124, -1221, -1194, -1137, -1055, -829, -535,
    -324, -130, 128, 306, 343, 458, 756, 1024, 1131, 1121, 989, 753, 582, 602, 678, 691, 698, 781,
    875, 918, 900, 864, 780, 668, 581, 535, 459, 321, 207, 165, 123, 27, -76, -94, -120, -238,
    -445, -688, -888, -1035, -1079, -1048, -1006, -1029, -1130, -1371, -1709, -2073, -2359, -2680,
    -3154, -3752, -4311, -4735, -5046, -5285, -5548, -5852, -6072, -5949, -5288, -4088, -2537,
    -838, 870, 2387, 3463, 3927, 3812, 3265, 2432, 1395, 224, -962, -1908, -2407, -2369, -1817,
    -822, 452, 1746, 2816, 3467, 3672, 3577, 3444, 3388, 3422, 3495, 3592, 3715, 3763, 3692, 3562,
    3432, 3244, 2978, 2742, 2605, 2481, 2414, 2484, 2696, 2966, 3211, 3300, 3004, 2329, 1372, 248,
    -902, -1836, -2436, -2741, -2774, -2496, -1979, -1354, -734, -166, 273, 467, 395, 92, -366,
    -942, -1574, -2166, -2736, -3263, -3645, -3783, -3779, -3720, -3610, -3462, -3278, -3012,
    -2660, -2314, -1991, -1629, -1237, -928, -755, -648, -550, -469, -443, -460, -476, -432, -293,
    0, 404, 849, 1264, 1638, 1946, 2139, 2236, 2243, 2187, 2018, 1797, 1583, 1440, 1385, 1354,
    1325, 1361, 1557, 1903, 2257, 2532, 2758, 2952, 3111, 3243, 3314, 3303, 3206, 3084, 2926, 2698,
    2382, 2060, 1804, 1560, 1239, 874, 558, 310, 126, -4, -92, -143, -116, -11, 45, 37, 27, 5, -71,
    -154, -201, -250, -294, -247, -97, 79, 196, 245, 165, 38, -79, -118, -216, -368, -510, -569,
    -577, -577, -546, -480, -409, -344, -280, -225, -191, -147, 2, 203, 451, 774, 1170, 1501, 1644,
    1664, 1627, 1549, 1426, 1339, 1320, 1303, 1205, 1053, 948, 920, 887, 816, 745, 654, 496, 356,
    296, 258, 117, -118, -327, -412, -323, -168, -137, -300, -510, -625, -703, -865, -1095, -1288,
    -1462, -1663, -1845, -1986, -2153, -2424, -2798, -3208, -3615, -4000, -4400, -4802, -5128,
    -5363, -5620, -5970, -6329, -6533, -6455, -5944, -4848, -3134, -1068, 864, 2290, 3106, 3446,
    3448, 3138, 2454, 1385, 131, -1005, -1828, -2338, -2458, -2066, -1073, 368, 1828, 2856, 3261,
    3241, 3138, 3166, 3309, 3480, 3625, 3759, 3818, 3765, 3568, 3325, 3131, 2987, 2827, 2560, 2228,
    1982, 2006, 2395, 2967, 3456, 3672, 3562, 3126, 2381, 1389, 275, -785, -1618, -2211, -2632,
    -2855, -2769, -2413, -1897, -1320, -795, -442, -348, -456, -759, -1180, -1649, -2086, -2539,
    -2996, -3390, -3648, -3814, -3926, -4009, -4021, -3949, -3768, -3520, -3257, -2950, -2532,
    -2043, -1609, -1321, -1124, -991, -882, -811, -861, -1018, -1106, -990, -718, -419, -104, 195,
    504, 796, 1070, 1258, 1367, 1434, 1444, 1336, 1154, 998, 863, 709, 614, 738, 1062, 1448, 1771,
    2040, 2277, 2490, 2649, 2666, 2568, 2479, 2385, 2167, 1828, 1506, 1271, 1066, 901, 758, 602,
    411, 256, 88, -132, -318, -380, -329, -291, -292, -320, -388, -502, -586, -629, -695, -799,
    -855, -825, -742, -628, -447, -242, -46, 120, 212, 190, 69, -129, -379, -664, -921, -1157,
    -1332, -1418, -1416, -1364, -1272, -1125, -950, -794, -626, -451, -227, 53, 347, 595, 723, 771,
    763, 741, 728, 714, 701, 679, 666, 674, 649, 553, 416, 258, 143, 84, 79, -10, -263, -577, -785,
    -847, -848, -883, -947, -1004, -982, -893, -793, -709, -615, -564, -597, -715, -837, -988,
    -1149, -1343, -1514, -1720, -1914, -2112, -2275, -2395, -2484, -2595, -2766, -2962, -3194,
    -3472, -3813, -4201, -4650, -5109, -5532, -5899, -6229, -6441, -6376, -5850, -4728, -3069,
    -1181, 486, 1641, 2323, 2700, 2798, 2552, 1938, 1051, 65, -772, -1351, -1642, -1564, -1009,
    -62, 989, 1815, 2249, 2295, 2206, 2270, 2483, 2706, 2894, 3136, 3449, 3694, 3735, 3569, 3346,
    3135, 2864, 2454, 1977, 1601, 1503, 1751, 2233, 2752, 3185, 3434, 3350, 2886, 2116, 1223, 321,
    -503, -1210, -1757, -2067, -2152, -2020, -1675, -1189, -758, -490, -393, -451, -663, -951,
    -1245, -1568, -1913, -2217, -2485, -2738, -2941, -3055, -3057, -2979, -2867, -2796, -2767,
    -2693, -2537, -2352, -2185, -1985, -1736, -1483, -1354, -1324, -1312, -1221, -1064, -908, -801,
    -700, -542, -303, -3, 342, 699, 984, 1157, 1216, 1238, 1251, 1242, 1175, 1107, 1066, 1090,
    1147, 1236, 1324, 1436, 1587, 1738, 1826, 1891, 1949, 1980, 1926, 1834, 1769, 1773, 1799, 1723,
    1533, 1319, 1203, 1138, 1060, 989, 961, 995, 1071, 1113, 1065, 860, 577, 288, 56, -129, -253,
    -306, -271, -186, -75, 47, 167, 277, 344, 407, 455, 476, 430, 351, 302, 281, 230, 99, -49,
    -197, -339, -489, -638, -753, -802, -725, -541, -340, -160, 41, 293, 596, 913, 1183, 1382,
    1478, 1514, 1482, 1434, 1357, 1249, 1126, 1032, 953, 852, 786, 813, 866, 847, 700, 494, 251,
    23, -165, -275, -415, -682, -962, -1045, -1028, -1214, -1432, -1138, -308, 395, 434, -61, -706,
    -1121, -1114, -881, -760, -800, -847, -974, -1340, -1775, -2048, -2210, -2337, -2298, -1967,
    -1644, -1746, -2286, -2859, -3107, -3142, -3189, -3372, -3656, -4035, -4420, -4834, -5228,
    -5492, -5334, -4586, -3296, -1772, -482, 370, 959, 1515, 1974, 2178, 2023, 1544, 908, 359, -82,
    -448, -550, -158, 584, 1264, 1630, 1659, 1526, 1504, 1773, 2264, 2819, 3332, 3778, 4107, 4303,
    4308, 4144, 3973, 3905, 3808, 3482, 2891, 2247, 1821, 1720, 1782, 1821, 1806, 1763, 1682, 1516,
    1281, 983, 713, 494, 240, -170, -650, -1065, -1288, -1292, -1083, -814, -588, -454, -391, -494,
    -669, -871, -1033, -1253, -1507, -1766, -1958, -2122, -2269, -2390, -2470, -2520, -2568, -2627,
    -2673, -2667, -2579, -2452, -2285, -2025, -1613, -1173, -801, -555, -355, -238, -157, -143,
    -186, -270, -310, -250, -110, 57, 244, 506, 833, 1184, 1480, 1676, 1804, 1867, 1878, 1777,
    1564, 1314, 1119, 1035, 983, 901, 773, 691, 676, 691, 781, 1006, 1361, 1692, 1935, 2062, 2074,
    1899, 1613, 1376, 1283, 1204, 1036, 800, 575, 335, 82, -134, -277, -385, -410, -321, -179, -44,
    81, 259, 444, 564, 526, 358, 122, -87, -234, -278, -190, -49, 57, 112, 164, 257, 374, 467, 453,
    362, 220, 22, -245, -506, -574, -463, -281, -147, -28, 114, 294, 491, 650, 780, 882, 964, 979,
    933, 857, 760, 627, 472, 363, 285, 182, -26, -299, -538, -660, -699, -696, -634, -482, -304,
    -143, -47, 3, 30, 50, 57, 2, -30, -20, 3, -6, -35, -73, -144, -256, -345, -392, -429, -499,
    -669, -911, -1154, -1261, -1231, -1170, -1192, -1252, -1291, -1279, -1247, -1185, -1097, -987,
    -888, -861, -930, -1071, -1257, -1463, -1654, -1743, -1774, -1877, -2146, -2516, -2836, -3079,
    -3253, -3425, -3439, -3139, -2455, -1588, -838, -413, -230, -113, 37, 110, 80, -49, -128, -150,
    -148, -208, -242, -82, 266, 553, 577, 382, 116, -70, -82, 85, 328, 585, 858, 1028, 968, 744,
    568, 552, 667, 836, 999, 1090, 1063, 1030, 1106, 1328, 1539, 1681, 1696, 1575, 1273, 962, 740,
    622, 564, 527, 460, 328, 190, 106, 137, 220, 268, 197, 53, -60, -139, -153, -144, -130, -145,
    -144, -173, -289, -434, -501, -507, -508, -526, -547, -592, -638, -651, -609, -538, -509, -602,
    -750, -859, -877, -845, -781, -660, -520, -379, -301, -293, -314, -302, -252, -199, -174, -180,
    -202, -230, -280, -361, -364, -226, -27, 142, 307, 471, 636, 804, 991, 1098, 1088, 1028, 935,
    871, 897, 984, 1006, 959, 932, 992, 1100, 1218, 1281, 1277, 1287, 1337, 1384, 1349, 1267, 1166,
    1065, 1001, 968, 961, 928, 854, 774, 748, 796, 824, 821, 784, 796, 856, 932, 980, 952, 927,
    931, 930, 853, 717, 576, 454, 348, 268, 190, 136, 100, 116, 153, 219, 288, 340, 338, 313, 266,
    204, 145, 105, 89, 56, 20, 8, 4, -19, -26, 8, 58, 127, 165, 121, 12, -26, 39, 110, 98, 19,
    -100, -219, -273, -281, -275, -244, -180, -123, -63, 15, 92, 113, 94, 75, 37, -23, -148, -336,
    -533, -637, -639, -612, -643, -706, -782, -824, -830, -800, -733, -654, -587, -522, -484, -507,
    -616, -790, -949, -1044, -1115, -1198, -1369, -1595, -1808, -1923, -1985, -2080, -2194, -2191,
    -2056, -1844, -1615, -1361, -1126, -996, -1006, -1157, -1402, -1664, -1865, -1978, -1967,
    -1838, -1588, -1261, -902, -534, -209, 85, 380, 666, 844, 895, 832, 648, 332, -61, -430, -708,
    -816, -736, -509, -234, 90, 432, 777, 1137, 1473, 1700, 1755, 1711, 1619, 1505, 1421, 1401,
    1382, 1287, 1123, 851, 484, 141, -35, -82, -67, 62, 274, 458, 587, 708, 772, 692, 551, 363,
    129, -105, -207, -226, -217, -119, 69, 267, 396, 472, 457, 370, 230, 10, -262, -493, -637,
    -755, -824, -843, -876, -921, -919, -893, -894, -900, -832, -743, -622, -489, -403, -377, -367,
    -300, -232, -169, -127, -79, -14, 93, 209, 328, 428, 524, 605, 719, 844, 933, 905, 772, 612,
    480, 415, 413, 424, 450, 506, 601, 700, 802, 952, 1135, 1294, 1423, 1529, 1620, 1641, 1603,
    1507, 1397, 1292, 1217, 1147, 1089, 1021, 971, 933, 919, 904, 901, 892, 890, 905, 920, 912,
    858, 746, 609, 472, 392, 377, 387, 376, 327, 251, 222, 224, 225, 212, 176, 150, 118, 81, -14,
    -140, -223, -246, -237, -237, -245, -291, -326, -299, -215, -121, -43, 40, 118, 207, 248, 259,
    235, 204, 168, 174, 233, 284, 333, 410, 524, 633, 727, 796, 786, 732, 672, 620, 565, 495, 385,
    239, 112, 54, 33, 66, 82, 94, 95, 127, 181, 259, 365, 461, 497, 503, 479, 413, 309, 200, 88,
    -36, -143, -209, -232, -217, -180, -143, -149, -173, -243, -331, -450, -547, -639, -755, -910,
    -1105, -1297, -1453, -1523, -1514, -1466, -1419, -1378, -1330, -1280, -1191, -1110, -1070,
    -1093, -1164, -1274, -1390, -1500, -1621, -1719, -1757, -1678, -1552, -1339, -1049, -722, -467,
    -319, -301, -399, -519, -536, -433, -292, -154, -12, 105, 191, 239, 270, 240, 128, 21, -3, 81,
    220, 375, 536, 680, 790, 876, 878, 804, 721, 699, 694, 690, 685, 714, 720, 767, 885, 1050,
    1186, 1236, 1199, 1078, 939, 794, 650, 496, 365, 248, 134, 26, -76, -147, -167, -134, -102,
    -98, -111, -143, -195, -250, -287, -313, -345, -390, -384, -336, -233, -98, 5, 33, 13, 41, 135,
    234, 317, 376, 430, 494, 576, 693, 821, 935, 1012, 1085, 1137, 1152, 1108, 1052, 1013, 1017,
    1037, 1037, 1012, 1002, 1036, 1101, 1178, 1239, 1259, 1230, 1206, 1200, 1201, 1191, 1196, 1183,
    1150, 1080, 1067, 1097, 1164, 1215, 1261, 1238, 1174, 1106, 1043, 974, 907, 865, 830, 773, 739,
    683, 596, 495, 412, 351, 332, 372, 441, 490, 539, 568, 592, 581, 574, 545, 526, 501, 481, 449,
    418, 401, 392, 419, 455, 524, 631, 739, 811, 855, 884, 918, 969, 1009, 1023, 1007, 981, 915,
    849, 822, 859, 906, 971, 1026, 1070, 1118, 1190, 1250, 1262, 1237, 1177, 1115, 1089, 1109,
    1122, 1105, 1070, 1034, 985, 911, 822, 717, 652, 618, 599, 546, 463, 346, 283, 297, 373, 459,
    521, 573, 539, 441, 307, 183, 52, -66, -148, -194, -229, -268, -308, -378, -447, -481, -447,
    -388, -338, -340, -391, -458, -508, -529, -552, -584, -638, -701, -755, -785, -813, -900, -953,
    -863, -678, -492, -391, -343, -393, -479, -563, -606, -565, -407, -241, -211, -248, -291, -369,
    -461, -508, -508, -539, -517, -488, -487, -504, -417, -281, -166, -91, -94, -199, -342, -468,
    -562, -586, -542, -516, -540, -554, -573, -583, -507, -392, -341, -360, -351, -332, -312, -256,
    -169, -101, -76, -102, -228, -387, -520, -622, -683, -652, -581, -563, -571, -586, -617, -645,
    -603, -547, -567, -639, -720, -787, -792, -715, -599, -468, -327, -167, -39, 68, 163, 207, 197,
    140, 46, -67, -132, -169, -235, -306, -325, -306, -302, -280, -209, -82, 32, 140, 245, 344,
    410, 461, 499, 530, 522, 494, 447, 388, 355, 373, 410, 399, 378, 382, 390, 377, 353, 314, 286,
    227, 151, 52, -22, -82, -138, -215, -269, -291, -251, -192, -169, -174, -194, -176, -132, -40,
    24, 46, 57, 111, 188, 234, 251, 256, 234, 182, 123, 80, 81, 93, 98, 90, 62, 25, -14, -11, 41,
    127, 226, 302, 349, 380, 431, 495, 551, 590, 649, 728, 809, 870, 880, 868, 884, 954, 1020,
    1049, 1039, 981, 867, 764, 705, 653, 598, 553, 521, 491, 466, 457, 431, 425, 455, 510, 571,
    670, 745, 763, 738, 691, 604, 477, 357, 242, 139, 57, 0, -70, -155, -248, -323, -380, -415,
    -430, -405, -340, -235, -127, -25, 23, 14, -61, -167, -259, -299, -270, -213, -158, -157, -192,
    -251, -268, -273, -282, -276, -236, -211, -237, -299, -349, -370, -382, -406, -401, -303, -161,
    -73, -47, -33, -33, -77, -179, -320, -438, -466, -451, -436, -436, -438, -458, -505, -551,
    -623, -687, -726, -739, -724, -690, -656, -702, -807, -917, -1046, -1137, -1151, -1104, -1092,
    -1124, -1170, -1219, -1222, -1168, -1086, -1033, -1010, -1062, -1167, -1276, -1362, -1424,
    -1444, -1451, -1453, -1448, -1385, -1359, -1414, -1480, -1484, -1452, -1407, -1343, -1289,
    -1214, -1140, -1126, -1199, -1263, -1248, -1154, -1019, -854, -706, -574, -478, -414, -445,
    -521, -614, -684, -697, -663, -624, -605, -617, -637, -686, -737, -770, -781, -759, -710, -606,
    -493, -367, -265, -203, -183, -177, -174, -223, -287, -316, -264, -179, -121, -94, -119, -202,
    -306, -379, -408, -379, -343, -291, -233, -184, -177, -195, -189, -159, -136, -138, -161, -206,
    -238, -234, -195, -169, -151, -143, -144, -134, -117, -87, -53, 6, 78, 140, 165, 139, 118, 103,
    84, 25, -22, -14, 33, 65, 64, 60, 85, 137, 214, 296, 374, 426, 438, 434, 456, 507, 561, 580,
    580, 588, 608, 643, 692, 742, 772, 813, 825, 781, 673, 607, 576, 568, 625, 761, 904, 999, 1067,
    1108, 1081, 1049, 1057, 1068, 1029, 956, 886, 811, 762, 752, 778, 835, 885, 927, 929, 915, 845,
    770, 692, 656, 611, 545, 459, 359, 248, 165, 179, 269, 367, 390, 369, 319, 257, 206, 205, 250,
    290, 289, 272, 243, 244, 275, 354, 410, 391, 286, 173, 99, 131, 236, 368, 470, 518, 518, 478,
    399, 318, 262, 287, 395, 510, 534, 447, 351, 293, 280, 297, 348, 358, 309, 280, 388, 543, 632,
    625, 499, 298, 119, 57, 102, 181, 266, 329, 307, 198, 16, -164, -259, -191, -19, 88, 44, -116,
    -234, -251, -186, -124, -101, -123, -172, -265, -370, -418, -367, -277, -243, -251, -304, -393,
    -514, -604, -605, -549, -505, -505, -551, -591, -677, -769, -833, -831, -782, -744, -696, -660,
    -619, -602, -622, -653, -648, -591, -538, -521, -533, -548, -543, -512, -472, -454, -494, -556,
    -616, -594, -496, -365, -279, -226, -222, -289, -396, -483, -505, -453, -366, -318, -350, -428,
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    102, -94, -9, 354, 750, 918, 806, 516, 248, 172, 274, 367, 406, 493, 604, 606, 512, 400, 318,
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    333, 316, 339, 355, 387, 389, 403, 399, 411, 420, 442, 479, 497, 468, 415, 395, 398, 394, 403,
    416, 457, 476, 476, 441, 405, 388, 377, 354, 347, 343, 351, 362, 373, 373, 369, 343, 306, 268,
    243, 217, 210, 242, 280, 279, 264, 231, 183, 170, 203, 246, 256, 246, 227, 201, 200, 207, 216,
    225, 245, 231, 212, 192, 180, 164, 161, 184, 187, 189, 189, 181, 165, 163, 171, 184, 190, 194,
    177, 168, 151, 164, 153, 158, 167, 184, 180, 155, 129, 109, 103, 102, 113, 117, 131, 130, 124,
    110, 107, 105, 102, 107, 97, 91, 92, 104, 93, 83, 92, 88, 70, 53, 54, 52, 81, 124, 144, 106,
    52, 22, 45, 102, 123, 92, 39, 20, 43, 83, 108, 112, 80, 72, 71, 93, 98, 84, 59, 56, 75, 94,
    118, 132, 107, 65, 28, 26, 20, 36, 54, 65, 57, 43, 24, 17, 31, 59, 77, 93, 74, 39, 4, 9, 32,
    51, 48, 9, -37, -37, -2, 40, 57, 57, 18, -27, -42, -28, -5, 17, 27, 27, 18, 10, -16, -12, 12,
    39, 37, 19, 3, -9, -6, 11, 47, 58, 42, 10, 4, 17, 40, 64, 79, 65, 40, 39, 52, 58, 69, 57, 33,
    37, 61, 84, 76, 69, 47, 34, 32, 33, 30, 49, 86, 93, 68, 21, -5, 7, 44, 85, 88, 55, 20, -2, 4,
    26, 33, 37, 11, -12, -24, -24, -27, -37, -31, -36, -54, -82, -98, -96, -87, -71, -65, -92,
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    -467, -450, -465, -470, -468, -471, -484, -501, -512, -512, -497, -482, -503, -504, -517, -544,
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    -59, -31, -3, 4, -24, -45, -73, -63, -50, -17, 1, 4, 3, -16, -30, -33, -5, 27, 35, 36, 36, 22,
    22, 14, 15, 21, 24, 34, 47, 67, 69, 68, 53, 60, 61, 72, 75, 98, 128, 147, 132, 101, 78, 95,
    127, 170, 180, 156, 122, 90, 86, 115, 149, 177, 180, 181, 176, 163, 160, 164, 175, 179, 175,
    179, 169, 181, 183, 190, 183, 194, 197, 206, 207, 215, 233, 246, 244, 240, 245, 267, 274, 277,
    280, 310, 336, 353, 338, 308, 290, 293, 320, 342, 359, 360, 369, 377, 367, 344, 340, 352, 372,
    398, 411, 408, 391, 373, 365, 369, 408, 450, 481, 487, 486, 478, 455, 445, 453, 478, 472, 478,
    472, 487, 504, 525, 529, 536, 538, 546, 541, 541, 556, 563, 575, 599, 611, 623, 623, 615, 606,
    608, 623, 629, 640, 642, 632, 640, 646, 662, 662, 681, 686, 681, 647, 623, 589, 602, 623, 646,
    650, 664, 666, 659, 649, 632, 608, 591, 601, 615, 614, 600, 585, 579, 587, 592, 595, 590, 575,
    562, 569, 585, 601, 592, 572, 542, 527, 537, 538, 526, 508, 501, 492, 487, 487, 492, 498, 504,
    503, 487, 468, 444, 433, 448, 477, 503, 508, 504, 487, 476, 473, 490, 490, 485, 459, 433, 414,
    405, 418, 419, 413, 400, 391, 382, 365, 351, 337, 337, 339, 357, 356, 350, 348, 352, 350, 353,
    338, 315, 298, 284, 277, 283, 292, 305, 302, 298, 300, 297, 305, 296, 312, 322, 334, 321, 305,
    292, 283, 287, 300, 300, 300, 291, 297, 286, 287, 287, 275, 269, 259, 272, 263, 255, 252, 258,
    259, 263, 252, 244, 239, 246, 245, 228, 206, 184, 169, 149, 153, 158, 163, 153, 141, 119, 110,
    94, 89, 79, 84, 91, 85, 71, 56, 51, 68, 86, 101, 98, 104, 84, 75, 73, 93, 99, 117, 132, 120,
    105, 87, 87, 96, 116, 134, 128, 113, 116, 125, 128, 132, 131, 128, 131, 138, 142, 159, 170,
    153, 136, 112, 111, 105, 126, 144, 143, 147, 139, 127, 109, 105, 109, 113, 113, 121, 128, 139,
    144, 144, 126, 119, 113, 135, 147, 157, 145, 136, 128, 124, 138, 149, 152, 149, 140, 135, 131,
    141, 161, 182, 174, 167, 154, 150, 152, 159, 184, 193, 180, 163, 152, 155, 154, 146, 144, 137,
    140, 125, 105, 80, 80, 93, 110, 118, 121, 106, 89, 65, 52, 39, 35, 43, 42, 38, 14, -6, -22,
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    -219, -221, -220, -228, -236, -233, -234, -234, -238, -233, -221, -213, -213, -225, -227, -218,
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    -216, -216, -210, -193, -187, -183, -178, -167, -161, -160, -144, -140, -126, -120, -115, -117,
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    -23, -14, -8, 31, 59, 89, 80, 65, 55, 58, 72, 91, 110, 116, 114, 111, 110, 106, 114, 109, 125,
    137, 159, 164, 160, 151, 148, 158, 176, 188, 202, 198, 194, 177, 162, 160, 159, 171, 173, 180,
    173, 175, 170, 174, 180, 189, 187, 183, 182, 184, 184, 184, 191, 198, 189, 193, 179, 175, 164,
    162, 159, 155, 153, 147, 150, 156, 171, 174, 171, 169, 159, 147, 139, 130, 133, 118, 115, 109,
    110, 111, 103, 88, 86, 97, 97, 96, 87, 78, 74, 64, 60, 47, 51, 58, 54, 45, 21, 3, -21, -27,
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    -28, -14, 3, 11, 9, 15, 17, 13, 1, 10, 25, 27, 27, 19, 19, 30, 37, 38, 28, 32, 38, 51, 67, 67,
    63, 48, 49, 47, 51, 57, 72, 77, 83, 73, 80, 79, 76, 56, 31, 21, 16, 19, 16, 15, 6, -16, -29,
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    -1, 9, 22, 39, 42, 40, 37, 30, 19, 2, 1, -5, -10, -23, -27, -27, -26, -18, -17, -14, -16, -30,
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    -347, -350, -357, -364, -365, -374, -370, -371, -374, -365, -349, -340, -336, -332, -326, -330,
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    -142, -129, -122, -121, -124, -139, -135, -154, -150, -155, -146, -143, -140, -136, -152, -148,
    -147, -124, -113, -108, -102, -106, -108, -114, -125, -133, -133, -115, -110, -101, -108, -121,
    -128, -115, -94, -69, -58, -46, -46, -37, -23, -11, 12, 23, 25, 24, 26, 40, 63, 75, 86, 92, 83,
    83, 81, 99, 111, 112, 115, 102, 97, 98, 117, 127, 134, 137, 143, 136, 133, 136, 138, 136, 136,
    135, 137, 146, 159, 168, 168, 173, 181, 176, 180, 186, 203, 217, 219, 211, 201, 198, 204, 215,
    224, 222, 227, 209, 209, 208, 223, 232, 227, 219, 214, 205, 219, 220, 228, 223, 218, 216, 211,
    208, 202, 207, 216, 214, 213, 199, 202, 200, 195, 188, 169, 169, 169, 172, 168, 159, 145, 130,
    120, 120, 127, 129, 129, 120, 110, 99, 89, 91, 88, 89, 81, 71, 61, 59, 61, 52, 50, 34, 28, 13,
    14, 20, 14, 4, -8, -3, 1, 1, -2, -17, -31, -39, -49, -43, -42, -32, -20, -24, -27, -41, -29,
    -33, -18, -26, -30, -35, -45, -51, -66, -64, -66, -54, -53, -39, -46, -48, -61, -52, -50, -42,
    -33, -35, -37, -45, -47, -38, -32, -35, -22, -21, -5, -1, 3, 9, 21, 32, 40, 40, 46, 54, 51, 59,
    60, 69, 57, 59, 45, 50, 48, 59, 57, 58, 48, 53, 43, 56, 59, 76, 81, 92, 96, 105, 104, 99, 101,
    111, 122, 127, 119, 125, 121, 127, 131, 131, 144, 144, 162, 163, 170, 174, 172, 173, 178, 181,
    186, 190, 192, 192, 185, 184, 175, 177, 187, 194, 196, 200, 198, 208, 212, 230, 234, 249, 246,
    248, 234, 239, 246, 252, 258, 255, 242, 229, 221, 223, 231, 229, 230, 223, 212, 207, 197, 197,
    196, 198, 201, 200, 196, 182, 181, 184, 180, 180, 178, 173, 167, 165, 164, 159, 164, 165, 181,
    176, 177, 174, 176, 178, 187, 188, 196, 185, 172, 152, 148, 153, 164, 160, 147, 138, 121, 127,
    118, 118, 107, 99, 91, 88, 83, 78, 70, 65, 64, 59, 50, 40, 25, 24, 16, 23, 8, -7, -16, -30,
    -30, -37, -30, -37, -44, -61, -78, -84, -97, -103, -102, -105, -95, -110, -125, -151, -164,
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    -383, -393, -383, -384, -381, -378, -381, -379, -380, -379, -378, -369, -369, -366, -370, -377,
    -364, -369, -358, -350, -339, -327, -327, -330, -330, -327, -340, -341, -344, -333, -327, -319,
    -320, -320, -322, -320, -310, -308, -297, -301, -307, -329, -331, -336, -318, -314, -312, -313,
    -314, -319, -327, -345, -349, -365, -368, -379, -382, -377, -369, -369, -360, -365, -361, -369,
    -363, -358, -355, -351, -354, -361, -368, -365, -360, -343, -337, -329, -324, -325, -312, -313,
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    -295, -288, -288, -282, -294, -292, -287, -282, -268, -271, -262, -252, -240, -236, -229, -233,
    -219, -212, -187, -167, -140, -122, -107, -103, -97, -92, -87, -78, -62, -43, -34, -21, -18,
    -6, 6, 24, 33, 39, 35, 29, 20, 20, 19, 26, 32, 33, 25, 23, 26, 32, 49, 60, 68, 72, 82, 86, 105,
    111, 128, 133, 141, 139, 134, 124, 124, 106, 108, 100, 111, 114, 124, 139, 148, 152, 162, 162,
    163, 171, 184, 206, 225, 246, 261, 271, 269, 271, 285, 288, 298, 299, 299, 296, 300, 311, 322,
    337, 349, 371, 378, 392, 396, 404, 400, 396, 381, 375, 352, 343, 324, 318, 311, 304, 300, 303,
    304, 310, 313, 324, 325, 329, 337, 349, 357, 355, 356, 357, 365, 372, 369, 366, 355, 345, 329,
    324, 319, 319, 326, 336, 343, 348, 353, 363, 367, 368, 371, 380, 382, 386, 384, 382, 379, 367,
    354, 342, 329, 325, 321, 326, 334, 334, 343, 347, 357, 356, 350, 349, 334, 324, 307, 304, 308,
    307, 307, 300, 292, 288, 281, 271, 271, 250, 252, 236, 249, 248, 250, 243, 233, 223, 208, 207,
    201, 198, 188, 176, 159, 147, 138, 126, 124, 123, 134, 148, 162, 173, 187, 183, 179, 178, 182,
    180, 176, 164, 157, 159, 152, 158, 153, 150, 143, 128, 110, 86, 70, 63, 53, 61, 47, 53, 40, 39,
    26, 21, 14, 9, 0, -15, -34, -53, -70, -83, -79, -67, -52, -35, -32, -24, -30, -19, -14, 7, 16,
    22, 25, 25, 25, 34, 36, 47, 45, 50, 44, 34, 17, -2, -2, 0, 18, 41, 64, 74, 83, 90, 95, 109,
    116, 127, 116, 110, 107, 93, 88, 77, 77, 71, 69, 67, 68, 68, 70, 70, 65, 57, 54, 37, 31, 16,
    24, 29, 27, 20, 9, 5, 2, 7, 16, 16, 14, 24, 29, 46, 48, 60, 56, 59, 69, 81, 94, 93, 92, 83, 84,
    79, 93, 106, 120, 116, 114, 99, 89, 84, 89, 93, 95, 90, 78, 61, 41, 30, 30, 27, 26, 22, 27, 38,
    44, 37, 35, 21, 24, 12, 15, 3, -4, -15, -25, -33, -45, -43, -49, -42, -51, -49, -61, -56, -48,
    -31, -6, 7, 17, 24, 38, 58, 72, 81, 83, 93, 74, 60, 33, 27, 19, 20, 6, 11, 16, 29, 35, 36, 40,
    45, 33, 18, -8, -21, -29, -38, -57, -77, -76, -77, -83, -106, -128, -149, -162, -170, -172,
    -167, -152, -164, -181, -207, -195, -179, -175, -189, -219, -246, -283, -312, -332, -329, -328,
    -327, -341, -344, -328, -312, -303, -301, -290, -281, -295, -309, -322, -319, -306, -313, -318,
    -318, -304, -289, -291, -305, -299, -308, -313, -336, -345, -341, -345, -365, -390, -402, -392,
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    -80, -92, -97, -99, -104, -111, -101, -97, -92, -105, -98, -91, -68, -65, -41, -20, 25, 43, 63,
    56, 58, 47, 43, 31, 24, 19, 6, -3, -16, -14, -8, -9, -1, -1, 22, 22, 35, 33, 32, 18, 12, -7,
    -10, -22, -11, -4, 10, 15, 35, 44, 59, 70, 70, 72, 56, 47, 31, 31, 51, 57, 76, 78, 90, 84, 67,
    63, 53, 55, 69, 79, 92, 91, 91, 98, 114, 141, 171, 192, 185, 173, 146, 134, 122, 116, 116, 123,
    129, 133, 136, 142, 152, 164, 167, 162, 149, 140, 126, 104, 87, 63, 60, 65, 79, 72, 67, 53, 53,
    33, 18, 0, -8, -11, -4, 8, 36, 64, 83, 81, 82, 88, 97, 88, 70, 42, 18, 7, -7, -18, -29, -18,
    -6, -7, -5, 16, 57, 96, 113, 122, 126, 115, 83, 42, 11, 9, 26, 47, 44, 36, 36, 43, 39, 31, 40,
    69, 94, 89, 76, 66, 85, 88, 80, 60, 61, 69, 57, 20, -12, -27, -26, -49, -81, -86, -76, -57,
    -45, -31, 2, 43, 68, 90, 88, 100, 90, 87, 61, 47, 39, 54, 68, 99, 135, 183, 209, 208, 199, 187,
    186, 189, 194, 216, 224, 231, 220, 210, 220, 223, 237, 236, 247, 245, 236, 209, 189, 193, 208,
    242, 261, 277, 283, 293, 300, 302, 309, 311, 309, 293, 268, 245, 230, 221, 226, 233, 250, 268,
    267, 264, 252, 247, 239, 229, 212, 207, 200, 202, 195, 207, 219, 236, 240, 251, 247, 249, 254,
    263, 283, 285, 304, 319, 335, 338, 337, 348, 356, 355, 348, 339, 342, 324, 310, 288, 287, 288,
    310, 327, 350, 355, 370, 367, 361, 346, 338, 347, 346, 346, 323, 318, 309, 294, 268, 241, 245,
    251, 259, 248, 240, 243, 251, 259, 276, 307, 343, 378, 384, 385, 366, 363, 369, 364, 367, 357,
    345, 311, 281, 253, 254, 270, 289, 315, 323, 328, 313, 302, 288, 281, 284, 285, 284, 258, 254,
    237, 232, 220, 222, 213, 198, 178, 157, 152, 149, 178, 202, 230, 243, 236, 228, 218, 207, 208,
    201, 195, 184, 163, 150, 121, 99, 82, 86, 104, 112, 125, 117, 115, 103, 98, 96, 93, 88, 94, 94,
    107, 106, 114, 105, 99, 80, 64, 49, 27, 1, -20, -31, -25, -22, -13, -10, 2, 0, -6, -23, -48,
    -76, -107, -143, -166, -184, -188, -195, -194, -186, -184, -177, -176, -161, -150, -132, -118,
    -110, -100, -97, -91, -85, -80, -69, -53, -40, -28, -32, -22, -27, -30, -33, -23, -2, 9, 30,
    44, 70, 87, 112, 114, 123, 122, 117, 99, 78, 62, 52, 45, 37, 36, 45, 64, 77, 90, 92, 101, 96,
    93, 86, 70, 67, 52, 41, 35, 30, 36, 38, 41, 47, 55, 57, 62, 64, 66, 68, 71, 77, 84, 96, 106,
    116, 118, 121, 125, 120, 113, 109, 111, 119, 118, 127, 140, 151, 165, 175, 189, 199, 204, 213,
    203, 204, 191, 182, 164, 152, 145, 155, 164, 174, 169, 161, 152, 145, 136, 140, 145, 147, 140,
    129, 118, 114, 108, 103, 88, 80, 70, 63, 50, 48, 56, 68, 71, 74, 75, 88, 99, 109, 125, 142,
    159, 177, 183, 187, 181, 178, 176, 164, 163, 163, 163, 162, 148, 140, 141, 145, 140, 134, 124,
    128, 119, 126, 123, 127, 141, 138, 148, 130, 133, 110, 103, 86, 75, 66, 65, 66, 59, 57, 65, 64,
    61, 52, 48, 44, 39, 37, 25, 13, -7, -23, -34, -40, -32, -32, -47, -63, -89, -101, -116, -118,
    -107, -105, -103, -115, -120, -115, -130, -122, -122, -104, -101, -100, -103, -115, -128, -150,
    -168, -171, -178, -169, -169, -169, -168, -177, -172, -172, -175, -183, -188, -201, -208, -214,
    -205, -195, -201, -207, -219, -211, -207, -197, -190, -177, -172, -165, -179, -171, -165, -142,
    -128, -117, -110, -101, -103, -98, -101, -85, -73, -64, -61, -60, -67, -58, -58, -38, -34, -14,
    -5, 4, -5, -9, -17, -25, -27, -30, -30, -50, -54, -62, -53, -48, -39, -33, -28, -26, -36, -33,
    -45, -42, -53, -56, -64, -64, -60, -56, -42, -30, -15, -14, -11, -15, -11, -6, 2, 12, 19, 27,
    21, 29, 21, 29, 27, 47, 45, 47, 35, 23, 16, 10, 16, 28, 39, 58, 59, 74, 83, 99, 105, 105, 102,
    86, 84, 68, 68, 60, 62, 62, 62, 66, 63, 70, 80, 91, 100, 93, 95, 88, 86, 81, 72, 79, 81, 87,
    91, 96, 99, 101, 95, 101, 101, 109, 108, 115, 110, 118, 126, 147, 156, 174, 190, 206, 215, 224,
    226, 224, 220, 214, 223, 231, 242, 243, 242, 238, 227, 223, 231, 229, 241, 237, 241, 231, 217,
    206, 199, 200, 200, 197, 194, 177, 152, 128, 104, 99, 94, 98, 103, 95, 83, 69, 65, 51, 55, 61,
    73, 78, 76, 74, 65, 61, 53, 48, 37, 39, 34, 29, 10, 1, -16, -30, -46, -59, -66, -76, -83, -88,
    -82, -82, -81, -77, -76, -66, -62, -55, -52, -52, -59, -66, -81, -95, -99, -107, -102, -112,
    -114, -118, -118, -124, -134, -138, -146, -151, -160, -172, -183, -198, -210, -217, -227, -231,
    -236, -243, -251, -257, -252, -251, -259, -269, -259, -258, -240, -235, -217, -218, -206, -212,
    -206, -204, -203, -203, -211, -211, -204, -194, -182, -164, -158, -149, -157, -162, -183, -192,
    -203, -193, -198, -194, -189, -195, -196, -209, -206, -203, -197, -195, -200, -198, -191, -188,
    -177, -173, -156, -131, -100, -84, -71, -75, -63, -61, -50, -58, -59, -71, -72, -79, -76, -59,
    -45, -28, -23, -15, -18, -26, -34, -42, -47, -39, -36, -34, -46, -55, -66, -79, -78, -93, -85,
    -88, -74, -67, -66, -58, -57, -44, -37, -24, -13, 0, 4, -3, -6, -9, -1, 6, 6, 5, 2, -3, -9,
    -12, -5, -2, 3, 7, 9, 9, 7, 9, 7, 11, 23, 34, 47, 57, 63, 58, 60, 58, 69, 74, 77, 79, 73, 73,
    70, 61, 55, 50, 51, 52, 52, 48, 37, 27, 7, -10, -33, -42, -49, -52, -60, -57, -71, -75, -92,
    -90, -88, -80, -84, -87, -96, -101, -101, -84, -76, -64, -65, -53, -47, -32, -30, -37, -58,
    -70, -85, -94, -95, -92, -90, -91, -96, -100, -112, -123, -142, -153, -160, -164, -173, -176,
    -186, -191, -198, -200, -200, -210, -212, -222, -240, -253, -265, -272, -280, -299, -309, -329,
    -340, -348, -360, -370, -376, -383, -396, -407, -422, -427, -425, -422, -417, -410, -398, -387,
    -386, -383, -380, -371, -372, -370, -397, -409, -427, -424, -424, -418, -405, -391, -372, -365,
    -366, -362, -361, -348, -350, -343, -344, -339, -351, -346, -348, -317, -303, -277, -279, -275,
    -298, -317, -330, -337, -336, -316, -306, -284, -288, -266, -272, -269, -287, -292, -309, -323,
    -336, -355, -365, -379, -382, -376, -363, -340, -326, -302, -290, -261, -248, -215, -206, -194,
    -184, -174, -154, -145, -128, -119, -97, -81, -73, -60, -63, -65, -82, -85, -86, -88, -101,
    -93, -92, -77, -84, -74, -67, -52, -34, -24, -15, -15, -34, -55, -74, -78, -67, -52, -40, -33,
    -29, -32, -24, -28, -26, -38, -46, -59, -84, -101, -109, -99, -83, -66, -53, -43, -44, -41,
    -40, -34, -27, -20, -18, -21, -27, -19, 2, 25, 58, 77, 101, 99, 105, 96, 110, 117, 143, 163,
    188, 199, 216, 233, 245, 268, 276, 290, 279, 269, 246, 237, 232, 241, 234, 240, 229, 239, 230,
    234, 231, 239, 237, 238, 219, 192, 172, 149, 133, 125, 125, 131, 128, 119, 116, 108, 98, 93,
    79, 77, 67, 58, 56, 47, 50, 56, 59, 74, 71, 83, 76, 77, 75, 73, 73, 73, 85, 93, 104, 104, 107,
    114, 123, 130, 129, 114, 112, 100, 106, 102, 103, 101, 105, 98, 101, 90, 99, 98, 99, 88, 85,
    71, 59, 29, 17, -3, -7, -18, -22, -36, -56, -74, -91, -96, -99, -98, -101, -118, -132, -151,
    -152, -147, -131, -123, -107, -108, -97, -85, -74, -60, -49, -33, -18, 5, 25, 34, 40, 46, 57,
    67, 68, 83, 96, 117, 123, 132, 134, 146, 151, 157, 160, 161, 155, 152, 145, 134, 134, 131, 128,
    121, 111, 112, 100, 100, 89, 98, 97, 99, 104, 102, 102, 100, 98, 99, 92, 96, 93, 86, 63, 49,
    33, 26, 14, 10, -2, -5, -10, -5, 2, 16, 29, 51, 63, 80, 87, 98, 106, 113, 113, 117, 118, 124,
    130, 135, 142, 152, 165, 174, 188, 197, 200, 200, 201, 212, 220, 234, 245, 253, 253, 248, 244,
    230, 225, 217, 219, 219, 214, 210, 192, 189, 185, 188, 191, 199, 198, 203, 203, 213, 219, 218,
    217, 207, 208, 203, 206, 214, 213, 225, 230, 244, 250, 249, 249, 237, 231, 223, 210, 209, 201,
    219, 219, 235, 251, 271, 287, 286, 291, 276, 268, 248, 236, 228, 223, 220, 218, 221, 216, 215,
    196, 188, 178, 180, 175, 167, 162, 152, 156, 149, 155, 157, 155, 160, 150, 156, 144, 137, 126,
    107, 91, 70, 58, 48, 31, 26, 19, 18, 11, -2, -10, -34, -46, -79, -94, -115, -115, -113, -100,
    -94, -92, -88, -90, -90, -95, -102, -105, -116, -127, -133, -139, -143, -136, -137, -135, -133,
    -133, -118, -117, -113, -111, -114, -112, -119, -122, -131, -139, -139, -137, -123, -119, -113,
    -115, -108, -107, -112, -117, -127, -131, -146, -152, -149, -134, -124, -109, -101, -92, -100,
    -108, -119, -135, -155, -175, -188, -192, -200, -203, -208, -207, -203, -200, -199, -203, -213,
    -213, -222, -219, -228, -229, -231, -235, -233, -231, -228, -223, -225, -228, -224, -220, -221,
    -214, -214, -209, -214, -209, -203, -191, -178, -155, -132, -116, -102, -97, -98, -110, -122,
    -135, -140, -142, -142, -138, -123, -113, -87, -68, -55, -54, -67, -82, -94, -107, -111, -124,
    -127, -139, -139, -148, -149, -145, -134, -127, -126, -130, -145, -158, -164, -173, -166, -159,
    -143, -136, -128, -132, -131, -133, -125, -120, -114, -105, -104, -104, -103, -90, -71, -39,
    -22, 3, -1, 10, 6, 16, 16, 32, 41, 58, 59, 63, 65, 71, 82, 93, 108, 124, 129, 134, 132, 133,
    142, 149, 161, 156, 145, 132, 119, 109, 103, 107, 116, 123, 123, 124, 114, 106, 89, 81, 65, 61,
    58, 50, 51, 43, 50, 49, 49, 51, 44, 32, 10, -2, -14, -21, -17, -13, -5, 2, 8, 12, 12, -2, -11,
    -13, -20, -22, -21, -20, -13, -18, -12, -14, -15, -20, -23, -33, -60, -74, -104, -110, -124,
    -117, -117, -113, -120, -121, -122, -127, -127, -129, -133, -146, -165, -178, -197, -204, -219,
    -209, -212, -212, -213, -215, -212, -223, -224, -241, -246, -267, -267, -287, -282, -295, -278,
    -278, -268, -280, -286, -304, -306, -314, -314, -313, -312, -314, -310, -300, -298, -283, -284,
    -265, -261, -257, -258, -258, -268, -270, -270, -264, -261, -260, -265, -264, -268, -277, -286,
    -288, -293, -282, -289, -283, -282, -286, -287, -289, -281, -289, -295, -309, -324, -337, -344,
    -346, -344, -340, -332, -321, -307, -286, -273, -257, -249, -236, -235, -244, -245, -255, -252,
    -250, -240, -235, -225, -226, -224, -225, -229, -226, -231, -226, -227, -226, -217, -211, -207,
    -207, -201, -193, -190, -187, -190, -189, -192, -192, -198, -195, -191, -172, -158, -125, -110,
    -84, -74, -55, -45, -37, -25, -25, -30, -45, -49, -59, -63, -70, -69, -62, -47, -39, -24, -18,
    -5, 2, 2, 7, 7, 5, 5, 7, 15, 34, 57, 76, 104, 122, 143, 146, 137, 131, 117, 115, 120, 124, 134,
    138, 154, 169, 190, 186, 184, 168, 154, 140, 125, 117, 111, 108, 110, 102, 104, 111, 121, 125,
    128, 125, 126, 125, 122, 110, 116, 116, 138, 151, 173, 192, 214, 221, 233, 226, 222, 201, 184,
    158, 143, 127, 114, 103, 97, 104, 104, 103, 83, 73, 43, 28, -2, -14, -33, -37, -45, -48, -51,
    -53, -52, -58, -70, -77, -81, -82, -92, -89, -97, -88, -87, -84, -77, -70, -64, -68, -77, -84,
    -91, -91, -104, -108, -120, -117, -114, -108, -104, -96, -88, -87, -79, -71, -68, -68, -71,
    -71, -64, -58, -46, -33, -17, -7, 2, -10, -17, -38, -50, -57, -77, -89, -108, -117, -138, -143,
    -156, -147, -170, -179, -197, -208, -214, -221, -229, -241, -243, -242, -239, -228, -229, -222,
    -229, -232, -230, -234, -223, -219, -213, -208, -205, -192, -191, -170, -149, -131, -115, -102,
    -97, -86, -85, -79, -76, -69, -58, -46, -45, -37, -44, -39, -42, -36, -32, -28, -30, -32, -35,
    -46, -45, -46, -34, -31, -26, -26, -25, -33, -30, -35, -43, -50, -62, -72, -81, -86, -87, -90,
    -92, -92, -91, -89, -88, -85, -83, -75, -66, -56, -39, -27, -11, 0, 13, 19, 28, 30, 44, 59, 74,
    84, 94, 110, 126, 140, 160, 181, 204, 228, 242, 258, 262, 274, 278, 280, 278, 276, 278, 280,
    286, 294, 298, 305, 315, 326, 325, 329, 329, 334, 337, 335, 335, 330, 332, 323, 324, 321, 322,
    318, 317, 310, 311, 309, 305, 311, 308, 322, 324, 328, 323, 325, 320, 329, 324, 338, 340, 345,
    348, 348, 345, 347, 337, 343, 337, 344, 347, 350, 352, 340, 332, 325, 310, 306, 285, 279, 271,
    266, 265, 264, 273, 282, 281, 280, 280, 268, 257, 244, 231, 225, 217, 222, 214, 217, 214, 215,
    215, 206, 199, 188, 180, 174, 165, 163, 161, 162, 158, 145, 142, 130, 134, 131, 125, 121, 115,
    121, 119, 120, 128, 129, 133, 128, 120, 115, 102, 98, 82, 72, 59, 59, 55, 56, 63, 60, 64, 58,
    61, 56, 54, 50, 48, 40, 37, 35, 26, 28, 15, 27, 15, 21, 10, 15, 7, 9, 10, 12, 13, 13, 17, 31,
    39, 51, 55, 72, 66, 79, 72, 81, 79, 83, 85, 93, 97, 111, 123, 137, 147, 158, 167, 173, 172,
    175, 174, 180, 179, 182, 174, 173, 164, 173, 173, 183, 183, 176, 177, 165, 156, 158, 150, 153,
    143, 139, 134, 133, 133, 140, 146, 142, 145, 132, 126, 121, 123, 139, 149, 164, 169, 179, 181,
    186, 191, 202, 218, 225, 234, 234, 236, 244, 248, 255, 269, 277, 290, 289, 289, 292, 284, 303,
    305, 317, 327, 333, 350, 353, 365, 366, 381, 391, 410, 411, 415, 405, 394, 378, 367, 364, 361,
    356, 348, 340, 340, 336, 329, 328, 318, 310, 299, 294, 286, 276, 273, 267, 253, 256, 248, 250,
    244, 244, 235, 229, 229, 226, 219, 211, 207, 202, 193, 205, 203, 219, 224, 231, 230, 225, 227,
    224, 231, 224, 225, 212, 201, 193, 183, 183, 179, 175, 175, 162, 157, 133, 127, 99, 89, 79, 73,
    64, 59, 55, 57, 52, 49, 40, 22, 8, -15, -22, -42, -42, -54, -57, -62, -69, -69, -78, -86, -99,
    -103, -107, -116, -124, -137, -145, -149, -159, -161, -174, -174, -175, -166, -163, -148, -147,
    -143, -143, -151, -147, -153, -161, -162, -161, -154, -150, -140, -130, -120, -117, -119, -122,
    -136, -142, -150, -157, -169, -181, -186, -190, -187, -188, -183, -182, -186, -182, -189, -188,
    -203, -213, -220, -226, -227, -229, -225, -232, -229, -232, -225, -223, -219, -216, -213, -215,
    -213, -207, -207, -205, -202, -190, -180, -174, -164, -168, -167, -176, -182, -188, -198, -200,
    -200, -202, -189, -188, -172, -161, -153, -149, -150, -154, -155, -160, -157, -161, -163, -171,
    -174, -180, -185, -179, -179, -158, -152, -139, -144, -137, -134, -123, -107, -95, -80, -76,
    -73, -72, -72, -62, -62, -55, -52, -46, -50, -41, -46, -30, -28, -8, -2, 15, 19, 35, 39, 53,
    63, 77, 83, 89, 88, 85, 87, 85, 87, 91, 93, 91, 89, 91, 92, 89, 84, 86, 97, 99, 108, 105, 109,
    123, 131, 134, 126, 109, 100, 85, 82, 79, 88, 101, 110, 117, 115, 118, 117, 121, 120, 129, 132,
    137, 141, 142, 145, 147, 148, 154, 150, 156, 157, 165, 155, 158, 149, 152, 143, 143, 143, 149,
    148, 148, 146, 121, 115, 87, 81, 59, 43, 28, 15, 10, 7, 12, 22, 18, 19, 8, 12, 7, 5, -3, -8,
    -25, -34, -40, -39, -39, -42, -41, -41, -40, -37, -45, -45, -57, -62, -76, -72, -70, -51, -43,
    -30, -35, -34, -47, -52, -68, -79, -85, -94, -91, -100, -99, -98, -90, -89, -81, -80, -89, -98,
    -116, -126, -146, -157, -168, -173, -182, -182, -183, -188, -193, -204, -204, -221, -223, -236,
    -244, -254, -261, -270, -270, -265, -257, -251, -245, -230, -225, -217, -211, -197, -197, -190,
    -198, -188, -186, -177, -176, -170, -164, -156, -151, -144, -146, -147, -150, -146, -143, -134,
    -118, -103, -95, -90, -86, -88, -98, -106, -117, -117, -117, -113, -112, -114, -121, -126,
    -134, -134, -142, -144, -146, -142, -140, -131, -141, -126, -135, -122, -124, -111, -100, -84,
    -75, -59, -60, -46, -41, -44, -38, -36, -26, -10, -8, 2, 1, 3, 4, 8, 17, 24, 27, 33, 38, 44,
    47, 72, 90, 113, 117, 128, 128, 136, 140, 144, 143, 148, 145, 146, 155, 169, 179, 196, 200,
    209, 211, 217, 232, 229, 230, 224, 210, 206, 189, 186, 182, 180, 175, 169, 164, 159, 153, 147,
    156, 154, 174, 182, 201, 214, 223, 236, 238, 239, 247, 243, 252, 249, 254, 250, 243, 236, 227,
    221, 222, 220, 232, 231, 245, 244, 241, 241, 228, 221, 216, 211, 202, 194, 186, 169, 158, 150,
    138, 134, 115, 109, 105, 96, 97, 92, 95, 88, 88, 82, 80, 77, 80, 84, 82, 75, 67, 59, 47, 39,
    24, 23, 3, 2, -21, -26, -39, -52, -50, -51, -44, -43, -45, -47, -52, -61, -68, -75, -86, -93,
    -96, -98, -90, -88, -81, -77, -85, -93, -113, -111, -124, -121, -115, -110, -105, -104, -105,
    -108, -118, -126, -139, -133, -137, -134, -137, -153, -165, -191, -201, -213, -212, -205, -200,
    -182, -174, -167, -169, -186, -204, -222, -233, -218, -206, -170, -147, -128, -121, -135, -144,
    -165, -184, -191, -194, -192, -194, -198, -203, -218, -219, -234, -235, -235, -216, -166, -99,
    -41, -71, -168, -291, -396, -455, -440, -375, -313, -264, -242, -242, -264, -285, -297, -315,
    -305, -297, -288, -279, -260, -230, -239, -247, -277, -308, -328, -342, -330, -327, -318, -320,
    -319, -312, -313, -294, -270, -251, -234, -216, -203, -198, -199, -207, -229, -242, -252, -254,
    -245, -238, -215, -203, -189, -186, -186, -195, -189, -190, -178, -170, -163, -150, -130, -122,
    -114, -116, -102, -98, -86, -76, -73, -67, -80, -83, -93, -80, -70, -61, -55, -48, -38, -31,
    -13, -11, -16, -26, -39, -48, -53, -39, -25, -2, 12, 23, 28, 29, 27, 24, 27, 33, 40, 45, 49,
    45, 47, 49, 58, 50, 48, 50, 45, 38, 26, 14, -6, -17, -29, -24, -34, -23, -35, -32, -41, -45,
    -56, -66, -79, -95, -110, -114, -111, -110, -107, -110, -127, -141, -159, -159, -163, -150,
    -143, -145, -156, -163, -155, -144, -129, -122, -113, -107, -103, -93, -100, -98, -97, -104,
    -107, -112, -99, -104, -111, -124, -137, -132, -129, -116, -118, -107, -112, -119, -123, -126,
    -129, -132, -129, -137, -136, -145, -148, -162, -164, -171, -192, -220, -224, -220, -211, -197,
    -187, -183, -176, -180, -174, -168, -157, -161, -174, -190, -212, -227, -223, -222, -211, -208,
    -207, -206, -198, -172, -157, -149, -138, -152, -147, -153, -132, -120, -97, -81, -77, -86,
    -104, -104, -103, -78, -66, -60, -75, -75, -82, -70, -57, -39, -26, -13, -11, -9, -21, -29,
    -51, -60, -59, -64, -67, -103, -127, -144, -122, -101, -78, -41, -37, -26, -23, -6, 13, 21, 44,
    45, 53, 69, 84, 95, 111, 109, 122, 126, 126, 122, 115, 136, 137, 159, 196, 213, 225, 235, 268,
    282, 321, 347, 362, 356, 358, 336, 316, 312, 330, 340, 348, 359, 338, 316, 319, 336, 352, 372,
    378, 356, 348, 376, 419, 469, 510, 516, 489, 475, 457, 421, 386, 369, 348, 338, 339, 320, 300,
    294, 317, 361, 423, 483, 495, 487, 507, 525, 542, 550, 553, 533, 539, 529, 510, 485, 484, 476,
    477, 479, 471, 443, 414, 418, 421, 425, 430, 434, 437, 451, 459, 466, 460, 442, 405, 357, 337,
    350, 366, 358, 341, 317, 318, 309, 299, 279, 260, 258, 243, 232, 195, 170, 148, 167, 187, 210,
    211, 205, 210, 222, 222, 206, 193, 185, 156, 159, 193, 227, 244, 248, 228, 215, 215, 250, 230,
    224, 218, 208, 193, 196, 194, 169, 191, 250, 300, 309, 314, 295, 289, 302, 316, 290, 286, 292,
    280, 249, 245, 217, 211, 200, 200, 168, 139, 126, 136, 158, 198, 217, 218, 212, 213, 232, 262,
    279, 253, 221, 176, 129, 90, 51, 18, -8, -13, -1, 4, 17, 19, 16, 30, 66, 92, 95, 100, 94, 110,
    144, 205, 226, 149, 23, -71, -51, 53, 126, 114, 25, -62, -82, -41, 60, 120, 126, 69, 34, 42,
    78, 96, 94, 69, 30, -29, -81, -104, -89, -45, -2, 11, -5, -55, -117, -132, -88, -43, -31, -47,
    -47, -77, -82, -61, -42, -55, -82, -123, -170, -187, -169, -141, -76, 29, 109, 134, 143, 124,
    89, 46, 15, 17, 48, 104, 119, 100, 76, 59, 53, 89, 123, 113, 112, 221, 449, 738, 896, 821, 595,
    386, 256, 230, 317, 434, 459, 397, 307, 205, 115, 76, 97, 147, 208, 226, 194, 158, 157, 139,
    101, 76, 83, 80, 60, 16, -45, -118, -188, -246, -272, -258, -230, -220, -219, -205, -219, -230,
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    218, 236, 125,
];