orchard/src/constants/fixed_bases/spend_auth_g.rs

use group::ff::PrimeField;
use pasta_curves::{arithmetic::CurveAffine, pallas};

/// Generator used as $\mathcal{G}^{\mathsf{Orchard}}$ in Spend authorization signatures.
pub const GENERATOR: ([u8; 32], [u8; 32]) = (
    [
        99, 201, 117, 184, 132, 114, 26, 141, 12, 161, 112, 123, 227, 12, 127, 12, 95, 68, 95, 62,
        124, 24, 141, 59, 6, 214, 241, 40, 179, 35, 85, 55,
    ],
    [
        201, 59, 12, 123, 129, 62, 227, 76, 216, 189, 5, 192, 254, 20, 201, 223, 251, 36, 214, 254,
        252, 188, 16, 123, 219, 102, 26, 223, 127, 53, 208, 26,
    ],
);

/// Full-width z-values for GENERATOR.
/// These can be reproduced by [`halo2_gadgets::ecc::chip::constants::find_zs_and_us`].
pub const Z: [u64; super::NUM_WINDOWS] = [
    49707, 15701, 45931, 163127, 41654, 212130, 34473, 25205, 4118, 10240, 12264, 22866, 203610,
    18808, 13851, 62448, 62380, 94497, 39496, 73216, 32037, 32774, 61690, 39173, 74580, 84678,
    23418, 103090, 34763, 19801, 54976, 196082, 131117, 20556, 58936, 139049, 49530, 488, 2129,
    44219, 64328, 38875, 58430, 34536, 84014, 15455, 38059, 15915, 26893, 100337, 120701, 98937,
    37075, 35293, 8351, 8361, 273432, 717, 3253, 40140, 28024, 95195, 41937, 200127, 95471, 103562,
    75737, 4182, 362357, 15219, 136680, 168274, 25085, 5925, 254392, 93041, 56204, 46757, 109788,
    100797, 80349, 87315, 77372, 96572, 18965,
];

/// Full-width u-values for GENERATOR.
/// These can be reproduced by [`halo2_gadgets::ecc::chip::constants::find_zs_and_us`].
pub const U: [[[u8; 32]; super::H]; super::NUM_WINDOWS] = [
    [
        [
            134, 139, 159, 167, 179, 203, 183, 86, 54, 69, 108, 127, 183, 40, 226, 188, 34, 72,
            235, 174, 120, 30, 214, 202, 46, 166, 177, 78, 133, 80, 221, 35,
        ],
        [
            128, 147, 194, 62, 34, 230, 94, 209, 44, 242, 88, 94, 91, 252, 184, 217, 72, 173, 32,
            128, 118, 158, 176, 67, 255, 192, 227, 150, 189, 56, 205, 10,
        ],
        [
            89, 235, 150, 72, 148, 202, 175, 172, 88, 248, 184, 63, 149, 194, 33, 149, 187, 218,
            51, 194, 131, 184, 34, 138, 62, 112, 115, 0, 197, 109, 145, 37,
        ],
        [
            55, 241, 4, 146, 234, 109, 232, 212, 90, 95, 84, 170, 84, 254, 20, 89, 80, 100, 143, 3,
            30, 229, 117, 35, 32, 249, 43, 36, 200, 74, 200, 13,
        ],
        [
            194, 23, 77, 68, 227, 113, 225, 181, 201, 67, 219, 25, 234, 73, 160, 104, 12, 6, 180,
            204, 185, 16, 224, 62, 83, 132, 193, 185, 69, 90, 67, 29,
        ],
        [
            156, 240, 85, 68, 24, 96, 228, 37, 250, 218, 25, 99, 51, 50, 37, 27, 23, 76, 42, 243,
            126, 23, 236, 249, 179, 94, 59, 83, 197, 193, 215, 32,
        ],
        [
            73, 145, 163, 254, 185, 142, 57, 198, 25, 48, 144, 127, 17, 171, 210, 170, 164, 88, 3,
            235, 37, 45, 124, 125, 44, 113, 141, 119, 93, 91, 163, 47,
        ],
        [
            144, 156, 74, 131, 227, 73, 40, 222, 73, 67, 210, 157, 154, 161, 96, 112, 61, 251, 210,
            2, 2, 199, 107, 190, 39, 133, 107, 181, 235, 217, 1, 32,
        ],
    ],
    [
        [
            204, 30, 193, 82, 109, 194, 174, 212, 203, 182, 251, 224, 85, 31, 240, 246, 163, 165,
            69, 160, 26, 78, 143, 50, 115, 92, 109, 71, 48, 205, 160, 15,
        ],
        [
            20, 52, 64, 133, 30, 26, 4, 37, 88, 2, 107, 192, 179, 203, 130, 109, 203, 163, 224, 31,
            238, 207, 238, 0, 79, 55, 35, 8, 69, 238, 155, 60,
        ],
        [
            129, 188, 56, 216, 72, 61, 212, 36, 171, 128, 228, 90, 229, 75, 126, 41, 186, 124, 100,
            62, 161, 224, 105, 69, 196, 160, 131, 35, 39, 217, 149, 40,
        ],
        [
            168, 4, 93, 175, 37, 163, 30, 50, 27, 141, 194, 23, 206, 18, 65, 85, 150, 36, 51, 169,
            206, 47, 128, 65, 151, 181, 117, 50, 74, 251, 37, 14,
        ],
        [
            143, 167, 209, 67, 187, 208, 101, 235, 49, 77, 89, 225, 7, 243, 50, 56, 150, 233, 186,
            94, 0, 161, 136, 54, 163, 101, 23, 180, 199, 82, 163, 32,
        ],
        [
            83, 85, 245, 163, 247, 47, 226, 3, 90, 35, 254, 250, 71, 176, 18, 214, 121, 5, 11, 162,
            55, 2, 116, 46, 36, 20, 81, 19, 209, 79, 84, 53,
        ],
        [
            181, 129, 189, 44, 171, 86, 12, 145, 21, 185, 255, 145, 238, 46, 220, 242, 242, 239, 5,
            39, 176, 87, 6, 205, 209, 13, 190, 26, 72, 252, 247, 47,
        ],
        [
            169, 151, 215, 50, 18, 225, 124, 186, 49, 5, 84, 177, 139, 69, 189, 88, 237, 39, 196,
            111, 251, 146, 226, 12, 207, 215, 254, 0, 246, 155, 86, 31,
        ],
    ],
    [
        [
            178, 207, 217, 160, 25, 246, 180, 59, 161, 29, 253, 55, 84, 14, 217, 170, 120, 167,
            203, 21, 147, 2, 190, 236, 198, 41, 99, 194, 47, 97, 213, 20,
        ],
        [
            45, 217, 42, 12, 249, 206, 77, 249, 191, 69, 78, 30, 201, 54, 60, 175, 218, 187, 222,
            73, 28, 240, 105, 118, 228, 192, 184, 161, 65, 230, 115, 35,
        ],
        [
            145, 233, 255, 221, 141, 221, 216, 67, 77, 53, 229, 49, 167, 130, 235, 235, 55, 39, 88,
            70, 146, 70, 243, 31, 156, 138, 246, 251, 13, 41, 2, 16,
        ],
        [
            44, 14, 167, 217, 244, 57, 222, 12, 243, 116, 172, 17, 218, 246, 161, 124, 209, 248,
            240, 97, 59, 176, 138, 242, 76, 23, 207, 179, 136, 243, 79, 12,
        ],
        [
            120, 239, 19, 236, 60, 149, 184, 181, 237, 83, 242, 22, 122, 53, 211, 43, 195, 217,
            208, 185, 53, 156, 105, 158, 161, 156, 47, 90, 67, 139, 159, 60,
        ],
        [
            249, 224, 188, 87, 191, 134, 192, 15, 207, 29, 167, 27, 149, 161, 44, 61, 81, 55, 15,
            30, 78, 203, 150, 136, 55, 222, 237, 245, 39, 227, 177, 29,
        ],
        [
            91, 228, 118, 231, 230, 113, 246, 243, 112, 73, 19, 146, 105, 173, 81, 28, 27, 59, 168,
            92, 82, 198, 192, 111, 208, 156, 210, 129, 148, 194, 13, 14,
        ],
        [
            224, 185, 193, 29, 240, 177, 244, 134, 56, 252, 24, 119, 213, 110, 191, 221, 105, 122,
            89, 30, 114, 196, 53, 33, 168, 48, 77, 85, 241, 128, 168, 51,
        ],
    ],
    [
        [
            79, 58, 209, 170, 171, 147, 19, 156, 23, 243, 181, 231, 92, 215, 234, 118, 17, 151,
            212, 115, 164, 220, 114, 178, 18, 147, 101, 201, 228, 162, 126, 54,
        ],
        [
            235, 245, 230, 232, 32, 231, 43, 206, 119, 97, 30, 131, 10, 3, 195, 93, 78, 158, 42,
            62, 53, 26, 42, 26, 123, 39, 164, 39, 149, 119, 79, 39,
        ],
        [
            78, 161, 190, 242, 222, 143, 16, 193, 35, 198, 206, 67, 37, 101, 231, 6, 62, 205, 36,
            2, 146, 11, 191, 111, 78, 107, 222, 19, 32, 194, 31, 28,
        ],
        [
            189, 36, 36, 147, 50, 162, 17, 179, 250, 219, 167, 100, 114, 56, 90, 184, 42, 49, 101,
            155, 213, 179, 140, 62, 245, 55, 81, 218, 11, 116, 203, 32,
        ],
        [
            170, 122, 46, 42, 82, 84, 63, 207, 174, 176, 7, 139, 74, 49, 198, 238, 243, 217, 155,
            175, 31, 22, 42, 49, 125, 6, 210, 80, 124, 138, 184, 42,
        ],
        [
            30, 149, 102, 115, 26, 193, 146, 161, 139, 248, 18, 9, 55, 231, 50, 78, 236, 158, 74,
            204, 173, 228, 73, 125, 75, 127, 42, 21, 202, 128, 69, 46,
        ],
        [
            33, 237, 143, 1, 212, 254, 16, 231, 202, 39, 42, 28, 134, 77, 246, 51, 31, 146, 160,
            11, 178, 194, 169, 251, 50, 131, 241, 132, 81, 122, 244, 58,
        ],
        [
            197, 18, 235, 234, 189, 238, 252, 93, 244, 246, 76, 251, 21, 250, 8, 118, 38, 40, 39,
            103, 96, 147, 112, 103, 188, 219, 33, 183, 6, 139, 186, 47,
        ],
    ],
    [
        [
            27, 179, 1, 219, 5, 237, 22, 195, 49, 31, 125, 207, 224, 185, 249, 141, 188, 16, 209,
            225, 213, 167, 101, 63, 245, 229, 177, 242, 28, 121, 227, 4,
        ],
        [
            209, 90, 156, 216, 151, 223, 46, 129, 150, 195, 74, 57, 16, 102, 32, 110, 156, 108, 48,
            128, 236, 231, 35, 169, 60, 210, 63, 240, 252, 175, 28, 22,
        ],
        [
            133, 6, 154, 178, 236, 58, 163, 25, 85, 197, 169, 75, 26, 103, 112, 168, 225, 245, 103,
            211, 223, 163, 79, 47, 253, 17, 114, 233, 127, 217, 94, 51,
        ],
        [
            252, 137, 21, 60, 226, 116, 238, 97, 66, 128, 128, 213, 51, 35, 35, 130, 77, 160, 200,
            226, 91, 25, 22, 133, 27, 188, 198, 159, 155, 4, 106, 4,
        ],
        [
            76, 129, 23, 15, 64, 93, 179, 128, 41, 202, 40, 164, 7, 199, 172, 203, 98, 179, 243,
            28, 66, 149, 80, 177, 112, 51, 81, 231, 178, 208, 16, 54,
        ],
        [
            100, 99, 114, 178, 31, 130, 16, 122, 18, 47, 103, 243, 55, 84, 112, 92, 156, 246, 119,
            91, 4, 173, 157, 48, 246, 132, 129, 162, 33, 42, 164, 38,
        ],
        [
            152, 167, 13, 134, 122, 121, 84, 244, 205, 49, 40, 241, 68, 223, 97, 107, 112, 216,
            124, 98, 232, 219, 187, 158, 28, 95, 222, 129, 219, 240, 233, 13,
        ],
        [
            255, 191, 150, 9, 220, 109, 94, 217, 202, 19, 194, 216, 152, 81, 167, 107, 204, 138,
            104, 200, 200, 253, 210, 14, 87, 133, 149, 93, 119, 137, 129, 45,
        ],
    ],
    [
        [
            162, 107, 4, 19, 49, 176, 93, 99, 15, 133, 159, 53, 191, 0, 79, 228, 236, 96, 145, 53,
            120, 10, 150, 94, 198, 49, 253, 119, 229, 116, 150, 13,
        ],
        [
            205, 164, 35, 49, 168, 151, 217, 138, 164, 143, 237, 170, 140, 153, 15, 171, 74, 89,
            60, 195, 13, 20, 170, 36, 66, 199, 45, 252, 18, 47, 204, 8,
        ],
        [
            95, 149, 177, 178, 217, 143, 235, 251, 203, 227, 33, 62, 147, 134, 228, 83, 84, 170,
            118, 91, 103, 94, 41, 99, 1, 95, 59, 67, 253, 146, 165, 5,
        ],
        [
            19, 184, 182, 93, 1, 4, 202, 21, 119, 77, 151, 12, 98, 255, 223, 34, 54, 162, 44, 199,
            13, 217, 159, 37, 147, 185, 89, 21, 251, 128, 21, 25,
        ],
        [
            190, 179, 248, 211, 188, 233, 181, 149, 178, 232, 28, 253, 234, 103, 160, 153, 252,
            188, 19, 132, 143, 227, 31, 109, 134, 85, 21, 104, 133, 39, 148, 13,
        ],
        [
            149, 40, 255, 15, 159, 19, 43, 100, 31, 196, 107, 209, 83, 25, 77, 122, 211, 27, 237,
            158, 74, 188, 198, 73, 86, 171, 73, 163, 110, 176, 37, 55,
        ],
        [
            25, 194, 88, 151, 108, 22, 157, 145, 11, 87, 6, 215, 227, 141, 203, 218, 34, 25, 236,
            49, 69, 170, 243, 13, 240, 210, 161, 186, 45, 32, 239, 12,
        ],
        [
            100, 133, 83, 207, 52, 184, 61, 180, 226, 133, 42, 161, 249, 216, 158, 39, 5, 185, 52,
            8, 212, 185, 49, 234, 32, 200, 23, 158, 19, 111, 74, 50,
        ],
    ],
    [
        [
            215, 206, 249, 236, 176, 248, 217, 12, 0, 204, 155, 112, 248, 215, 200, 248, 8, 250,
            61, 104, 22, 109, 196, 54, 27, 3, 0, 203, 187, 116, 69, 45,
        ],
        [
            82, 29, 122, 199, 191, 205, 105, 136, 96, 93, 249, 65, 104, 197, 48, 64, 166, 175, 144,
            96, 114, 186, 147, 65, 1, 35, 87, 134, 90, 145, 230, 24,
        ],
        [
            154, 172, 87, 147, 10, 166, 129, 223, 224, 162, 95, 194, 248, 41, 234, 174, 177, 221,
            64, 244, 202, 201, 225, 138, 179, 110, 80, 104, 84, 39, 26, 43,
        ],
        [
            75, 226, 94, 205, 107, 248, 174, 164, 95, 115, 20, 62, 241, 202, 80, 182, 248, 213,
            115, 216, 142, 165, 182, 8, 151, 156, 170, 110, 219, 237, 63, 3,
        ],
        [
            49, 234, 64, 230, 146, 237, 191, 49, 112, 45, 60, 43, 252, 216, 195, 70, 153, 146, 225,
            144, 9, 226, 23, 158, 136, 113, 247, 108, 62, 144, 108, 9,
        ],
        [
            103, 21, 127, 107, 59, 109, 133, 160, 143, 88, 92, 94, 63, 60, 176, 30, 201, 130, 24,
            59, 22, 197, 68, 223, 207, 57, 45, 122, 91, 202, 196, 35,
        ],
        [
            52, 102, 244, 254, 244, 16, 81, 190, 173, 244, 154, 38, 64, 214, 63, 97, 169, 9, 167,
            51, 246, 33, 109, 247, 50, 220, 114, 64, 13, 179, 177, 30,
        ],
        [
            144, 221, 225, 200, 23, 166, 32, 166, 176, 75, 198, 254, 19, 193, 245, 128, 7, 12, 208,
            85, 254, 120, 147, 143, 63, 184, 236, 60, 26, 253, 251, 35,
        ],
    ],
    [
        [
            75, 83, 105, 13, 6, 123, 42, 108, 212, 123, 233, 193, 139, 45, 132, 88, 44, 242, 39,
            25, 1, 235, 41, 93, 161, 218, 156, 90, 105, 43, 114, 46,
        ],
        [
            113, 216, 156, 147, 163, 145, 14, 155, 250, 78, 89, 11, 16, 228, 91, 223, 129, 87, 8,
            161, 204, 28, 0, 75, 59, 172, 225, 121, 76, 165, 42, 36,
        ],
        [
            195, 34, 156, 131, 184, 36, 15, 228, 23, 198, 79, 88, 138, 166, 168, 21, 16, 35, 82,
            123, 87, 247, 59, 42, 195, 113, 128, 240, 223, 247, 79, 25,
        ],
        [
            197, 57, 189, 78, 132, 12, 150, 148, 108, 113, 199, 232, 67, 154, 65, 201, 151, 136,
            175, 146, 0, 126, 215, 68, 183, 100, 207, 132, 39, 238, 74, 28,
        ],
        [
            213, 35, 155, 170, 77, 61, 206, 127, 232, 164, 11, 133, 55, 141, 203, 73, 112, 37, 27,
            8, 250, 18, 169, 233, 171, 174, 218, 9, 15, 227, 192, 24,
        ],
        [
            134, 99, 90, 204, 109, 34, 78, 239, 97, 108, 119, 18, 165, 166, 98, 20, 155, 15, 193,
            71, 34, 134, 45, 232, 229, 4, 167, 6, 75, 99, 2, 54,
        ],
        [
            4, 136, 7, 177, 132, 128, 188, 128, 221, 121, 213, 198, 133, 42, 219, 156, 145, 179,
            35, 254, 88, 233, 96, 90, 206, 150, 181, 191, 254, 218, 217, 31,
        ],
        [
            183, 202, 252, 66, 36, 234, 250, 116, 96, 15, 72, 88, 124, 136, 8, 156, 204, 151, 89,
            171, 185, 139, 47, 215, 117, 207, 44, 117, 226, 84, 248, 5,
        ],
    ],
    [
        [
            48, 78, 243, 80, 211, 5, 172, 75, 113, 98, 154, 247, 185, 52, 36, 155, 5, 244, 149, 7,
            84, 162, 39, 0, 233, 219, 188, 229, 84, 18, 154, 34,
        ],
        [
            135, 176, 3, 156, 231, 35, 196, 24, 109, 104, 169, 210, 121, 247, 72, 214, 141, 15,
            155, 221, 249, 30, 196, 117, 108, 229, 219, 116, 233, 89, 208, 61,
        ],
        [
            108, 238, 126, 36, 119, 110, 54, 206, 165, 24, 218, 88, 206, 201, 226, 190, 28, 76,
            125, 62, 87, 21, 15, 158, 2, 233, 41, 18, 242, 223, 192, 6,
        ],
        [
            169, 95, 111, 93, 78, 167, 161, 2, 54, 29, 206, 209, 119, 196, 7, 36, 248, 233, 68, 45,
            243, 58, 155, 147, 32, 175, 221, 168, 144, 79, 126, 18,
        ],
        [
            229, 0, 65, 205, 148, 179, 229, 116, 253, 143, 119, 111, 142, 63, 235, 124, 140, 243,
            182, 164, 15, 57, 219, 23, 114, 237, 116, 213, 200, 235, 227, 55,
        ],
        [
            9, 233, 193, 136, 60, 112, 74, 107, 87, 12, 113, 20, 8, 8, 94, 195, 227, 83, 178, 77,
            143, 104, 211, 169, 253, 62, 8, 196, 81, 39, 96, 13,
        ],
        [
            223, 12, 147, 224, 113, 27, 48, 142, 243, 199, 244, 62, 255, 20, 63, 79, 12, 37, 159,
            81, 80, 172, 136, 23, 107, 186, 180, 33, 148, 49, 128, 10,
        ],
        [
            100, 248, 42, 239, 155, 107, 80, 255, 126, 96, 195, 152, 204, 166, 14, 46, 114, 152,
            200, 111, 94, 233, 117, 247, 89, 83, 34, 2, 189, 3, 245, 4,
        ],
    ],
    [
        [
            26, 254, 208, 112, 167, 15, 77, 90, 124, 14, 227, 31, 204, 94, 253, 228, 223, 252, 114,
            141, 234, 26, 108, 144, 115, 131, 19, 142, 25, 148, 80, 53,
        ],
        [
            95, 154, 56, 85, 66, 246, 97, 207, 254, 117, 98, 51, 204, 68, 9, 1, 157, 25, 113, 175,
            12, 172, 33, 67, 212, 17, 238, 76, 166, 43, 6, 30,
        ],
        [
            48, 204, 33, 34, 141, 223, 27, 151, 244, 225, 206, 129, 54, 211, 251, 18, 168, 186,
            214, 141, 37, 229, 219, 62, 187, 87, 66, 140, 181, 233, 161, 35,
        ],
        [
            143, 158, 2, 174, 102, 73, 205, 247, 110, 78, 131, 38, 192, 195, 70, 193, 14, 166, 232,
            42, 142, 222, 35, 147, 189, 77, 50, 220, 23, 56, 126, 38,
        ],
        [
            10, 84, 87, 89, 169, 77, 97, 156, 0, 100, 41, 191, 232, 88, 138, 82, 220, 123, 231, 59,
            142, 115, 196, 116, 217, 80, 178, 117, 237, 250, 11, 32,
        ],
        [
            152, 88, 228, 103, 64, 4, 197, 110, 204, 4, 0, 131, 250, 205, 206, 83, 180, 179, 98,
            51, 213, 11, 237, 149, 150, 226, 123, 62, 129, 198, 28, 58,
        ],
        [
            188, 254, 66, 154, 178, 61, 236, 232, 27, 107, 131, 38, 104, 160, 49, 57, 3, 111, 18,
            106, 158, 91, 57, 220, 174, 59, 138, 227, 176, 49, 171, 15,
        ],
        [
            92, 116, 148, 172, 212, 215, 137, 153, 48, 241, 40, 25, 45, 204, 141, 58, 235, 146,
            155, 248, 50, 112, 4, 206, 228, 70, 94, 117, 128, 150, 213, 18,
        ],
    ],
    [
        [
            155, 96, 199, 129, 161, 131, 9, 109, 43, 95, 79, 108, 230, 168, 172, 51, 244, 183, 203,
            211, 198, 95, 64, 184, 12, 184, 190, 250, 108, 77, 202, 61,
        ],
        [
            151, 114, 132, 115, 19, 130, 213, 126, 140, 64, 58, 149, 171, 26, 245, 47, 253, 9, 212,
            80, 154, 3, 206, 254, 158, 241, 87, 90, 67, 8, 29, 59,
        ],
        [
            231, 100, 245, 101, 53, 146, 235, 219, 228, 106, 101, 51, 85, 110, 51, 78, 221, 149,
            223, 78, 184, 47, 144, 234, 161, 28, 6, 48, 41, 228, 253, 57,
        ],
        [
            239, 82, 160, 74, 136, 231, 198, 194, 99, 192, 170, 182, 36, 125, 149, 58, 9, 239, 91,
            146, 54, 104, 94, 42, 147, 4, 61, 79, 185, 11, 51, 1,
        ],
        [
            56, 89, 137, 88, 196, 32, 115, 15, 6, 53, 123, 43, 42, 27, 226, 220, 196, 131, 211,
            126, 14, 174, 191, 229, 172, 6, 210, 189, 92, 66, 79, 26,
        ],
        [
            236, 153, 243, 131, 143, 123, 164, 95, 214, 160, 21, 150, 12, 71, 118, 170, 92, 166,
            223, 162, 133, 58, 93, 2, 31, 57, 197, 190, 66, 169, 112, 18,
        ],
        [
            137, 13, 132, 54, 102, 120, 119, 177, 34, 217, 123, 89, 76, 242, 218, 72, 236, 129, 33,
            42, 148, 242, 221, 33, 252, 74, 219, 142, 25, 82, 162, 62,
        ],
        [
            0, 132, 243, 70, 85, 72, 216, 242, 225, 170, 56, 212, 52, 143, 154, 202, 248, 33, 148,
            236, 117, 24, 29, 63, 148, 233, 28, 74, 59, 44, 221, 6,
        ],
    ],
    [
        [
            122, 45, 241, 68, 72, 20, 58, 84, 181, 215, 45, 12, 74, 54, 17, 144, 144, 97, 82, 103,
            81, 123, 158, 238, 167, 173, 212, 8, 90, 63, 188, 59,
        ],
        [
            190, 69, 211, 175, 56, 60, 42, 23, 208, 231, 241, 96, 205, 55, 222, 210, 178, 240, 230,
            118, 210, 253, 59, 206, 104, 165, 221, 249, 237, 74, 42, 33,
        ],
        [
            69, 202, 255, 56, 181, 188, 225, 92, 19, 165, 74, 192, 67, 249, 139, 35, 87, 125, 27,
            228, 61, 78, 56, 144, 42, 255, 159, 217, 53, 99, 10, 62,
        ],
        [
            17, 213, 190, 3, 139, 251, 81, 49, 133, 14, 185, 61, 240, 132, 117, 99, 240, 125, 104,
            191, 248, 27, 77, 11, 130, 122, 237, 184, 35, 100, 180, 3,
        ],
        [
            236, 29, 195, 209, 34, 84, 144, 163, 206, 89, 168, 108, 27, 11, 70, 115, 204, 213, 254,
            154, 127, 24, 198, 242, 246, 223, 181, 250, 165, 119, 22, 62,
        ],
        [
            60, 247, 191, 168, 239, 211, 60, 148, 241, 31, 18, 170, 16, 159, 36, 114, 42, 255, 166,
            224, 203, 137, 29, 159, 207, 121, 83, 18, 65, 177, 147, 58,
        ],
        [
            142, 74, 131, 209, 60, 216, 199, 80, 41, 112, 74, 182, 191, 182, 44, 195, 255, 209,
            212, 108, 139, 121, 174, 211, 221, 158, 186, 94, 7, 171, 195, 6,
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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    [
        [
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        [
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        [
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        [
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        [
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        [
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    [
        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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    [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        ],
        [
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        [
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        [
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    [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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    [
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        [
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        [
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        [
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        [
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        [
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        [
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    [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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    [
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        [
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        ],
        [
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        [
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        [
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        [
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        [
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        [
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    [
        [
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        ],
        [
            22, 50, 40, 200, 159, 100, 214, 73, 77, 69, 163, 2, 110, 139, 27, 106, 154, 229, 182,
            137, 7, 168, 187, 202, 17, 19, 160, 25, 162, 17, 89, 48,
        ],
        [
            164, 44, 83, 249, 124, 41, 132, 94, 96, 167, 55, 81, 204, 189, 223, 195, 250, 225, 16,
            205, 0, 3, 130, 36, 165, 36, 166, 132, 92, 91, 67, 63,
        ],
        [
            74, 250, 76, 30, 147, 188, 232, 26, 69, 89, 236, 235, 117, 199, 87, 31, 17, 223, 161,
            198, 244, 125, 157, 12, 237, 115, 191, 191, 71, 169, 248, 8,
        ],
        [
            199, 31, 247, 17, 166, 210, 80, 23, 60, 82, 40, 177, 153, 123, 9, 176, 227, 228, 80,
            110, 191, 176, 172, 159, 234, 227, 133, 97, 160, 201, 8, 45,
        ],
        [
            76, 132, 117, 193, 103, 234, 31, 11, 42, 125, 132, 21, 248, 178, 136, 13, 191, 20, 46,
            6, 95, 231, 230, 95, 29, 223, 70, 180, 205, 75, 70, 29,
        ],
        [
            252, 10, 50, 84, 120, 20, 243, 48, 252, 113, 112, 249, 255, 250, 144, 178, 245, 108,
            209, 169, 102, 254, 1, 34, 254, 141, 201, 39, 18, 66, 213, 37,
        ],
        [
            216, 43, 15, 51, 184, 164, 7, 189, 92, 219, 230, 192, 138, 49, 17, 116, 209, 106, 26,
            208, 1, 207, 209, 130, 200, 28, 194, 68, 159, 151, 92, 59,
        ],
    ],
    [
        [
            130, 227, 156, 234, 103, 13, 183, 24, 209, 108, 219, 46, 240, 126, 63, 210, 226, 125,
            54, 73, 152, 148, 106, 3, 165, 179, 217, 171, 135, 178, 187, 25,
        ],
        [
            249, 123, 230, 251, 192, 186, 61, 109, 88, 101, 236, 21, 188, 172, 133, 102, 200, 159,
            0, 83, 252, 97, 5, 193, 171, 41, 51, 40, 232, 17, 197, 47,
        ],
        [
            230, 209, 96, 28, 233, 75, 176, 21, 83, 187, 216, 27, 42, 240, 129, 127, 124, 226, 24,
            47, 194, 225, 110, 93, 108, 50, 169, 242, 24, 163, 130, 38,
        ],
        [
            133, 62, 95, 11, 93, 161, 179, 247, 32, 25, 89, 217, 173, 147, 63, 62, 162, 228, 178,
            45, 146, 101, 13, 17, 171, 246, 125, 143, 194, 108, 30, 58,
        ],
        [
            246, 216, 189, 144, 11, 240, 154, 125, 249, 154, 103, 59, 40, 198, 29, 207, 162, 186,
            17, 160, 63, 218, 136, 217, 105, 228, 71, 36, 45, 244, 135, 30,
        ],
        [
            219, 147, 219, 20, 99, 77, 100, 59, 113, 73, 90, 255, 236, 117, 72, 139, 43, 36, 149,
            4, 112, 41, 98, 157, 60, 2, 220, 9, 118, 181, 189, 46,
        ],
        [
            4, 109, 33, 143, 207, 231, 44, 77, 113, 223, 222, 247, 110, 52, 82, 202, 123, 213, 168,
            77, 249, 194, 9, 158, 7, 158, 246, 204, 165, 198, 9, 63,
        ],
        [
            84, 44, 128, 238, 129, 148, 169, 143, 203, 17, 195, 37, 152, 129, 162, 175, 39, 140,
            217, 131, 143, 238, 67, 49, 14, 235, 52, 228, 147, 63, 54, 35,
        ],
    ],
    [
        [
            191, 200, 71, 7, 129, 246, 124, 225, 156, 59, 22, 9, 148, 195, 71, 78, 147, 151, 234,
            102, 64, 121, 202, 224, 245, 27, 80, 223, 176, 227, 26, 17,
        ],
        [
            157, 66, 240, 109, 254, 70, 22, 27, 239, 237, 53, 115, 128, 155, 233, 187, 164, 148,
            232, 0, 41, 157, 202, 126, 95, 253, 77, 150, 3, 247, 218, 58,
        ],
        [
            228, 151, 252, 188, 162, 217, 229, 108, 43, 184, 35, 147, 108, 83, 94, 28, 151, 48,
            103, 150, 181, 98, 147, 212, 14, 134, 229, 37, 192, 112, 24, 16,
        ],
        [
            83, 208, 193, 201, 178, 111, 198, 23, 126, 42, 70, 132, 206, 197, 226, 122, 89, 140,
            131, 139, 135, 216, 52, 136, 76, 217, 147, 230, 129, 245, 176, 59,
        ],
        [
            244, 45, 69, 232, 83, 171, 220, 246, 253, 139, 1, 48, 15, 253, 251, 59, 222, 181, 17,
            129, 4, 237, 150, 59, 232, 244, 106, 254, 81, 244, 254, 18,
        ],
        [
            188, 199, 14, 197, 255, 152, 21, 31, 227, 236, 205, 79, 82, 104, 52, 214, 2, 218, 180,
            90, 116, 189, 195, 244, 167, 62, 194, 36, 107, 184, 11, 43,
        ],
        [
            91, 136, 16, 71, 244, 127, 17, 108, 158, 203, 244, 225, 158, 108, 74, 143, 209, 88,
            216, 76, 60, 162, 103, 218, 6, 86, 220, 238, 109, 6, 112, 28,
        ],
        [
            210, 145, 15, 69, 76, 180, 168, 134, 197, 134, 121, 248, 13, 45, 162, 58, 191, 117,
            233, 85, 161, 132, 243, 111, 26, 158, 207, 5, 173, 101, 203, 39,
        ],
    ],
    [
        [
            91, 229, 184, 51, 211, 97, 48, 184, 113, 20, 161, 108, 173, 224, 151, 36, 98, 116, 190,
            236, 239, 208, 45, 65, 41, 218, 22, 78, 21, 159, 68, 26,
        ],
        [
            154, 217, 229, 180, 214, 167, 164, 163, 231, 131, 232, 179, 73, 218, 83, 161, 164, 155,
            38, 217, 38, 83, 173, 123, 185, 195, 136, 28, 222, 105, 248, 44,
        ],
        [
            239, 18, 84, 25, 24, 214, 58, 20, 152, 95, 143, 93, 97, 219, 36, 109, 132, 217, 17, 55,
            49, 1, 18, 121, 131, 145, 4, 217, 250, 134, 88, 14,
        ],
        [
            253, 67, 150, 157, 135, 33, 201, 53, 183, 45, 159, 132, 171, 98, 41, 58, 140, 134, 11,
            145, 25, 241, 71, 213, 88, 135, 55, 47, 244, 112, 235, 43,
        ],
        [
            203, 78, 141, 190, 49, 209, 195, 175, 45, 64, 143, 120, 102, 235, 159, 161, 245, 198,
            29, 126, 9, 86, 92, 60, 63, 99, 217, 169, 217, 25, 97, 57,
        ],
        [
            233, 223, 245, 147, 242, 164, 19, 19, 137, 245, 19, 241, 36, 159, 136, 111, 211, 191,
            185, 125, 216, 176, 166, 33, 218, 175, 100, 57, 180, 168, 33, 21,
        ],
        [
            191, 125, 108, 252, 109, 113, 20, 141, 133, 231, 150, 20, 101, 219, 222, 38, 99, 160,
            59, 92, 97, 181, 71, 115, 51, 165, 119, 92, 118, 44, 127, 60,
        ],
        [
            113, 88, 23, 85, 9, 181, 218, 205, 196, 189, 218, 69, 235, 215, 199, 177, 88, 46, 80,
            177, 124, 126, 188, 209, 80, 154, 254, 177, 249, 6, 34, 45,
        ],
    ],
    [
        [
            49, 171, 43, 141, 243, 56, 203, 14, 8, 164, 117, 204, 211, 2, 98, 215, 247, 219, 40,
            10, 65, 77, 198, 28, 168, 165, 187, 204, 93, 58, 182, 38,
        ],
        [
            76, 41, 75, 64, 104, 7, 90, 39, 75, 212, 84, 97, 109, 16, 221, 105, 175, 57, 203, 170,
            160, 193, 20, 250, 41, 48, 135, 95, 210, 60, 239, 18,
        ],
        [
            11, 48, 231, 185, 24, 69, 14, 2, 119, 209, 228, 104, 103, 135, 156, 250, 144, 116, 172,
            233, 164, 53, 176, 174, 97, 86, 41, 34, 69, 64, 80, 45,
        ],
        [
            206, 62, 81, 203, 222, 175, 138, 11, 37, 103, 16, 242, 2, 233, 61, 206, 100, 119, 153,
            92, 27, 168, 76, 186, 61, 115, 161, 236, 188, 105, 53, 39,
        ],
        [
            184, 121, 255, 112, 144, 174, 21, 210, 228, 37, 104, 55, 37, 190, 74, 219, 138, 97,
            143, 89, 102, 179, 145, 166, 45, 48, 254, 158, 171, 154, 179, 29,
        ],
        [
            6, 225, 64, 102, 192, 218, 125, 198, 151, 71, 85, 123, 214, 160, 161, 13, 126, 187,
            146, 117, 142, 61, 67, 33, 247, 101, 92, 227, 237, 171, 178, 46,
        ],
        [
            214, 175, 191, 1, 36, 44, 95, 190, 226, 11, 238, 183, 89, 58, 32, 159, 7, 43, 143, 126,
            30, 154, 77, 11, 225, 220, 100, 206, 57, 69, 147, 59,
        ],
        [
            132, 71, 64, 13, 36, 95, 197, 166, 181, 130, 188, 161, 21, 134, 156, 60, 229, 202, 115,
            252, 142, 193, 144, 9, 148, 49, 152, 217, 94, 10, 200, 16,
        ],
    ],
    [
        [
            169, 185, 107, 159, 236, 0, 234, 249, 163, 24, 243, 22, 89, 24, 72, 31, 99, 20, 210,
            52, 203, 224, 58, 131, 135, 126, 139, 241, 11, 223, 180, 41,
        ],
        [
            100, 111, 163, 64, 52, 18, 196, 37, 86, 14, 150, 151, 192, 192, 213, 66, 5, 175, 208,
            15, 99, 225, 99, 23, 255, 115, 41, 53, 244, 241, 232, 62,
        ],
        [
            203, 172, 162, 221, 207, 144, 7, 120, 39, 125, 39, 231, 4, 167, 167, 147, 197, 4, 221,
            168, 11, 32, 252, 185, 253, 56, 198, 125, 180, 217, 48, 14,
        ],
        [
            151, 198, 41, 131, 85, 85, 153, 167, 214, 190, 207, 57, 232, 116, 153, 110, 242, 143,
            87, 149, 148, 79, 202, 50, 254, 93, 181, 118, 241, 36, 47, 30,
        ],
        [
            169, 132, 214, 252, 163, 226, 40, 236, 102, 76, 39, 197, 196, 64, 76, 131, 131, 239,
            125, 186, 226, 201, 133, 168, 63, 255, 217, 34, 32, 14, 87, 27,
        ],
        [
            152, 171, 139, 173, 78, 7, 26, 26, 41, 52, 127, 102, 29, 98, 192, 1, 192, 245, 215,
            144, 80, 63, 44, 223, 64, 223, 246, 42, 138, 196, 82, 56,
        ],
        [
            181, 29, 217, 137, 178, 103, 44, 244, 146, 108, 167, 194, 209, 98, 153, 191, 200, 209,
            197, 121, 30, 99, 180, 251, 16, 70, 185, 48, 28, 225, 29, 4,
        ],
        [
            6, 12, 109, 251, 112, 60, 35, 12, 42, 207, 70, 3, 142, 241, 196, 126, 220, 203, 68,
            249, 158, 166, 46, 67, 32, 23, 192, 239, 36, 44, 206, 25,
        ],
    ],
    [
        [
            94, 19, 121, 58, 184, 157, 237, 59, 227, 107, 130, 65, 168, 219, 76, 58, 226, 235, 146,
            109, 35, 2, 8, 52, 110, 145, 135, 173, 45, 18, 40, 18,
        ],
        [
            73, 20, 152, 96, 153, 114, 82, 42, 234, 214, 83, 47, 117, 62, 120, 141, 43, 72, 95, 94,
            222, 242, 227, 94, 53, 78, 58, 66, 227, 164, 108, 36,
        ],
        [
            15, 203, 0, 206, 129, 153, 3, 46, 221, 28, 232, 197, 225, 202, 69, 64, 15, 85, 203, 4,
            165, 83, 252, 98, 130, 126, 118, 166, 132, 113, 254, 3,
        ],
        [
            27, 247, 153, 83, 213, 195, 61, 103, 248, 197, 36, 170, 167, 29, 42, 61, 58, 108, 9,
            162, 63, 63, 78, 234, 102, 112, 223, 115, 109, 89, 205, 11,
        ],
        [
            230, 87, 100, 238, 166, 118, 76, 72, 206, 16, 128, 19, 196, 235, 19, 85, 25, 180, 143,
            88, 79, 67, 74, 18, 42, 0, 182, 167, 5, 82, 141, 58,
        ],
        [
            242, 225, 221, 181, 10, 42, 4, 246, 169, 149, 20, 171, 248, 249, 181, 206, 171, 85,
            200, 89, 186, 144, 18, 113, 211, 76, 54, 13, 175, 5, 23, 57,
        ],
        [
            124, 90, 7, 105, 198, 10, 101, 152, 215, 14, 162, 242, 28, 138, 77, 181, 216, 134, 209,
            125, 207, 40, 23, 247, 132, 101, 202, 184, 108, 234, 30, 23,
        ],
        [
            113, 101, 162, 46, 79, 205, 213, 191, 24, 206, 128, 228, 42, 66, 147, 106, 8, 211, 6,
            57, 131, 108, 24, 46, 80, 206, 180, 58, 149, 204, 118, 61,
        ],
    ],
    [
        [
            251, 19, 185, 65, 96, 235, 128, 183, 255, 41, 247, 142, 148, 237, 175, 76, 168, 5, 48,
            90, 246, 162, 79, 83, 10, 170, 36, 227, 89, 13, 167, 62,
        ],
        [
            56, 166, 248, 151, 90, 187, 224, 187, 156, 41, 254, 99, 77, 25, 30, 149, 121, 164, 64,
            17, 55, 129, 219, 217, 125, 235, 138, 13, 220, 168, 152, 1,
        ],
        [
            165, 106, 214, 186, 223, 37, 21, 54, 151, 110, 55, 189, 197, 11, 61, 209, 156, 123,
            169, 180, 84, 10, 149, 134, 72, 186, 24, 177, 182, 246, 164, 19,
        ],
        [
            73, 95, 93, 223, 114, 216, 130, 77, 25, 212, 228, 134, 143, 89, 68, 90, 11, 213, 48,
            205, 242, 51, 247, 151, 216, 45, 159, 152, 184, 225, 221, 41,
        ],
        [
            40, 171, 76, 37, 66, 223, 82, 113, 211, 247, 233, 118, 209, 240, 160, 244, 13, 51, 194,
            152, 58, 168, 231, 12, 185, 25, 186, 175, 64, 12, 231, 6,
        ],
        [
            179, 90, 55, 174, 72, 152, 204, 148, 24, 250, 29, 50, 143, 98, 133, 199, 241, 225, 133,
            171, 33, 49, 178, 167, 35, 162, 79, 159, 26, 232, 0, 8,
        ],
        [
            125, 6, 204, 17, 50, 201, 101, 165, 28, 107, 109, 206, 143, 215, 105, 123, 175, 164,
            63, 159, 21, 11, 234, 96, 159, 43, 88, 18, 159, 33, 88, 38,
        ],
        [
            221, 140, 167, 49, 28, 116, 206, 121, 79, 136, 80, 60, 181, 7, 95, 177, 32, 126, 87,
            128, 168, 124, 129, 166, 189, 214, 255, 44, 221, 83, 103, 48,
        ],
    ],
    [
        [
            100, 19, 245, 99, 127, 23, 39, 14, 128, 145, 57, 217, 20, 253, 209, 74, 223, 24, 220,
            142, 19, 167, 130, 239, 220, 226, 211, 66, 177, 44, 34, 25,
        ],
        [
            253, 114, 38, 89, 223, 86, 164, 50, 35, 154, 30, 159, 194, 152, 119, 36, 118, 25, 244,
            85, 63, 29, 152, 56, 150, 14, 250, 231, 157, 94, 53, 1,
        ],
        [
            122, 133, 104, 47, 162, 156, 2, 203, 65, 211, 188, 21, 95, 196, 233, 189, 85, 11, 82,
            62, 121, 185, 128, 178, 117, 221, 41, 246, 177, 224, 168, 53,
        ],
        [
            15, 47, 113, 92, 78, 129, 107, 39, 106, 27, 10, 4, 193, 207, 48, 209, 184, 128, 128,
            54, 167, 37, 99, 169, 88, 131, 209, 43, 191, 232, 246, 43,
        ],
        [
            151, 100, 55, 80, 35, 25, 142, 78, 150, 69, 94, 12, 237, 225, 126, 108, 106, 133, 11,
            118, 58, 8, 195, 87, 124, 129, 2, 8, 228, 8, 235, 41,
        ],
        [
            154, 75, 9, 198, 211, 209, 244, 131, 49, 126, 187, 157, 54, 92, 229, 166, 249, 72, 229,
            168, 92, 24, 17, 154, 4, 213, 211, 179, 26, 60, 115, 57,
        ],
        [
            148, 168, 89, 36, 108, 105, 22, 194, 209, 232, 199, 64, 79, 100, 96, 148, 205, 137, 20,
            98, 107, 79, 12, 200, 56, 4, 93, 151, 129, 18, 90, 2,
        ],
        [
            173, 118, 232, 220, 163, 182, 149, 237, 184, 151, 108, 87, 139, 99, 14, 144, 174, 120,
            101, 207, 198, 189, 108, 99, 145, 73, 114, 141, 90, 97, 136, 36,
        ],
    ],
];

pub fn generator() -> pallas::Affine {
    pallas::Affine::from_xy(
        pallas::Base::from_repr(GENERATOR.0).unwrap(),
        pallas::Base::from_repr(GENERATOR.1).unwrap(),
    )
    .unwrap()
}

#[cfg(test)]
mod tests {
    use super::super::{NUM_WINDOWS, ORCHARD_PERSONALIZATION};
    use super::*;
    use group::Curve;
    use halo2_gadgets::ecc::chip::constants::{test_lagrange_coeffs, test_zs_and_us};
    use pasta_curves::{
        arithmetic::{CurveAffine, CurveExt},
        pallas,
    };

    #[test]
    fn generator() {
        let hasher = pallas::Point::hash_to_curve(ORCHARD_PERSONALIZATION);
        let point = hasher(b"G");
        let coords = point.to_affine().coordinates().unwrap();

        assert_eq!(*coords.x(), pallas::Base::from_repr(GENERATOR.0).unwrap());
        assert_eq!(*coords.y(), pallas::Base::from_repr(GENERATOR.1).unwrap());
    }

    #[test]
    fn lagrange_coeffs() {
        let base = super::generator();
        test_lagrange_coeffs(base, NUM_WINDOWS);
    }

    #[test]
    fn z() {
        let base = super::generator();
        test_zs_and_us(base, &Z, &U, NUM_WINDOWS);
    }
}