darkfi_sdk/crypto/constants/fixed_bases/

nullifier_k.rs

/* This file is part of DarkFi (https://dark.fi)
 *
 * Copyright (C) 2020-2025 Dyne.org foundation
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Affero General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */

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

pub const GENERATOR: ([u8; 32], [u8; 32]) = (
    [
        117, 202, 71, 228, 167, 106, 111, 211, 155, 219, 181, 204, 146, 177, 126, 94, 207, 201,
        244, 250, 113, 85, 55, 46, 141, 25, 168, 156, 22, 170, 231, 37,
    ],
    [
        204, 1, 224, 26, 226, 220, 184, 45, 51, 180, 193, 193, 158, 164, 224, 95, 117, 255, 8, 32,
        68, 115, 4, 136, 132, 51, 26, 27, 133, 31, 92, 21,
    ],
);

/// Full-width z-values for GENERATOR
pub const Z: [u64; super::NUM_WINDOWS] = [
    34374, 173069, 40776, 220066, 45494, 37762, 5245, 11979, 33386, 238556, 128731, 12128, 89982,
    85351, 9804, 12820, 80455, 100009, 24382, 17854, 26367, 7067, 102106, 64293, 114999, 172304,
    36687, 11287, 66386, 41470, 182654, 12214, 36528, 16257, 26179, 15660, 106189, 211703, 12936,
    2506, 149799, 82965, 117810, 98881, 296, 146201, 63200, 31766, 78221, 6587, 27974, 126041,
    19927, 79339, 210060, 127148, 10109, 19815, 107452, 10296, 642, 11828, 3985, 2984, 30806,
    12554, 1815, 19894, 16790, 33748, 12879, 1742, 30858, 118563, 26855, 75617, 10167, 17660,
    33638, 89236, 50234, 30489, 67488, 50229, 29277,
];

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

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 halo2_gadgets::ecc::chip::constants::{test_lagrange_coeffs, test_zs_and_us};
    use pasta_curves::{arithmetic::CurveExt, group::Curve};

    #[test]
    fn generator() {
        let hasher = pallas::Point::hash_to_curve(ORCHARD_PERSONALIZATION);
        let point = hasher(b"K");
        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);
    }
}