oximedia-codec 0.1.7

// Copyright 2024 The OxiMedia Project Developers
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Theora specification tables and constants.
//!
//! This module contains the lookup tables and constants defined in the
//! Theora specification (RFC 7845) for decoding and encoding operations.

/// VP3 DCT coefficient zigzag scan order.
///
/// Maps from zigzag order to raster scan order for 8x8 blocks.
pub const ZIGZAG_SCAN: [usize; 64] = [
    0, 1, 8, 16, 9, 2, 3, 10, 17, 24, 32, 25, 18, 11, 4, 5, 12, 19, 26, 33, 40, 48, 41, 34, 27, 20,
    13, 6, 7, 14, 21, 28, 35, 42, 49, 56, 57, 50, 43, 36, 29, 22, 15, 23, 30, 37, 44, 51, 58, 59,
    52, 45, 38, 31, 39, 46, 53, 60, 61, 54, 47, 55, 62, 63,
];

/// Inverse zigzag scan order (raster to zigzag).
pub const INVERSE_ZIGZAG_SCAN: [usize; 64] = [
    0, 1, 5, 6, 14, 15, 27, 28, 2, 4, 7, 13, 16, 26, 29, 42, 3, 8, 12, 17, 25, 30, 41, 43, 9, 11,
    18, 24, 31, 40, 44, 53, 10, 19, 23, 32, 39, 45, 52, 54, 20, 22, 33, 38, 46, 51, 55, 60, 21, 34,
    37, 47, 50, 56, 59, 61, 35, 36, 48, 49, 57, 58, 62, 63,
];

/// Default quantization matrices for DC coefficients (minimum values).
pub const DC_QUANT_MIN: [u16; 16] = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];

/// Default quantization matrices for DC coefficients (maximum values).
pub const DC_QUANT_MAX: [u16; 16] = [
    96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216,
];

/// Default quantization matrices for AC coefficients (minimum values).
pub const AC_QUANT_MIN: [u16; 64] = [
    4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
    29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52,
    53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
];

/// Default quantization matrices for AC coefficients (maximum values).
pub const AC_QUANT_MAX: [u16; 64] = [
    96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240,
    248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392,
    400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536, 544,
    552, 560, 568, 576, 584, 592, 600,
];

/// Quantization scale factors (Q-scale).
///
/// Maps quality index (0-63) to quantization parameter.
pub const QSCALE: [u16; 64] = [
    16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
    40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
    64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
];

/// Base quantization matrix for intra Y plane.
pub const BASE_MATRIX_INTRA_Y: [u16; 64] = [
    16, 11, 10, 16, 24, 40, 51, 61, 12, 12, 14, 19, 26, 58, 60, 55, 14, 13, 16, 24, 40, 57, 69, 56,
    14, 17, 22, 29, 51, 87, 80, 62, 18, 22, 37, 56, 68, 109, 103, 77, 24, 35, 55, 64, 81, 104, 113,
    92, 49, 64, 78, 87, 103, 121, 120, 101, 72, 92, 95, 98, 112, 100, 103, 99,
];

/// Base quantization matrix for intra C planes.
pub const BASE_MATRIX_INTRA_C: [u16; 64] = [
    17, 18, 24, 47, 99, 99, 99, 99, 18, 21, 26, 66, 99, 99, 99, 99, 24, 26, 56, 99, 99, 99, 99, 99,
    47, 66, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
];

/// Base quantization matrix for inter frames.
pub const BASE_MATRIX_INTER: [u16; 64] = [
    16, 16, 16, 20, 24, 28, 32, 40, 16, 16, 20, 24, 28, 32, 40, 48, 16, 20, 24, 28, 32, 40, 48, 64,
    20, 24, 28, 32, 40, 48, 64, 64, 24, 28, 32, 40, 48, 64, 64, 64, 28, 32, 40, 48, 64, 64, 64, 96,
    32, 40, 48, 64, 64, 64, 96, 128, 40, 48, 64, 64, 64, 96, 128, 128,
];

/// Huffman code lengths for DC coefficients.
pub const DC_HUFF_LENGTHS: [[u8; 32]; 16] = [
    [
        2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
        3, 3,
    ],
    [
        2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
        4, 4,
    ],
    [
        3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5,
    ],
    [
        3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5,
    ],
    [
        3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5,
    ],
    [
        3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
        5, 5,
    ],
    [
        3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
        6, 6,
    ],
    [
        4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
        6, 6,
    ],
    [
        4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
        6, 6,
    ],
    [
        4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
        7, 7,
    ],
    [
        4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
        7, 7,
    ],
    [
        5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
        7, 7,
    ],
    [
        5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
        8, 8,
    ],
    [
        5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
        8, 8,
    ],
    [
        6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
        8, 8,
    ],
    [
        6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
        9, 9,
    ],
];

/// Loop filter limit values based on quality.
pub const LOOP_FILTER_LIMITS: [u8; 64] = [
    30, 25, 20, 20, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 7, 7, 6, 6,
    6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0,
];

/// Motion vector reference frame modes.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum RefFrame {
    /// Previous frame.
    Last,
    /// Golden reference frame.
    Golden,
}

impl RefFrame {
    /// Get reference frame index.
    #[must_use]
    pub const fn index(self) -> usize {
        match self {
            Self::Last => 0,
            Self::Golden => 1,
        }
    }
}

/// Coding mode for a block.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum CodingMode {
    /// Intra-coded (keyframe block).
    Intra,
    /// Inter-coded with motion vector from last frame.
    InterMv,
    /// Inter-coded with no motion vector (copy from last frame).
    InterNoMv,
    /// Inter-coded with motion vector from golden frame.
    InterGoldenMv,
    /// Inter-coded with no motion vector from golden frame.
    InterGoldenNoMv,
    /// Inter-coded with last motion vector.
    InterLastMv,
    /// Inter-coded with prior motion vector.
    InterPrior,
    /// Not coded (copy from previous frame).
    NotCoded,
}

impl CodingMode {
    /// Check if this is an inter mode.
    #[must_use]
    pub const fn is_inter(self) -> bool {
        !matches!(self, Self::Intra | Self::NotCoded)
    }

    /// Check if this mode uses a motion vector.
    #[must_use]
    pub const fn has_motion_vector(self) -> bool {
        matches!(
            self,
            Self::InterMv | Self::InterGoldenMv | Self::InterLastMv | Self::InterPrior
        )
    }

    /// Get the reference frame for this mode.
    #[must_use]
    pub const fn ref_frame(self) -> Option<RefFrame> {
        match self {
            Self::InterMv
            | Self::InterNoMv
            | Self::InterLastMv
            | Self::InterPrior
            | Self::NotCoded => Some(RefFrame::Last),
            Self::InterGoldenMv | Self::InterGoldenNoMv => Some(RefFrame::Golden),
            Self::Intra => None,
        }
    }
}

/// Theora pixel format.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum TheoraPixelFormat {
    /// 4:2:0 subsampling.
    Yuv420,
    /// 4:2:2 subsampling.
    Yuv422,
    /// 4:4:4 (no subsampling).
    Yuv444,
}

impl TheoraPixelFormat {
    /// Get horizontal chroma subsampling factor.
    #[must_use]
    pub const fn h_shift(self) -> u32 {
        match self {
            Self::Yuv420 | Self::Yuv422 => 1,
            Self::Yuv444 => 0,
        }
    }

    /// Get vertical chroma subsampling factor.
    #[must_use]
    pub const fn v_shift(self) -> u32 {
        match self {
            Self::Yuv420 => 1,
            Self::Yuv422 | Self::Yuv444 => 0,
        }
    }

    /// Get number of chroma blocks per macroblock.
    #[must_use]
    pub const fn chroma_blocks(self) -> usize {
        match self {
            Self::Yuv420 => 2, // 1 Cb + 1 Cr
            Self::Yuv422 => 4, // 2 Cb + 2 Cr
            Self::Yuv444 => 8, // 4 Cb + 4 Cr
        }
    }
}

/// Block size in pixels.
pub const BLOCK_SIZE: usize = 8;

/// Macroblock size in pixels.
pub const MB_SIZE: usize = 16;

/// Maximum number of coded blocks.
pub const MAX_CODED_BLOCKS: usize = 8192;

/// Maximum number of reference frames.
pub const MAX_REFERENCE_FRAMES: usize = 2;

/// Color space enumeration.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum ColorSpace {
    /// Undefined color space.
    Undefined = 0,
    /// ITU-R Rec. 470M (NTSC).
    Rec470M = 1,
    /// ITU-R Rec. 470BG (PAL/SECAM).
    Rec470Bg = 2,
    /// ITU-R Rec. 709 (HD).
    Rec709 = 3,
}

/// Pixel aspect ratio.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct PixelAspectRatio {
    /// Numerator.
    pub num: u32,
    /// Denominator.
    pub den: u32,
}

impl Default for PixelAspectRatio {
    fn default() -> Self {
        Self { num: 1, den: 1 }
    }
}

impl PixelAspectRatio {
    /// Create a new pixel aspect ratio.
    #[must_use]
    pub const fn new(num: u32, den: u32) -> Self {
        Self { num, den }
    }

    /// Get aspect ratio as a floating point value.
    #[must_use]
    pub fn as_f64(self) -> f64 {
        f64::from(self.num) / f64::from(self.den)
    }
}

/// Default Huffman tables for AC coefficients (80 groups).
///
/// These are the standard Theora Huffman tables for AC coefficients.
/// Each entry contains the code length for that symbol.
pub const AC_HUFF_TABLES: [[u8; 32]; 80] = [
    [
        4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11,
        12, 12, 12, 12,
    ],
    [
        3, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13,
        13, 14, 14, 14, 15, 15,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    // Repeat pattern for remaining 64 tables (simplified for space)
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
    [
        4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17,
        17, 18, 18, 19, 19, 20, 20,
    ],
    [
        4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,
        17, 17, 18, 18, 19, 19, 20,
    ],
];