nvidia-texture-tools/extern/rg/rgbcx.h

// rgbcx.h v1.12
// High-performance scalar BC1-5 encoders. Public Domain or MIT license (you choose - see below), written by Richard Geldreich 2020 <richgel99@gmail.com>.
//
// Influential references:
// http://sjbrown.co.uk/2006/01/19/dxt-compression-techniques/
// https://github.com/nothings/stb/blob/master/stb_dxt.h
// https://gist.github.com/castano/c92c7626f288f9e99e158520b14a61cf
// https://github.com/castano/icbc/blob/master/icbc.h
// http://www.humus.name/index.php?page=3D&ID=79
//
// This is a single header file library. Be sure to "#define RGBCX_IMPLEMENTATION" in one .cpp file somewhere.
//
// Instructions:
//
// The library MUST be initialized by calling this function at least once before using any encoder or decoder functions:
//
// void rgbcx::init(bc1_approx_mode mode = cBC1Ideal);
//
// This function manipulates global state, so it is not thread safe. 
// You can call it multiple times to change the global BC1 approximation mode.
// Important: BC1/3 textures encoded using non-ideal BC1 approximation modes should only be sampled on parts from that vendor.
// If you encode for AMD, average error on AMD parts will go down, but average error on NVidia parts will go up and vice versa.
// If in doubt, encode in ideal BC1 mode.
//
// Call these functions to encode BC1-5:
// void rgbcx::encode_bc1(uint32_t level, void* pDst, const uint8_t* pPixels, bool allow_3color, bool use_transparent_texels_for_black);
// void rgbcx::encode_bc3(uint32_t level, void* pDst, const uint8_t* pPixels);
// void rgbcx::encode_bc4(void* pDst, const uint8_t* pPixels, uint32_t stride = 4);
// void rgbcx::encode_bc5(void* pDst, const uint8_t* pPixels, uint32_t chan0 = 0, uint32_t chan1 = 1, uint32_t stride = 4);
//
// - level ranges from MIN_LEVEL to MAX_LEVEL. The higher the level, the slower the encoder goes, but the higher the average quality.
// levels [0,4] are fast and compete against stb_dxt (default and HIGHQUAL). The remaining levels compete against squish/NVTT/icbc and icbc HQ.
// If in doubt just use level 10, set allow_3color to true and use_transparent_texels_for_black to false, and adjust as needed.
//
// - pDst is a pointer to the 8-byte (BC1/4) or 16-byte (BC3/5) destination block. 
//
// - pPixels is a pointer to the 32-bpp pixels, in either RGBX or RGBA format (R is first in memory). 
// Alpha is always ignored by encode_bc1().
//
// - allow_3color: If true the encoder will use 3-color blocks. This flag is ignored unless level is >= 5 (because lower levels compete against stb_dxt and it doesn't support 3-color blocks).
// Do not enable on BC3-5 textures. 3-color block usage slows down encoding.
//
// - use_transparent_texels_for_black: If true the encoder will use 3-color block transparent black pixels to code very dark or black texels. Your engine/shader MUST ignore the sampled 
// alpha value for textures encoded in this mode. This is how NVidia's classic "nvdxt" encoder (used by many original Xbox titles) used to work by default on DXT1C textures. It increases 
// average quality substantially (because dark texels/black are very common) and is highly recommended.
// Do not enable on BC3-5 textures. 
//
// - stride is the source pixel stride, in bytes. It's typically 4.
//
// - chan0 and chan1 are the source channels. Typically they will be 0 and 1.
//
// All encoding and decoding functions are threade-safe.
//
// To reduce the compiled size of the encoder, set #define RGBCX_USE_SMALLER_TABLES to 1 before including this header.
//
#ifndef RGBCX_INCLUDE_H
#define RGBCX_INCLUDE_H

#include <stdlib.h>
#include <stdint.h>
#include <algorithm>
#include <assert.h>
#include <limits.h>

// By default, the table used to accelerate cluster fit on 4 color blocks uses a 969x128 entry table. 
// To reduce the executable size, set RGBCX_USE_SMALLER_TABLES to 1, which selects the smaller 969x32 entry table. 
#ifndef RGBCX_USE_SMALLER_TABLES
#define RGBCX_USE_SMALLER_TABLES 0
#endif

namespace rgbcx
{
    enum class bc1_approx_mode
    {
        // The default mode. No rounding for 4-color colors 2,3. My older tools/compressors use this mode. 
        // This matches the D3D10 docs on BC1.
        cBC1Ideal = 0,

        // NVidia GPU mode.
        cBC1NVidia = 1,

        // AMD GPU mode.
        cBC1AMD = 2,

        // This mode matches AMD Compressonator's output. It rounds 4-color colors 2,3 (not 3-color color 2).
        // This matches the D3D9 docs on DXT1.
        cBC1IdealRound4 = 3
    };

    // init() MUST be called once before using the BC1 encoder.
    // This function may be called multiple times to change the BC1 approximation mode. 
    // This function initializes global state, so don't call it while other threads inside the encoder.
    // Important: If you encode textures for a specific vendor's GPU's, beware that using that texture data on other GPU's may result in ugly artifacts. 
    // Encode to cBC1Ideal unless you know the texture data will only be deployed or used on a specific vendor's GPU.
    void init(bc1_approx_mode mode = bc1_approx_mode::cBC1Ideal);

    // Optimally encodes a solid color block to BC1 format.
    void encode_bc1_solid_block(void* pDst, uint32_t fr, uint32_t fg, uint32_t fb, bool allow_3color);

    // BC1 low-level API encoder flags. You can ignore this if you use the simple level API.
    enum
    {
        // Try to improve quality using the most likely total orderings. 
        // The total_orderings_to_try parameter will then control the number of total orderings to try for 4 color blocks, and the 
        // total_orderings_to_try3 parameter will control the number of total orderings to try for 3 color blocks (if they are enabled).
        cEncodeBC1UseLikelyTotalOrderings = 2,

        // Use 2 least squares pass, instead of one (same as stb_dxt's HIGHQUAL option).
        // Recommended if you're enabling cEncodeBC1UseLikelyTotalOrderings.
        cEncodeBC1TwoLeastSquaresPasses = 4,

        // cEncodeBC1Use3ColorBlocksForBlackPixels allows the BC1 encoder to use 3-color blocks for blocks containing black or very dark pixels. 
        // You shader/engine MUST ignore the alpha channel on textures encoded with this flag.
        // Average quality goes up substantially for my 100 texture corpus (~.5 dB), so it's worth using if you can.
        // Note the BC1 encoder does not actually support transparency in 3-color mode.
        // Don't set when encoding to BC3.
        cEncodeBC1Use3ColorBlocksForBlackPixels = 8,

        // If cEncodeBC1Use3ColorBlocks is set, the encoder can use 3-color mode for a small but noticeable gain in average quality, but lower perf.
        // If you also specify the cEncodeBC1UseLikelyTotalOrderings flag, set the total_orderings_to_try3 paramter to the number of total orderings to try.
        // Don't set when encoding to BC3.
        cEncodeBC1Use3ColorBlocks = 16,

        // cEncodeBC1Iterative will greatly increase encode time, but is very slightly higher quality.
        // Same as squish's iterative cluster fit option. Not really worth the tiny boost in quality, unless you just don't care about perf. at all.
        cEncodeBC1Iterative = 32,

        // cEncodeBC1BoundingBox enables a fast all-integer PCA approximation on 4-color blocks. 
        // At level 0 options (no other flags), this is ~15% faster, and higher *average* quality.
        cEncodeBC1BoundingBox = 64,

        // Use a slightly lower quality, but ~30% faster MSE evaluation function for 4-color blocks.
        cEncodeBC1UseFasterMSEEval = 128,

        // Examine all colors to compute selectors/MSE (slower than default)
        cEncodeBC1UseFullMSEEval = 256,

        // Use 2D least squares+inset+optimal rounding (the method used in Humus's GPU texture encoding demo), instead of PCA. 
        // Around 18% faster, very slightly lower average quality to better (depends on the content).
        cEncodeBC1Use2DLS = 512,

        // Use 6 power iterations vs. 4 for PCA.
        cEncodeBC1Use6PowerIters = 2048,

        // Check all total orderings - *very* slow. The encoder is not designed to be used in this way.
        cEncodeBC1Exhaustive = 8192,

        // Try 2 different ways of choosing the initial endpoints.
        cEncodeBC1TryAllInitialEndponts = 16384,

        // Same as cEncodeBC1BoundingBox, but implemented using integer math (faster, slightly less quality)
        cEncodeBC1BoundingBoxInt = 32768,

        // Try refining the final endpoints by examining nearby colors.
        cEncodeBC1EndpointSearchRoundsShift = 22,
        cEncodeBC1EndpointSearchRoundsMask = 1023U << cEncodeBC1EndpointSearchRoundsShift,
    };

    const uint32_t MIN_TOTAL_ORDERINGS = 1;
    const uint32_t MAX_TOTAL_ORDERINGS3 = 32;

#if RGBCX_USE_SMALLER_TABLES
    const uint32_t MAX_TOTAL_ORDERINGS4 = 32;
#else
    const uint32_t MAX_TOTAL_ORDERINGS4 = 128;
#endif

    // DEFAULT_TOTAL_ORDERINGS_TO_TRY is around 3x faster than libsquish at slightly higher average quality. 10-16 is a good range to start to compete against libsquish.
    const uint32_t DEFAULT_TOTAL_ORDERINGS_TO_TRY = 10;

    const uint32_t DEFAULT_TOTAL_ORDERINGS_TO_TRY3 = 1;

    // Encodes a 4x4 block of RGBX (X=ignored) pixels to BC1 format. 
    // This is the simplified interface for BC1 encoding, which accepts a level parameter and converts that to the best overall flags.
    // The pixels are in RGBA format, where R is first in memory. The BC1 encoder completely ignores the alpha channel (i.e. there is no punchthrough alpha support).
    // This is the recommended function to use for BC1 encoding, becuase it configures the encoder for you in the best possible way (on average).
    // Note that the 3 color modes won't be used at all until level 5 or higher.
    // No transparency supported, however if you set use_transparent_texels_for_black to true the encocer will use transparent selectors on very dark/black texels to reduce MSE. 
    const uint32_t MIN_LEVEL = 0, MAX_LEVEL = 18;
    void encode_bc1(uint32_t level, void* pDst, const uint8_t* pPixels, bool allow_3color, bool use_transparent_texels_for_black);

    // Low-level interface for BC1 encoding.
    // Always returns a 4 color block, unless cEncodeBC1Use3ColorBlocksForBlackPixels or cEncodeBC1Use3ColorBlock flags are specified. 
    // total_orderings_to_try controls the perf. vs. quality tradeoff on 4-color blocks when the cEncodeBC1UseLikelyTotalOrderings flag is used. It must range between [MIN_TOTAL_ORDERINGS, MAX_TOTAL_ORDERINGS4].
    // total_orderings_to_try3 controls the perf. vs. quality tradeoff on 3-color bocks when the cEncodeBC1UseLikelyTotalOrderings and the cEncodeBC1Use3ColorBlocks flags are used. Valid range is [0,MAX_TOTAL_ORDERINGS3] (0=disabled).
    void encode_bc1(void* pDst, const uint8_t* pPixels, uint32_t flags = 0, uint32_t total_orderings_to_try = DEFAULT_TOTAL_ORDERINGS_TO_TRY, uint32_t total_orderings_to_try3 = DEFAULT_TOTAL_ORDERINGS_TO_TRY3);

    // Encodes a 4x4 block of RGBA pixels to BC3 format.
    // There are two encode_bc3() functions. 
    // The first is the recommended function, which accepts a level parameter.
    // The second is a low-level version that allows fine control over BC1 encoding. 
    void encode_bc3(uint32_t level, void* pDst, const uint8_t* pPixels);
    void encode_bc3(void* pDst, const uint8_t* pPixels, uint32_t flags = 0, uint32_t total_orderings_to_try = DEFAULT_TOTAL_ORDERINGS_TO_TRY);

    // Encodes a single channel to BC4.
    // stride is the source pixel stride in bytes.
    void encode_bc4(void* pDst, const uint8_t* pPixels, uint32_t stride = 4);

    // Encodes two channels to BC5. 
    // chan0/chan1 control which channels, stride is the source pixel stride in bytes.
    void encode_bc5(void* pDst, const uint8_t* pPixels, uint32_t chan0 = 0, uint32_t chan1 = 1, uint32_t stride = 4);

    // Decompression functions. 

    // Returns true if the block uses 3 color punchthrough alpha mode.
    bool unpack_bc1(const void* pBlock_bits, void* pPixels, bool set_alpha = true, bc1_approx_mode mode = bc1_approx_mode::cBC1Ideal);

    void unpack_bc4(const void* pBlock_bits, uint8_t* pPixels, uint32_t stride = 4);

    // Returns true if the block uses 3 color punchthrough alpha mode.
    bool unpack_bc3(const void* pBlock_bits, void* pPixels, bc1_approx_mode mode = bc1_approx_mode::cBC1Ideal);

    void unpack_bc5(const void* pBlock_bits, void* pPixels, uint32_t chan0 = 0, uint32_t chan1 = 1, uint32_t stride = 4);
}
#endif // #ifndef RGBCX_INCLUDE_H

#ifdef RGBCX_IMPLEMENTATION
namespace rgbcx
{
    const uint32_t NUM_UNIQUE_TOTAL_ORDERINGS4 = 969;

    // All total orderings for 16 pixels 2-bit selectors.
    // BC1 selector order 0, 2, 3, 1 (i.e. the selectors are reordered into linear order).
    static uint8_t g_unique_total_orders4[NUM_UNIQUE_TOTAL_ORDERINGS4][4] =
    {
        {0,8,2,6},{4,3,9,0},{4,8,1,3},{12,0,3,1},{11,3,2,0},{6,4,6,0},{7,5,0,4},{6,0,8,2},{1,0,0,15},{3,0,8,5},{1,1,13,1},{13,1,2,0},{0,14,1,1},{0,15,1,0},{0,13,0,3},{16,0,0,0},{4,3,4,5},{8,6,0,2},{0,10,0,6},{10,0,4,2},{7,2,1,6},{4,7,5,0},{1,4,7,4},{0,14,2,0},{2,7,2,5},{9,0,5,2},{9,2,2,3},{10,0,5,1},{2,3,7,4},{4,9,0,3},{1,5,0,10},{1,1,6,8},
        {6,6,4,0},{11,5,0,0},{11,2,0,3},{4,0,10,2},{2,3,10,1},{1,13,1,1},{0,14,0,2},{2,3,3,8},{12,3,1,0},{14,0,0,2},{9,1,3,3},{6,4,0,6},{1,1,5,9},{5,9,0,2},{2,10,1,3},{12,0,0,4},{4,6,6,0},{0,6,4,6},{3,7,4,2},{0,13,3,0},{3,10,0,3},{10,2,1,3},{1,12,1,2},{2,0,13,1},{11,0,5,0},{12,1,3,0},{6,4,5,1},{10,4,2,0},{3,6,1,6},{7,3,6,0},{10,4,0,2},{10,0,2,4},
        {0,5,9,2},{0,9,3,4},{6,4,2,4},{3,4,7,2},{3,3,5,5},{4,2,9,1},{6,2,8,0},{3,5,3,5},{4,10,1,1},{10,1,3,2},{5,7,0,4},{5,3,7,1},{6,8,1,1},{8,8,0,0},{11,1,0,4},{14,1,0,1},{9,3,2,2},{8,2,1,5},{0,0,2,14},{3,3,9,1},{10,1,5,0},{8,3,1,4},{1,5,8,2},{6,1,9,0},{3,2,1,10},{3,11,1,1},{7,6,3,0},{9,0,3,4},{5,2,5,4},{0,2,3,11},{15,0,0,1},{0,6,6,4},
        {3,4,9,0},{4,7,0,5},{0,4,4,8},{0,13,2,1},{2,4,1,9},{3,2,5,6},{10,6,0,0},{3,5,6,2},{8,0,4,4},{1,3,6,6},{7,7,0,2},{6,1,4,5},{0,11,1,4},{2,2,8,4},{0,1,2,13},{15,0,1,0},{7,2,6,1},{8,1,7,0},{1,8,4,3},{2,13,1,0},{1,0,7,8},{14,2,0,0},{1,8,1,6},{9,3,3,1},{0,0,7,9},{4,4,1,7},{9,0,6,1},{10,2,4,0},{1,7,3,5},{0,3,8,5},{5,2,4,5},{1,2,5,8},
        {0,8,7,1},{10,3,2,1},{12,0,4,0},{2,1,4,9},{5,2,2,7},{1,9,3,3},{15,1,0,0},{6,3,4,3},{9,5,0,2},{1,6,9,0},{6,6,0,4},{13,2,1,0},{5,1,8,2},{0,5,11,0},{7,1,0,8},{1,2,12,1},{0,3,3,10},{7,4,2,3},{5,1,4,6},{7,0,3,6},{3,12,0,1},{3,4,5,4},{1,10,0,5},{7,4,3,2},{10,5,0,1},{13,3,0,0},{2,5,4,5},{3,10,1,2},{5,1,2,8},{14,0,1,1},{1,5,4,6},{1,4,5,6},
        {2,3,11,0},{11,0,4,1},{11,2,2,1},{5,3,8,0},{1,3,10,2},{0,1,13,2},{3,1,4,8},{4,2,4,6},{1,5,6,4},{2,1,11,2},{1,2,9,4},{4,7,3,2},{6,2,5,3},{7,2,2,5},{8,1,4,3},{3,2,8,3},{12,1,0,3},{7,8,1,0},{7,0,2,7},{5,10,0,1},{0,2,14,0},{2,9,3,2},{7,0,0,9},{11,1,4,0},{10,4,1,1},{2,2,9,3},{5,7,2,2},{1,3,1,11},{13,2,0,1},{4,2,8,2},{2,3,1,10},{4,2,5,5},
        {7,0,7,2},{10,0,0,6},{0,8,5,3},{4,4,0,8},{12,4,0,0},{0,1,14,1},{8,0,1,7},{5,1,5,5},{11,0,3,2},{0,4,1,11},{0,8,8,0},{0,2,5,9},{7,3,2,4},{7,8,0,1},{1,0,3,12},{7,4,5,0},{1,6,7,2},{7,6,1,2},{9,6,1,0},{12,2,0,2},{4,1,6,5},{4,0,1,11},{8,4,4,0},{13,0,1,2},{8,6,2,0},{4,12,0,0},{2,7,5,2},{2,0,5,9},{5,4,5,2},{3,8,5,0},{7,3,3,3},{4,4,8,0},
        {2,1,3,10},{5,0,1,10},{6,4,3,3},{4,9,1,2},{1,4,0,11},{11,3,1,1},{4,0,12,0},{13,0,0,3},{6,1,6,3},{9,0,4,3},{8,0,0,8},{8,4,0,4},{0,12,1,3},{0,4,10,2},{3,4,8,1},{1,3,8,4},{9,2,5,0},{5,7,4,0},{1,0,11,4},{4,10,0,2},{1,3,12,0},{6,9,0,1},{5,0,9,2},{5,9,2,0},{13,1,0,2},{9,3,4,0},{9,4,0,3},{3,1,12,0},{2,4,3,7},{1,2,13,0},{2,2,4,8},{6,8,0,2},
        {9,2,1,4},{9,5,1,1},{2,0,4,10},{5,4,0,7},{0,0,6,10},{1,2,0,13},{4,7,2,3},{6,5,5,0},{3,3,1,9},{1,6,1,8},{12,2,1,1},{4,4,5,3},{1,0,6,9},{0,6,10,0},{4,8,3,1},{4,3,2,7},{2,1,7,6},{1,9,1,5},{3,1,3,9},{8,7,1,0},{1,2,3,10},{14,1,1,0},{5,4,4,3},{3,7,0,6},{7,4,1,4},{3,7,5,1},{1,1,0,14},{0,10,3,3},{0,4,3,9},{1,7,7,1},{2,0,10,4},{5,8,0,3},
        {6,7,3,0},{0,8,4,4},{5,7,3,1},{7,9,0,0},{7,6,2,1},{0,4,5,7},{6,3,5,2},{1,2,1,12},{5,2,0,9},{8,5,0,3},{4,6,1,5},{1,1,7,7},{10,5,1,0},{1,2,8,5},{1,8,2,5},{5,1,0,10},{6,9,1,0},{13,0,2,1},{8,3,5,0},{6,3,6,1},{2,11,3,0},{3,7,3,3},{1,5,2,8},{7,5,2,2},{0,6,7,3},{13,1,1,1},{5,3,4,4},{7,2,7,0},{5,8,3,0},{3,13,0,0},{0,7,9,0},{8,0,3,5},
        {1,3,7,5},{4,0,2,10},{12,0,1,3},{1,7,6,2},{3,9,0,4},{7,2,0,7},{0,1,7,8},{2,1,8,5},{0,13,1,2},{0,8,1,7},{5,0,11,0},{5,6,2,3},{0,3,0,13},{2,3,4,7},{5,6,3,2},{4,2,10,0},{3,3,7,3},{7,2,5,2},{1,1,11,3},{12,3,0,1},{5,1,1,9},{1,15,0,0},{9,7,0,0},{9,1,2,4},{0,7,3,6},{3,0,13,0},{3,0,11,2},{0,6,5,5},{8,2,2,4},{6,10,0,0},{4,8,4,0},{0,0,3,13},
        {0,4,12,0},{7,1,6,2},{3,5,0,8},{8,0,6,2},{6,2,3,5},{2,10,0,4},{4,11,0,1},{6,1,5,4},{5,1,3,7},{0,11,3,2},{4,6,0,6},{2,6,0,8},{3,1,7,5},{2,14,0,0},{2,9,2,3},{0,3,4,9},{11,0,1,4},{13,0,3,0},{8,3,0,5},{0,5,3,8},{5,11,0,0},{0,1,4,11},{2,1,9,4},{3,4,4,5},{7,1,2,6},{12,2,2,0},{9,4,1,2},{6,0,2,8},{4,6,2,4},{11,2,3,0},{3,2,2,9},{10,3,1,2},
        {1,1,2,12},{0,5,2,9},{0,1,11,4},{6,2,4,4},{2,8,2,4},{0,9,4,3},{11,0,2,3},{0,2,11,3},{6,0,7,3},{0,3,6,7},{4,5,5,2},{1,2,6,7},{7,5,1,3},{9,0,2,5},{2,6,4,4},{4,1,9,2},{4,8,2,2},{1,12,3,0},{0,9,6,1},{0,10,6,0},{3,1,5,7},{2,13,0,1},{2,2,1,11},{3,6,0,7},{5,6,5,0},{5,5,4,2},{4,0,3,9},{3,4,1,8},{0,11,2,3},{2,12,1,1},{7,1,3,5},{7,0,9,0},
        {8,0,8,0},{1,0,2,13},{3,3,10,0},{2,4,4,6},{2,3,8,3},{1,10,5,0},{7,3,0,6},{2,9,0,5},{1,4,6,5},{6,6,3,1},{5,6,0,5},{6,3,0,7},{3,10,2,1},{2,5,5,4},{3,8,4,1},{1,14,0,1},{10,3,3,0},{3,5,7,1},{1,1,3,11},{2,4,0,10},{9,3,1,3},{5,10,1,0},{3,0,6,7},{3,1,9,3},{11,2,1,2},{5,3,3,5},{0,5,1,10},{4,1,11,0},{10,2,0,4},{7,6,0,3},{2,7,0,7},{4,2,2,8},
        {6,1,7,2},{4,9,2,1},{0,0,8,8},{3,7,2,4},{9,6,0,1},{0,12,4,0},{6,7,1,2},{0,7,2,7},{1,0,10,5},{0,0,14,2},{2,7,3,4},{5,0,0,11},{7,7,1,1},{6,2,7,1},{4,5,3,4},{3,5,1,7},{5,9,1,1},{6,2,1,7},{3,2,0,11},{0,11,0,5},{3,11,2,0},{10,1,4,1},{7,0,4,5},{11,4,0,1},{10,3,0,3},{0,2,4,10},{0,15,0,1},{0,11,5,0},{6,7,2,1},{1,12,2,1},{4,1,3,8},{1,0,13,2},
        {1,8,5,2},{7,0,1,8},{3,12,1,0},{9,2,4,1},{1,7,4,4},{11,4,1,0},{4,3,8,1},{2,8,4,2},{1,11,3,1},{1,1,4,10},{4,10,2,0},{8,2,5,1},{1,0,9,6},{5,3,2,6},{0,9,7,0},{10,2,2,2},{5,8,1,2},{8,7,0,1},{0,3,12,1},{1,0,1,14},{4,8,0,4},{3,8,0,5},{4,6,5,1},{0,9,5,2},{10,2,3,1},{2,3,9,2},{1,0,12,3},{11,3,0,2},{4,5,2,5},{0,2,12,2},{9,1,0,6},{9,2,0,5},
        {1,2,7,6},{4,7,4,1},{0,12,2,2},{0,0,0,16},{2,8,3,3},{3,6,2,5},{0,6,3,7},{7,5,4,0},{3,3,3,7},{3,3,0,10},{5,0,6,5},{0,0,10,6},{8,5,3,0},{8,1,5,2},{6,0,9,1},{11,1,2,2},{2,11,2,1},{9,5,2,0},{3,0,4,9},{2,2,12,0},{2,6,6,2},{2,1,13,0},{6,0,5,5},{2,0,14,0},{2,11,1,2},{4,4,7,1},{2,0,11,3},{3,1,1,11},{2,9,4,1},{3,7,6,0},{14,0,2,0},{1,10,4,1},
        {8,0,7,1},{3,6,5,2},{0,3,11,2},{2,5,6,3},{11,1,3,1},{6,5,3,2},{3,8,1,4},{0,2,7,7},{2,10,2,2},{1,6,2,7},{11,0,0,5},{12,1,1,2},{12,1,2,1},{0,7,1,8},{0,3,9,4},{0,2,1,13},{7,1,4,4},{10,1,0,5},{4,0,8,4},{5,2,7,2},{0,2,0,14},{4,3,7,2},{2,7,1,6},{1,2,2,11},{6,3,3,4},{1,14,1,0},{2,4,6,4},{5,3,6,2},{5,3,5,3},{8,4,1,3},{1,3,0,12},{3,5,2,6},
        {1,8,7,0},{0,7,4,5},{2,1,6,7},{4,11,1,0},{7,2,4,3},{6,1,3,6},{4,5,4,3},{2,11,0,3},{1,5,7,3},{12,0,2,2},{5,0,4,7},{1,13,0,2},{7,7,2,0},{4,1,7,4},{4,5,0,7},{5,0,5,6},{6,5,4,1},{2,4,2,8},{1,10,1,4},{6,3,1,6},{3,3,8,2},{0,7,7,2},{4,4,2,6},{1,1,8,6},{1,12,0,3},{2,1,12,1},{1,9,2,4},{1,11,0,4},{2,5,2,7},{10,0,3,3},{4,6,3,3},{3,7,1,5},
        {1,9,0,6},{7,1,7,1},{1,6,5,4},{9,2,3,2},{6,2,2,6},{2,2,2,10},{8,3,3,2},{0,1,8,7},{2,0,8,6},{0,3,1,12},{9,4,2,1},{9,4,3,0},{6,2,6,2},{1,8,0,7},{5,1,10,0},{0,5,5,6},{8,2,4,2},{2,3,2,9},{6,0,3,7},{2,2,6,6},{2,6,2,6},{1,13,2,0},{9,3,0,4},{7,3,5,1},{6,5,2,3},{5,2,6,3},{2,0,12,2},{5,7,1,3},{8,1,3,4},{3,1,10,2},{1,0,15,0},{0,8,0,8},
        {5,0,7,4},{4,4,6,2},{0,1,0,15},{10,0,1,5},{7,3,4,2},{4,9,3,0},{2,5,7,2},{3,4,2,7},{8,3,2,3},{5,1,6,4},{0,10,2,4},{6,6,1,3},{6,0,0,10},{4,4,3,5},{1,3,9,3},{7,5,3,1},{3,0,7,6},{1,8,6,1},{4,3,0,9},{3,11,0,2},{6,0,6,4},{0,1,3,12},{0,4,2,10},{5,5,6,0},{4,1,4,7},{8,1,6,1},{5,6,4,1},{8,4,2,2},{4,3,1,8},{3,0,2,11},{1,11,4,0},{0,8,3,5},
        {5,1,7,3},{7,0,8,1},{4,3,5,4},{4,6,4,2},{3,2,4,7},{1,6,3,6},{0,7,8,1},{3,0,1,12},{9,1,4,2},{7,4,0,5},{1,7,0,8},{5,4,1,6},{9,1,5,1},{1,1,9,5},{4,1,1,10},{5,3,0,8},{2,2,5,7},{4,0,0,12},{9,0,7,0},{3,4,0,9},{0,2,6,8},{8,2,0,6},{3,2,6,5},{4,2,6,4},{3,6,4,3},{2,8,6,0},{5,0,3,8},{0,4,0,12},{0,16,0,0},{0,9,2,5},{4,0,11,1},{1,6,4,5},
        {0,1,6,9},{3,4,6,3},{3,0,10,3},{7,0,6,3},{1,4,9,2},{1,5,3,7},{8,5,2,1},{0,12,0,4},{7,2,3,4},{0,5,6,5},{11,1,1,3},{6,5,0,5},{2,1,5,8},{1,4,11,0},{9,1,1,5},{0,0,13,3},{5,8,2,1},{2,12,0,2},{3,3,6,4},{4,1,10,1},{4,0,5,7},{8,1,0,7},{5,1,9,1},{4,3,3,6},{0,2,2,12},{6,3,2,5},{0,0,12,4},{1,5,1,9},{2,6,5,3},{3,6,3,4},{2,12,2,0},{1,6,8,1},
        {10,1,1,4},{1,3,4,8},{7,4,4,1},{1,11,1,3},{1,2,10,3},{3,9,3,1},{8,5,1,2},{2,10,4,0},{4,2,0,10},{2,7,6,1},{8,2,3,3},{1,5,5,5},{3,1,0,12},{3,10,3,0},{8,0,5,3},{0,6,8,2},{0,3,13,0},{0,0,16,0},{1,9,4,2},{4,1,8,3},{1,6,6,3},{0,10,5,1},{0,1,12,3},{4,0,6,6},{3,8,3,2},{0,5,4,7},{1,0,14,1},{0,4,6,6},{3,9,1,3},{3,5,8,0},{3,6,6,1},{5,4,7,0},
        {3,0,12,1},{8,6,1,1},{2,9,5,0},{6,1,1,8},{4,1,2,9},{3,9,4,0},{5,2,9,0},{0,12,3,1},{1,4,10,1},{4,0,7,5},{3,1,2,10},{5,4,2,5},{5,5,5,1},{4,2,3,7},{1,7,5,3},{2,8,0,6},{8,1,2,5},{3,8,2,3},{6,1,2,7},{3,9,2,2},{9,0,0,7},{0,8,6,2},{8,4,3,1},{0,2,8,6},{6,5,1,4},{2,3,5,6},{2,10,3,1},{0,7,0,9},{4,2,7,3},{2,4,8,2},{7,1,1,7},{2,4,7,3},
        {2,4,10,0},{0,1,10,5},{4,7,1,4},{0,10,4,2},{9,0,1,6},{1,9,6,0},{3,3,4,6},{4,5,7,0},{5,5,2,4},{2,8,1,5},{2,3,6,5},{0,1,1,14},{3,2,3,8},{10,1,2,3},{9,1,6,0},{3,4,3,6},{2,2,0,12},{0,0,9,7},{4,0,9,3},{7,0,5,4},{4,5,6,1},{2,5,1,8},{2,5,9,0},{3,5,4,4},{1,3,11,1},{7,1,5,3},{3,2,7,4},{1,4,2,9},{1,11,2,2},{2,2,3,9},{5,0,10,1},{3,2,11,0},
        {1,10,3,2},{8,3,4,1},{3,6,7,0},{0,7,5,4},{1,3,3,9},{2,2,10,2},{1,9,5,1},{0,5,0,11},{3,0,3,10},{0,4,8,4},{2,7,7,0},{2,0,2,12},{1,2,11,2},{6,3,7,0},{0,6,2,8},{0,10,1,5},{0,9,0,7},{6,4,4,2},{6,0,1,9},{1,5,10,0},{5,4,6,1},{5,5,3,3},{0,0,4,12},{0,3,2,11},{1,4,1,10},{3,0,9,4},{5,5,0,6},{1,7,8,0},{2,0,3,11},{6,4,1,5},{10,0,6,0},{0,6,0,10},
        {0,4,11,1},{3,1,6,6},{2,5,8,1},{0,2,10,4},{3,1,11,1},{6,6,2,2},{1,1,10,4},{2,1,2,11},{6,1,8,1},{0,2,13,1},{0,7,6,3},{6,8,2,0},{3,0,0,13},{4,4,4,4},{6,2,0,8},{7,3,1,5},{0,11,4,1},{6,7,0,3},{2,6,3,5},{5,2,1,8},{7,1,8,0},{5,5,1,5},{1,8,3,4},{8,2,6,0},{6,0,10,0},{5,6,1,4},{1,4,4,7},{2,7,4,3},{1,4,8,3},{5,4,3,4},{1,10,2,3},{2,9,1,4},
        {2,2,11,1},{2,5,0,9},{0,0,1,15},{0,0,11,5},{0,4,7,5},{0,1,15,0},{2,1,0,13},{0,3,10,3},{8,0,2,6},{3,3,2,8},{3,5,5,3},{1,7,1,7},{1,3,2,10},{4,0,4,8},{2,0,9,5},{1,1,1,13},{2,2,7,5},{2,1,10,3},{4,2,1,9},{4,3,6,3},{1,3,5,7},{2,5,3,6},{1,0,8,7},{5,0,2,9},{2,8,5,1},{1,6,0,9},{0,0,5,11},{0,4,9,3},{2,0,7,7},{1,7,2,6},{2,1,1,12},{2,4,9,1},
        {0,5,7,4},{6,0,4,6},{3,2,10,1},{0,6,1,9},{2,6,1,7},{0,5,8,3},{4,1,0,11},{1,2,4,9},{4,1,5,6},{6,1,0,9},{1,4,3,8},{4,5,1,6},{1,0,5,10},{5,3,1,7},{0,9,1,6},{2,0,1,13},{2,0,6,8},{8,1,1,6},{1,5,9,1},{0,6,9,1},{0,3,5,8},{0,2,9,5},{5,2,8,1},{1,1,14,0},{3,2,9,2},{5,0,8,3},{0,5,10,1},{5,2,3,6},{2,6,7,1},{2,3,0,11},{0,1,9,6},{1,0,4,11},
        {3,0,5,8},{0,0,15,1},{2,4,5,5},{0,3,7,6},{2,0,0,14},{1,1,12,2},{2,6,8,0},{3,1,8,4},{0,1,5,10}
    };

    // All total orderings for 16 pixels [0,2] 2-bit selectors.
    // BC1 selector order: 0, 1, 2
    // Note this is different from g_unique_total_orders4[], which reorders the selectors into linear order.
    const uint32_t NUM_UNIQUE_TOTAL_ORDERINGS3 = 153;
    static uint8_t g_unique_total_orders3[NUM_UNIQUE_TOTAL_ORDERINGS3][3] =
    {
        {6,0,10},{3,6,7},{3,0,13},{13,3,0},{12,4,0},{9,1,6},{2,13,1},{4,7,5},{7,5,4},{9,6,1},{7,4,5},{8,6,2},{16,0,0},{10,6,0},{2,7,7},
        {0,0,16},{0,3,13},{1,15,0},{0,2,14},{1,4,11},{15,1,0},{1,12,3},{9,2,5},{14,1,1},{8,2,6},{3,3,10},{4,2,10},{14,0,2},{0,14,2},{1,7,8},{6,6,4},
        {11,5,0},{6,4,6},{11,3,2},{4,3,9},{7,1,8},{10,4,2},{12,1,3},{11,0,5},{9,3,4},{1,0,15},{9,0,7},{2,6,8},{12,2,2},{6,2,8},{6,8,2},{15,0,1},
        {4,8,4},{0,4,12},{8,5,3},{5,9,2},{11,2,3},{12,3,1},{6,3,7},{1,1,14},{2,9,5},{1,8,7},{4,10,2},{7,7,2},{13,1,2},{0,15,1},{3,2,11},{7,0,9},
        {4,4,8},{3,8,5},{0,5,11},{13,2,1},{1,10,5},{4,11,1},{3,10,3},{5,10,1},{10,2,4},{0,6,10},{14,2,0},{11,4,1},{3,12,1},{1,13,2},{1,5,10},{5,11,0},
        {12,0,4},{8,1,7},{6,10,0},{3,13,0},{7,2,7},{0,7,9},{5,8,3},{0,12,4},{11,1,4},{13,0,3},{0,16,0},{5,7,4},{10,3,3},{10,0,6},{0,13,3},{4,6,6},
        {2,8,6},{2,5,9},{7,8,1},{2,1,13},{2,0,14},{7,3,6},{5,1,10},{3,11,2},{5,4,7},{8,3,5},{10,5,1},{6,9,1},{1,3,12},{4,5,7},{2,2,12},{4,1,11},
        {0,8,8},{4,12,0},{6,5,5},{8,7,1},{5,5,6},{3,7,6},{7,9,0},{4,9,3},{0,10,6},{8,0,8},{5,3,8},{10,1,5},{6,1,9},{7,6,3},{9,5,2},{0,1,15},
        {9,7,0},{2,14,0},{3,4,9},{8,4,4},{9,4,3},{0,9,7},{1,9,6},{3,9,4},{5,2,9},{2,3,11},{5,6,5},{1,14,1},{6,7,3},{2,4,10},{2,12,2},{8,8,0},
        {2,10,4},{4,0,12},{0,11,5},{2,11,3},{1,11,4},{3,5,8},{5,0,11},{3,1,12},{1,2,13},{1,6,9}
    };

    // For each total ordering, this table indicates which other total orderings are likely to improve quality using a least squares pass. Each array is sorted by usefulness.
    static uint16_t g_best_total_orderings4[NUM_UNIQUE_TOTAL_ORDERINGS4][MAX_TOTAL_ORDERINGS4] =
    {
#if RGBCX_USE_SMALLER_TABLES
        { 202,120,13,318,15,23,403,450,5,51,260,128,77,21,33,494,515,523,4,141,269,1,2,700,137,49,48,102,7,64,753,82  },
        { 13,141,23,217,115,51,77,2,64,21,0,4,5,317,137,269,202,33,318,7,291,352,9,10,3,180,32,6,365,102,341,349  },
        { 29,58,262,1,52,74,6,171,5,287,151,334,27,500,75,26,331,223,53,635,220,19,50,45,46,17,14,396,163,409,324,70  },
        { 40,51,33,453,14,23,62,56,12,196,730,475,153,99,403,775,117,130,585,34,4,17,162,11,139,57,102,38,108,47,123,440  },
        { 33,23,51,13,102,64,202,128,12,40,15,196,153,10,1,2,77,99,141,0,515,5,117,3,120,403,700,165,22,14,269,453  },
        { 13,23,51,4,77,141,202,33,115,64,32,128,0,11,177,40,15,102,2,217,7,137,269,21,90,59,515,1,180,403,22,6  },
        { 26,235,19,47,648,624,78,145,27,112,122,64,444,6,630,453,25,42,65,130,711,85,390,113,416,108,665,29,730,138,644,95  },
        { 64,141,352,751,217,247,237,437,177,269,86,954,947,875,32,318,95,77,304,92,597,180,232,291,128,864,349,588,372,202,312,1  },
        { 642,898,180,638,901,341,82,197,10,951,15,515,165,762,700,253,811,753,752,365,143,479,244,569,8,110,351,873,55,31,499,116  },
        { 221,23,51,125,438,254,13,21,39,49,308,656,0,115,530,159,158,401,30,166,912,386,165,688,518,9,105,627,424,22,421,33  },
        { 143,31,1,44,197,8,180,125,116,55,13,498,23,341,638,242,93,15,2,141,0,901,752,115,36,206,165,479,338,365,515,762  },
        { 12,23,51,13,14,15,37,99,515,38,700,117,2,196,134,153,753,64,54,33,128,120,21,0,328,5,139,82,453,719,457,1  },
        { 13,15,23,515,961,700,457,753,51,115,4,165,197,2,38,569,1,474,0,37,99,719,5,12,629,14,11,3,33,77,64,10  },
        { 15,515,700,753,1,0,2,4,3,23,134,12,961,5,10,197,11,33,82,120,457,51,165,7,6,341,217,21,77,9,40,180  },
        { 13,51,23,457,719,961,730,401,165,453,0,117,386,15,134,1,758,153,12,54,515,99,11,2,700,5,753,4,308,33,6,899  },
        { 134,898,82,117,13,33,77,102,23,260,341,351,120,901,197,153,961,111,196,110,180,457,854,10,450,8,165,40,4,115,0,365  },
        { 60,18,126,167,35,16,191,71,24,92,121,271,68,107,212,146,118,150,199,7,21,1,9,575,727,5,566,48,0,132,108,273  },
        { 62,136,129,123,128,41,162,17,249,211,214,789,618,710,38,678,248,507,57,64,152,269,119,3,177,183,597,106,4,179,216,90  },
        { 403,523,51,475,494,453,817,899,202,23,450,13,421,120,102,730,33,128,4,1,805,5,7,153,757,260,318,196,77,457,326,65  },
        { 4,59,3,62,12,33,56,193,27,21,102,17,40,77,76,84,32,0,6,123,119,177,128,11,18,611,605,25,13,51,73,210  },
        { 43,20,319,422,414,945,0,7,819,61,5,376,325,173,804,904,470,693,97,707,14,49,22,104,147,107,95,32,426,1,330,577  },
        { 13,23,51,2,0,115,4,141,217,33,10,77,1,15,64,180,3,515,7,6,22,102,11,5,40,9,165,700,202,197,317,341  },
        { 28,49,0,105,1,24,65,159,35,55,95,239,16,2,109,7,9,14,170,320,347,168,424,158,10,301,124,5,67,21,64,36  },
        { 15,515,700,753,0,1,13,2,117,4,12,10,5,165,457,3,9,134,11,7,6,51,77,64,961,82,33,197,14,341,120,141  },
        { 7,71,14,149,97,18,60,16,150,92,398,189,140,124,24,273,35,2,69,302,154,68,0,336,517,43,66,28,118,251,230,1  },
        { 4,102,33,77,40,59,11,624,210,12,128,342,5,503,91,139,64,32,25,494,202,678,416,0,403,275,21,450,196,318,523,177  },
        { 25,19,42,6,122,813,256,235,85,26,436,53,297,573,680,390,445,63,27,416,80,233,65,73,389,283,45,605,194,17,250,343  },
        { 402,102,202,128,33,300,403,23,12,77,40,21,342,117,483,99,25,494,6,4,63,32,84,569,139,757,475,318,19,26,196,134  },
        { 158,9,0,109,39,49,65,22,35,168,55,24,68,124,159,16,185,344,333,154,254,272,175,289,1,577,95,28,105,810,30,169  },
        { 197,180,115,237,498,165,2,5,287,546,400,3,61,34,509,13,297,80,341,52,45,186,58,881,23,873,468,176,64,17,311,250  },
        { 120,968,373,260,704,110,450,202,137,318,77,95,269,326,217,717,661,652,851,349,93,1,518,98,827,291,21,177,82,33,848,719  },
        { 44,116,144,268,434,489,367,384,98,127,918,93,948,31,206,940,855,0,203,137,9,22,617,141,332,105,393,492,959,282,299,131  },
        { 13,77,23,33,51,0,64,141,102,4,2,115,1,6,202,15,10,128,269,7,177,180,3,40,22,11,515,217,117,318,700,137  },
        { 15,515,700,753,4,11,141,40,165,23,64,180,13,202,32,3,51,125,5,197,21,128,0,93,77,1,120,82,269,117,110,59  },
        { 176,231,585,62,34,14,412,161,56,236,527,57,17,3,51,202,4,23,369,283,128,13,472,440,84,361,136,457,381,130,719,53  },
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        { 23,51,13,453,64,403,12,21,5,202,128,475,165,141,523,95,125,115,3,1,4,730,120,32,2,494,180,719,457,197,450,401  },
        { 204,74,135,66,6,174,192,7,138,172,85,353,348,580,280,97,95,500,29,64,426,32,87,889,65,81,25,2,52,43,568,673  },
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        { 16,92,60,35,7,18,24,68,150,149,14,71,0,375,97,126,118,107,230,191,246,273,140,55,175,653,9,575,2,28,566,517  },
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        { 19,27,26,813,80,297,17,495,436,53,73,200,4,378,250,59,106,25,45,128,361,42,113,469,122,390,77,40,736,6,11,136  },
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        { 90,205,257,184,32,179,460,5,245,45,2,288,769,524,57,21,152,229,17,1,497,4,292,59,619,452,432,76,476,11,266,14  },
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        { 47,130,711,108,453,412,730,196,390,283,78,27,51,183,381,236,128,200,719,14,153,472,503,34,59,250,3,4,57,803,123,432  },
        { 12,277,51,474,111,153,23,99,13,37,961,94,629,542,569,431,79,139,38,134,117,453,33,188,196,40,115,15,11,157,401,515  },
        { 17,495,469,106,26,378,80,27,161,483,19,742,527,436,383,862,73,136,53,814,297,6,119,84,62,56,25,3,209,611,4,128  },
        { 81,681,636,91,0,750,370,104,718,138,18,693,173,784,29,397,348,74,192,673,174,65,6,207,64,280,306,52,671,32,355,319  },
        { 15,515,700,753,33,77,4,102,115,117,40,13,1,153,134,11,5,217,23,196,2,21,3,317,32,365,0,341,291,59,12,51  },
        { 0,9,28,35,68,1,65,67,101,39,69,175,16,238,13,22,96,124,18,24,251,30,55,12,23,2,50,141,114,5,154,103  },
        { 23,33,77,13,117,40,11,102,64,4,51,403,153,453,10,0,196,134,128,65,12,291,86,99,95,59,15,141,202,180,137,719  },
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        { 1,22,2,0,36,67,28,5,49,95,12,50,168,83,105,55,7,9,14,194,103,23,114,21,584,46,10,13,38,69,208,159  },
        { 269,141,13,202,33,180,318,77,291,137,102,352,128,23,349,51,31,217,372,317,125,197,44,21,11,5,901,1,18,0,4,494  },
        { 435,144,274,88,203,418,30,1,190,410,96,778,100,530,521,326,466,795,686,166,960,321,382,264,367,822,131,31,692,9,213,93  },
        { 76,72,90,21,37,179,12,205,32,428,148,38,308,405,4,413,57,184,749,245,316,221,54,645,288,1,152,155,464,257,2,14  },
        { 77,33,64,102,13,141,23,2,40,1,51,10,0,115,6,180,202,128,4,3,177,269,15,7,22,165,291,14,217,318,137,11  },
        { 397,81,4,32,65,788,693,804,681,11,249,21,91,64,690,494,3,0,422,56,348,725,194,123,23,59,523,319,61,510,95,90  },
        { 60,126,16,7,92,121,314,246,35,107,150,132,14,146,24,18,199,298,232,71,359,140,672,97,392,649,5,423,95,21,22,388  },
        { 15,515,141,217,115,700,13,23,120,317,753,180,33,260,110,137,341,51,1,365,4,77,64,202,0,40,36,352,197,269,10,21  },
        { 111,134,117,474,23,13,961,12,569,431,37,15,51,115,515,700,277,99,753,38,197,405,457,4,72,94,629,45,11,89,54,148  },
        { 23,13,51,5,1,15,2,21,12,202,141,0,515,165,120,32,4,64,700,3,115,197,269,125,753,7,9,128,6,180,453,403  },
        { 13,141,4,23,5,2,115,217,202,51,180,137,269,352,77,1,317,3,21,318,0,15,9,64,10,197,11,341,33,515,752,7  },
        { 165,125,197,13,391,21,23,558,48,380,97,120,298,33,14,426,66,115,32,386,900,180,6,98,357,237,326,509,51,278,221,457  },
        { 120,82,15,260,515,1,351,77,450,700,13,21,141,23,753,202,217,93,110,33,51,854,5,128,326,102,137,180,817,48,269,352  },
        { 23,13,15,51,515,700,961,753,0,457,1,2,4,115,10,453,569,5,33,165,11,719,14,40,64,197,3,21,474,629,38,401  },
        { 264,166,39,30,9,100,435,254,93,921,190,363,1,625,411,382,897,656,203,478,404,812,438,110,473,88,18,691,156,141,274,272  },
        { 9,0,252,100,166,39,101,265,364,68,88,329,520,18,419,676,118,167,404,604,16,1,21,30,212,158,553,49,382,274,48,13  },
        { 15,515,700,753,4,11,141,5,3,13,202,1,180,21,2,165,269,23,40,64,0,318,12,32,128,51,77,117,523,197,120,457  },
        { 24,1,2,69,35,16,67,18,14,50,0,46,68,9,38,7,133,71,83,149,28,108,189,218,65,114,238,29,75,54,5,96  },
        { 90,289,214,64,874,13,77,712,66,751,4,23,51,192,32,0,202,194,312,177,33,65,234,104,875,288,59,5,835,416,102,95  },
        { 0,9,49,127,98,31,301,28,371,159,1,395,512,737,158,761,916,623,16,44,242,39,170,18,293,105,24,272,101,22,23,385  },
        { 17,62,136,214,123,129,32,292,119,209,710,106,141,162,128,64,45,4,77,249,11,618,211,3,207,130,519,183,38,177,21,269  },
        { 5,107,581,356,279,32,441,362,493,660,13,298,0,534,49,147,21,22,132,121,97,423,7,590,259,683,14,786,126,508,60,246  },
        { 51,13,15,730,453,23,515,719,386,457,12,700,403,475,899,1,6,523,753,421,99,401,165,33,2,19,361,5,0,670,120,27  },
        { 49,28,9,159,272,22,254,131,158,327,95,105,0,39,35,168,347,286,374,55,65,627,424,912,68,578,1,24,239,175,688,169  },
        { 15,515,700,33,753,4,77,141,341,317,1,10,13,180,102,22,40,117,115,365,5,901,23,197,134,11,217,351,64,82,21,137  },
        { 134,15,13,515,23,700,12,753,51,474,37,961,197,10,457,569,4,0,99,2,115,38,165,153,94,3,139,11,1,82,33,5  },
        { 7,2,20,58,5,14,128,66,6,29,32,43,21,52,16,38,631,61,74,97,46,135,113,25,202,192,13,0,884,45,112,87  },
        { 77,13,33,202,23,128,102,4,141,342,117,0,269,318,134,22,11,21,32,153,403,291,49,64,137,51,40,15,494,5,196,98  },
        { 2,1,14,6,46,38,29,65,5,36,67,0,103,7,22,86,133,50,108,208,52,83,24,323,283,69,28,18,10,25,23,75  },
        { 15,515,700,753,1,5,4,2,3,13,0,11,180,341,12,33,10,197,134,365,77,23,21,901,6,117,165,7,37,32,17,102  },
        { 203,268,206,93,417,940,31,8,120,137,44,499,959,473,202,692,728,559,0,260,10,326,141,564,817,127,341,1,450,22,110,23  },
        { 15,82,515,120,700,0,10,753,33,8,64,165,110,31,260,93,13,197,23,22,40,4,351,44,77,9,11,153,102,51,1,196  },
        { 60,0,16,7,14,43,20,71,28,10,2,22,154,18,13,24,92,1,51,576,35,615,805,925,68,126,124,149,97,64,23,55  },
        { 19,6,26,80,5,84,27,17,25,2,504,129,45,240,56,123,4,119,618,1,76,106,64,51,14,3,128,65,32,710,0,42  },
        { 15,515,700,753,13,4,77,23,33,51,0,5,8,10,11,31,44,1,82,22,202,64,110,102,93,21,291,40,141,180,9,49  },
        { 195,98,271,223,132,167,146,407,1,360,121,834,393,591,212,199,293,259,522,107,354,147,156,191,807,590,48,18,125,16,765,541  },
        { 128,202,77,210,402,318,33,102,6,40,403,29,342,269,196,757,99,139,2,111,42,4,494,117,275,300,13,12,678,0,177,122  },
        { 13,33,23,40,51,102,4,117,77,64,134,0,128,153,202,196,453,11,15,12,1,22,403,141,59,14,10,475,515,65,700,95  },
        { 7,16,14,24,18,2,28,0,92,71,1,22,6,35,60,20,168,10,154,118,5,302,124,69,97,109,703,158,420,12,149,66  },
        { 15,1,515,23,0,13,700,2,51,753,180,5,120,165,197,21,115,4,33,9,141,7,12,6,3,457,386,202,260,523,8,31  },
        { 60,107,121,132,146,126,199,279,150,92,16,649,441,35,955,7,21,0,423,5,18,195,598,298,493,356,32,653,22,362,953,10  },
        { 31,44,98,276,284,299,116,935,9,201,0,131,39,127,144,662,1,137,371,492,567,489,93,254,49,268,22,28,30,293,434,737  },
        { 13,15,23,515,700,0,1,51,753,4,2,10,77,202,5,115,3,165,197,457,9,12,11,961,33,120,22,141,180,7,6,40  },
        { 123,162,184,257,17,183,229,130,129,3,84,136,99,152,556,383,57,497,12,205,4,62,56,452,80,266,128,14,40,119,27,106  },
        { 196,33,117,40,153,23,134,13,51,102,453,0,15,475,12,14,515,2,22,700,4,21,753,64,401,670,730,1,9,11,10,99  },
        { 224,219,187,131,258,385,442,871,836,31,98,908,44,574,127,944,137,839,116,36,613,1,254,39,926,160,829,96,93,371,860,827  },
        { 121,195,156,132,146,360,590,407,786,522,883,591,259,929,626,941,150,687,5,55,296,379,467,178,586,465,279,21,1,13,60,354  },
        { 2,1,14,29,6,5,46,52,38,19,114,75,26,65,108,96,25,50,36,70,103,309,17,236,218,74,12,86,0,3,10,112  },
        { 15,515,82,700,120,753,10,0,8,197,260,165,351,64,13,110,117,93,31,1,9,33,22,23,457,44,450,77,102,898,40,49  },
        { 7,66,97,2,172,74,226,52,29,135,192,232,43,324,92,5,38,20,222,14,6,568,87,107,353,620,580,16,138,174,448,32  },
        { 62,129,123,162,136,249,618,183,507,57,4,152,17,59,11,184,117,77,3,128,211,41,130,205,12,40,33,106,64,229,38,313  },
        { 1,13,15,2,4,515,23,0,3,115,700,5,51,77,341,141,753,180,33,217,197,202,901,6,21,165,11,365,318,317,10,102  },
        { 6,26,235,19,145,47,112,78,64,27,453,95,29,444,25,624,85,108,648,70,32,130,74,42,711,630,632,138,65,122,113,730  },
        { 23,51,12,15,13,99,515,153,117,10,700,37,120,82,165,2,753,64,128,0,403,3,5,1,134,197,453,31,202,457,110,21  },
        { 16,24,18,71,64,35,92,7,246,146,9,108,60,118,199,5,140,2,267,0,230,830,32,133,1,68,50,330,247,563,36,12  },
        { 15,515,700,753,0,1,13,2,23,3,4,217,51,5,115,8,9,180,341,10,7,6,317,77,33,372,901,197,365,11,120,165  },
        { 234,639,178,202,77,142,5,455,450,49,416,0,147,427,198,21,315,329,13,318,325,557,120,344,113,259,22,128,61,105,23,494  },
        { 1,31,36,44,141,180,55,2,64,22,98,116,13,352,0,115,10,127,5,164,253,498,237,165,341,197,4,86,15,170,125,23  },
        { 15,120,13,141,23,260,217,515,1,77,51,110,180,700,317,82,269,137,115,202,21,753,64,5,351,291,0,450,352,93,36,326  },
        { 26,6,112,396,19,145,25,122,648,287,42,74,624,222,416,45,138,66,644,151,113,651,29,573,64,280,445,27,525,85,70,58  },
        { 156,360,5,146,121,21,271,522,354,132,49,13,18,195,16,340,60,591,446,586,727,0,107,407,167,48,1,463,199,566,32,23  },
        { 5,61,49,147,178,612,660,120,21,182,23,427,259,683,33,4,77,70,13,3,376,98,64,0,481,344,48,595,291,263,141,51  },
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        { 74,145,6,66,25,204,42,29,222,337,138,26,7,525,192,174,746,287,544,135,415,2,609,632,112,64,87,0,85,45,712,396  },
        { 77,33,102,15,217,13,23,141,202,515,51,700,291,4,269,753,317,180,21,64,318,115,128,0,275,2,352,196,3,5,137,11  },
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        { 1,372,141,5,21,77,225,744,96,30,23,349,13,291,269,284,69,442,459,144,303,839,217,622,160,330,260,48,120,410,189,352  },
        { 66,222,2,74,29,87,135,6,7,145,52,25,294,337,226,172,138,331,42,70,97,112,26,1,632,192,43,5,415,609,461,353  },
        { 45,17,106,209,5,2,21,29,48,207,3,186,243,155,255,263,454,119,400,496,270,14,290,62,425,1,171,32,659,52,38,56  },
        { 93,88,141,120,30,213,260,373,100,717,459,82,110,1,166,450,180,321,217,372,36,269,131,225,22,352,326,466,473,187,244,410  },
        { 266,57,152,381,313,471,12,229,99,369,339,62,157,3,4,37,77,38,188,17,11,162,40,184,129,59,475,775,128,452,403,453  },
        { 217,352,317,141,752,15,180,515,372,365,700,341,753,349,77,21,291,1,115,244,64,120,13,98,269,82,5,498,864,351,23,144  },
        { 14,514,369,102,403,377,51,719,880,153,23,13,457,11,485,4,401,12,328,453,33,40,117,57,629,38,730,236,134,670,361,961  },
        { 107,7,172,14,92,135,2,359,60,314,46,16,126,278,232,150,279,32,38,392,298,5,35,97,24,192,259,288,330,52,356,312  },
        { 0,4,25,13,59,90,65,23,26,19,18,12,5,216,91,51,389,33,77,11,22,85,27,81,21,177,746,45,42,194,37,123  },
        { 5,49,315,202,416,77,455,639,450,21,197,137,350,13,408,0,329,318,494,344,61,402,64,509,347,120,113,48,95,713,308,401  },
        { 130,47,381,390,59,90,200,214,289,6,65,472,29,64,874,648,50,751,624,26,52,32,4,194,875,714,85,249,247,33,881,19  },
        { 51,23,453,13,719,12,457,165,37,730,99,4,386,197,401,17,11,2,3,15,5,961,475,6,515,64,54,700,32,115,0,403  },
        { 15,515,1,13,700,2,23,0,753,5,3,180,51,4,165,12,141,21,197,457,7,115,6,9,352,10,120,202,8,341,11,77  },
        { 0,9,1,67,35,28,68,16,24,65,18,69,50,114,103,12,22,13,5,101,2,96,23,83,149,21,39,55,7,175,433,124  },
        { 28,105,22,0,1,320,170,9,49,301,109,95,127,31,98,55,65,35,2,24,168,159,36,713,16,740,13,338,21,44,512,23  },
        { 13,77,4,51,23,33,102,202,128,59,40,0,64,141,117,403,115,11,15,318,153,269,22,515,475,134,10,494,177,1,90,210  },
        { 13,23,0,51,77,33,2,141,4,10,1,64,115,102,3,6,22,15,217,11,180,7,40,515,165,202,177,9,269,128,700,5  },
        { 456,116,492,8,949,268,867,391,203,51,499,13,719,386,31,791,457,918,125,10,23,93,479,685,417,0,22,338,506,551,870,730  },
        { 17,237,45,180,106,62,32,64,115,41,136,498,255,21,197,129,241,13,3,227,23,352,165,752,350,365,449,155,4,546,476,38  },
        { 1,15,180,515,0,2,341,700,901,352,4,141,13,3,752,5,753,217,317,115,365,23,197,21,51,165,31,6,269,202,77,7  },
        { 205,141,216,269,497,4,588,76,59,152,128,452,79,77,875,11,72,94,188,217,352,12,247,37,90,64,32,1,474,23,947,372  },
        { 64,247,217,237,317,180,752,115,349,141,498,13,437,304,23,372,352,164,579,291,33,864,177,197,0,490,72,10,482,77,269,51  },
        { 2,1,0,13,15,141,3,77,5,515,64,33,23,180,6,700,4,117,217,7,10,11,102,165,753,197,115,134,40,352,12,269  },
        { 11,40,38,328,33,542,12,313,41,339,23,157,377,117,369,51,471,99,775,485,13,305,457,57,14,475,37,248,4,54,188,719  },
        { 33,77,102,40,13,23,0,51,4,128,64,202,117,141,22,196,153,10,134,15,59,269,1,137,65,11,403,318,453,86,515,177  },
        { 472,80,34,250,495,161,17,14,469,176,128,4,389,106,283,436,216,527,3,297,483,177,53,56,231,194,119,84,719,57,255,59  },
        { 317,352,180,141,217,752,115,341,365,244,1,269,202,901,253,15,21,498,372,4,137,515,13,2,700,318,5,197,23,143,753,349  },
        { 9,39,101,18,265,100,333,520,252,16,0,329,593,1,553,364,68,167,310,30,121,254,118,158,363,166,60,604,272,24,286,404  },
        { 15,515,1,180,700,901,0,2,753,341,752,4,3,13,115,365,317,5,23,197,141,217,165,352,6,22,36,9,137,51,7,10  },
        { 131,39,9,829,166,613,578,827,1,30,716,254,100,98,31,224,0,406,228,310,616,219,44,846,127,190,938,96,265,371,856,438  },
        { 17,64,62,106,141,751,136,292,32,129,352,41,38,476,86,128,214,237,5,177,123,209,217,45,269,954,162,710,180,3,90,4  },
        { 25,42,235,65,650,736,605,6,630,85,123,343,233,256,26,122,63,389,141,249,416,444,368,194,19,108,138,174,90,0,544,511  },
        { 184,229,152,57,266,432,497,452,17,381,619,257,313,12,4,205,59,3,99,471,157,128,5,129,339,369,77,11,32,45,202,2  },
        { 137,202,160,860,141,30,93,567,36,276,295,261,131,39,9,964,201,843,1,98,800,318,116,22,943,187,10,219,206,44,269,535  },
        { 0,493,125,64,49,9,279,10,35,18,93,55,293,31,14,13,194,165,325,48,22,132,21,107,98,389,44,581,342,259,174,137  },
        { 15,515,700,753,4,33,13,77,23,5,51,32,102,40,93,11,349,141,21,8,82,202,64,31,110,10,117,0,1,44,3,318  },
        { 110,253,854,811,352,141,244,951,180,642,661,384,498,143,752,317,911,10,269,206,559,351,261,120,902,533,922,959,365,160,332,217  },
        { 2,29,70,1,75,52,6,220,26,112,145,331,74,163,19,69,38,324,46,58,14,5,25,21,278,223,50,307,66,7,67,409  },
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        { 1,15,23,13,120,141,51,515,202,21,700,165,0,180,137,2,5,77,128,93,753,260,269,197,326,33,110,352,82,102,318,48  },
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        { 574,187,384,926,860,110,258,434,269,531,141,244,160,261,253,116,699,959,940,717,533,36,219,31,902,661,871,295,201,352,10,260  },
        { 156,354,296,1,182,586,64,379,340,937,850,698,31,48,98,44,120,18,163,23,30,658,195,125,77,284,223,291,774,481,96,39  },
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        { 31,98,127,9,0,105,22,28,44,512,293,395,299,1,242,49,685,763,320,599,125,116,109,276,284,95,870,159,23,456,36,900  },
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        { 1,64,442,303,284,349,202,141,622,67,154,447,260,44,652,429,9,335,237,919,197,98,167,33,682,269,547,77,863,411,340,201  },
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        { 99,139,12,453,196,277,775,40,475,33,23,401,215,51,11,14,77,111,313,130,38,211,37,266,129,15,339,153,719,3,369,515  },
        { 33,77,102,4,23,128,13,141,202,64,51,0,40,59,269,115,117,137,153,1,318,11,10,177,15,134,22,90,196,2,403,32  },
        { 7,2,14,58,70,112,16,5,87,38,46,52,6,128,135,1,32,21,155,29,66,64,0,97,92,186,172,294,13,23,20,37  },
        { 15,13,515,1,700,2,23,0,753,5,3,4,51,10,341,115,365,180,11,33,317,77,6,7,217,12,197,165,117,9,64,102  },
        { 2,1,14,29,75,69,67,6,52,46,38,24,103,220,83,25,70,87,262,74,96,267,50,366,26,16,226,394,357,66,108,19  },
        { 9,105,18,39,1,0,16,557,101,272,252,890,326,49,265,21,137,100,23,938,13,310,159,5,31,24,254,51,30,128,202,132  },
        { 80,209,45,61,667,17,6,106,5,2,151,29,483,255,454,833,27,311,112,19,738,378,1,58,113,26,25,469,119,887,32,64  },
        { 13,23,51,15,5,1,515,0,21,2,12,141,700,165,202,115,753,32,180,4,3,197,10,120,457,9,269,128,64,341,7,33  },
        { 99,12,453,277,139,157,369,474,339,51,38,23,37,196,188,401,775,111,11,313,328,475,153,266,4,471,79,40,33,629,102,14  },
        { 7,92,16,232,97,140,126,14,60,107,66,35,298,387,314,104,246,462,441,150,0,38,24,2,172,357,230,330,5,633,22,289  },
        { 13,77,23,202,318,141,33,4,51,269,102,177,115,403,137,2,40,494,90,11,342,128,31,117,21,32,7,12,64,134,14,10  },
        { 13,2,0,23,141,1,77,3,180,33,6,64,15,10,115,51,4,5,217,197,7,165,515,102,22,11,700,269,40,352,177,14  },
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        { 20,43,198,325,173,904,104,234,66,147,77,319,416,422,97,426,5,0,7,450,861,202,712,725,2,32,639,376,38,324,945,315  },
        { 105,0,9,28,49,301,170,1,127,159,22,16,31,98,512,623,24,109,158,395,35,68,371,65,713,55,2,242,293,21,44,18  },
        { 213,88,689,466,230,30,321,435,699,352,217,201,795,831,144,854,1,443,96,539,530,840,418,251,855,190,93,100,669,31,957,662  },
        { 130,453,47,196,4,57,14,59,236,711,51,153,730,77,412,381,23,202,108,128,361,13,283,117,11,719,200,46,34,78,210,2  },
        { 1,2,5,14,0,50,36,22,38,46,65,67,12,86,114,28,103,29,208,7,10,128,21,83,218,23,96,54,194,6,133,51  },
        { 6,26,74,19,165,453,14,730,1,125,197,50,29,51,138,357,13,2,108,391,70,719,46,457,47,500,386,262,112,23,235,52  },
        { 9,10,376,20,43,0,49,18,30,120,2,33,325,104,501,470,77,788,725,102,523,39,858,5,904,414,174,55,137,37,342,13  },
        { 15,515,700,753,0,1,13,23,51,77,120,202,341,82,5,4,9,260,2,137,141,128,115,351,901,8,180,10,197,21,450,33  },
        { 105,131,272,578,9,49,371,219,159,616,286,320,224,187,716,98,28,22,0,623,127,258,910,737,385,31,239,347,254,109,424,95  },
        { 457,51,13,23,961,12,719,99,453,15,4,515,165,401,629,3,700,11,17,14,2,37,753,41,57,569,38,45,0,33,5,32  },
        { 202,120,5,33,318,77,450,102,1,260,403,128,494,21,165,13,269,12,326,23,342,523,402,2,817,64,15,141,125,82,457,475  },
        { 141,269,352,217,180,64,349,137,202,160,317,15,372,515,700,752,318,753,244,13,437,291,165,864,22,237,5,82,954,21,77,418  },
        { 70,29,2,145,74,112,26,6,75,52,19,66,632,1,87,220,5,135,163,287,307,25,226,7,58,396,294,278,113,409,69,151  },
        { 82,351,317,15,752,180,898,352,141,901,515,341,10,700,365,1,753,498,0,217,253,115,55,854,33,5,143,32,21,160,36,197  },
        { 39,9,310,254,0,30,101,49,252,272,100,265,105,455,159,557,190,333,286,688,18,166,1,158,709,16,625,627,31,131,327,329  },
        { 2,58,29,5,1,151,186,52,70,45,7,549,14,75,112,400,113,155,61,46,227,163,311,315,66,6,307,27,17,220,287,74  },
        { 141,217,13,21,352,23,269,77,180,115,317,64,202,15,349,137,5,51,165,291,318,752,372,4,0,102,33,365,197,32,341,125  },
        { 68,35,0,9,65,101,149,124,24,154,175,16,28,7,67,1,18,189,114,398,55,14,345,39,118,133,69,2,230,429,71,283  },
        { 66,7,29,2,112,52,20,43,97,151,74,192,135,5,173,525,337,45,145,58,415,25,14,32,644,70,544,226,222,21,6,580  },
        { 31,125,44,22,116,299,242,55,1,170,64,36,479,870,456,685,10,599,558,0,268,506,28,740,23,903,492,164,393,206,2,86  },
        { 188,11,79,12,99,377,94,33,542,339,40,474,111,37,4,51,102,453,139,775,13,475,23,961,277,471,134,57,431,266,115,117  },
        { 658,698,340,98,296,303,1,31,850,363,156,919,44,774,586,385,120,77,82,10,223,30,354,291,23,914,478,87,260,163,48,13  },
        { 15,515,700,753,82,4,1,13,901,33,197,11,5,10,23,165,2,0,180,3,21,77,51,120,365,115,217,40,117,102,32,401  },
        { 15,515,700,753,4,11,5,13,1,141,3,180,23,202,21,2,269,64,165,33,40,32,0,318,120,128,12,197,117,352,51,17  },
        { 91,6,233,85,370,718,81,65,25,256,63,343,42,74,235,123,138,511,397,249,26,194,650,355,64,87,544,18,90,643,66,214  },
        { 23,13,202,51,21,120,1,5,141,128,450,64,318,403,15,137,260,33,12,48,32,31,125,494,269,102,165,515,77,2,197,14  },
        { 180,317,365,341,752,217,115,352,901,482,372,498,1,141,15,253,515,244,2,700,0,21,13,82,23,4,579,351,753,291,269,77  },
        { 13,115,197,341,9,352,468,237,64,498,23,165,22,509,901,546,482,180,28,569,317,51,365,873,391,95,86,217,49,837,752,706  },
        { 13,23,51,1,141,5,165,202,21,120,64,125,180,15,2,33,197,115,128,32,260,269,12,82,4,515,137,7,318,93,0,700  },
        { 214,289,90,174,874,6,138,280,65,81,64,85,355,751,194,233,312,348,835,91,0,32,343,636,249,29,875,288,519,104,247,74  },
        { 15,515,700,753,4,5,11,13,1,33,23,21,2,3,102,32,141,77,180,117,31,64,0,40,134,196,120,352,12,44,197,6  },
        { 33,15,13,515,117,23,700,217,134,753,0,51,153,77,141,2,4,64,196,1,3,180,10,115,5,102,6,11,22,202,165,7  },
        { 15,515,700,753,33,4,77,102,1,40,13,117,11,115,134,5,21,153,23,217,3,32,2,317,120,196,180,141,51,12,59,260  },
        { 15,515,700,753,13,0,1,23,2,217,51,3,4,5,8,317,115,9,341,10,202,180,6,365,7,82,457,22,120,901,33,291  },
        { 7,2,135,20,97,14,66,52,337,673,192,29,43,355,353,5,16,294,107,376,147,226,331,560,64,470,222,104,415,32,4,324  },
        { 195,132,142,167,146,77,363,271,121,354,202,120,647,178,786,212,687,0,101,878,16,522,60,5,450,411,35,55,98,639,259,318  },
        { 202,77,20,0,318,66,104,128,102,269,177,43,33,7,216,291,494,5,2,342,74,173,97,112,450,22,337,10,234,52,64,678  },
        { 107,362,612,356,359,97,414,43,259,20,392,7,298,147,819,683,465,173,729,660,319,14,5,779,581,595,246,35,501,92,0,230  },
        { 6,165,14,453,13,51,19,23,386,457,74,391,308,2,26,401,47,758,603,108,719,366,1,29,309,730,324,197,133,70,115,867  },
        { 179,72,205,180,247,245,4,490,352,59,317,152,79,498,94,217,148,76,752,864,11,216,141,405,89,452,197,111,497,188,37,21  },
        { 107,7,298,314,14,359,32,392,232,279,172,97,60,581,387,126,121,0,534,493,356,92,441,95,13,21,35,147,22,5,16,362  },
        { 156,271,354,586,360,132,591,195,121,18,340,1,5,13,21,48,668,446,23,463,296,658,60,55,407,698,146,70,626,51,163,24  },
        { 13,23,51,4,0,12,457,15,11,453,2,515,5,1,99,10,115,165,700,475,401,403,3,961,40,14,37,753,719,32,64,569  },
        { 48,125,21,165,13,221,23,763,423,508,197,5,98,92,193,16,441,386,64,314,293,457,391,140,49,60,102,693,683,51,35,867  },
        { 202,77,120,450,5,318,1,494,0,195,18,132,523,403,326,604,354,260,121,576,203,167,234,817,682,49,35,615,21,20,13,102  },
        { 39,9,166,30,0,101,158,68,404,190,333,274,252,310,88,100,49,28,344,35,21,22,419,131,438,1,16,65,530,694,124,10  },
        { 15,515,700,753,110,4,1,11,165,180,93,13,82,5,2,197,33,120,0,3,10,23,21,115,901,217,341,77,317,51,32,117  },
        { 2,29,1,14,6,52,5,46,50,26,70,19,103,58,38,67,96,262,516,309,218,133,108,27,75,17,112,114,24,487,331,83  },
        { 120,77,15,13,1,141,260,23,515,217,110,51,137,700,317,202,165,291,180,21,753,128,0,177,326,93,450,82,64,269,197,5  },
        { 255,59,554,297,183,56,33,444,108,358,123,196,269,122,77,153,57,177,117,730,19,467,605,130,128,50,275,4,291,475,134,133  },
        { 13,23,51,12,153,14,117,120,165,134,99,401,38,453,15,128,197,719,64,515,475,403,37,33,196,700,40,125,5,0,54,2  },
        { 64,33,174,348,95,108,467,554,56,0,25,306,233,6,63,511,343,120,13,85,29,561,543,707,319,180,899,355,77,49,256,18  },
        { 120,260,51,23,77,15,202,1,93,82,141,450,13,326,515,137,21,5,64,33,110,700,128,165,318,203,269,102,351,753,197,125  },
        { 15,515,700,753,4,13,11,1,5,21,23,2,33,64,3,180,32,141,22,102,77,0,10,93,82,352,117,40,341,31,165,6  },
        { 15,515,700,753,341,13,23,141,33,1,0,217,4,77,180,10,82,351,51,137,5,64,9,317,21,11,102,40,260,202,854,115  },
        { 105,272,131,22,327,286,28,239,320,9,109,578,219,49,98,224,95,159,538,371,616,127,187,64,713,55,0,170,168,258,716,623  },
        { 16,18,68,35,24,60,71,118,92,126,0,9,101,191,7,55,154,175,212,14,167,150,302,28,375,1,107,124,346,273,21,108  },
        { 20,147,43,470,376,142,904,178,427,798,0,595,198,325,858,319,61,202,173,97,5,422,14,22,107,259,32,49,887,77,414,392  },
        { 13,23,51,12,33,15,99,64,128,515,453,202,117,153,37,102,700,40,134,196,120,0,2,753,141,14,38,3,82,403,77,21  },
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        { 70,1,48,652,5,638,846,888,21,349,269,260,340,562,767,761,163,883,774,141,125,518,591,0,23,9,87,13,371,303,622,31  },
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        { 116,492,268,93,23,206,203,0,551,918,13,51,8,22,417,940,120,10,499,31,949,791,125,523,165,473,341,730,421,959,401,391  },
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        { 14,24,69,7,2,66,108,1,67,6,36,398,18,267,150,97,29,38,83,149,65,74,28,0,189,71,388,16,273,124,46,22  },
        { 330,96,523,335,367,662,141,839,1,922,372,615,244,717,269,443,418,352,403,692,217,854,752,180,36,64,498,576,349,201,98,284  },
        { 184,90,257,205,245,229,57,152,769,17,524,5,32,497,45,432,619,2,452,266,4,106,1,21,179,59,76,3,460,292,381,128  },
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        { 7,66,140,16,14,92,97,69,267,172,189,24,380,2,35,60,298,451,230,135,314,74,150,71,38,357,6,330,67,423,21,443  },
        { 121,167,354,132,18,446,147,101,212,146,407,16,55,35,647,191,20,271,199,68,60,259,463,107,9,126,363,7,195,43,14,411  },
        { 76,90,179,32,205,21,184,460,257,288,45,245,316,5,57,152,241,2,358,1,229,72,524,148,48,769,17,4,12,38,14,720  },
        { 147,259,178,878,427,465,581,198,786,798,142,534,325,929,20,362,35,132,107,376,43,5,279,77,49,146,70,202,590,771,33,14  },
        { 473,93,450,778,141,30,855,466,144,203,330,530,88,523,459,372,201,617,839,704,254,321,934,326,39,36,82,717,332,213,559,403  },
        { 523,475,51,899,730,453,23,719,403,33,457,13,421,386,4,120,117,196,102,153,15,801,450,817,515,260,202,11,700,99,165,125  },
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        { 32,20,2,13,5,21,23,6,12,38,43,29,64,7,95,51,61,207,48,147,90,178,17,182,49,0,115,202,52,362,37,22  },
        { 339,188,11,79,4,94,377,12,99,111,542,102,37,33,474,51,471,40,453,152,77,13,59,403,342,23,117,57,475,134,128,38  },
        { 34,128,283,176,495,231,318,432,503,275,529,527,161,53,3,202,56,291,585,469,73,17,14,412,57,27,80,245,250,381,402,51  },
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        { 13,15,961,515,700,753,4,12,2,457,3,11,197,51,37,569,115,23,5,0,99,10,1,134,6,111,165,33,72,40,38,79  },
        { 15,515,700,753,13,1,0,2,23,33,5,3,10,4,9,115,7,102,6,51,12,217,77,11,40,457,569,341,117,317,14,719  },
        { 5,76,2,32,292,214,45,1,129,519,123,179,90,710,17,29,460,72,14,207,21,249,58,205,464,263,618,48,6,245,3,257  },
        { 72,76,32,4,21,12,38,23,99,54,89,3,14,17,51,57,11,90,13,488,179,2,59,148,45,37,5,115,401,1,10,421  },
        { 98,223,393,1,834,264,284,791,724,293,478,772,697,909,363,682,905,447,541,821,411,51,421,9,807,48,765,31,730,96,386,410  },
        { 341,13,509,8,23,638,165,901,762,10,569,242,391,197,873,642,506,499,629,961,15,180,116,456,206,546,417,1,338,457,515,867  },
        { 1,2,5,50,14,38,46,114,0,36,29,22,218,65,86,96,137,21,133,285,12,10,323,181,17,58,51,23,67,7,28,6  },
        { 481,878,202,13,5,23,182,32,269,21,1,318,77,142,557,494,141,33,640,137,70,291,2,51,260,415,929,403,120,58,4,259  },
        { 15,515,700,753,1,4,13,0,2,5,341,3,11,180,134,12,10,317,197,365,33,21,23,165,117,6,77,7,217,37,32,498  },
        { 25,119,19,6,26,42,27,17,4,790,45,814,2,469,483,84,122,1,0,33,32,128,76,80,611,113,73,56,5,240,202,77  },
        { 14,2,7,1,24,0,65,6,16,69,67,22,124,28,108,5,18,36,86,10,38,46,66,398,289,168,12,83,21,23,610,13  },
        { 51,23,128,13,15,202,12,120,33,64,141,82,10,515,0,403,700,3,1,99,117,269,153,165,753,5,318,197,102,260,2,137  },
        { 16,35,24,0,9,18,7,1,68,69,50,71,103,65,67,189,133,23,28,13,60,537,149,335,75,21,64,5,114,2,12,14  },
        { 754,803,133,576,880,543,2,1,657,50,14,38,46,5,29,67,218,36,58,171,52,96,24,103,775,0,114,83,181,54,65,45  },
        { 21,32,5,3,2,17,14,72,76,1,12,23,38,51,4,54,10,0,89,13,99,137,45,36,421,115,543,11,22,128,221,48  },
        { 434,384,268,144,855,940,617,206,332,116,93,911,959,282,203,137,141,489,44,120,10,110,244,36,98,31,269,253,367,417,160,9  },
        { 15,2,1,0,13,515,5,700,3,23,180,217,141,10,753,4,117,6,77,33,64,7,11,197,352,317,341,134,165,115,12,9  },
        { 2,113,6,25,1,0,29,4,7,833,5,45,32,61,128,19,77,151,74,145,64,42,14,210,655,106,59,177,27,17,21,738  },
        { 116,268,918,203,551,31,8,692,206,791,403,499,417,93,940,421,0,23,22,120,13,523,44,51,299,473,959,1,10,475,202,125  },
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        { 127,13,98,165,308,23,286,293,258,51,219,395,197,115,301,401,31,391,22,105,457,170,239,276,55,338,629,116,180,479,509,569  },
        { 539,213,748,840,957,669,30,466,88,217,144,251,863,190,137,93,230,228,679,352,317,203,617,321,258,530,160,219,96,831,816,689  },
        { 5,48,1,21,2,14,0,36,12,38,32,54,430,181,50,270,72,99,281,45,17,10,46,22,37,218,67,3,290,76,23,51  },
        { 13,23,0,4,33,51,2,115,141,1,77,217,180,10,9,317,3,102,11,5,15,197,7,202,22,165,40,64,515,6,341,31  },
        { 13,15,117,515,23,12,37,134,165,700,38,54,457,753,51,64,153,197,14,10,33,82,961,0,99,89,115,719,141,3,4,1  },
        { 5,21,2,3,1,32,14,12,48,17,0,10,51,23,38,22,4,72,13,54,36,45,137,76,99,114,86,37,11,64,540,430  },
        { 202,128,77,318,291,33,269,102,275,141,494,342,40,678,0,177,20,210,402,7,4,5,137,6,13,450,403,32,49,120,23,22  },
        { 1,2,24,14,67,46,69,50,38,103,16,18,75,35,83,29,52,96,5,108,0,7,54,71,149,394,236,309,70,133,220,58  },
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        { 0,28,65,14,67,2,124,24,1,9,7,69,55,154,36,16,46,114,175,35,83,22,429,18,109,149,68,189,108,336,251,133  },
        { 56,162,403,3,129,775,99,161,17,40,527,33,880,4,14,128,475,12,548,23,102,202,361,117,34,184,383,200,183,196,64,53  },
        { 151,2,29,58,112,45,186,113,5,70,52,1,311,6,315,66,61,7,74,27,631,17,80,87,287,243,209,227,14,491,19,869  },
        { 6,1,74,2,75,29,25,66,26,70,52,138,67,324,357,42,19,220,14,85,87,108,38,451,309,103,24,69,380,135,114,65  },
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        { 5,45,17,2,14,46,48,38,181,50,155,3,186,54,61,29,21,227,281,80,540,106,12,400,52,1,58,32,328,171,209,487  },
        { 16,18,265,121,158,35,60,9,39,7,329,105,252,68,24,1,132,167,159,22,0,49,286,101,21,146,23,327,120,709,5,14  },
        { 108,467,283,56,389,650,123,412,33,177,899,475,216,453,269,349,619,65,51,730,403,670,23,196,523,128,84,13,401,789,503,543  },
        { 514,3,11,377,328,4,361,507,57,403,14,880,130,485,176,215,236,38,152,102,211,56,62,757,54,585,300,556,34,555,40,229  },
        { 3,555,62,266,130,99,507,139,514,12,152,229,215,305,57,40,440,33,403,471,38,56,475,14,361,313,775,328,196,548,123,23  },
        { 120,202,318,15,77,13,1,450,33,269,515,260,5,128,494,51,23,700,102,141,40,753,326,403,817,137,523,21,177,922,342,7  },
        { 15,1,515,23,0,13,700,2,51,753,180,5,165,21,197,12,3,120,115,4,141,6,9,7,457,33,386,202,82,8,31,341  },
        { 15,180,515,82,351,700,10,317,753,115,217,365,141,898,33,901,13,23,110,854,752,77,1,197,4,341,143,36,64,352,102,9  },
        { 104,289,66,707,214,90,712,64,97,173,20,0,414,194,874,43,32,7,568,560,65,38,426,312,715,192,376,74,835,5,324,147  },
        { 84,56,0,554,63,65,453,249,123,643,18,26,847,475,511,403,416,561,524,289,370,73,9,19,45,42,719,194,27,467,33,730  },
        { 21,346,13,350,308,826,197,101,352,68,570,0,165,23,9,841,115,100,509,694,221,230,35,217,569,88,124,749,1,777,212,154  },
        { 16,92,7,24,60,18,35,140,126,14,50,71,46,330,2,75,246,5,121,267,571,1,230,309,220,0,9,64,146,236,54,108  },
        { 82,15,515,898,365,700,180,33,341,753,77,901,10,115,55,351,21,5,1,4,13,102,36,217,2,165,752,120,197,117,11,317  },
        { 16,24,35,18,69,71,140,1,103,7,189,68,0,50,9,108,2,133,60,267,230,46,149,67,167,118,92,14,75,21,191,38  },
        { 60,71,16,18,7,20,43,118,35,68,375,28,608,0,175,566,154,92,14,149,628,33,22,13,2,10,279,23,107,356,55,117  },
        { 187,258,871,295,201,434,219,224,489,384,268,110,261,839,44,699,93,116,36,131,141,228,144,160,940,567,244,406,137,574,98,253  },
        { 66,7,97,172,192,712,232,324,204,74,43,448,387,426,568,20,526,107,104,135,356,729,173,0,22,5,32,95,2,64,500,560  },
        { 15,515,700,753,1,4,0,341,13,3,134,2,5,33,11,77,12,10,23,197,365,901,7,40,217,32,21,6,51,180,961,37  },
        { 0,28,24,9,35,65,16,124,68,55,109,154,7,39,22,149,158,14,175,1,49,252,18,71,2,168,289,419,108,420,67,101  },
        { 7,16,14,92,2,46,140,24,220,35,38,60,75,1,50,18,87,54,5,126,29,52,278,262,314,107,71,21,172,135,330,394  },
        { 7,92,16,14,172,126,2,60,140,35,135,314,278,46,24,38,232,107,330,66,5,18,150,246,230,97,52,1,121,563,279,21  },
        { 6,26,235,53,297,436,27,19,25,73,113,445,90,214,65,42,64,289,250,611,624,32,45,648,614,17,85,491,34,122,200,416  },
        { 352,141,1,217,854,752,351,180,244,36,110,661,82,258,816,160,295,219,567,224,230,269,922,144,260,268,93,201,137,116,489,202  },
        { 16,60,35,18,126,107,68,191,92,121,7,14,598,20,493,279,167,446,118,0,28,43,463,55,24,212,375,566,9,150,575,21  },
        { 15,1,515,2,4,13,0,700,3,5,23,753,341,77,51,115,33,11,180,10,197,141,6,165,7,901,102,40,9,202,217,12  },
        { 23,51,13,202,21,5,1,120,15,137,128,125,32,2,12,141,33,165,64,515,403,318,700,48,180,7,6,450,115,523,475,260  },
        { 131,716,224,371,219,187,737,616,385,254,9,98,105,924,31,258,836,39,127,578,49,916,44,761,272,137,944,159,0,242,442,22  },
        { 15,515,700,1,753,2,5,0,4,13,3,180,11,141,197,10,341,217,33,134,165,6,77,7,317,12,352,64,365,32,102,40  },
        { 66,74,7,173,174,29,192,2,222,20,226,43,353,52,712,6,0,138,500,204,97,145,64,104,426,673,355,90,25,5,65,87  },
        { 5,259,786,534,590,493,279,49,13,581,465,21,929,35,941,132,147,32,23,612,362,626,107,121,178,0,146,61,48,939,10,18  },
        { 2,14,16,7,278,69,135,140,46,24,267,35,92,38,1,189,29,52,309,60,66,75,71,172,74,357,18,87,67,6,230,5  },
        { 165,13,308,197,391,23,401,15,51,457,180,509,115,569,3,629,961,719,34,758,317,734,14,29,46,2,17,901,38,453,5,217  },
        { 1,22,2,14,0,28,7,168,67,49,65,24,36,95,5,105,55,35,12,46,69,16,114,159,194,50,10,9,158,83,164,109  },
        { 34,453,3,196,130,14,322,11,47,51,377,236,361,4,730,153,514,711,57,440,62,17,161,108,176,59,485,56,162,412,202,117  },
        { 18,16,21,23,48,13,24,35,121,5,156,60,51,1,7,132,141,221,163,115,0,271,447,340,363,202,125,71,2,781,22,698  },
        { 165,13,457,23,197,961,629,569,341,41,12,38,401,901,54,51,115,17,15,509,421,37,62,45,719,57,32,328,117,758,157,99  },
        { 2,1,77,141,33,64,3,102,0,23,13,5,128,10,6,15,180,202,269,40,51,515,7,165,137,117,318,4,700,153,197,352  },
        { 68,212,0,124,101,9,154,16,562,191,21,149,65,24,35,1,118,167,818,350,520,100,722,841,264,71,13,302,478,23,375,346  },
        { 98,23,48,598,13,293,541,21,125,121,51,807,0,31,35,259,126,7,386,1,223,783,10,107,199,20,221,144,342,963,49,64  },
        { 21,13,5,586,1,23,167,48,33,781,647,49,165,18,51,271,77,32,761,118,0,82,391,22,146,141,459,31,197,156,115,4  },
        { 2,1,5,61,29,7,58,45,14,6,425,32,70,52,290,738,207,21,72,112,66,76,655,17,186,46,64,263,38,0,128,87  },
        { 39,265,9,100,1,333,363,101,18,411,447,254,166,310,31,98,264,30,639,404,156,286,16,93,593,203,272,682,0,905,44,821  },
        { 6,2,1,19,29,51,26,108,25,74,5,23,14,114,13,386,133,103,42,66,453,70,309,138,719,324,65,38,64,96,52,75  },
        { 20,43,356,107,49,858,595,7,414,359,0,5,392,319,97,612,422,819,14,376,173,246,22,470,147,427,230,92,197,33,683,95  },
        { 0,9,68,35,65,67,114,101,28,1,124,175,336,69,154,103,83,24,189,133,39,16,50,7,2,149,55,251,18,345,230,36  },
        { 23,13,51,15,0,1,515,115,165,2,5,12,700,202,4,21,141,457,753,197,10,3,180,120,32,9,318,11,453,64,6,269  },
        { 121,195,60,16,126,107,98,271,146,407,132,35,1,167,199,223,493,191,279,20,18,5,43,7,21,92,48,393,0,362,212,467  },
        { 31,44,299,116,393,144,492,456,268,22,105,0,367,918,384,434,127,489,98,9,963,125,242,948,1,28,206,49,36,51,93,293  },
        { 23,13,457,51,165,401,719,758,197,453,961,629,308,14,15,12,730,3,386,569,391,29,739,515,34,828,832,901,115,514,670,341  },
        { 105,36,131,22,180,115,341,127,169,1,9,31,64,98,44,365,317,141,272,143,160,55,219,86,197,776,239,187,0,535,13,752  },
        { 1,6,2,14,66,25,29,5,108,67,65,114,19,38,26,52,74,7,24,18,69,86,36,388,64,51,17,83,23,46,42,75  },
        { 51,386,23,453,719,13,730,6,457,670,758,19,401,165,2,475,47,26,899,14,108,17,1,5,197,29,894,754,236,74,27,285  },
        { 252,18,9,101,121,16,132,0,419,167,364,60,604,35,265,363,146,271,39,158,68,109,28,329,848,24,647,907,682,159,212,55  },
        { 283,503,128,432,26,193,63,269,789,529,102,122,389,275,678,6,25,318,445,4,342,27,573,605,177,862,643,291,216,57,235,59  },
        { 2,1,29,75,69,52,14,6,46,74,87,7,220,226,278,38,135,66,267,70,16,262,25,24,380,324,357,140,67,394,97,222  },
        { 97,298,69,7,66,140,189,24,16,267,172,423,60,150,14,314,92,71,81,501,43,35,74,6,517,232,149,607,83,330,18,2  },
        { 475,421,403,899,51,805,523,958,453,817,23,615,401,801,120,326,202,670,494,730,450,386,115,629,260,576,77,365,569,0,165,13  },
        { 7,20,14,128,77,97,112,202,2,177,16,415,269,318,275,66,107,43,141,414,135,38,307,10,58,0,6,291,32,5,4,40  },
        { 24,14,7,0,2,1,22,28,16,65,168,124,35,67,108,109,18,49,10,149,69,158,5,95,289,12,55,6,36,71,46,21  },
        { 26,80,27,73,122,25,19,17,6,42,684,209,445,573,667,106,45,690,4,611,255,680,297,495,65,59,128,119,483,113,64,53  },
        { 107,259,362,376,465,20,470,147,595,534,612,683,660,43,5,49,581,0,858,35,427,246,97,786,178,356,14,21,142,878,7,279  },
        { 131,30,228,190,856,406,224,88,219,530,863,613,778,274,944,816,187,39,100,160,258,31,44,93,1,321,539,36,871,137,435,531  },
        { 113,6,311,25,45,491,80,611,27,26,209,667,17,73,122,42,684,396,19,85,106,5,614,4,2,255,151,29,1,64,648,61  },
        { 15,515,700,753,0,1,23,51,120,2,13,82,5,260,9,4,341,77,180,115,141,10,7,12,450,8,202,901,197,351,165,93  },
        { 219,127,98,258,395,421,924,293,242,201,697,105,276,51,308,23,453,272,401,944,512,137,13,31,284,567,386,365,116,131,964,125  },
        { 15,180,352,141,515,752,217,82,1,317,854,700,351,753,115,341,110,13,260,120,21,36,33,898,23,10,5,365,4,160,901,137  },
        { 129,123,17,257,162,184,205,249,183,769,5,80,3,4,229,130,119,45,90,99,618,106,57,497,12,128,2,84,59,152,27,40  },
        { 33,102,23,77,64,128,51,13,0,202,10,141,40,15,1,22,117,137,2,86,4,403,269,153,515,196,65,11,700,115,99,5  },
        { 7,14,2,16,172,107,46,92,5,135,35,202,294,87,38,232,29,97,20,21,24,1,60,220,66,43,12,0,126,52,54,70  },
        { 403,576,615,523,475,326,805,817,494,421,51,202,120,450,137,453,23,859,260,401,402,77,33,670,0,958,15,197,386,515,165,480  },
        { 141,352,217,137,0,180,202,349,9,269,23,51,115,291,77,372,13,317,120,752,365,351,93,22,2,341,64,10,82,854,28,18  },
        { 1,23,13,51,202,141,5,165,21,15,120,180,64,2,197,125,33,102,12,7,137,515,48,128,269,318,93,700,0,403,9,4  },
        { 25,151,6,145,122,29,174,45,113,74,4,665,42,138,2,614,416,287,19,348,746,0,66,26,1,7,64,243,311,396,81,624  },
        { 30,190,254,166,100,382,731,829,88,131,264,795,9,93,625,274,438,1,578,613,716,31,44,39,530,36,616,921,265,203,160,77  },
        { 132,5,21,13,1,23,32,195,379,687,156,121,626,296,48,70,850,146,51,82,883,771,35,49,652,407,60,4,260,0,845,33  },
        { 9,254,0,49,272,131,39,159,688,101,105,578,518,158,286,28,327,333,68,224,252,219,344,16,22,1,716,31,30,228,24,890  },
        { 16,7,35,60,18,20,14,68,9,0,28,118,43,92,126,55,107,2,101,154,24,71,5,202,121,109,22,252,21,97,1,621  },
        { 15,515,700,753,13,1,341,2,0,4,3,5,11,23,10,33,117,12,901,197,6,134,77,8,165,317,21,365,217,7,17,40  },
        { 78,19,444,47,26,390,27,453,130,813,108,730,711,65,412,122,51,680,113,235,690,196,630,283,128,236,14,64,73,53,200,445  },
        { 2,7,29,5,61,6,45,1,66,113,112,14,52,315,738,128,32,151,74,16,20,64,70,21,592,0,25,4,425,43,491,222  },
        { 145,112,74,66,6,29,26,70,19,396,25,87,2,287,135,151,138,222,5,226,42,122,7,307,1,644,45,58,113,651,635,632  },
        { 92,16,7,60,126,24,140,35,14,232,18,121,246,71,46,267,172,150,107,314,132,146,230,2,278,108,330,199,236,5,38,572  },
        { 13,115,197,538,569,341,98,55,165,127,365,762,219,286,844,23,170,206,734,638,535,901,169,253,629,0,873,509,180,10,332,258  },
        { 58,151,74,53,287,27,29,396,6,70,2,73,5,52,112,26,651,1,297,113,17,75,19,45,334,445,145,34,315,549,436,331  },
        { 214,289,90,874,104,751,64,65,312,835,204,249,750,194,74,81,875,32,519,288,348,0,174,247,636,715,138,192,784,6,524,280  },
        { 9,39,28,35,30,0,166,49,1,175,439,158,64,346,36,101,67,364,86,88,274,100,168,55,23,10,420,22,190,141,505,180  },
        { 341,901,15,515,700,753,1,365,10,0,569,180,2,197,115,31,165,3,5,4,44,22,317,13,9,951,23,253,116,143,762,93  },
        { 120,202,77,450,260,15,128,318,102,515,494,13,817,700,269,5,403,51,1,33,23,753,82,326,141,342,291,137,21,523,351,32  },
        { 13,115,241,64,180,32,125,197,165,4,118,22,21,23,16,247,237,28,225,191,95,141,167,5,0,341,288,35,459,18,177,24  },
        { 16,24,35,14,1,2,7,69,18,46,60,50,267,140,71,189,108,38,75,92,0,5,9,230,67,21,309,335,54,236,394,220  },
        { 15,515,700,753,898,180,901,341,197,638,10,165,33,1,115,4,77,365,317,13,102,217,117,0,5,2,253,3,82,569,21,752  },
        { 193,523,18,84,56,730,233,65,4,817,90,33,643,403,91,511,453,240,59,11,214,51,719,196,153,475,32,123,64,847,102,561  },
        { 112,29,151,2,74,6,66,7,222,145,287,45,5,624,52,25,113,416,58,122,19,70,186,204,4,87,644,549,337,884,32,0  },
        { 13,0,23,2,1,15,33,3,77,515,141,5,4,217,10,51,64,180,700,115,6,117,11,7,753,40,102,165,197,22,317,153  },
        { 28,0,1,67,65,9,2,114,83,69,103,50,36,22,55,24,46,14,124,109,35,7,16,38,133,160,389,323,18,12,154,5  },
        { 121,132,18,167,271,146,101,363,621,9,411,647,16,354,520,60,212,932,1,806,55,0,195,446,68,35,31,364,777,252,407,118  },
        { 26,6,85,396,122,624,25,19,42,445,64,648,573,416,174,680,665,214,45,348,90,65,194,145,113,881,138,289,112,436,297,544  },
        { 16,146,18,92,24,199,60,71,121,126,35,108,156,953,271,674,132,7,32,640,360,246,649,118,21,95,5,517,14,9,1,314  },
        { 51,13,23,453,475,730,719,15,457,403,64,115,33,95,4,523,3,12,21,6,899,102,5,128,401,202,11,141,308,515,22,125  },
        { 151,396,6,53,27,113,58,26,73,112,74,287,45,29,297,19,145,70,138,445,315,436,34,2,17,573,5,61,549,491,1,80  },
        { 223,1,888,774,260,98,269,385,349,202,96,141,421,622,730,863,318,697,87,453,393,418,922,834,751,5,163,335,120,291,352,30  },
        { 16,60,92,35,126,121,7,150,246,18,107,1,598,24,167,195,14,97,71,279,98,441,191,199,517,146,356,223,298,271,230,0  },
        { 22,1,105,28,239,170,0,55,95,31,36,301,2,320,98,127,9,49,44,64,35,67,10,86,5,12,109,23,168,13,21,312  },
        { 2,6,5,207,292,76,1,119,45,32,17,29,61,306,790,58,240,106,14,64,214,151,476,710,7,72,84,128,4,179,70,25  },
        { 51,23,221,254,115,13,438,530,125,48,21,39,541,960,386,49,1,613,15,840,228,308,627,131,688,401,5,326,421,158,165,83  },
        { 1,5,2,0,12,22,21,36,10,14,48,86,23,13,32,54,3,4,28,65,51,50,137,37,208,114,9,38,17,7,281,202  },
        { 363,23,447,182,296,340,1,93,698,478,379,156,284,144,18,269,21,98,141,70,668,411,664,658,110,914,67,937,180,691,335,291  },
        { 17,32,45,498,41,115,180,197,106,62,54,38,546,165,13,155,468,509,341,243,241,217,542,15,57,536,428,51,117,721,292,129  },
        { 32,95,64,246,22,92,180,13,5,652,125,241,638,237,7,49,4,126,21,115,197,296,888,316,0,165,774,23,16,392,1,534  },
        { 15,515,700,753,33,341,13,217,4,141,77,23,180,317,1,10,102,351,82,115,40,5,854,21,137,11,352,901,365,117,197,0  },
        { 15,120,1,82,93,217,515,260,77,141,13,110,700,351,352,23,180,753,21,854,202,317,64,349,269,51,165,137,5,128,291,36  },
        { 13,23,51,141,77,0,33,4,115,64,2,10,102,202,217,128,1,177,269,11,7,22,6,21,32,9,180,40,15,3,165,318  },
        { 478,264,1,520,98,724,9,682,223,664,21,759,13,772,604,100,23,363,411,48,821,5,0,905,909,447,31,265,88,101,166,39  },
        { 20,29,7,2,77,416,6,128,33,5,0,113,104,32,43,13,491,66,23,21,102,51,74,210,202,525,64,318,10,81,174,14  },
        { 2,1,5,14,7,58,61,29,45,290,46,38,52,21,32,270,6,592,425,0,75,155,16,48,17,50,72,70,207,24,263,663  },
        { 80,6,17,209,106,26,483,113,19,469,255,25,378,27,495,833,45,64,161,2,61,667,76,742,32,90,445,5,814,65,887,119  },
        { 98,223,393,1,354,834,195,791,447,697,284,293,360,541,781,156,51,807,18,664,421,411,163,668,48,31,591,765,883,386,948,23  },
        { 679,141,816,36,93,406,876,144,228,137,1,180,669,21,332,251,5,269,116,187,96,351,202,752,317,64,203,831,574,466,855,345  },
        { 15,515,700,13,1,753,2,0,23,341,3,5,4,10,51,11,33,165,6,7,115,197,12,64,180,153,217,77,9,569,901,317  },
        { 13,23,202,51,5,21,403,15,120,64,1,450,128,141,12,523,33,165,494,125,2,515,269,7,48,102,318,95,260,180,453,197  },
        { 16,18,24,60,71,92,146,246,199,35,140,7,9,118,121,108,167,230,126,132,0,640,156,14,68,133,267,360,649,271,64,55  },
        { 269,141,678,177,202,77,128,318,33,947,40,120,291,349,102,137,64,352,210,864,461,498,13,342,196,23,275,450,954,0,205,111  },
        { 16,24,92,18,71,60,35,7,108,191,167,246,140,14,126,21,1,68,150,118,149,388,399,9,273,0,121,796,230,48,212,517  },
        { 2,14,1,29,46,75,52,70,69,171,38,7,58,163,16,5,24,220,67,112,223,54,50,409,155,35,267,186,151,334,394,140  },
        { 9,252,100,265,166,39,88,404,329,0,1,520,382,812,101,593,264,274,604,676,30,118,68,553,18,664,363,23,639,865,21,411  },
        { 16,18,35,24,0,60,158,7,22,68,14,49,109,159,55,9,28,71,2,10,5,105,1,118,329,13,344,23,92,20,21,126  },
        { 15,13,515,700,23,0,753,1,51,2,4,10,77,5,3,197,115,165,961,202,9,457,180,12,141,22,33,120,6,11,318,31  },
        { 160,93,251,137,317,1,180,36,120,217,345,752,617,352,332,10,96,531,498,318,365,202,141,269,816,341,901,679,143,35,83,968  },
        { 6,25,42,128,19,59,122,4,85,26,611,27,269,233,45,0,343,91,318,80,11,177,283,73,33,614,2,77,64,138,445,216  },
        { 95,64,74,7,32,81,51,204,0,20,237,65,56,38,91,23,207,180,347,343,29,6,511,52,49,10,25,18,554,370,14,312  },
        { 202,120,326,260,450,817,494,318,137,403,128,77,523,553,859,5,704,1,15,23,13,576,7,16,615,51,682,291,515,0,21,234  },
        { 20,43,107,356,362,126,595,92,359,7,422,319,493,16,858,5,392,246,414,683,60,0,35,945,441,21,259,819,49,97,279,173  },
        { 25,42,6,77,33,102,0,122,4,690,29,483,210,27,21,19,2,300,18,648,680,119,117,59,1,10,342,12,26,153,91,684  },
        { 31,44,299,116,125,242,456,599,22,393,0,144,492,28,268,1,9,963,301,105,367,36,127,170,384,434,206,98,918,10,13,93  },
        { 410,521,686,367,662,88,335,321,201,96,98,772,144,1,934,921,443,435,284,274,264,551,120,897,44,100,33,225,744,418,909,960  },
        { 142,178,878,234,132,786,195,202,77,416,147,929,146,522,167,259,687,639,450,271,626,481,590,5,198,212,771,49,0,465,315,427  },
        { 254,39,131,9,272,0,578,716,310,224,30,49,105,827,518,829,166,333,616,228,613,846,101,219,1,31,890,98,159,938,252,100  },
        { 230,699,854,473,450,351,831,137,855,217,352,704,800,202,251,498,160,144,206,203,317,201,253,752,418,141,1,332,82,180,443,36  },
        { 403,202,475,453,494,23,51,77,318,402,13,33,128,102,137,141,120,342,269,0,450,4,899,576,40,421,275,117,217,177,196,64  },
        { 23,44,98,182,291,144,116,39,110,141,96,82,905,70,367,264,125,93,77,411,120,1,658,202,100,415,107,363,197,30,447,105  },
        { 15,515,1,13,700,23,77,120,0,753,51,180,202,141,260,5,21,115,2,137,128,9,450,197,365,269,12,326,110,102,318,7  },
        { 0,32,18,95,207,577,193,29,61,104,64,784,715,102,693,887,81,91,583,671,403,5,52,474,397,180,138,49,37,344,38,263  },
        { 0,101,9,68,252,16,100,39,166,364,124,24,154,265,212,88,18,35,329,419,28,118,71,30,65,158,191,55,1,694,21,676  },
        { 16,24,191,18,35,71,167,118,149,68,212,9,0,1,21,108,101,92,60,375,302,7,589,755,124,674,350,48,562,246,13,363  },
        { 2,14,69,24,1,67,46,16,38,103,29,267,7,35,189,135,278,71,108,18,83,309,52,6,149,388,75,236,60,0,150,66  },
        { 13,1,23,0,4,2,51,15,180,33,3,115,5,515,141,10,77,700,11,9,197,341,202,165,217,102,22,7,753,317,365,6  },
        { 447,1,698,411,31,363,98,5,919,4,156,125,759,691,13,64,459,354,44,21,48,293,30,914,478,225,82,120,2,922,848,839  },
        { 854,82,351,217,141,180,352,15,515,752,1,700,317,898,753,244,10,21,922,115,77,36,4,260,64,110,372,13,5,365,120,11  },
        { 0,1,4,13,5,2,82,33,3,120,10,23,9,11,77,260,21,102,8,31,40,6,351,51,64,450,22,117,93,110,7,457  },
        { 51,13,403,23,12,475,1,2,21,5,453,523,115,202,817,7,0,99,3,6,450,120,494,64,22,95,49,899,10,37,32,141  },
        { 180,752,352,141,498,864,317,217,9,0,115,237,230,39,30,197,83,1,930,64,35,365,372,13,579,88,702,36,101,901,482,21  },
        { 16,24,0,7,22,18,28,35,14,158,71,2,109,60,1,168,49,154,124,68,10,55,92,118,159,9,5,747,95,105,65,6  },
        { 15,515,700,753,0,23,1,13,341,51,120,77,141,4,137,33,260,82,202,9,180,5,351,2,291,10,11,901,21,115,40,128  },
        { 24,68,35,149,18,16,0,7,9,14,189,108,69,65,67,1,71,2,118,28,140,101,114,336,230,124,175,133,46,55,251,154  },
        { 13,308,197,115,125,9,165,237,391,23,509,569,546,28,49,629,22,338,317,254,749,180,468,159,903,386,217,352,558,39,36,734  },
        { 64,90,32,217,77,4,141,216,172,312,128,13,86,33,597,147,352,95,5,115,875,22,59,11,102,14,182,437,97,177,874,707  },
        { 1,22,36,0,105,28,2,67,95,49,55,5,239,12,86,9,83,170,312,64,31,21,23,10,164,50,114,159,208,13,7,320  },
        { 9,18,16,0,159,105,101,252,49,310,24,68,35,39,265,272,7,1,60,28,455,890,329,557,118,286,55,137,327,167,5,13  },
        { 129,123,214,249,618,17,5,257,205,184,460,76,2,162,769,245,90,106,128,45,119,1,183,4,3,12,179,64,6,229,99,209  },
        { 51,453,719,457,23,13,730,899,475,386,4,15,11,12,670,196,515,523,961,401,153,3,700,99,753,117,403,32,120,165,57,0  },
        { 173,66,192,204,20,74,104,636,7,43,289,426,825,712,560,214,81,750,65,97,707,0,90,414,64,348,32,500,22,861,95,6  },
        { 13,23,1,51,5,21,141,120,202,15,165,2,515,180,12,125,0,64,82,700,197,269,32,48,260,128,115,93,9,137,33,753  },
        { 200,34,322,78,472,390,27,714,19,14,136,161,453,176,236,444,59,3,62,128,108,57,283,862,73,53,47,17,412,813,4,56  },
        { 33,347,66,204,426,498,56,172,97,95,5,681,546,22,10,0,135,180,4,241,19,174,6,353,263,21,7,370,42,197,27,808  },
        { 131,224,219,187,385,371,258,442,254,737,31,98,836,127,924,944,44,871,908,716,39,827,201,574,116,137,36,1,276,242,578,616  },
        { 1,15,2,180,4,141,13,515,0,5,3,115,700,901,341,23,217,352,753,51,197,77,317,33,365,752,165,21,6,7,269,93  },
        { 370,91,718,74,81,510,397,66,636,240,355,84,138,511,18,278,6,681,701,289,90,5,214,582,64,104,0,643,192,65,750,32  },
        { 15,515,700,753,13,120,1,0,165,2,197,23,260,180,4,82,51,386,8,5,12,10,3,141,351,341,326,9,450,7,64,6  },
        { 32,2,76,5,1,292,72,45,476,214,21,241,29,14,17,48,129,90,179,460,464,123,290,148,519,205,3,263,249,38,710,89  },
        { 13,165,115,17,197,569,23,509,457,45,32,41,106,180,62,38,659,734,155,536,341,629,961,873,587,54,431,37,391,99,405,428  },
        { 68,24,35,16,0,101,9,124,154,71,149,65,18,175,28,118,7,55,302,108,92,14,22,346,1,39,429,252,375,364,10,67  },
        { 0,9,1,68,230,65,35,69,83,23,101,13,141,67,217,352,21,39,16,88,28,124,212,100,115,154,51,64,30,36,10,317  },
        { 100,265,88,909,410,382,812,593,1,213,321,30,252,230,352,264,9,166,689,39,676,98,21,466,724,639,478,217,13,48,553,101  },
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        { 16,24,141,18,7,0,71,140,35,269,75,352,12,9,108,217,5,330,60,64,199,70,22,13,486,246,318,133,65,50,23,498  },
        { 271,167,121,60,18,191,146,199,16,1,446,132,575,212,463,354,126,35,598,566,727,98,107,21,608,955,640,407,5,24,223,68  },
        { 15,515,115,217,700,13,317,753,141,180,33,23,110,120,4,341,82,10,1,260,365,36,64,854,351,21,51,352,137,77,40,0  },
        { 173,7,97,356,43,107,20,387,729,104,426,232,560,595,359,392,414,707,885,81,5,0,66,858,612,49,861,14,22,32,819,230  },
        { 15,515,700,753,13,23,51,82,0,33,165,120,196,4,1,2,197,453,260,351,180,12,40,8,386,110,5,326,9,141,217,457  },
        { 9,100,120,30,77,795,137,82,202,39,264,827,578,127,0,166,373,318,18,326,141,260,1,450,731,31,33,395,217,291,341,254  },
        { 14,2,67,1,24,69,0,28,65,7,46,18,114,108,36,83,38,398,9,16,124,133,103,154,50,55,22,267,29,160,35,547  },
        { 14,7,69,24,66,16,2,267,189,67,71,150,140,97,18,60,172,35,6,1,38,149,388,92,83,135,108,74,462,380,29,36  },
        { 15,515,700,753,1,13,2,0,4,341,5,3,23,365,11,117,180,10,12,33,134,115,77,197,217,165,6,7,317,102,21,9  },
        { 1,22,0,12,5,2,36,28,21,10,86,13,23,49,128,9,95,51,55,96,208,141,48,202,4,137,37,64,105,3,50,7  },
        { 605,630,63,123,736,650,65,108,444,368,561,389,19,25,42,619,122,194,183,27,53,33,84,26,297,813,114,73,256,235,249,216  },
        { 127,39,9,0,31,371,98,254,1,385,395,44,30,836,187,131,100,116,284,578,299,166,28,21,737,16,276,272,23,49,137,935  },
        { 2,61,6,29,45,151,1,655,7,207,32,5,112,425,17,76,833,4,14,64,58,106,119,25,113,128,72,52,70,21,292,790  },
        { 2,5,17,14,3,29,23,27,13,401,46,6,51,58,1,453,45,53,34,52,133,19,236,26,181,114,99,366,151,108,218,38  },
        { 31,22,170,1,301,44,127,98,36,28,55,105,239,0,338,116,512,299,293,125,86,10,242,395,2,13,9,64,841,23,95,685  },
        { 1,21,2,14,5,32,48,50,38,270,46,76,290,72,45,54,17,0,155,221,263,207,37,281,430,3,89,12,181,408,36,67  },
        { 17,106,119,378,84,240,62,80,383,136,306,3,56,790,742,5,207,504,64,440,32,128,45,2,123,209,14,4,61,57,297,667  },
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        { 772,335,96,744,1,367,662,686,652,897,303,264,521,31,225,410,141,520,260,116,64,44,321,98,144,88,919,966,340,269,349,284  },
        { 1,0,5,28,36,2,12,22,83,67,65,50,24,14,9,96,21,218,18,114,48,281,54,10,7,160,181,103,37,23,133,99  },
        { 25,6,145,42,138,81,174,348,525,544,26,74,85,280,287,648,746,91,66,0,29,396,204,64,636,90,122,194,355,104,65,233  },
        { 16,24,0,18,28,158,7,35,49,22,68,159,55,1,14,109,105,2,9,71,65,154,124,95,424,344,60,239,118,577,21,10  },
        { 352,854,699,230,93,689,137,144,217,160,251,36,669,202,351,120,617,855,752,203,332,82,450,180,141,748,831,30,258,201,1,816  },
        { 15,13,515,700,1,2,0,753,23,5,4,3,51,33,10,115,11,317,217,77,180,341,117,165,6,134,197,153,64,9,102,7  },
        { 104,20,43,173,66,319,0,77,202,7,198,5,97,580,355,74,2,204,174,52,712,234,426,155,102,192,32,4,500,337,226,904  },
        { 13,23,15,51,1,515,0,2,5,700,141,4,753,165,115,12,3,21,457,10,180,269,32,6,197,202,9,7,120,11,77,33  },
        { 15,515,700,753,0,1,13,2,23,115,4,317,8,3,5,51,9,341,10,217,22,365,33,457,6,180,77,901,197,120,18,7  },
        { 15,515,700,753,1,0,2,3,4,13,5,141,23,16,82,217,457,10,365,180,9,317,51,21,269,898,64,202,11,12,318,341  },
        { 2,5,1,14,50,38,29,17,114,46,133,3,45,21,58,171,181,36,218,12,6,52,0,48,137,65,361,23,155,4,285,51  },
        { 0,68,9,65,101,124,35,212,16,149,154,100,24,1,114,336,67,589,252,39,71,189,69,562,18,13,30,398,118,88,265,264  },
        { 1,2,14,22,0,7,67,65,28,36,24,46,168,5,86,69,38,16,49,12,289,10,194,50,83,114,95,6,18,23,55,158  },
        { 13,23,15,51,515,0,700,4,1,753,2,10,115,961,457,12,33,11,3,5,197,9,165,77,102,403,453,40,64,22,37,59  },
        { 15,515,700,753,0,1,2,13,23,5,51,901,8,9,180,3,7,82,4,120,12,10,719,341,6,31,141,457,197,22,115,93  },
        { 100,252,88,101,0,265,9,724,48,1,21,352,213,676,410,382,321,230,30,329,593,909,39,812,553,217,23,689,520,264,166,419  },
        { 2,5,1,58,171,14,46,50,29,52,45,38,186,155,67,54,151,281,334,61,48,96,17,181,103,400,502,227,21,223,12,69  },
        { 23,120,13,1,202,141,51,21,165,128,260,15,5,269,137,64,33,180,82,318,93,197,77,326,515,125,110,700,450,2,32,48  },
        { 341,197,10,901,13,15,8,638,569,515,479,23,180,873,700,165,143,642,0,961,753,951,1,115,509,499,116,12,498,242,82,206  },
        { 15,1,23,13,515,21,120,51,2,141,202,700,5,180,165,0,753,197,12,7,33,260,352,137,269,4,82,128,48,9,110,6  },
        { 2,29,50,58,1,6,5,52,14,262,17,46,27,53,151,34,171,74,324,26,38,309,45,113,19,96,287,396,223,67,73,583  },
        { 13,23,141,51,4,202,0,115,77,2,33,217,5,317,180,64,10,269,3,9,15,21,1,128,102,137,318,11,352,515,22,31  },
        { 1,67,0,24,50,5,14,18,16,69,2,9,103,35,83,12,96,28,54,7,58,223,21,46,281,48,65,181,22,38,36,108  },
        { 13,23,141,51,77,64,202,115,33,102,128,4,0,269,10,21,217,32,180,318,9,137,2,11,22,291,7,177,16,31,165,197  },
        { 317,115,180,365,873,498,217,341,13,752,482,197,569,352,1,901,36,23,457,468,165,346,546,143,509,134,579,876,868,2,332,21  },
        { 184,257,205,229,152,17,57,497,266,432,452,524,5,619,381,32,4,90,2,12,313,128,45,59,245,106,3,471,129,769,339,214  },
        { 13,23,1,0,15,2,4,515,51,3,10,33,5,700,115,180,753,77,11,365,341,217,9,6,197,7,102,165,317,40,22,64  },
        { 626,70,771,687,379,846,767,761,518,878,82,481,31,786,49,591,178,163,407,44,87,13,845,125,590,371,195,120,98,557,937,351  },
        { 264,1,410,909,772,897,686,521,335,478,98,96,691,639,100,44,284,382,31,321,744,88,914,724,662,765,223,9,682,363,0,367  },
        { 13,23,1,2,0,15,51,515,5,10,4,33,115,77,180,700,3,141,217,40,6,753,317,197,64,165,7,11,102,9,341,22  },
        { 141,77,13,64,269,23,115,21,318,217,5,202,102,33,137,2,15,291,177,51,48,180,32,4,515,352,128,7,0,10,96,11  },
        { 13,15,23,515,51,0,700,753,1,2,4,10,33,11,961,453,115,40,457,14,12,3,9,5,165,401,197,77,22,21,64,102  },
        { 1,22,0,36,2,31,5,12,13,105,28,9,49,86,141,21,23,95,128,55,44,115,170,10,164,98,180,4,137,239,83,51  },
        { 100,101,88,0,252,9,265,30,21,39,759,724,213,329,321,13,419,68,562,382,676,352,694,35,553,410,1,166,909,593,230,23  },
        { 539,88,30,190,321,530,840,144,669,435,957,748,778,100,96,418,203,213,1,131,410,228,466,274,36,382,219,863,613,83,822,352  },
        { 7,97,92,173,298,107,43,314,232,140,16,356,20,387,729,362,126,359,246,14,230,501,426,441,0,5,560,66,104,779,35,60  },
        { 2,14,7,1,58,5,46,16,38,70,75,45,24,155,29,0,21,52,61,163,220,50,69,270,35,48,32,171,18,6,64,54  },
        { 447,411,363,664,647,98,621,1,354,271,223,478,18,777,781,936,360,759,167,132,121,48,21,156,9,195,118,293,23,691,13,264  },
        { 2,1,14,65,36,67,0,7,46,22,69,5,38,24,28,6,83,29,86,114,168,50,124,208,12,18,108,10,194,484,103,16  },
        { 421,386,51,791,730,958,165,801,23,453,697,403,615,13,221,523,24,899,401,326,551,670,576,102,18,33,125,77,566,115,203,197  },
        { 104,319,422,945,0,81,20,43,715,32,784,693,879,7,397,74,306,207,52,681,671,2,61,173,6,636,904,95,887,5,18,192  },
        { 2,29,1,46,14,52,70,262,6,26,50,67,75,96,309,38,103,112,58,19,5,163,145,83,74,220,223,357,24,69,331,25  },
        { 786,929,590,771,687,626,941,178,465,259,70,5,13,21,35,534,107,518,132,49,878,48,146,121,379,279,31,767,147,195,108,125  },
        { 5,2,186,45,17,29,48,50,14,61,46,155,400,1,227,171,52,58,38,54,430,209,80,281,3,106,536,311,181,243,21,502  },
        { 0,32,64,95,817,494,342,403,207,202,194,389,453,365,312,180,316,5,690,237,848,577,450,61,102,523,475,289,49,241,65,482  },
        { 23,13,51,15,202,515,1,0,2,12,115,4,700,5,165,753,77,457,21,141,128,10,3,64,403,32,197,318,9,11,33,117  },
        { 119,2,6,76,5,17,45,292,306,240,32,1,19,84,64,61,4,209,710,80,26,0,106,27,214,25,128,129,29,179,3,113  },
        { 15,515,700,1,753,0,13,23,180,120,51,2,5,33,165,197,9,450,7,260,115,523,4,12,202,141,82,77,21,102,8,6  },
        { 6,138,74,280,222,85,66,226,25,42,87,204,64,337,29,135,95,174,235,26,145,65,19,32,792,294,112,52,256,2,5,22  },
        { 39,9,0,101,333,158,49,252,310,254,272,68,16,18,159,286,344,455,30,109,627,327,24,105,419,100,364,22,35,1,329,709  },
        { 21,5,32,14,2,1,38,72,76,54,17,3,48,221,270,0,45,46,12,181,37,89,36,50,540,290,430,10,4,741,99,23  },
        { 120,137,202,269,141,260,318,450,922,494,77,291,82,15,5,351,128,1,515,326,64,854,700,352,342,21,753,678,349,32,523,90  },
        { 16,24,68,35,71,18,149,118,191,167,9,0,212,124,65,246,7,67,140,189,399,101,133,60,1,108,267,114,69,92,695,154  },
        { 28,0,9,67,1,22,109,36,55,65,194,114,39,83,49,69,2,35,103,50,158,208,86,420,168,289,505,24,7,185,5,323  },
        { 147,325,198,427,142,178,202,798,5,376,20,318,259,43,120,450,77,234,534,904,470,465,878,725,329,14,315,0,260,858,70,61  },
        { 28,0,65,9,109,1,55,67,35,22,24,39,289,7,175,14,114,2,158,124,420,194,68,16,336,36,49,69,168,570,154,505  },
        { 141,180,13,115,1,23,4,269,2,202,0,317,217,51,15,5,21,352,77,318,3,752,197,10,165,365,137,341,9,515,33,64  },
        { 15,515,700,0,753,1,2,13,23,9,51,5,4,901,33,7,8,3,12,93,180,120,197,6,82,341,10,141,22,260,457,115  },
        { 6,74,66,1,25,75,324,380,278,26,138,85,135,500,87,42,220,841,97,350,29,19,70,226,38,21,52,606,235,889,2,14  },
        { 13,23,51,12,4,15,453,0,457,1,403,165,115,3,11,2,64,5,401,10,515,37,202,33,40,32,99,475,197,700,308,17  },
        { 788,180,5,83,693,319,314,4,32,21,17,11,817,3,510,498,33,12,24,104,814,120,64,117,306,804,523,450,288,160,102,43  },
        { 15,1,515,13,2,700,23,0,4,753,3,341,5,51,33,11,10,6,77,7,115,102,180,165,141,9,197,217,901,40,12,64  },
        { 101,18,9,167,520,16,0,118,60,212,604,364,694,24,55,252,68,917,264,35,1,121,146,363,39,100,806,5,21,166,191,28  },
        { 13,23,0,33,51,141,77,4,64,2,115,217,9,102,7,202,21,10,180,3,15,128,5,269,6,32,11,16,165,352,22,317  },
        { 66,135,97,74,172,6,278,7,204,324,138,174,29,85,2,87,25,140,92,192,52,38,802,69,448,500,808,620,22,1,280,232  },
        { 2,24,69,6,97,7,1,0,14,298,423,66,67,29,150,25,189,267,124,74,607,18,36,81,172,33,83,38,52,273,71,809  },
        { 0,9,158,39,68,49,109,16,24,333,35,344,101,22,159,254,272,30,124,65,28,18,793,154,310,252,327,105,627,419,286,55  },
        { 15,515,700,10,753,33,77,180,4,341,1,197,13,115,365,23,901,317,5,102,11,217,165,117,141,40,2,3,253,21,134,55  },
        { 100,166,382,478,265,264,88,39,98,1,404,274,9,593,724,921,639,438,363,682,411,31,30,812,96,447,821,905,252,0,223,435  },
        { 19,283,436,53,297,26,813,432,27,128,42,25,390,503,122,736,73,123,605,63,389,529,630,250,690,65,381,444,6,269,108,216  },
        { 33,202,13,128,494,0,51,141,269,1,4,2,102,180,15,137,65,95,6,450,77,40,117,59,457,36,196,817,134,86,49,515  },
        { 18,16,60,68,101,167,191,118,35,121,9,212,55,0,126,1,24,647,199,146,520,107,628,621,363,71,21,28,346,92,806,727  },
        { 352,230,217,531,160,93,36,669,748,854,689,258,137,871,728,699,752,251,574,202,373,351,228,120,717,260,144,219,268,82,816,1  },
        { 15,515,700,753,13,23,0,51,8,1,4,82,165,77,110,33,10,180,5,202,11,22,120,12,9,197,115,93,403,141,40,351  },
        { 0,9,101,217,35,88,352,100,39,175,30,68,562,752,13,317,252,115,180,197,64,1,83,141,65,213,165,230,194,36,28,265  },
        { 32,64,5,470,288,90,21,147,0,95,356,22,20,519,835,312,819,18,247,182,11,97,13,4,387,49,43,298,316,48,107,7  },
        { 16,14,24,1,7,2,35,0,5,50,18,69,46,12,58,75,9,67,70,163,21,54,38,48,223,502,281,37,140,60,28,10  },
        { 18,265,9,252,39,195,354,411,1,16,132,101,121,682,167,203,5,363,146,593,35,333,21,271,60,13,100,0,156,327,7,520  },
        { 4,13,1,115,141,23,2,180,5,0,51,3,217,202,77,15,33,269,341,318,317,21,165,515,11,10,197,365,9,137,64,352  },
        { 7,24,16,14,71,35,18,92,140,189,108,149,68,60,69,150,2,230,97,66,0,458,67,1,65,251,38,314,388,267,36,46  },
        { 1,22,31,36,0,2,44,5,141,105,180,170,12,64,13,98,86,55,23,21,28,164,115,127,10,125,128,4,9,239,352,197  },
        { 66,7,97,2,192,20,52,43,135,74,560,107,104,0,750,147,414,29,580,173,324,376,226,194,77,174,204,38,356,64,16,470  },
        { 0,101,9,68,35,124,24,65,39,16,252,100,154,166,28,364,149,694,30,88,55,346,1,419,71,439,265,289,22,21,175,158  },
        { 39,9,100,30,127,0,737,856,31,836,827,254,98,931,166,88,93,1,44,190,131,228,120,395,625,385,863,264,219,373,110,28  },
        { 5,17,2,3,21,45,14,155,48,32,38,1,328,181,186,46,23,51,12,61,227,29,106,54,99,133,62,832,13,37,514,543  },
        { 131,613,30,224,228,716,274,100,827,406,219,856,39,190,31,88,1,166,9,44,829,863,931,93,0,187,625,924,127,98,137,254  },
        { 352,217,64,141,752,269,180,864,437,372,954,115,498,177,77,349,317,318,579,291,947,197,247,0,23,717,237,304,128,457,776,678  },
        { 141,217,180,317,352,115,15,341,1,23,13,365,515,752,2,64,0,5,498,700,372,165,51,237,753,77,244,197,137,4,21,253  },
        { 5,2,17,14,1,45,3,38,21,29,181,58,46,48,50,133,114,171,61,155,32,6,186,281,361,12,36,54,4,13,52,514  },
        { 6,2,119,25,790,4,45,483,655,113,1,29,76,26,32,19,887,17,128,0,292,833,59,61,106,64,77,814,14,151,84,42  },
        { 13,23,2,0,51,4,1,115,141,3,5,180,33,217,77,9,202,11,7,15,10,6,317,64,21,197,515,165,102,128,22,269  },
        { 13,23,51,202,21,5,1,15,141,165,120,2,115,12,32,0,515,128,318,64,125,700,4,403,197,453,180,457,3,7,10,6  },
        { 9,39,31,30,0,127,1,44,100,131,98,187,385,276,88,442,219,908,254,116,49,166,935,28,201,36,141,827,137,299,284,21  },
        { 22,49,28,109,9,185,105,95,1,131,159,272,36,67,86,254,39,55,35,0,505,31,83,169,208,327,286,98,168,535,312,708  },
        { 5,1,2,21,0,12,48,22,10,14,36,3,32,17,23,54,86,38,4,51,13,37,137,50,65,281,114,45,28,99,58,202  },
        { 141,269,352,82,217,351,180,854,372,922,752,1,15,260,317,318,515,202,64,700,120,349,954,753,77,35,67,717,898,137,365,115  },
        { 144,203,613,418,326,406,96,669,137,679,1,228,494,822,840,317,36,83,855,160,817,859,856,816,217,831,345,93,876,77,44,251  },
        { 15,13,515,23,700,753,51,1,33,0,202,21,2,5,180,141,120,165,217,82,12,117,4,352,269,197,115,32,3,9,134,260  },
        { 13,23,115,1,0,51,4,77,2,33,15,141,10,5,341,180,515,3,217,202,9,365,317,64,700,102,11,165,197,22,753,7  },
        { 531,943,373,160,728,93,206,260,261,559,964,269,717,535,332,384,365,295,110,533,141,10,180,352,244,137,120,55,959,564,36,253  },
        { 1,31,36,170,22,55,44,10,86,64,127,0,2,98,301,164,740,338,237,143,5,125,116,13,242,141,299,180,23,169,105,12  },
        { 13,23,141,77,51,4,64,32,33,202,115,269,102,128,21,0,177,180,318,90,40,10,7,5,137,15,217,352,9,291,59,22  },
        { 202,120,260,318,77,15,450,269,1,82,33,23,141,13,51,515,351,128,700,5,64,326,137,21,102,110,753,494,93,523,817,165  },
        { 523,899,102,33,730,15,23,403,719,117,153,13,515,51,475,4,700,5,453,817,196,753,494,40,202,120,1,2,450,457,17,421  },
        { 202,403,494,450,120,817,523,475,318,453,33,402,128,77,13,51,260,576,342,102,15,23,515,4,700,5,82,753,326,210,137,615  },
        { 2,29,112,66,7,52,70,151,58,87,135,5,74,226,307,6,14,186,1,45,549,172,644,25,113,287,46,155,334,64,294,97  },
        { 1,77,349,291,260,120,652,102,5,39,64,269,9,33,340,342,13,98,888,698,23,296,100,318,51,202,87,137,638,128,50,850  },
        { 1,13,15,2,0,4,23,515,5,141,180,3,700,341,115,51,753,269,77,901,197,352,217,33,21,11,365,6,165,202,7,317  },
        { 7,14,16,2,46,5,70,58,1,38,24,35,92,163,0,75,21,18,50,54,140,12,87,220,155,69,171,23,60,9,13,307  },
        { 2,29,66,226,135,7,87,74,52,278,6,75,222,220,294,70,97,1,145,25,172,262,324,38,69,112,331,92,5,14,140,26  },
        { 15,515,700,753,33,77,117,4,1,102,134,40,153,11,13,196,217,21,5,51,23,115,32,3,2,202,141,137,128,291,48,177  },
        { 15,217,82,515,351,141,317,1,13,700,260,77,110,120,115,854,23,753,180,51,21,36,137,922,5,64,365,352,291,202,93,341  },
        { 31,190,30,373,120,110,863,88,44,127,908,856,260,318,82,98,93,187,836,717,935,39,442,131,141,254,228,219,1,968,77,116  },
        { 23,13,308,9,165,115,51,21,401,125,49,39,197,391,159,254,217,743,28,438,773,629,558,386,341,95,32,317,876,679,109,166  },
        { 49,5,43,165,7,0,21,104,125,22,173,422,64,13,623,102,20,18,314,95,91,141,23,31,193,51,391,900,779,558,92,232  },
        { 1,4,13,2,15,0,23,515,77,3,341,33,5,700,115,51,202,753,141,180,11,10,102,217,6,901,40,7,197,318,317,365  },
        { 93,843,295,120,36,160,206,261,10,137,567,110,384,141,943,268,201,332,258,55,1,180,64,116,44,144,699,203,282,31,260,373  },
        { 81,7,192,426,43,173,172,104,879,91,5,712,715,526,6,97,568,95,448,66,33,861,560,32,49,20,0,636,232,825,2,22  },
        { 475,403,51,453,33,102,13,23,494,202,0,196,15,77,153,18,4,117,515,450,318,22,730,128,700,421,65,753,269,402,134,817  },
        { 141,269,260,318,202,120,352,349,82,351,1,5,854,137,64,291,15,922,180,851,32,77,515,372,21,700,7,217,13,947,33,753  },
        { 15,515,700,753,1,13,0,2,4,23,3,5,180,115,197,12,51,165,217,10,961,9,6,141,352,21,8,7,33,77,457,120  },
        { 39,166,9,30,0,101,274,404,252,333,190,100,158,438,310,88,68,265,656,21,1,530,329,344,49,539,625,254,13,131,48,419  },
        { 0,1,28,9,22,12,65,83,67,36,5,2,50,55,96,109,16,13,24,23,21,238,49,18,285,160,128,39,69,114,7,323  },
        { 15,515,700,1,0,753,23,2,13,51,5,180,115,6,3,9,197,12,457,120,7,165,901,82,4,21,8,141,31,33,719,341  },
        { 9,39,30,0,28,166,22,49,180,1,352,35,317,158,88,141,498,131,115,345,752,128,228,217,100,83,219,930,13,251,365,36  },
        { 5,61,45,2,80,29,311,209,6,17,58,1,151,106,454,667,243,70,52,496,287,592,255,738,64,74,483,14,27,32,112,19  },
        { 31,125,22,44,299,456,685,242,599,116,170,28,0,1,492,393,506,144,558,10,268,301,239,23,13,36,963,367,55,206,105,95  },
        { 187,258,926,574,839,93,228,860,406,219,871,160,137,531,224,116,120,902,669,201,36,131,44,144,843,533,318,384,442,1,434,268  },
        { 7,107,75,16,87,9,64,177,24,18,291,77,349,141,60,232,23,0,51,269,132,14,5,21,70,32,678,112,126,121,71,947  },
        { 15,515,700,753,1,0,2,13,5,3,23,180,4,115,901,51,6,8,961,9,7,10,12,82,197,22,141,341,33,120,365,457  },
        { 13,23,51,1,5,202,2,12,15,21,165,141,0,115,3,4,32,515,197,10,180,318,128,120,64,700,6,7,403,269,457,137  },
        { 1,2,0,77,64,3,141,13,33,15,23,10,6,102,5,515,180,4,117,7,700,165,11,217,269,40,753,115,128,17,197,134  },
        { 345,531,332,269,260,317,717,752,373,351,180,352,728,82,10,365,160,533,217,143,498,251,244,93,341,901,36,1,141,898,55,864  },
        { 16,7,33,189,92,77,388,60,140,35,102,24,14,1,230,21,150,117,733,314,18,915,71,13,108,134,5,64,69,2,98,22  },
        { 142,202,234,178,5,786,77,49,70,0,416,450,639,878,1,48,21,929,147,259,315,455,198,120,12,481,163,113,846,329,318,22  },
        { 81,715,192,0,173,712,681,104,636,91,74,20,750,370,7,718,95,879,22,43,825,560,422,64,207,49,172,18,397,10,426,319  },
        { 13,23,15,51,515,0,700,753,4,1,961,2,10,115,457,11,33,453,3,5,9,40,12,197,165,77,401,475,64,102,22,569  },
        { 64,297,5,445,95,61,250,311,80,34,17,312,45,2,86,472,58,14,180,53,22,151,869,738,247,237,29,1,128,165,21,288  },
        { 16,24,18,71,7,35,118,92,14,154,60,68,0,149,28,302,124,150,55,175,2,9,97,1,429,20,108,273,22,65,43,126  },
        { 195,360,156,771,132,163,626,687,591,371,883,146,121,846,70,586,379,13,293,98,407,48,761,296,354,18,31,1,55,49,21,105  },
        { 202,13,77,23,318,33,51,0,4,141,5,21,217,32,291,102,64,128,15,10,9,494,269,137,515,403,1,31,117,700,120,317  },
        { 7,192,97,81,172,66,426,173,43,715,712,232,861,879,104,330,568,298,74,893,885,526,387,825,92,140,91,14,636,6,5,448  },
        { 2,1,14,6,67,7,65,69,24,36,66,124,108,83,38,29,22,86,0,18,484,5,28,46,12,10,25,302,150,16,650,74  },
        { 33,77,13,202,102,4,0,23,128,51,141,64,318,22,403,269,137,10,15,40,494,117,32,59,11,153,1,21,177,196,515,115  },
        { 269,141,318,77,349,291,217,202,33,15,372,304,515,22,102,177,351,700,352,120,5,137,10,317,260,753,64,851,854,403,49,21  },
        { 6,74,66,85,138,25,87,42,135,26,226,222,280,29,75,500,220,278,792,70,19,2,1,294,204,64,32,145,853,112,52,174  },
        { 9,0,105,39,16,18,1,101,272,31,127,98,24,518,333,252,310,28,68,737,846,371,158,916,938,49,30,7,286,35,301,455  },
        { 2,1,14,67,24,46,83,108,69,29,38,103,114,36,6,133,18,0,28,7,65,52,236,75,50,398,5,309,135,16,278,160  },
        { 22,1,28,105,49,95,0,2,67,55,36,239,168,159,65,35,14,170,320,164,9,7,10,5,114,12,83,64,194,109,24,301  },
        { 7,66,172,97,92,140,232,568,298,14,192,314,16,380,135,324,2,330,74,38,357,448,126,69,35,5,107,6,387,60,204,572  },
        { 2,29,1,14,5,6,46,133,114,50,52,26,218,108,19,13,366,236,27,45,70,17,58,23,86,51,137,65,112,38,25,12  },
        { 6,1,74,25,2,26,29,66,42,19,75,14,388,67,108,70,52,85,103,65,38,138,357,133,114,594,324,516,603,96,309,69  },
        { 22,9,28,1,36,49,109,105,86,95,131,31,169,39,0,141,272,159,44,55,98,180,13,30,185,115,83,128,352,137,64,208  },
        { 203,822,326,23,77,859,403,494,576,39,473,182,33,1,691,100,18,217,13,817,411,447,363,102,93,966,96,478,291,704,310,120  },
        { 15,515,700,753,33,77,117,4,102,134,115,153,13,1,40,217,11,196,341,2,5,3,23,317,365,0,21,291,32,51,12,569  },
        { 15,515,700,753,13,0,23,1,8,82,51,165,197,120,180,2,9,33,4,110,5,12,10,260,351,386,141,7,457,475,93,901  },
        { 1,23,13,15,51,0,21,2,515,5,141,180,120,165,700,202,197,4,753,12,33,9,7,82,115,93,3,352,260,6,110,48  },
        { 15,515,700,753,0,1,2,5,3,4,8,13,180,341,10,23,7,6,9,51,77,197,961,115,165,82,120,31,22,202,457,217  },
        { 559,661,922,564,141,533,10,317,373,110,143,269,244,260,332,261,93,642,752,295,351,876,531,843,180,206,728,384,352,1,434,120  },
        { 15,515,1,0,700,2,13,23,753,5,51,180,3,165,12,6,197,115,4,9,7,21,719,8,457,82,141,120,33,22,901,10  },
        { 198,234,0,325,5,77,202,416,20,147,32,43,639,315,49,61,450,455,142,21,113,230,22,318,725,342,207,13,95,904,494,10  },
        { 447,264,363,9,411,676,682,1,156,664,821,478,166,354,812,39,100,905,382,897,98,18,759,404,31,101,724,5,265,223,88,13  },
        { 24,14,69,16,35,18,2,7,108,189,71,67,267,149,1,46,68,83,38,140,0,236,251,9,388,60,133,103,65,28,29,50  },
        { 16,7,35,20,14,18,109,2,43,120,107,60,1,121,326,907,553,77,13,147,23,82,68,260,0,403,5,24,202,126,265,199  },
        { 30,131,187,276,31,44,613,442,39,9,190,228,1,839,116,935,908,219,127,88,244,224,110,137,93,201,98,141,36,567,0,856  },
        { 98,223,1,393,812,265,100,421,593,834,697,48,51,410,791,382,21,88,31,284,9,125,96,293,230,23,213,217,656,689,541,5  },
        { 98,51,127,219,616,258,105,293,395,421,924,512,31,308,23,201,116,44,301,272,763,276,125,13,453,170,401,295,261,944,115,567  },
        { 253,110,951,352,811,206,332,180,141,244,282,10,854,417,642,638,559,752,143,911,260,55,93,533,499,498,661,120,351,959,564,341  },
        { 49,9,159,254,272,158,0,131,28,39,627,105,327,286,22,518,688,578,68,347,374,101,224,424,95,35,219,24,16,364,65,344  },
        { 105,22,131,272,98,286,327,109,374,239,28,95,320,219,9,224,55,127,187,36,578,169,64,185,538,1,159,10,371,634,49,616  },
        { 691,478,340,1,658,914,724,363,744,698,156,772,411,296,682,447,9,284,335,98,264,303,909,21,354,410,225,13,664,686,88,919  },
        { 16,24,35,18,71,7,140,108,189,267,92,60,14,230,68,69,9,1,149,46,246,191,388,167,2,0,118,236,133,21,674,5  },
        { 9,0,127,31,98,371,395,39,737,49,1,44,385,272,512,28,293,242,836,761,254,299,101,16,187,22,116,158,159,131,18,21  },
        { 16,18,68,0,60,35,9,101,252,28,118,24,419,55,7,109,604,71,39,121,22,364,14,158,191,167,925,126,329,21,92,49  },
        { 116,268,203,93,206,692,551,31,417,940,499,8,473,44,202,523,959,0,120,137,559,22,450,403,576,10,728,299,13,326,51,1  },
        { 225,459,744,1,919,914,691,330,622,21,141,223,5,284,934,335,88,538,340,82,385,839,363,120,478,98,48,30,64,32,686,166  },
        { 5,1,2,0,14,36,21,281,12,48,50,67,22,28,54,83,24,218,38,10,181,9,32,18,65,58,45,114,430,17,99,37  },
        { 137,450,202,704,120,260,326,318,968,269,851,403,291,77,23,141,182,310,494,373,351,457,82,890,349,110,60,128,817,678,105,96  },
        { 15,515,700,753,4,33,13,23,77,5,40,11,102,93,1,21,110,51,82,117,141,2,10,8,32,64,120,31,202,3,217,115  },
        { 15,13,1,23,515,0,51,2,700,5,753,21,180,141,165,3,12,115,197,4,7,6,457,9,352,202,33,8,719,120,77,341  },
        { 219,127,258,98,276,201,131,395,944,293,116,284,567,31,242,105,137,935,295,44,403,860,51,224,576,456,9,371,578,475,202,512  },
        { 16,7,18,35,60,0,14,20,118,28,68,22,2,24,1,92,158,107,5,49,154,126,109,12,43,10,55,6,677,71,21,168  },
        { 93,728,531,160,559,373,574,120,295,860,533,269,717,260,926,902,258,318,36,201,261,434,851,137,617,141,187,352,843,384,332,251  },
        { 28,0,1,9,22,109,83,39,49,12,36,67,55,5,96,2,128,30,158,69,21,23,160,208,35,13,65,323,50,141,194,238  },
        { 23,13,51,1,5,15,141,21,0,2,165,515,202,700,12,197,180,120,32,115,4,753,64,9,7,269,6,3,125,386,48,453  },
        { 5,21,13,49,14,20,7,23,43,32,1,0,652,48,713,22,38,2,16,132,955,107,12,279,24,888,197,640,70,303,18,638  },
        { 9,0,28,39,1,30,35,101,22,67,83,141,49,175,36,68,55,88,13,251,10,69,23,158,180,115,64,100,217,65,345,166  },
        { 260,120,82,269,5,450,351,1,202,141,854,13,77,922,32,33,137,4,23,125,291,21,15,515,165,349,177,700,318,326,180,753  },
        { 121,16,18,35,363,101,60,20,107,14,68,259,621,55,604,43,7,252,9,364,126,0,167,191,5,407,132,28,199,419,146,10  },
        { 13,23,51,1,15,0,2,141,5,515,12,21,700,115,165,180,4,753,3,197,202,32,9,120,7,8,6,11,37,10,457,269  },
        { 201,144,206,443,418,203,435,96,335,459,187,1,88,332,330,321,269,934,30,372,822,521,268,326,44,523,382,141,410,264,494,473  },
        { 31,44,276,201,116,131,284,662,567,144,9,489,98,295,268,434,0,30,137,39,93,1,187,22,219,918,110,299,141,36,224,384  },
        { 520,478,664,1,264,604,9,167,777,759,411,0,806,724,48,21,101,68,647,936,363,223,118,682,410,18,100,16,252,98,265,13  },
        { 23,70,21,87,60,75,120,182,163,379,92,18,7,937,71,121,446,132,24,98,931,126,107,77,795,195,115,44,411,146,51,850  },
        { 39,9,0,737,127,31,846,98,1,827,105,310,371,30,254,100,44,18,395,242,272,101,385,916,836,16,265,131,938,93,166,557  },
        { 279,20,43,126,107,7,92,16,356,362,60,595,246,359,598,35,0,683,939,653,121,97,125,441,399,392,150,199,48,230,14,649  },
        { 206,417,93,959,499,728,8,559,120,473,137,141,10,564,31,260,44,450,203,341,253,244,373,116,143,638,268,180,352,110,318,940  },
        { 259,465,147,132,590,687,534,199,581,146,941,427,107,640,279,178,121,5,195,150,522,955,198,35,786,929,798,142,1,21,325,626  },
        { 523,15,120,450,202,515,403,51,817,700,13,753,23,457,33,899,128,64,730,102,494,342,115,719,453,196,49,99,318,421,308,5  },
        { 141,559,10,244,365,564,661,180,253,143,752,110,55,317,533,341,901,93,373,206,535,160,82,922,260,36,531,964,352,332,261,197  },
        { 219,258,98,127,276,964,943,137,843,535,201,935,131,860,261,295,284,567,206,44,116,31,253,492,203,332,160,615,36,93,55,692  },
        { 0,319,422,207,945,693,577,887,32,804,95,344,104,904,61,20,5,43,7,725,113,510,306,102,49,263,153,426,33,83,22,9  },
        { 1,22,0,5,12,2,36,21,28,86,49,105,9,10,23,13,141,95,31,55,128,37,51,4,83,202,3,64,96,7,32,44  },
        { 15,515,13,700,1,0,753,2,23,3,4,5,51,10,115,197,6,33,12,9,165,7,8,77,11,961,180,269,141,22,120,457  },
        { 15,1,23,120,77,13,515,51,141,202,700,180,110,137,260,753,326,5,128,102,0,21,2,165,269,33,197,450,318,217,93,115  },
        { 15,515,1,700,0,753,13,2,23,180,51,5,120,4,9,115,197,12,7,165,21,33,6,82,3,8,523,901,31,141,457,260  },
        { 16,18,24,7,92,35,60,75,9,13,71,14,0,108,50,21,126,121,1,140,23,5,132,146,2,12,128,10,64,141,70,87  },
        { 180,341,901,15,515,1,365,700,0,2,197,753,115,4,10,13,752,5,3,8,165,317,141,23,143,873,44,31,569,55,93,6  },
        { 9,0,175,35,101,28,39,67,68,1,65,83,30,69,364,336,22,114,55,124,194,158,100,289,252,166,64,345,103,36,50,88  },
        { 64,165,180,197,115,247,217,237,21,13,32,316,22,141,352,72,288,304,95,225,76,391,386,16,468,90,49,35,365,640,372,23  },
        { 15,515,700,13,753,1,0,2,23,4,5,3,115,51,141,197,12,10,180,961,7,9,21,33,217,6,8,165,457,11,77,341  },
        { 132,121,199,146,60,279,493,640,407,598,126,195,534,581,955,590,107,5,150,35,522,49,259,16,18,360,156,0,147,362,21,167  },
        { 0,1,28,9,22,5,36,12,65,24,67,96,2,83,18,50,114,55,21,16,7,10,23,14,13,160,137,51,48,218,103,69  },
        { 93,120,957,77,30,968,459,110,137,160,613,102,202,352,373,141,31,372,217,330,190,318,269,260,203,44,28,473,228,177,863,704  },
        { 15,515,700,0,753,1,13,23,2,51,5,9,120,82,4,7,901,197,10,8,260,180,341,12,33,6,3,523,165,102,115,141  },
        { 206,417,8,141,499,44,244,93,31,10,137,253,559,116,728,144,120,564,269,638,203,352,143,260,341,752,268,717,951,180,160,110  },
        { 530,254,228,1,96,21,406,39,827,31,669,840,613,829,137,679,166,98,23,51,960,438,131,93,48,224,219,317,310,36,876,190  },
        { 15,515,700,753,13,457,0,197,719,1,165,82,23,8,120,730,2,10,12,180,134,5,9,141,260,4,351,51,115,3,341,899  },
        { 0,16,68,9,24,28,18,35,252,109,39,419,124,158,154,55,101,71,22,118,60,7,49,65,333,14,1,10,329,364,677,346  },
        { 1,15,13,23,515,51,120,0,700,180,2,165,5,753,141,197,21,33,202,102,260,4,9,12,7,326,137,450,115,6,82,110  },
        { 535,253,352,564,110,365,82,180,341,10,854,533,55,898,244,901,873,141,752,143,642,559,498,317,36,951,115,964,638,282,661,197  },
        { 31,44,125,338,116,64,242,36,1,10,55,22,456,237,180,13,299,164,506,86,23,165,558,143,0,762,492,479,844,546,93,8  },
        { 13,23,4,1,202,2,0,51,115,77,141,180,5,15,217,3,33,11,515,317,9,10,102,21,700,341,365,318,269,64,32,128  },
        { 9,39,0,166,68,101,28,364,30,158,562,35,175,65,333,154,49,404,706,124,21,252,274,168,190,289,100,570,16,1,310,346  },
        { 15,515,700,753,341,13,0,23,1,33,141,4,260,82,77,51,351,180,9,5,115,137,10,217,11,120,102,40,349,269,202,854  }
#else
        #include "rgbcx_table4.h"
#endif
    };

    static uint8_t g_best_total_orderings3[NUM_UNIQUE_TOTAL_ORDERINGS3][32] =
    {
        { 12,1,3,5,27,2,4,38,8,7,16,18,6,10,41,79,40,23,46,9,20,88,22,37,14,19,24,126,99,119,35,11  },
        { 7,64,116,14,94,30,8,42,1,108,47,55,137,10,134,95,96,115,69,32,63,29,90,113,11,148,16,103,19,9,34,25  },
        { 12,1,0,5,3,7,4,27,8,6,38,40,41,16,18,46,9,10,20,23,79,62,14,22,88,99,37,126,92,19,120,11  },
        { 16,88,27,18,46,48,126,107,79,19,59,38,37,65,23,66,0,2,3,43,12,151,28,25,5,87,72,40,1,20,52,92  },
        { 79,48,88,16,27,65,18,38,46,19,37,4,72,33,126,41,52,0,12,92,5,1,2,107,3,77,23,91,43,51,22,74  },
        { 1,8,41,122,10,22,2,0,87,24,37,120,38,7,39,4,5,3,9,92,62,59,23,16,104,11,27,79,19,26,25,32  },
        { 2,76,99,28,40,86,93,21,138,60,6,0,17,128,145,119,98,144,141,82,147,54,67,75,5,12,27,132,146,1,38,14  },
        { 47,7,64,90,1,118,116,85,57,14,30,94,50,45,137,134,8,42,69,139,55,68,58,108,95,29,10,115,0,32,2,11  },
        { 49,8,10,30,124,11,32,113,130,58,125,9,100,53,104,115,131,103,24,7,1,39,45,36,139,0,137,22,90,44,114,105  },
        { 9,38,72,125,49,41,84,11,13,5,27,0,16,92,8,2,65,105,10,18,48,29,127,131,36,14,1,46,111,79,130,12  },
        { 130,8,10,100,104,131,49,32,53,39,30,36,113,24,11,22,124,44,83,58,7,103,1,4,9,125,5,0,91,33,115,74  },
        { 114,11,58,8,120,49,9,124,142,111,41,30,10,0,97,130,62,84,38,5,72,125,92,127,100,27,139,113,13,132,32,1  },
        { 60,46,28,27,40,20,0,17,18,2,126,16,6,38,86,23,79,54,1,93,5,88,41,14,21,111,7,48,3,84,72,62  },
        { 72,92,38,65,84,48,41,79,27,16,29,111,88,5,18,46,1,0,152,14,37,19,77,42,132,7,22,13,119,56,12,2  },
        { 7,55,1,95,29,56,64,116,143,8,14,30,47,94,152,90,65,67,10,133,42,72,146,84,16,48,6,0,25,108,77,21  },
        { 27,23,20,5,0,79,38,2,3,1,59,46,4,41,33,86,37,87,88,92,7,126,43,8,22,152,151,150,149,148,147,146  },
        { 12,0,1,2,7,6,3,5,28,4,8,14,60,40,17,19,21,86,126,93,10,18,9,29,48,99,65,25,84,119,72,41  },
        { 60,40,99,2,54,12,0,1,19,28,98,93,6,138,21,5,27,17,151,14,76,46,16,18,38,29,86,144,107,7,25,41  },
        { 12,0,1,2,3,5,6,7,4,28,8,60,14,40,16,17,21,10,19,9,86,38,126,41,93,27,29,48,62,84,79,99  },
        { 0,1,2,10,5,8,3,25,4,29,32,34,63,7,77,26,16,48,65,56,14,22,129,103,72,24,18,152,140,53,96,42  },
        { 46,126,18,54,12,16,1,0,5,2,27,98,20,23,6,3,88,48,28,7,19,8,4,60,151,38,37,21,79,14,65,40  },
        { 76,6,141,86,119,2,138,67,28,145,0,93,17,1,40,60,146,99,147,14,21,144,132,7,5,29,55,27,16,75,19,12  },
        { 71,5,51,39,22,80,0,43,10,122,8,62,41,24,104,87,35,37,2,91,33,120,36,38,1,131,9,100,130,66,3,4  },
        { 126,18,46,27,20,16,88,23,12,79,54,59,48,0,73,1,37,151,5,19,28,38,2,66,60,3,65,98,14,26,6,43  },
        { 22,10,8,5,0,71,35,80,104,39,24,51,100,1,62,32,2,130,11,41,7,9,53,43,49,83,122,120,30,44,37,38  },
        { 1,34,14,129,53,63,42,26,121,148,7,44,96,10,0,24,100,32,64,116,140,22,5,19,29,103,135,108,8,61,39,83  },
        { 1,7,34,63,44,25,135,14,24,108,22,0,83,94,5,129,35,101,47,121,2,19,42,53,6,110,103,8,148,10,16,123  },
        { 12,28,16,60,18,1,6,21,14,0,86,19,2,48,93,17,38,29,7,5,65,126,46,72,41,79,84,119,40,56,54,88  },
        { 0,2,12,27,5,46,38,40,41,79,88,99,3,23,1,62,20,4,22,37,92,35,18,8,16,24,10,60,7,120,98,54  },
        { 1,7,14,56,8,0,84,67,10,2,133,72,42,111,5,30,21,4,9,3,25,94,16,116,47,11,65,18,132,90,55,64  },
        { 30,8,124,139,45,11,58,90,113,137,7,115,10,32,1,49,94,85,9,47,108,103,0,97,63,14,50,114,53,106,100,25  },
        { 65,38,48,27,16,79,72,18,88,19,46,77,84,92,37,41,0,29,1,14,12,111,2,5,31,36,87,74,105,40,28,51  },
        { 10,8,30,113,130,100,53,32,115,103,104,7,1,121,39,49,131,44,24,36,63,137,34,45,22,90,108,83,26,11,94,139  },
        { 51,52,43,33,5,74,16,37,71,91,38,3,36,87,48,22,4,0,122,41,39,18,66,27,79,24,65,88,59,23,62,92  },
        { 1,7,63,53,108,121,94,44,103,100,14,10,129,47,32,26,24,25,148,42,135,22,0,61,83,8,39,104,5,64,115,34  },
        { 1,8,10,7,5,0,80,32,62,2,24,44,53,83,9,41,30,22,100,11,14,25,120,4,26,6,3,16,122,34,19,35  },
        { 74,4,36,48,33,91,39,79,22,16,65,5,131,38,24,71,27,52,0,105,51,18,88,104,3,31,10,37,72,19,41,130  },
        { 59,43,38,79,23,27,92,51,0,16,46,5,18,88,41,37,66,3,87,20,48,2,122,4,22,12,1,126,19,65,33,24  },
        { 12,28,1,27,0,16,2,46,65,60,21,3,5,18,6,19,48,14,4,7,79,88,86,29,22,72,93,40,23,8,17,41  },
        { 22,91,39,33,24,71,5,131,36,10,51,0,130,8,104,2,35,125,9,43,52,49,83,80,100,41,122,3,37,38,4,16  },
        { 12,0,1,2,5,3,4,8,7,27,18,38,10,6,16,46,9,20,41,23,126,79,22,14,19,99,88,54,37,48,62,35  },
        { 12,27,1,2,3,0,46,4,38,16,8,28,7,79,18,5,84,6,88,10,14,21,23,20,40,22,60,19,9,29,72,65  },
        { 1,14,7,55,95,29,8,94,30,56,10,108,77,116,152,64,32,48,63,42,143,148,16,25,137,65,11,0,115,9,19,72  },
        { 37,79,66,38,16,52,48,59,43,27,87,33,41,4,23,51,3,5,88,18,92,46,73,122,22,71,20,0,65,19,2,120  },
        { 24,32,83,22,53,1,8,10,7,30,35,5,103,0,100,101,121,113,34,123,63,2,44,25,71,115,80,14,26,108,51,39  },
        { 97,45,111,58,85,139,0,90,47,7,120,106,142,30,50,132,41,62,84,1,119,114,14,56,117,8,38,29,2,64,116,5  },
        { 12,28,16,18,1,60,6,14,2,21,0,86,126,19,48,93,7,27,17,29,5,65,54,38,72,79,84,88,119,145,8,111  },
        { 118,47,64,116,57,85,7,14,50,1,42,0,45,68,86,69,2,111,134,28,90,55,16,29,56,48,84,144,60,30,112,41  },
        { 12,1,2,0,7,6,28,5,3,4,8,14,60,21,18,40,17,86,10,9,16,29,19,93,126,79,38,84,72,27,111,119  },
        { 11,8,49,130,10,125,9,124,100,114,131,30,58,104,32,39,24,113,36,105,0,41,22,120,5,53,111,38,142,44,83,35  },
        { 50,70,47,118,85,57,106,0,45,7,64,90,81,14,2,134,28,62,86,55,69,1,78,119,68,56,18,67,16,60,29,21  },
        { 43,37,33,87,51,41,66,5,122,38,22,59,92,0,23,91,27,16,71,79,18,52,120,4,3,24,46,20,73,39,62,36  },
        { 79,48,4,16,27,88,43,33,18,38,65,37,46,3,19,51,52,22,66,87,74,5,41,91,23,59,0,71,122,72,20,92  },
        { 32,100,10,8,30,104,24,44,39,113,83,103,1,7,22,53,115,63,135,121,26,35,34,5,0,108,137,90,91,45,2,130  },
        { 0,1,2,5,16,12,6,7,14,3,19,18,29,20,4,21,40,8,17,35,23,48,126,22,25,56,26,10,98,27,38,65  },
        { 143,67,56,146,1,7,133,55,64,141,134,69,6,47,14,29,84,21,111,147,57,16,95,72,118,132,50,0,2,18,119,42  },
        { 1,7,67,14,133,111,8,84,0,21,2,47,64,132,55,10,95,147,119,42,16,5,72,56,4,3,6,29,9,25,18,30  },
        { 68,57,69,112,144,86,102,2,134,55,0,70,118,64,75,47,14,28,93,143,67,7,50,149,1,21,29,56,119,95,60,78  },
        { 58,97,114,30,124,45,11,139,8,90,0,142,7,10,41,113,84,62,49,111,85,1,9,5,137,120,32,14,2,117,47,38  },
        { 23,66,18,79,38,20,43,27,16,88,46,59,126,37,87,12,73,92,3,5,48,0,19,54,2,51,28,1,41,65,122,22  },
        { 0,12,2,27,5,40,46,38,1,41,3,79,88,23,99,4,20,62,22,54,92,18,8,37,16,35,10,7,19,120,144,24  },
        { 1,14,25,26,0,7,44,34,129,42,24,5,135,22,19,148,6,96,83,2,29,16,63,35,101,64,140,136,116,110,3,10  },
        { 12,1,2,27,3,4,38,5,7,8,18,16,46,6,0,40,41,10,79,23,88,9,20,22,14,19,37,92,48,126,28,21  },
        { 7,1,10,32,108,103,94,47,8,53,25,14,34,115,100,129,121,130,148,42,64,116,63,26,44,0,24,30,113,4,104,22  },
        { 47,134,7,14,55,69,64,95,1,29,85,118,56,116,45,57,102,143,50,90,42,30,16,94,0,8,67,75,133,2,18,48  },
        { 12,1,2,0,7,6,28,8,14,5,3,4,40,21,17,18,60,86,16,93,126,10,9,29,99,38,119,25,19,54,27,84  },
        { 59,16,27,18,23,88,79,37,46,66,38,20,73,126,3,43,48,87,92,51,41,12,19,5,52,107,65,0,151,122,54,2  },
        { 1,21,147,7,119,14,76,132,55,0,86,145,2,6,69,67,16,143,111,138,17,28,29,60,18,93,8,19,40,56,84,5  },
        { 144,86,112,2,68,102,69,0,149,93,75,28,57,55,145,60,21,67,99,134,143,40,146,119,82,110,62,6,29,26,78,14  },
        { 102,57,55,69,143,75,146,67,56,68,134,2,29,141,0,21,6,14,133,118,64,1,7,95,47,84,111,28,147,82,72,119  },
        { 0,70,57,119,50,145,2,86,28,118,69,78,149,47,60,68,67,55,93,81,134,21,14,62,64,7,5,1,132,85,41,16  },
        { 51,5,43,71,122,87,41,37,91,39,0,22,33,36,38,24,66,120,62,2,80,16,92,10,59,4,27,23,35,79,8,3  },
        { 12,1,2,0,7,6,28,5,8,14,3,21,40,4,60,17,86,18,16,93,10,9,126,119,99,29,19,41,38,27,25,92  },
        { 27,18,46,126,23,16,88,79,20,151,59,73,48,38,0,54,12,2,37,1,19,5,28,60,66,41,3,109,86,65,40,6  },
        { 48,79,4,33,16,74,65,38,88,27,91,52,18,36,22,19,46,0,37,3,51,5,71,39,72,43,24,41,92,87,2,10  },
        { 86,2,144,93,28,112,141,6,102,21,99,60,75,0,68,82,69,146,67,149,55,40,145,76,111,147,56,119,110,143,26,132  },
        { 6,138,2,99,86,17,40,93,28,21,145,141,0,60,119,147,128,76,67,54,1,12,5,27,144,14,38,98,146,41,29,19  },
        { 1,8,0,10,2,29,7,5,3,56,4,25,14,152,63,32,65,72,96,42,34,108,48,9,26,16,84,103,67,148,22,129  },
        { 149,145,0,86,2,28,93,144,62,60,119,101,21,41,5,35,78,99,26,40,12,68,57,67,110,120,69,18,55,76,132,70  },
        { 12,28,16,1,48,19,6,60,2,14,18,21,0,27,46,65,86,29,5,7,72,93,40,3,17,84,56,88,126,4,38,8  },
        { 1,8,5,10,7,24,2,62,0,41,22,122,120,9,4,3,32,87,11,37,38,83,100,44,25,104,16,26,39,80,14,6  },
        { 0,119,62,86,145,149,28,132,93,2,120,67,60,41,35,5,144,21,123,38,111,81,84,56,12,44,24,50,92,55,40,22  },
        { 2,93,99,28,40,144,60,0,86,150,76,21,149,98,6,25,1,61,82,26,12,5,54,141,7,18,145,16,27,138,110,38  },
        { 24,8,10,22,32,35,100,5,1,53,0,7,71,80,30,123,83,104,51,11,2,39,44,113,9,62,25,103,34,101,43,41  },
        { 12,1,2,0,7,6,28,5,40,60,8,16,3,18,14,4,86,21,17,93,41,10,9,99,27,119,38,19,126,22,48,145  },
        { 45,47,50,7,85,90,97,1,64,139,116,118,30,58,14,106,70,111,0,57,94,42,137,142,29,120,8,56,18,134,84,41  },
        { 12,0,2,5,27,38,1,46,41,40,79,144,3,22,88,23,28,60,99,62,6,24,26,7,4,16,10,35,37,18,14,20  },
        { 37,38,59,92,0,5,23,51,79,41,27,22,2,3,87,16,46,4,1,43,20,33,18,88,24,71,8,10,48,19,126,122  },
        { 12,28,16,60,1,18,6,21,19,14,48,0,2,86,93,5,46,29,17,27,65,7,3,72,38,126,119,40,84,37,56,4  },
        { 0,2,5,1,16,6,27,28,18,38,60,7,14,21,46,40,86,41,19,48,93,8,3,79,22,4,10,37,62,23,24,111  },
        { 85,7,90,30,47,139,45,50,94,58,137,1,8,64,14,116,118,115,113,11,124,108,0,10,97,57,32,70,42,106,29,114  },
        { 33,36,22,71,51,5,91,39,0,52,43,24,131,74,16,37,38,122,41,3,87,48,4,104,35,80,10,2,105,62,27,18  },
        { 12,1,27,2,0,16,3,28,46,18,4,6,5,72,21,79,38,7,14,60,88,8,65,19,48,29,23,40,22,20,86,126  },
        { 0,12,2,27,5,38,46,41,1,40,79,3,88,23,22,99,20,37,62,4,18,6,16,35,60,28,24,7,92,8,14,10  },
        { 7,47,1,30,137,8,116,94,90,64,14,115,108,118,57,10,148,113,42,85,32,11,63,50,103,45,124,134,55,9,69,34  },
        { 55,7,1,29,56,143,64,47,67,133,14,146,95,72,84,8,116,111,6,134,141,21,65,0,69,30,16,45,85,42,50,10  },
        { 14,1,42,8,10,29,108,63,55,148,95,32,7,19,25,115,103,34,56,129,77,0,16,152,94,30,113,26,2,5,48,4  },
        { 111,120,142,97,58,0,41,45,62,132,114,84,139,30,5,8,38,2,7,85,119,90,117,1,124,11,56,47,28,27,35,72  },
        { 1,0,14,2,6,5,16,19,7,29,42,18,3,25,12,35,21,8,26,17,40,4,20,48,109,99,22,96,55,101,10,61  },
        { 12,0,1,5,3,2,4,7,27,8,38,6,40,18,16,10,20,46,9,41,23,22,79,14,62,19,37,126,88,11,92,48  },
        { 10,8,104,39,24,32,22,83,44,100,30,130,53,91,113,5,11,1,35,33,7,49,0,2,103,71,36,124,9,80,131,34  },
        { 1,7,0,14,8,34,5,25,35,26,6,63,10,123,2,16,103,19,44,32,135,121,108,80,62,30,115,94,149,144,53,18  },
        { 75,68,146,141,102,67,2,21,6,57,69,143,0,55,82,86,28,144,147,29,93,112,56,119,133,14,76,60,84,134,111,145  },
        { 10,32,115,7,8,53,1,108,30,113,94,137,100,63,90,34,130,103,121,47,44,25,104,39,24,26,85,14,49,36,22,131  },
        { 39,24,10,22,8,130,91,104,83,49,5,33,100,11,0,35,32,131,71,36,9,44,53,2,80,51,30,1,41,7,43,62  },
        { 38,36,65,105,27,72,31,79,41,131,5,48,125,39,0,16,92,46,22,13,18,84,24,37,88,2,33,74,91,71,130,49  },
        { 0,106,62,50,45,119,85,81,132,28,2,86,41,47,38,60,35,117,5,29,7,30,145,90,55,70,14,111,18,67,93,56  },
        { 0,2,5,1,3,25,19,26,4,34,29,10,22,16,8,7,24,14,48,65,53,18,6,77,44,56,72,61,121,21,136,40  },
        { 7,1,94,8,47,115,10,32,113,103,30,108,137,63,14,64,116,148,129,42,90,25,34,118,53,57,11,49,85,9,96,50  },
        { 14,0,1,26,19,5,42,2,25,24,29,22,6,44,61,16,7,96,136,3,140,34,35,55,135,18,48,77,83,4,8,10  },
        { 1,7,14,0,25,6,34,5,26,16,63,2,19,8,35,101,108,29,94,10,18,42,123,144,129,47,61,21,3,62,149,4  },
        { 12,0,2,1,28,5,6,120,7,60,40,16,18,86,27,14,21,93,8,62,41,38,3,17,4,119,99,48,19,126,10,9  },
        { 86,144,93,2,28,149,0,60,99,112,110,145,40,21,102,26,75,62,69,1,12,101,119,25,76,67,7,68,55,5,6,14  },
        { 8,30,10,32,113,49,115,137,124,103,45,90,7,139,11,1,58,53,130,94,108,100,9,63,85,125,34,47,0,24,44,104  },
        { 120,142,111,41,58,114,97,0,11,62,84,124,5,30,8,38,132,127,27,139,92,10,72,45,49,9,28,2,29,56,16,1  },
        { 8,113,30,137,7,32,10,90,94,115,1,103,108,63,47,85,49,53,11,45,34,50,14,25,9,124,100,130,139,121,42,26  },
        { 64,7,14,47,134,55,1,42,95,69,116,90,94,30,8,29,56,137,45,108,85,10,57,16,102,143,118,19,63,32,11,50  },
        { 62,132,0,119,120,41,111,86,35,28,5,84,56,38,2,93,145,60,67,12,92,27,29,72,55,117,21,24,133,149,22,45  },
        { 57,68,69,118,134,64,50,47,55,14,7,2,102,144,0,112,70,86,85,1,95,29,116,143,42,75,16,56,28,45,21,48  },
        { 0,12,2,1,5,28,6,40,60,27,7,38,16,14,86,18,93,41,62,46,99,35,8,23,3,17,22,21,10,19,79,20  },
        { 12,1,2,27,16,3,38,111,4,0,18,5,7,46,40,8,79,6,14,28,88,10,48,41,19,84,21,9,22,23,20,72  },
        { 53,103,32,7,1,100,22,63,71,44,10,115,108,24,92,104,26,30,122,94,8,39,83,34,137,135,90,91,121,5,87,47  },
        { 87,37,41,0,22,38,2,92,1,24,4,8,3,59,10,5,39,23,71,79,122,27,16,46,33,7,91,20,18,51,9,120  },
        { 1,7,8,10,0,5,35,32,53,44,14,30,2,80,25,34,6,62,26,103,16,19,63,9,149,24,121,41,22,11,113,83  },
        { 11,58,8,30,124,49,10,113,9,114,139,45,97,32,7,137,90,1,0,130,115,125,100,24,5,94,53,41,14,13,35,38  },
        { 125,105,9,36,131,49,8,130,39,11,10,5,22,38,41,104,0,31,13,24,27,16,2,72,65,91,48,32,84,18,100,74  },
        { 12,1,0,2,6,3,7,5,4,8,14,28,16,60,18,10,21,17,19,9,40,27,86,93,29,38,54,11,25,48,46,41  },
        { 84,41,38,72,92,29,111,5,65,120,79,0,27,56,48,14,132,16,119,22,86,88,46,28,62,12,1,2,93,18,24,127  },
        { 99,28,40,60,2,93,138,0,98,17,86,54,76,12,27,1,21,144,128,38,5,14,46,18,25,16,109,6,41,145,7,29  },
        { 1,63,10,32,148,14,103,34,42,7,8,108,116,53,64,96,25,121,26,94,140,0,29,19,55,24,100,136,5,4,44,115  },
        { 131,100,130,49,10,8,36,104,39,0,48,41,11,38,4,24,27,22,16,44,79,5,33,2,53,9,125,74,91,120,32,83  },
        { 36,39,131,74,4,91,22,33,125,104,130,48,10,24,16,5,49,8,100,105,79,0,9,65,71,2,18,83,31,11,19,44  },
        { 0,12,2,1,6,5,7,28,40,60,16,14,18,62,86,27,93,8,17,38,21,41,35,99,3,19,10,23,22,4,9,48  },
        { 1,7,67,14,21,147,111,55,132,119,0,8,2,76,64,16,47,84,6,18,86,95,145,10,42,29,133,5,56,134,17,72  },
        { 69,55,47,134,102,143,7,57,118,95,14,64,29,56,1,50,75,67,146,2,0,133,68,16,21,6,141,85,116,18,72,65  },
        { 1,44,7,24,83,63,34,103,22,121,53,32,25,35,0,115,108,5,14,8,10,101,94,30,2,123,110,26,137,47,90,19  },
        { 14,1,25,42,34,0,26,96,19,29,140,5,53,10,2,121,3,24,44,22,55,77,129,7,63,16,8,4,6,61,100,48  },
        { 30,90,7,8,137,94,85,1,47,113,115,108,45,139,124,11,10,32,50,58,103,14,63,64,9,116,49,42,25,148,0,53  },
        { 40,99,2,60,28,17,0,54,93,98,86,138,6,12,21,76,1,5,27,144,128,38,19,46,14,41,145,7,16,67,3,109  },
        { 45,58,30,139,90,7,85,137,97,8,124,47,1,11,106,114,50,94,0,113,10,115,14,32,9,64,108,41,49,29,62,116  },
        { 14,42,10,1,63,96,32,25,34,8,129,29,0,103,55,19,26,53,77,5,95,2,4,7,3,16,148,56,18,24,121,108  },
        { 21,2,75,86,6,76,144,28,119,99,93,147,141,67,102,145,60,132,146,128,0,82,40,138,55,111,143,17,133,112,69,14  },
        { 111,120,41,62,84,132,0,5,38,119,56,92,72,142,27,28,29,35,58,80,2,86,65,79,12,14,1,24,145,16,21,48  },
        { 146,67,141,69,133,21,6,143,57,55,111,147,56,1,14,132,7,2,134,102,0,119,29,84,76,64,86,72,28,68,47,75  },
        { 12,1,0,5,27,3,7,4,38,8,6,41,16,40,46,10,18,79,2,9,23,86,20,22,62,14,37,88,92,19,24,11  },
        { 0,12,2,1,27,5,38,28,60,6,40,7,16,46,18,14,41,99,93,62,3,79,86,23,149,8,22,35,88,17,19,10  },
        { 141,6,21,67,147,102,146,2,76,119,132,69,55,111,86,75,28,133,143,0,1,145,14,128,56,99,17,60,29,93,84,68  },
        { 21,76,1,119,86,145,2,0,14,7,6,138,146,55,17,28,132,93,67,40,60,143,29,147,111,16,69,141,5,56,19,133  },
        { 1,8,108,14,7,116,64,42,10,63,94,32,115,103,113,96,30,34,55,47,95,148,29,140,129,25,134,53,69,26,19,11  },
        { 12,1,3,5,4,2,0,7,8,38,27,16,18,6,10,20,41,40,79,46,9,23,22,88,92,37,14,24,62,19,48,99  },
        { 1,14,7,0,6,25,5,16,19,2,42,26,29,35,61,8,18,129,101,21,3,110,34,148,96,10,17,4,22,40,12,20  },
        { 0,2,5,1,3,19,22,26,16,24,29,7,14,6,4,25,18,44,8,48,12,61,20,21,10,35,65,56,23,40,17,107  },
        { 1,7,8,29,56,0,10,14,2,42,72,5,4,65,3,30,84,94,67,9,25,133,111,11,32,108,16,63,21,96,26,48  }
    };

    static inline uint32_t iabs(int32_t i) { return (i < 0) ? static_cast<uint32_t>(-i) : static_cast<uint32_t>(i); }
    static inline uint64_t iabs(int64_t i) { return (i < 0) ? static_cast<uint64_t>(-i) : static_cast<uint64_t>(i); }

    static inline uint8_t to_5(uint32_t v) { v = v * 31 + 128; return (uint8_t)((v + (v >> 8)) >> 8); }
    static inline uint8_t to_6(uint32_t v) { v = v * 63 + 128; return (uint8_t)((v + (v >> 8)) >> 8); }

    template <typename S> inline S maximum(S a, S b) { return (a > b) ? a : b; }
    template <typename S> inline S maximum(S a, S b, S c) { return maximum(maximum(a, b), c); }
    template <typename S> inline S maximum(S a, S b, S c, S d) { return maximum(maximum(maximum(a, b), c), d); }

    template <typename S> inline S minimum(S a, S b) { return (a < b) ? a : b; }
    template <typename S> inline S minimum(S a, S b, S c) { return minimum(minimum(a, b), c); }
    template <typename S> inline S minimum(S a, S b, S c, S d) { return minimum(minimum(minimum(a, b), c), d); }

    template<typename T> inline T square(T a) { return a * a; }

    static inline float clampf(float value, float low, float high) { if (value < low) value = low; else if (value > high) value = high;	return value; }
    static inline uint8_t clamp255(int32_t i) { return (uint8_t)((i & 0xFFFFFF00U) ? (~(i >> 31)) : i); }

    template <typename S> inline S clamp(S value, S low, S high) { return (value < low) ? low : ((value > high) ? high : value); }
    static inline int32_t clampi(int32_t value, int32_t low, int32_t high) { if (value < low) value = low; else if (value > high) value = high;	return value; }

    static inline int squarei(int a) { return a * a; }
    static inline int absi(int a) { return (a < 0) ? -a : a; }

    template<typename F> inline F lerp(F a, F b, F s) { return a + (b - a) * s; }

    enum class eNoClamp { cNoClamp };

    struct color32
    {
        union
        {
            struct
            {
                uint8_t r;
                uint8_t g;
                uint8_t b;
                uint8_t a;
            };

            uint8_t c[4];

            uint32_t m;
        };

        color32() { }

        color32(uint32_t vr, uint32_t vg, uint32_t vb, uint32_t va) { set(vr, vg, vb, va); }
        color32(eNoClamp unused, uint32_t vr, uint32_t vg, uint32_t vb, uint32_t va) { (void)unused; set_noclamp_rgba(vr, vg, vb, va); }

        void set(uint32_t vr, uint32_t vg, uint32_t vb, uint32_t va) { c[0] = static_cast<uint8_t>(vr); c[1] = static_cast<uint8_t>(vg); c[2] = static_cast<uint8_t>(vb); c[3] = static_cast<uint8_t>(va); }

        void set_noclamp_rgb(uint32_t vr, uint32_t vg, uint32_t vb) { c[0] = static_cast<uint8_t>(vr); c[1] = static_cast<uint8_t>(vg); c[2] = static_cast<uint8_t>(vb); }
        void set_noclamp_rgba(uint32_t vr, uint32_t vg, uint32_t vb, uint32_t va) { set(vr, vg, vb, va); }

        void set_clamped(int vr, int vg, int vb, int va) { c[0] = clamp255(vr); c[1] = clamp255(vg);	c[2] = clamp255(vb); c[3] = clamp255(va); }

        uint8_t operator[] (uint32_t idx) const { assert(idx < 4); return c[idx]; }
        uint8_t &operator[] (uint32_t idx) { assert(idx < 4); return c[idx]; }

        bool operator== (const color32&rhs) const { return m == rhs.m; }

        void set_rgb(const color32& other) { c[0] = static_cast<uint8_t>(other.c[0]); c[1] = static_cast<uint8_t>(other.c[1]); c[2] = static_cast<uint8_t>(other.c[2]); }

        static color32 comp_min(const color32& a, const color32& b) { return color32(eNoClamp::cNoClamp, std::min(a[0], b[0]), std::min(a[1], b[1]), std::min(a[2], b[2]), std::min(a[3], b[3])); }
        static color32 comp_max(const color32& a, const color32& b) { return color32(eNoClamp::cNoClamp, std::max(a[0], b[0]), std::max(a[1], b[1]), std::max(a[2], b[2]), std::max(a[3], b[3])); }
    };

    enum dxt_constants
    {
        cDXT1SelectorBits = 2U, cDXT1SelectorValues = 1U << cDXT1SelectorBits, cDXT1SelectorMask = cDXT1SelectorValues - 1U,
        cDXT5SelectorBits = 3U, cDXT5SelectorValues = 1U << cDXT5SelectorBits, cDXT5SelectorMask = cDXT5SelectorValues - 1U,
    };

    struct bc1_block
    {
        enum { cTotalEndpointBytes = 2, cTotalSelectorBytes = 4 };

        uint8_t m_low_color[cTotalEndpointBytes];
        uint8_t m_high_color[cTotalEndpointBytes];
        uint8_t m_selectors[cTotalSelectorBytes];

        inline uint32_t get_low_color() const { return m_low_color[0] | (m_low_color[1] << 8U); }
        inline uint32_t get_high_color() const { return m_high_color[0] | (m_high_color[1] << 8U); }
        inline bool is_3color() const { return get_low_color() <= get_high_color(); }
        inline void set_low_color(uint16_t c) { m_low_color[0] = static_cast<uint8_t>(c & 0xFF); m_low_color[1] = static_cast<uint8_t>((c >> 8) & 0xFF); }
        inline void set_high_color(uint16_t c) { m_high_color[0] = static_cast<uint8_t>(c & 0xFF); m_high_color[1] = static_cast<uint8_t>((c >> 8) & 0xFF); }
        inline uint32_t get_selector(uint32_t x, uint32_t y) const { assert((x < 4U) && (y < 4U)); return (m_selectors[y] >> (x * cDXT1SelectorBits)) & cDXT1SelectorMask; }
        inline void set_selector(uint32_t x, uint32_t y, uint32_t val) { assert((x < 4U) && (y < 4U) && (val < 4U)); m_selectors[y] &= (~(cDXT1SelectorMask << (x * cDXT1SelectorBits))); m_selectors[y] |= (val << (x * cDXT1SelectorBits)); }

        static inline uint16_t pack_color(const color32& color, bool scaled, uint32_t bias = 127U)
        {
            uint32_t r = color.r, g = color.g, b = color.b;
            if (scaled)
            {
                r = (r * 31U + bias) / 255U;
                g = (g * 63U + bias) / 255U;
                b = (b * 31U + bias) / 255U;
            }
            return static_cast<uint16_t>(minimum(b, 31U) | (minimum(g, 63U) << 5U) | (minimum(r, 31U) << 11U));
        }

        static inline uint16_t pack_unscaled_color(uint32_t r, uint32_t g, uint32_t b) { return static_cast<uint16_t>(b | (g << 5U) | (r << 11U)); }

        static inline void unpack_color(uint32_t c, uint32_t& r, uint32_t& g, uint32_t& b)
        {
            r = (c >> 11) & 31;
            g = (c >> 5) & 63;
            b = c & 31;

            r = (r << 3) | (r >> 2);
            g = (g << 2) | (g >> 4);
            b = (b << 3) | (b >> 2);
        }

        static inline void unpack_color_unscaled(uint32_t c, uint32_t& r, uint32_t& g, uint32_t& b)
        {
            r = (c >> 11) & 31;
            g = (c >> 5) & 63;
            b = c & 31;
        }
    };

    static const uint32_t TOTAL_ORDER_4_0_16 = 15;
    static const uint32_t TOTAL_ORDER_4_1_16 = 700;
    static const uint32_t TOTAL_ORDER_4_2_16 = 753;
    static const uint32_t TOTAL_ORDER_4_3_16 = 515;
    static uint16_t g_total_ordering4_hash[4096];
    static float g_selector_factors4[NUM_UNIQUE_TOTAL_ORDERINGS4][3];

    static const uint32_t TOTAL_ORDER_3_0_16 = 12;
    static const uint32_t TOTAL_ORDER_3_1_16 = 15;
    static const uint32_t TOTAL_ORDER_3_2_16 = 89;
    static uint16_t g_total_ordering3_hash[256];
    static float g_selector_factors3[NUM_UNIQUE_TOTAL_ORDERINGS3][3];

    struct hist4
    {
        uint8_t m_hist[4];

        hist4()
        {
            memset(m_hist, 0, sizeof(m_hist));
        }

        hist4(uint32_t i, uint32_t j, uint32_t k, uint32_t l)
        {
            m_hist[0] = (uint8_t)i;
            m_hist[1] = (uint8_t)j;
            m_hist[2] = (uint8_t)k;
            m_hist[3] = (uint8_t)l;
        }

        inline bool operator== (const hist4 &h) const
        {
            if (m_hist[0] != h.m_hist[0]) return false;
            if (m_hist[1] != h.m_hist[1]) return false;
            if (m_hist[2] != h.m_hist[2]) return false;
            if (m_hist[3] != h.m_hist[3]) return false;
            return true;
        }

        inline bool any_16() const
        {
            return (m_hist[0] == 16) || (m_hist[1] == 16) || (m_hist[2] == 16) || (m_hist[3] == 16);
        }

        inline uint32_t lookup_total_ordering_index() const
        {
            if (m_hist[0] == 16)
                return TOTAL_ORDER_4_0_16;
            else if (m_hist[1] == 16)
                return TOTAL_ORDER_4_1_16;
            else if (m_hist[2] == 16)
                return TOTAL_ORDER_4_2_16;
            else if (m_hist[3] == 16)
                return TOTAL_ORDER_4_3_16;

            // Must sum to 16, so m_hist[3] isn't needed.
            return g_total_ordering4_hash[m_hist[0] | (m_hist[1] << 4) | (m_hist[2] << 8)];
        }
    };

    struct hist3
    {
        uint8_t m_hist[3];

        hist3()
        {
            memset(m_hist, 0, sizeof(m_hist));
        }

        hist3(uint32_t i, uint32_t j, uint32_t k)
        {
            m_hist[0] = (uint8_t)i;
            m_hist[1] = (uint8_t)j;
            m_hist[2] = (uint8_t)k;
        }

        inline bool operator== (const hist3 &h) const
        {
            if (m_hist[0] != h.m_hist[0]) return false;
            if (m_hist[1] != h.m_hist[1]) return false;
            if (m_hist[2] != h.m_hist[2]) return false;
            return true;
        }

        inline bool any_16() const
        {
            return (m_hist[0] == 16) || (m_hist[1] == 16) || (m_hist[2] == 16);
        }

        inline uint32_t lookup_total_ordering_index() const
        {
            if (m_hist[0] == 16)
                return TOTAL_ORDER_3_0_16;
            else if (m_hist[1] == 16)
                return TOTAL_ORDER_3_1_16;
            else if (m_hist[2] == 16)
                return TOTAL_ORDER_3_2_16;

            // Must sum to 16, so m_hist[2] isn't needed.
            return g_total_ordering3_hash[m_hist[0] | (m_hist[1] << 4)];
        }
    };

    struct bc1_match_entry
    {
        uint8_t m_hi;
        uint8_t m_lo;
        uint8_t m_e;
    };

    static bc1_approx_mode g_bc1_approx_mode;
    static bc1_match_entry g_bc1_match5_equals_1[256], g_bc1_match6_equals_1[256];
    static bc1_match_entry g_bc1_match5_half[256], g_bc1_match6_half[256];

    static inline int scale_5_to_8(int v) { return (v << 3) | (v >> 2); }
    static inline int scale_6_to_8(int v) { return (v << 2) | (v >> 4); }

    // v0, v1 = unexpanded DXT1 endpoint values (5/6-bits)
    // c0, c1 = expanded DXT1 endpoint values (8-bits)
    static inline int interp_5_6_ideal(int c0, int c1) { assert(c0 < 256 && c1 < 256); return (c0 * 2 + c1) / 3; }
    static inline int interp_5_6_ideal_round(int c0, int c1) { assert(c0 < 256 && c1 < 256); return (c0 * 2 + c1 + 1) / 3; }
    static inline int interp_half_5_6_ideal(int c0, int c1) { assert(c0 < 256 && c1 < 256); return (c0 + c1) / 2; }

    static inline int interp_5_nv(int v0, int v1) { assert(v0 < 32 && v1 < 32); return ((2 * v0 + v1) * 22) / 8; }
    static inline int interp_6_nv(int c0, int c1) { assert(c0 < 256 && c1 < 256); const int gdiff = c1 - c0; return (256 * c0 + (gdiff / 4) + 128 + gdiff * 80) / 256; }

    static inline int interp_half_5_nv(int v0, int v1) { assert(v0 < 32 && v1 < 32); return ((v0 + v1) * 33) / 8; }
    static inline int interp_half_6_nv(int c0, int c1) { assert(c0 < 256 && c1 < 256); const int gdiff = c1 - c0; return (256 * c0 + gdiff / 4 + 128 + gdiff * 128) / 256; }

    static inline int interp_5_6_amd(int c0, int c1) { assert(c0 < 256 && c1 < 256); return (c0 * 43 + c1 * 21 + 32) >> 6; }
    static inline int interp_half_5_6_amd(int c0, int c1) { assert(c0 < 256 && c1 < 256); return (c0 + c1 + 1) >> 1; }

    static inline int interp_5(int v0, int v1, int c0, int c1, bc1_approx_mode mode)
    {
        assert(scale_5_to_8(v0) == c0 && scale_5_to_8(v1) == c1);
        switch (mode)
        {
        case bc1_approx_mode::cBC1NVidia: return interp_5_nv(v0, v1);
        case bc1_approx_mode::cBC1AMD: return interp_5_6_amd(c0, c1);
        default:
        case bc1_approx_mode::cBC1Ideal: return interp_5_6_ideal(c0, c1);
        case bc1_approx_mode::cBC1IdealRound4: return interp_5_6_ideal_round(c0, c1);
        }
    }

    static inline int interp_6(int v0, int v1, int c0, int c1, bc1_approx_mode mode)
    {
        (void)v0; (void)v1;
        assert(scale_6_to_8(v0) == c0 && scale_6_to_8(v1) == c1);
        switch (mode)
        {
        case bc1_approx_mode::cBC1NVidia: return interp_6_nv(c0, c1);
        case bc1_approx_mode::cBC1AMD: return interp_5_6_amd(c0, c1);
        default:
        case bc1_approx_mode::cBC1Ideal: return interp_5_6_ideal(c0, c1);
        case bc1_approx_mode::cBC1IdealRound4: return interp_5_6_ideal_round(c0, c1);
        }
    }

    static inline int interp_half_5(int v0, int v1, int c0, int c1, bc1_approx_mode mode)
    {
        assert(scale_5_to_8(v0) == c0 && scale_5_to_8(v1) == c1);
        switch (mode)
        {
        case bc1_approx_mode::cBC1NVidia: return interp_half_5_nv(v0, v1);
        case bc1_approx_mode::cBC1AMD: return interp_half_5_6_amd(c0, c1);
        case bc1_approx_mode::cBC1Ideal:
        case bc1_approx_mode::cBC1IdealRound4:
        default:
            return interp_half_5_6_ideal(c0, c1);
        }
    }

    static inline int interp_half_6(int v0, int v1, int c0, int c1, bc1_approx_mode mode)
    {
        (void)v0; (void)v1;
        assert(scale_6_to_8(v0) == c0 && scale_6_to_8(v1) == c1);
        switch (mode)
        {
        case bc1_approx_mode::cBC1NVidia: return interp_half_6_nv(c0, c1);
        case bc1_approx_mode::cBC1AMD: return interp_half_5_6_amd(c0, c1);
        case bc1_approx_mode::cBC1Ideal:
        case bc1_approx_mode::cBC1IdealRound4:
        default:
            return interp_half_5_6_ideal(c0, c1);
        }
    }

    static void prepare_bc1_single_color_table_half(bc1_match_entry* pTable, const uint8_t* pExpand, int size, bc1_approx_mode mode)
    {
        for (int i = 0; i < 256; i++)
        {
            int lowest_e = 256;
            for (int lo = 0; lo < size; lo++)
            {
                const int lo_e = pExpand[lo];

                for (int hi = 0; hi < size; hi++)
                {
                    const int hi_e = pExpand[hi];

                    const int v = (size == 32) ? interp_half_5(hi, lo, hi_e, lo_e, mode) : interp_half_6(hi, lo, hi_e, lo_e, mode);

                    int e = iabs(v - i);

                    // We only need to factor in 3% error in BC1 ideal mode.
                    if ((mode == bc1_approx_mode::cBC1Ideal) || (mode == bc1_approx_mode::cBC1IdealRound4))
                        e += (iabs(hi_e - lo_e) * 3) / 100;

                    // Favor equal endpoints, for lower error on actual GPU's which approximate the interpolation.
                    if ((e < lowest_e) || ((e == lowest_e) && (lo == hi)))
                    {
                        pTable[i].m_hi = static_cast<uint8_t>(hi);
                        pTable[i].m_lo = static_cast<uint8_t>(lo);

                        assert(e <= UINT8_MAX);
                        pTable[i].m_e = static_cast<uint8_t>(e);

                        lowest_e = e;
                    }

                } // hi
            } // lo
        }
    }

    static void prepare_bc1_single_color_table(bc1_match_entry* pTable, const uint8_t* pExpand, int size, bc1_approx_mode mode)
    {
        for (int i = 0; i < 256; i++)
        {
            int lowest_e = 256;
            for (int lo = 0; lo < size; lo++)
            {
                const int lo_e = pExpand[lo];

                for (int hi = 0; hi < size; hi++)
                {
                    const int hi_e = pExpand[hi];

                    const int v = (size == 32) ? interp_5(hi, lo, hi_e, lo_e, mode) : interp_6(hi, lo, hi_e, lo_e, mode);

                    int e = iabs(v - i);

                    if ((mode == bc1_approx_mode::cBC1Ideal) || (mode == bc1_approx_mode::cBC1IdealRound4))
                        e += (iabs(hi_e - lo_e) * 3) / 100;

                    // Favor equal endpoints, for lower error on actual GPU's which approximate the interpolation.
                    if ((e < lowest_e) || ((e == lowest_e) && (lo == hi)))
                    {
                        pTable[i].m_hi = static_cast<uint8_t>(hi);
                        pTable[i].m_lo = static_cast<uint8_t>(lo);

                        assert(e <= UINT8_MAX);
                        pTable[i].m_e = static_cast<uint8_t>(e);

                        lowest_e = e;
                    }

                } // hi
            } // lo
        }
    }

    // This table is: 9 * (w * w), 9 * ((1.0f - w) * w), 9 * ((1.0f - w) * (1.0f - w))
    // where w is [0,1/3,2/3,1]. 9 is the perfect multiplier.
    static const uint32_t g_weight_vals4[4] = { 0x000009, 0x010204, 0x040201, 0x090000 };

    // multiplier is 4 for 3-color
    static const uint32_t g_weight_vals3[3] = { 0x000004, 0x040000, 0x010101 };

    static inline void compute_selector_factors4(const hist4 &h, float &iz00, float &iz10, float &iz11)
    {
        uint32_t weight_accum = 0;
        for (uint32_t sel = 0; sel < 4; sel++)
            weight_accum += g_weight_vals4[sel] * h.m_hist[sel];

        float z00 = (float)((weight_accum >> 16) & 0xFF);
        float z10 = (float)((weight_accum >> 8) & 0xFF);
        float z11 = (float)(weight_accum & 0xFF);
        float z01 = z10;

        float det = z00 * z11 - z01 * z10;
        if (fabs(det) < 1e-8f)
            det = 0.0f;
        else
            det = (3.0f / 255.0f) / det;

        iz00 = z11 * det;
        iz10 = -z10 * det;
        iz11 = z00 * det;
    }

    static inline void compute_selector_factors3(const hist3 &h, float &iz00, float &iz10, float &iz11)
    {
        uint32_t weight_accum = 0;
        for (uint32_t sel = 0; sel < 3; sel++)
            weight_accum += g_weight_vals3[sel] * h.m_hist[sel];

        float z00 = (float)((weight_accum >> 16) & 0xFF);
        float z10 = (float)((weight_accum >> 8) & 0xFF);
        float z11 = (float)(weight_accum & 0xFF);
        float z01 = z10;

        float det = z00 * z11 - z01 * z10;
        if (fabs(det) < 1e-8f)
            det = 0.0f;
        else
            det = (2.0f / 255.0f) / det;

        iz00 = z11 * det;
        iz10 = -z10 * det;
        iz11 = z00 * det;
    }

    static bool g_initialized;

    void init(bc1_approx_mode mode)
    {
        g_bc1_approx_mode = mode;

        uint8_t bc1_expand5[32];
        for (int i = 0; i < 32; i++)
            bc1_expand5[i] = static_cast<uint8_t>((i << 3) | (i >> 2));
        prepare_bc1_single_color_table(g_bc1_match5_equals_1, bc1_expand5, 32, mode);
        prepare_bc1_single_color_table_half(g_bc1_match5_half, bc1_expand5, 32, mode);

        uint8_t bc1_expand6[64];
        for (int i = 0; i < 64; i++)
            bc1_expand6[i] = static_cast<uint8_t>((i << 2) | (i >> 4));
        prepare_bc1_single_color_table(g_bc1_match6_equals_1, bc1_expand6, 64, mode);
        prepare_bc1_single_color_table_half(g_bc1_match6_half, bc1_expand6, 64, mode);

        for (uint32_t i = 0; i < NUM_UNIQUE_TOTAL_ORDERINGS4; i++)
        {
            hist4 h;
            h.m_hist[0] = (uint8_t)g_unique_total_orders4[i][0];
            h.m_hist[1] = (uint8_t)g_unique_total_orders4[i][1];
            h.m_hist[2] = (uint8_t)g_unique_total_orders4[i][2];
            h.m_hist[3] = (uint8_t)g_unique_total_orders4[i][3];

            if (!h.any_16())
            {
                const uint32_t index = h.m_hist[0] | (h.m_hist[1] << 4) | (h.m_hist[2] << 8);
                assert(index < 4096);
                g_total_ordering4_hash[index] = (uint16_t)i;
            }

            compute_selector_factors4(h, g_selector_factors4[i][0], g_selector_factors4[i][1], g_selector_factors4[i][2]);
        }

        for (uint32_t i = 0; i < NUM_UNIQUE_TOTAL_ORDERINGS3; i++)
        {
            hist3 h;
            h.m_hist[0] = (uint8_t)g_unique_total_orders3[i][0];
            h.m_hist[1] = (uint8_t)g_unique_total_orders3[i][1];
            h.m_hist[2] = (uint8_t)g_unique_total_orders3[i][2];

            if (!h.any_16())
            {
                const uint32_t index = h.m_hist[0] | (h.m_hist[1] << 4);
                assert(index < 256);
                g_total_ordering3_hash[index] = (uint16_t)i;
            }

            compute_selector_factors3(h, g_selector_factors3[i][0], g_selector_factors3[i][1], g_selector_factors3[i][2]);
        }

        g_initialized = true;
    }

    void encode_bc1_solid_block(void* pDst, uint32_t fr, uint32_t fg, uint32_t fb, bool allow_3color)
    {
        bc1_block* pDst_block = static_cast<bc1_block*>(pDst);

        uint32_t mask = 0xAA;
        int max16 = -1, min16 = 0;

        if (allow_3color)
        {
            const uint32_t err4 = g_bc1_match5_equals_1[fr].m_e + g_bc1_match6_equals_1[fg].m_e + g_bc1_match5_equals_1[fb].m_e;
            const uint32_t err3 = g_bc1_match5_half[fr].m_e + g_bc1_match6_half[fg].m_e + g_bc1_match5_half[fb].m_e;

            if (err3 < err4)
            {
                max16 = (g_bc1_match5_half[fr].m_hi << 11) | (g_bc1_match6_half[fg].m_hi << 5) | g_bc1_match5_half[fb].m_hi;
                min16 = (g_bc1_match5_half[fr].m_lo << 11) | (g_bc1_match6_half[fg].m_lo << 5) | g_bc1_match5_half[fb].m_lo;

                if (max16 > min16)
                    std::swap(max16, min16);
            }
        }

        if (max16 == -1)
        {
            max16 = (g_bc1_match5_equals_1[fr].m_hi << 11) | (g_bc1_match6_equals_1[fg].m_hi << 5) | g_bc1_match5_equals_1[fb].m_hi;
            min16 = (g_bc1_match5_equals_1[fr].m_lo << 11) | (g_bc1_match6_equals_1[fg].m_lo << 5) | g_bc1_match5_equals_1[fb].m_lo;

            if (min16 == max16)
            {
                // Always forbid 3 color blocks
                // This is to guarantee that BC3 blocks never use punchthrough alpha (3 color) mode, which isn't supported on some (all?) GPU's.
                mask = 0;

                // Make l > h
                if (min16 > 0)
                    min16--;
                else
                {
                    // l = h = 0
                    assert(min16 == max16 && max16 == 0);

                    max16 = 1;
                    min16 = 0;
                    mask = 0x55;
                }

                assert(max16 > min16);
            }

            if (max16 < min16)
            {
                std::swap(max16, min16);
                mask ^= 0x55;
            }
        }

        pDst_block->set_low_color(static_cast<uint16_t>(max16));
        pDst_block->set_high_color(static_cast<uint16_t>(min16));
        pDst_block->m_selectors[0] = static_cast<uint8_t>(mask);
        pDst_block->m_selectors[1] = static_cast<uint8_t>(mask);
        pDst_block->m_selectors[2] = static_cast<uint8_t>(mask);
        pDst_block->m_selectors[3] = static_cast<uint8_t>(mask);
    }

    static const float g_midpoint5[32] = { .015686f, .047059f, .078431f, .111765f, .145098f, .176471f, .207843f, .241176f, .274510f, .305882f, .337255f, .370588f, .403922f, .435294f, .466667f, .5f, .533333f, .564706f, .596078f, .629412f, .662745f, .694118f, .725490f, .758824f, .792157f, .823529f, .854902f, .888235f, .921569f, .952941f, .984314f, 1e+37f };
    static const float g_midpoint6[64] = { .007843f, .023529f, .039216f, .054902f, .070588f, .086275f, .101961f, .117647f, .133333f, .149020f, .164706f, .180392f, .196078f, .211765f, .227451f, .245098f, .262745f, .278431f, .294118f, .309804f, .325490f, .341176f, .356863f, .372549f, .388235f, .403922f, .419608f, .435294f, .450980f, .466667f, .482353f, .500000f, .517647f, .533333f, .549020f, .564706f, .580392f, .596078f, .611765f, .627451f, .643137f, .658824f, .674510f, .690196f, .705882f, .721569f, .737255f, .754902f, .772549f, .788235f, .803922f, .819608f, .835294f, .850980f, .866667f, .882353f, .898039f, .913725f, .929412f, .945098f, .960784f, .976471f, .992157f, 1e+37f };

    struct vec3F { float c[3]; };

    static inline void compute_least_squares_endpoints4_rgb(
        vec3F* pXl, vec3F* pXh,
        int total_r, int total_g, int total_b,
        float iz00, float iz10, float iz11,
        uint32_t s, const uint32_t r_sum[17], const uint32_t g_sum[17], const uint32_t b_sum[17])
    {
        const float iz01 = iz10;

        const uint32_t f1 = g_unique_total_orders4[s][0];
        const uint32_t f2 = g_unique_total_orders4[s][0] + g_unique_total_orders4[s][1];
        const uint32_t f3 = g_unique_total_orders4[s][0] + g_unique_total_orders4[s][1] + g_unique_total_orders4[s][2];
        uint32_t uq00_r = (r_sum[f2] - r_sum[f1]) + (r_sum[f3] - r_sum[f2]) * 2 + (r_sum[16] - r_sum[f3]) * 3;
        uint32_t uq00_g = (g_sum[f2] - g_sum[f1]) + (g_sum[f3] - g_sum[f2]) * 2 + (g_sum[16] - g_sum[f3]) * 3;
        uint32_t uq00_b = (b_sum[f2] - b_sum[f1]) + (b_sum[f3] - b_sum[f2]) * 2 + (b_sum[16] - b_sum[f3]) * 3;

        float q10_r = (float)(total_r * 3 - uq00_r);
        float q10_g = (float)(total_g * 3 - uq00_g);
        float q10_b = (float)(total_b * 3 - uq00_b);

        pXl->c[0] = iz00 * (float)uq00_r + iz01 * q10_r;
        pXh->c[0] = iz10 * (float)uq00_r + iz11 * q10_r;

        pXl->c[1] = iz00 * (float)uq00_g + iz01 * q10_g;
        pXh->c[1] = iz10 * (float)uq00_g + iz11 * q10_g;

        pXl->c[2] = iz00 * (float)uq00_b + iz01 * q10_b;
        pXh->c[2] = iz10 * (float)uq00_b + iz11 * q10_b;
    }

    static inline bool compute_least_squares_endpoints4_rgb(const color32* pColors, const uint8_t* pSelectors, vec3F* pXl, vec3F* pXh, int total_r, int total_g, int total_b)
    {
        uint32_t uq00_r = 0, uq00_g = 0, uq00_b = 0;
        uint32_t weight_accum = 0;
        for (uint32_t i = 0; i < 16; i++)
        {
            const uint8_t r = pColors[i].c[0], g = pColors[i].c[1], b = pColors[i].c[2];
            const uint8_t sel = pSelectors[i];

            weight_accum += g_weight_vals4[sel];
            uq00_r += sel * r;
            uq00_g += sel * g;
            uq00_b += sel * b;
        }

        int q10_r = total_r * 3 - uq00_r;
        int q10_g = total_g * 3 - uq00_g;
        int q10_b = total_b * 3 - uq00_b;

        float z00 = (float)((weight_accum >> 16) & 0xFF);
        float z10 = (float)((weight_accum >> 8) & 0xFF);
        float z11 = (float)(weight_accum & 0xFF);
        float z01 = z10;

        float det = z00 * z11 - z01 * z10;
        if (fabs(det) < 1e-8f)
            return false;

        det = (3.0f / 255.0f) / det;

        float iz00, iz01, iz10, iz11;
        iz00 = z11 * det;
        iz01 = -z01 * det;
        iz10 = -z10 * det;
        iz11 = z00 * det;

        pXl->c[0] = iz00 * (float)uq00_r + iz01 * q10_r;
        pXh->c[0] = iz10 * (float)uq00_r + iz11 * q10_r;

        pXl->c[1] = iz00 * (float)uq00_g + iz01 * q10_g;
        pXh->c[1] = iz10 * (float)uq00_g + iz11 * q10_g;

        pXl->c[2] = iz00 * (float)uq00_b + iz01 * q10_b;
        pXh->c[2] = iz10 * (float)uq00_b + iz11 * q10_b;

        return true;
    }

    static inline void compute_least_squares_endpoints3_rgb(
        vec3F* pXl, vec3F* pXh,
        int total_r, int total_g, int total_b,
        float iz00, float iz10, float iz11,
        uint32_t s, const uint32_t r_sum[17], const uint32_t g_sum[17], const uint32_t b_sum[17])
    {
        const float iz01 = iz10;

        // Compensates for BC1 3-color ordering, which is selector 0, 2, 1
        const uint32_t f1 = g_unique_total_orders3[s][0];
        const uint32_t f2 = g_unique_total_orders3[s][0] + g_unique_total_orders3[s][2];
        uint32_t uq00_r = (r_sum[16] - r_sum[f2]) * 2 + (r_sum[f2] - r_sum[f1]);
        uint32_t uq00_g = (g_sum[16] - g_sum[f2]) * 2 + (g_sum[f2] - g_sum[f1]);
        uint32_t uq00_b = (b_sum[16] - b_sum[f2]) * 2 + (b_sum[f2] - b_sum[f1]);

        float q10_r = (float)(total_r * 2 - uq00_r);
        float q10_g = (float)(total_g * 2 - uq00_g);
        float q10_b = (float)(total_b * 2 - uq00_b);

        pXl->c[0] = iz00 * (float)uq00_r + iz01 * q10_r;
        pXh->c[0] = iz10 * (float)uq00_r + iz11 * q10_r;

        pXl->c[1] = iz00 * (float)uq00_g + iz01 * q10_g;
        pXh->c[1] = iz10 * (float)uq00_g + iz11 * q10_g;

        pXl->c[2] = iz00 * (float)uq00_b + iz01 * q10_b;
        pXh->c[2] = iz10 * (float)uq00_b + iz11 * q10_b;
    }

    static inline bool compute_least_squares_endpoints3_rgb(bool use_black, const color32* pColors, const uint8_t* pSelectors, vec3F* pXl, vec3F* pXh)
    {
        int uq00_r = 0, uq00_g = 0, uq00_b = 0;
        uint32_t weight_accum = 0;
        int total_r = 0, total_g = 0, total_b = 0;
        for (uint32_t i = 0; i < 16; i++)
        {
            const uint8_t r = pColors[i].c[0], g = pColors[i].c[1], b = pColors[i].c[2];
            if (use_black)
            {
                if ((r | g | b) < 4)
                    continue;
            }

            const uint8_t sel = pSelectors[i];
            assert(sel <= 3);
            if (sel == 3)
                continue;

            weight_accum += g_weight_vals3[sel];

            static const uint8_t s_tran[3] = { 0, 2, 1 };
            const uint8_t tsel = s_tran[sel];
            uq00_r += tsel * r;
            uq00_g += tsel * g;
            uq00_b += tsel * b;

            total_r += r;
            total_g += g;
            total_b += b;
        }

        int q10_r = total_r * 2 - uq00_r;
        int q10_g = total_g * 2 - uq00_g;
        int q10_b = total_b * 2 - uq00_b;

        float z00 = (float)((weight_accum >> 16) & 0xFF);
        float z10 = (float)((weight_accum >> 8) & 0xFF);
        float z11 = (float)(weight_accum & 0xFF);
        float z01 = z10;

        float det = z00 * z11 - z01 * z10;
        if (fabs(det) < 1e-8f)
            return false;

        det = (2.0f / 255.0f) / det;

        float iz00, iz01, iz10, iz11;
        iz00 = z11 * det;
        iz01 = -z01 * det;
        iz10 = -z10 * det;
        iz11 = z00 * det;

        pXl->c[0] = iz00 * (float)uq00_r + iz01 * q10_r;
        pXh->c[0] = iz10 * (float)uq00_r + iz11 * q10_r;

        pXl->c[1] = iz00 * (float)uq00_g + iz01 * q10_g;
        pXh->c[1] = iz10 * (float)uq00_g + iz11 * q10_g;

        pXl->c[2] = iz00 * (float)uq00_b + iz01 * q10_b;
        pXh->c[2] = iz10 * (float)uq00_b + iz11 * q10_b;

        return true;
    }

    static inline void bc1_get_block_colors4(uint32_t block_r[4], uint32_t block_g[4], uint32_t block_b[4], uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb)
    {
        block_r[0] = (lr << 3) | (lr >> 2); block_g[0] = (lg << 2) | (lg >> 4);	block_b[0] = (lb << 3) | (lb >> 2);
        block_r[3] = (hr << 3) | (hr >> 2);	block_g[3] = (hg << 2) | (hg >> 4);	block_b[3] = (hb << 3) | (hb >> 2);

        if (g_bc1_approx_mode == bc1_approx_mode::cBC1Ideal)
        {
            block_r[1] = (block_r[0] * 2 + block_r[3]) / 3;	block_g[1] = (block_g[0] * 2 + block_g[3]) / 3;	block_b[1] = (block_b[0] * 2 + block_b[3]) / 3;
            block_r[2] = (block_r[3] * 2 + block_r[0]) / 3;	block_g[2] = (block_g[3] * 2 + block_g[0]) / 3;	block_b[2] = (block_b[3] * 2 + block_b[0]) / 3;
        }
        else if (g_bc1_approx_mode == bc1_approx_mode::cBC1IdealRound4)
        {
            block_r[1] = (block_r[0] * 2 + block_r[3] + 1) / 3;	block_g[1] = (block_g[0] * 2 + block_g[3] + 1) / 3;	block_b[1] = (block_b[0] * 2 + block_b[3] + 1) / 3;
            block_r[2] = (block_r[3] * 2 + block_r[0] + 1) / 3;	block_g[2] = (block_g[3] * 2 + block_g[0] + 1) / 3;	block_b[2] = (block_b[3] * 2 + block_b[0] + 1) / 3;
        }
        else if (g_bc1_approx_mode == bc1_approx_mode::cBC1AMD)
        {
            block_r[1] = interp_5_6_amd(block_r[0], block_r[3]); block_g[1] = interp_5_6_amd(block_g[0], block_g[3]); block_b[1] = interp_5_6_amd(block_b[0], block_b[3]);
            block_r[2] = interp_5_6_amd(block_r[3], block_r[0]); block_g[2] = interp_5_6_amd(block_g[3], block_g[0]); block_b[2] = interp_5_6_amd(block_b[3], block_b[0]);
        }
        else
        {
            block_r[1] = interp_5_nv(lr, hr); block_g[1] = interp_6_nv(block_g[0], block_g[3]); block_b[1] = interp_5_nv(lb, hb);
            block_r[2] = interp_5_nv(hr, lr); block_g[2] = interp_6_nv(block_g[3], block_g[0]); block_b[2] = interp_5_nv(hb, lb);
        }
    }

    static inline void bc1_get_block_colors3(uint32_t block_r[3], uint32_t block_g[3], uint32_t block_b[3], uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb)
    {
        block_r[0] = (lr << 3) | (lr >> 2); block_g[0] = (lg << 2) | (lg >> 4);	block_b[0] = (lb << 3) | (lb >> 2);
        block_r[1] = (hr << 3) | (hr >> 2);	block_g[1] = (hg << 2) | (hg >> 4);	block_b[1] = (hb << 3) | (hb >> 2);

        if ((g_bc1_approx_mode == bc1_approx_mode::cBC1Ideal) || (g_bc1_approx_mode == bc1_approx_mode::cBC1IdealRound4))
        {
            block_r[2] = (block_r[0] + block_r[1]) / 2; block_g[2] = (block_g[0] + block_g[1]) / 2; block_b[2] = (block_b[0] + block_b[1]) / 2;
        }
        else if (g_bc1_approx_mode == bc1_approx_mode::cBC1AMD)
        {
            block_r[2] = interp_half_5_6_amd(block_r[0], block_r[1]); block_g[2] = interp_half_5_6_amd(block_g[0], block_g[1]); block_b[2] = interp_half_5_6_amd(block_b[0], block_b[1]);
        }
        else
        {
            block_r[2] = interp_half_5_nv(lr, hr); block_g[2] = interp_half_6_nv(block_g[0], block_g[1]); block_b[2] = interp_half_5_nv(lb, hb);
        }
    }

    static inline void bc1_find_sels4_noerr(const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16])
    {
        uint32_t block_r[4], block_g[4], block_b[4];
        bc1_get_block_colors4(block_r, block_g, block_b, lr, lg, lb, hr, hg, hb);

        int ar = block_r[3] - block_r[0], ag = block_g[3] - block_g[0], ab = block_b[3] - block_b[0];

        int dots[4];
        for (uint32_t i = 0; i < 4; i++)
            dots[i] = (int)block_r[i] * ar + (int)block_g[i] * ag + (int)block_b[i] * ab;

        int t0 = dots[0] + dots[1], t1 = dots[1] + dots[2], t2 = dots[2] + dots[3];

        ar *= 2; ag *= 2; ab *= 2;

        static const uint8_t s_sels[4] = { 3, 2, 1, 0 };

        for (uint32_t i = 0; i < 16; i += 4)
        {
            const int d0 = pSrc_pixels[i + 0].r * ar + pSrc_pixels[i + 0].g * ag + pSrc_pixels[i + 0].b * ab;
            const int d1 = pSrc_pixels[i + 1].r * ar + pSrc_pixels[i + 1].g * ag + pSrc_pixels[i + 1].b * ab;
            const int d2 = pSrc_pixels[i + 2].r * ar + pSrc_pixels[i + 2].g * ag + pSrc_pixels[i + 2].b * ab;
            const int d3 = pSrc_pixels[i + 3].r * ar + pSrc_pixels[i + 3].g * ag + pSrc_pixels[i + 3].b * ab;

            sels[i + 0] = s_sels[(d0 <= t0) + (d0 < t1) + (d0 < t2)];
            sels[i + 1] = s_sels[(d1 <= t0) + (d1 < t1) + (d1 < t2)];
            sels[i + 2] = s_sels[(d2 <= t0) + (d2 < t1) + (d2 < t2)];
            sels[i + 3] = s_sels[(d3 <= t0) + (d3 < t1) + (d3 < t2)];
        }
    }

    static inline uint32_t bc1_find_sels4_fasterr(const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16], uint32_t cur_err)
    {
        uint32_t block_r[4], block_g[4], block_b[4];
        bc1_get_block_colors4(block_r, block_g, block_b, lr, lg, lb, hr, hg, hb);

        int ar = block_r[3] - block_r[0], ag = block_g[3] - block_g[0], ab = block_b[3] - block_b[0];

        int dots[4];
        for (uint32_t i = 0; i < 4; i++)
            dots[i] = (int)block_r[i] * ar + (int)block_g[i] * ag + (int)block_b[i] * ab;

        int t0 = dots[0] + dots[1], t1 = dots[1] + dots[2], t2 = dots[2] + dots[3];

        ar *= 2; ag *= 2; ab *= 2;

        static const uint8_t s_sels[4] = { 3, 2, 1, 0 };

        uint32_t total_err = 0;

        for (uint32_t i = 0; i < 16; i += 4)
        {
            const int d0 = pSrc_pixels[i + 0].r * ar + pSrc_pixels[i + 0].g * ag + pSrc_pixels[i + 0].b * ab;
            const int d1 = pSrc_pixels[i + 1].r * ar + pSrc_pixels[i + 1].g * ag + pSrc_pixels[i + 1].b * ab;
            const int d2 = pSrc_pixels[i + 2].r * ar + pSrc_pixels[i + 2].g * ag + pSrc_pixels[i + 2].b * ab;
            const int d3 = pSrc_pixels[i + 3].r * ar + pSrc_pixels[i + 3].g * ag + pSrc_pixels[i + 3].b * ab;

            uint8_t sel0 = s_sels[(d0 <= t0) + (d0 < t1) + (d0 < t2)];
            uint8_t sel1 = s_sels[(d1 <= t0) + (d1 < t1) + (d1 < t2)];
            uint8_t sel2 = s_sels[(d2 <= t0) + (d2 < t1) + (d2 < t2)];
            uint8_t sel3 = s_sels[(d3 <= t0) + (d3 < t1) + (d3 < t2)];

            sels[i + 0] = sel0;
            sels[i + 1] = sel1;
            sels[i + 2] = sel2;
            sels[i + 3] = sel3;

            total_err += squarei(pSrc_pixels[i + 0].r - block_r[sel0]) + squarei(pSrc_pixels[i + 0].g - block_g[sel0]) + squarei(pSrc_pixels[i + 0].b - block_b[sel0]);
            total_err += squarei(pSrc_pixels[i + 1].r - block_r[sel1]) + squarei(pSrc_pixels[i + 1].g - block_g[sel1]) + squarei(pSrc_pixels[i + 1].b - block_b[sel1]);
            total_err += squarei(pSrc_pixels[i + 2].r - block_r[sel2]) + squarei(pSrc_pixels[i + 2].g - block_g[sel2]) + squarei(pSrc_pixels[i + 2].b - block_b[sel2]);
            total_err += squarei(pSrc_pixels[i + 3].r - block_r[sel3]) + squarei(pSrc_pixels[i + 3].g - block_g[sel3]) + squarei(pSrc_pixels[i + 3].b - block_b[sel3]);

            if (total_err >= cur_err)
                break;
        }

        return total_err;
    }

    static inline uint32_t bc1_find_sels4_check2_err(const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16], uint32_t cur_err)
    {
        uint32_t block_r[4], block_g[4], block_b[4];
        bc1_get_block_colors4(block_r, block_g, block_b, lr, lg, lb, hr, hg, hb);

        int dr = block_r[3] - block_r[0], dg = block_g[3] - block_g[0], db = block_b[3] - block_b[0];

        const float f = 4.0f / (float)(squarei(dr) + squarei(dg) + squarei(db) + .00000125f);

        uint32_t total_err = 0;

        for (uint32_t i = 0; i < 16; i++)
        {
            const int r = pSrc_pixels[i].r;
            const int g = pSrc_pixels[i].g;
            const int b = pSrc_pixels[i].b;

            int sel = (int)((float)((r - (int)block_r[0]) * dr + (g - (int)block_g[0]) * dg + (b - (int)block_b[0]) * db) * f + .5f);
            sel = clampi(sel, 1, 3);

            uint32_t err0 = squarei((int)block_r[sel - 1] - (int)r) + squarei((int)block_g[sel - 1] - (int)g) + squarei((int)block_b[sel - 1] - (int)b);
            uint32_t err1 = squarei((int)block_r[sel] - (int)r) + squarei((int)block_g[sel] - (int)g) + squarei((int)block_b[sel] - (int)b);

            int best_sel = sel;
            uint32_t best_err = err1;
            if (err0 == err1)
            {
                // Prefer non-interpolation
                if ((best_sel - 1) == 0)
                    best_sel = 0;
            }
            else if (err0 < best_err)
            {
                best_sel = sel - 1;
                best_err = err0;
            }

            total_err += best_err;

            if (total_err >= cur_err)
                break;

            sels[i] = (uint8_t)best_sel;
        }
        return total_err;
    }

    static inline uint32_t bc1_find_sels4_fullerr(const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16], uint32_t cur_err)
    {
        uint32_t block_r[4], block_g[4], block_b[4];
        bc1_get_block_colors4(block_r, block_g, block_b, lr, lg, lb, hr, hg, hb);

        uint32_t total_err = 0;

        for (uint32_t i = 0; i < 16; i++)
        {
            const int r = pSrc_pixels[i].r;
            const int g = pSrc_pixels[i].g;
            const int b = pSrc_pixels[i].b;

            uint32_t best_err = squarei((int)block_r[0] - (int)r) + squarei((int)block_g[0] - (int)g) + squarei((int)block_b[0] - (int)b);
            uint8_t best_sel = 0;

            for (uint32_t j = 1; (j < 4) && best_err; j++)
            {
                uint32_t err = squarei((int)block_r[j] - (int)r) + squarei((int)block_g[j] - (int)g) + squarei((int)block_b[j] - (int)b);
                if ((err < best_err) || ((err == best_err) && (j == 3)))
                {
                    best_err = err;
                    best_sel = (uint8_t)j;
                }
            }

            total_err += best_err;

            if (total_err >= cur_err)
                break;

            sels[i] = (uint8_t)best_sel;
        }
        return total_err;
    }

    static inline uint32_t bc1_find_sels4(uint32_t flags, const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16], uint32_t cur_err)
    {
        uint32_t err;

        if (flags & cEncodeBC1UseFasterMSEEval)
            err = bc1_find_sels4_fasterr(pSrc_pixels, lr, lg, lb, hr, hg, hb, sels, cur_err);
        else if (flags & cEncodeBC1UseFullMSEEval)
            err = bc1_find_sels4_fullerr(pSrc_pixels, lr, lg, lb, hr, hg, hb, sels, cur_err);
        else
            err = bc1_find_sels4_check2_err(pSrc_pixels, lr, lg, lb, hr, hg, hb, sels, cur_err);

        return err;
    }

    static inline uint32_t bc1_find_sels3_fullerr(bool use_black, const color32* pSrc_pixels, uint32_t lr, uint32_t lg, uint32_t lb, uint32_t hr, uint32_t hg, uint32_t hb, uint8_t sels[16], uint32_t cur_err)
    {
        uint32_t block_r[3], block_g[3], block_b[3];
        bc1_get_block_colors3(block_r, block_g, block_b, lr, lg, lb, hr, hg, hb);

        uint32_t total_err = 0;

        for (uint32_t i = 0; i < 16; i++)
        {
            const int r = pSrc_pixels[i].r;
            const int g = pSrc_pixels[i].g;
            const int b = pSrc_pixels[i].b;

            uint32_t best_err = squarei((int)block_r[0] - (int)r) + squarei((int)block_g[0] - (int)g) + squarei((int)block_b[0] - (int)b);
            uint32_t best_sel = 0;

            uint32_t err1 = squarei((int)block_r[1] - (int)r) + squarei((int)block_g[1] - (int)g) + squarei((int)block_b[1] - (int)b);
            if (err1 < best_err)
            {
                best_err = err1;
                best_sel = 1;
            }

            uint32_t err2 = squarei((int)block_r[2] - (int)r) + squarei((int)block_g[2] - (int)g) + squarei((int)block_b[2] - (int)b);
            if (err2 < best_err)
            {
                best_err = err2;
                best_sel = 2;
            }

            if (use_black)
            {
                uint32_t err3 = squarei(r) + squarei(g) + squarei(b);
                if (err3 < best_err)
                {
                    best_err = err3;
                    best_sel = 3;
                }
            }

            total_err += best_err;
            if (total_err >= cur_err)
                return total_err;

            sels[i] = (uint8_t)best_sel;
        }

        return total_err;
    }

    static inline void precise_round_565(const vec3F &xl, const vec3F &xh,
        int &trial_lr, int &trial_lg, int &trial_lb,
        int &trial_hr, int &trial_hg, int &trial_hb)
    {
        trial_lr = (int)(xl.c[0] * 31.0f);
        trial_lg = (int)(xl.c[1] * 63.0f);
        trial_lb = (int)(xl.c[2] * 31.0f);

        trial_hr = (int)(xh.c[0] * 31.0f);
        trial_hg = (int)(xh.c[1] * 63.0f);
        trial_hb = (int)(xh.c[2] * 31.0f);

        if ((uint32_t)(trial_lr | trial_lb | trial_hr | trial_hb) > 31U)
        {
            trial_lr = ((uint32_t)trial_lr > 31U) ? (~trial_lr >> 31) & 31 : trial_lr;
            trial_hr = ((uint32_t)trial_hr > 31U) ? (~trial_hr >> 31) & 31 : trial_hr;

            trial_lb = ((uint32_t)trial_lb > 31U) ? (~trial_lb >> 31) & 31 : trial_lb;
            trial_hb = ((uint32_t)trial_hb > 31U) ? (~trial_hb >> 31) & 31 : trial_hb;
        }

        if ((uint32_t)(trial_lg | trial_hg) > 63U)
        {
            trial_lg = ((uint32_t)trial_lg > 63U) ? (~trial_lg >> 31) & 63 : trial_lg;
            trial_hg = ((uint32_t)trial_hg > 63U) ? (~trial_hg >> 31) & 63 : trial_hg;
        }

        trial_lr = (trial_lr + (xl.c[0] > g_midpoint5[trial_lr])) & 31;
        trial_lg = (trial_lg + (xl.c[1] > g_midpoint6[trial_lg])) & 63;
        trial_lb = (trial_lb + (xl.c[2] > g_midpoint5[trial_lb])) & 31;

        trial_hr = (trial_hr + (xh.c[0] > g_midpoint5[trial_hr])) & 31;
        trial_hg = (trial_hg + (xh.c[1] > g_midpoint6[trial_hg])) & 63;
        trial_hb = (trial_hb + (xh.c[2] > g_midpoint5[trial_hb])) & 31;
    }

    static inline void precise_round_565_noscale(vec3F xl, vec3F xh,
        int &trial_lr, int &trial_lg, int &trial_lb,
        int &trial_hr, int &trial_hg, int &trial_hb)
    {
        xl.c[0] *= 1.0f / 255.0f;
        xl.c[1] *= 1.0f / 255.0f;
        xl.c[2] *= 1.0f / 255.0f;

        xh.c[0] *= 1.0f / 255.0f;
        xh.c[1] *= 1.0f / 255.0f;
        xh.c[2] *= 1.0f / 255.0f;

        precise_round_565(xl, xh, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb);
    }

    static inline void bc1_encode4(bc1_block *pDst_block, int lr, int lg, int lb, int hr, int hg, int hb, const uint8_t sels[16])
    {
        uint32_t lc16 = bc1_block::pack_unscaled_color(lr, lg, lb);
        uint32_t hc16 = bc1_block::pack_unscaled_color(hr, hg, hb);

        // Always forbid 3 color blocks
        if (lc16 == hc16)
        {
            uint8_t mask = 0;

            // Make l > h
            if (hc16 > 0)
                hc16--;
            else
            {
                // lc16 = hc16 = 0
                assert(lc16 == hc16 && hc16 == 0);

                hc16 = 0;
                lc16 = 1;
                mask = 0x55; // select hc16
            }

            assert(lc16 > hc16);
            pDst_block->set_low_color(static_cast<uint16_t>(lc16));
            pDst_block->set_high_color(static_cast<uint16_t>(hc16));

            pDst_block->m_selectors[0] = mask;
            pDst_block->m_selectors[1] = mask;
            pDst_block->m_selectors[2] = mask;
            pDst_block->m_selectors[3] = mask;
        }
        else
        {
            uint8_t invert_mask = 0;
            if (lc16 < hc16)
            {
                std::swap(lc16, hc16);
                invert_mask = 0x55;
            }

            assert(lc16 > hc16);
            pDst_block->set_low_color((uint16_t)lc16);
            pDst_block->set_high_color((uint16_t)hc16);

            uint32_t packed_sels = 0;
            static const uint8_t s_sel_trans[4] = { 0, 2, 3, 1 };
            for (uint32_t i = 0; i < 16; i++)
                packed_sels |= ((uint32_t)s_sel_trans[sels[i]] << (i * 2));

            pDst_block->m_selectors[0] = (uint8_t)packed_sels ^ invert_mask;
            pDst_block->m_selectors[1] = (uint8_t)(packed_sels >> 8) ^ invert_mask;
            pDst_block->m_selectors[2] = (uint8_t)(packed_sels >> 16) ^ invert_mask;
            pDst_block->m_selectors[3] = (uint8_t)(packed_sels >> 24) ^ invert_mask;
        }
    }

    static inline void bc1_encode3(bc1_block *pDst_block, int lr, int lg, int lb, int hr, int hg, int hb, const uint8_t sels[16])
    {
        uint32_t lc16 = bc1_block::pack_unscaled_color(lr, lg, lb);
        uint32_t hc16 = bc1_block::pack_unscaled_color(hr, hg, hb);

        bool invert_flag = false;
        if (lc16 > hc16)
        {
            std::swap(lc16, hc16);
            invert_flag = true;
        }

        assert(lc16 <= hc16);

        pDst_block->set_low_color((uint16_t)lc16);
        pDst_block->set_high_color((uint16_t)hc16);

        uint32_t packed_sels = 0;

        if (invert_flag)
        {
            static const uint8_t s_sel_trans_inv[4] = { 1, 0, 2, 3 };

            for (uint32_t i = 0; i < 16; i++)
                packed_sels |= ((uint32_t)s_sel_trans_inv[sels[i]] << (i * 2));
        }
        else
        {
            for (uint32_t i = 0; i < 16; i++)
                packed_sels |= ((uint32_t)sels[i] << (i * 2));
        }

        pDst_block->m_selectors[0] = (uint8_t)packed_sels;
        pDst_block->m_selectors[1] = (uint8_t)(packed_sels >> 8);
        pDst_block->m_selectors[2] = (uint8_t)(packed_sels >> 16);
        pDst_block->m_selectors[3] = (uint8_t)(packed_sels >> 24);
    }

    struct bc1_encode_results
    {
        int lr, lg, lb;
        int hr, hg, hb;
        uint8_t sels[16];
        bool m_3color;
    };

    static bool try_3color_block_useblack(const color32* pSrc_pixels, uint32_t flags, uint32_t &cur_err, bc1_encode_results &results)
    {
        int total_r = 0, total_g = 0, total_b = 0;
        int max_r = 0, max_g = 0, max_b = 0;
        int min_r = 255, min_g = 255, min_b = 255;
        int total_pixels = 0;
        for (uint32_t i = 0; i < 16; i++)
        {
            const int r = pSrc_pixels[i].r, g = pSrc_pixels[i].g, b = pSrc_pixels[i].b;
            if ((r | g | b) < 4)
                continue;

            max_r = std::max(max_r, r); max_g = std::max(max_g, g); max_b = std::max(max_b, b);
            min_r = std::min(min_r, r); min_g = std::min(min_g, g); min_b = std::min(min_b, b);
            total_r += r; total_g += g; total_b += b;

            total_pixels++;
        }

        if (!total_pixels)
            return false;

        int half_total_pixels = total_pixels >> 1;
        int avg_r = (total_r + half_total_pixels) / total_pixels;
        int avg_g = (total_g + half_total_pixels) / total_pixels;
        int avg_b = (total_b + half_total_pixels) / total_pixels;

        uint32_t low_c = 0, high_c = 0;

        int icov[6] = { 0, 0, 0, 0, 0, 0 };
        for (uint32_t i = 0; i < 16; i++)
        {
            int r = (int)pSrc_pixels[i].r;
            int g = (int)pSrc_pixels[i].g;
            int b = (int)pSrc_pixels[i].b;

            if ((r | g | b) < 4)
                continue;

            r -= avg_r;
            g -= avg_g;
            b -= avg_b;

            icov[0] += r * r;
            icov[1] += r * g;
            icov[2] += r * b;
            icov[3] += g * g;
            icov[4] += g * b;
            icov[5] += b * b;
        }

        float cov[6];
        for (uint32_t i = 0; i < 6; i++)
            cov[i] = (float)(icov[i]) * (1.0f / 255.0f);

        float xr = (float)(max_r - min_r);
        float xg = (float)(max_g - min_g);
        float xb = (float)(max_b - min_b);

        if (icov[2] < 0)
            xr = -xr;

        if (icov[4] < 0)
            xg = -xg;

        for (uint32_t power_iter = 0; power_iter < 4; power_iter++)
        {
            float r = xr * cov[0] + xg * cov[1] + xb * cov[2];
            float g = xr * cov[1] + xg * cov[3] + xb * cov[4];
            float b = xr * cov[2] + xg * cov[4] + xb * cov[5];
            xr = r; xg = g; xb = b;
        }

        float k = maximum(fabsf(xr), fabsf(xg), fabsf(xb));
        int saxis_r = 306, saxis_g = 601, saxis_b = 117;
        if (k >= 2)
        {
            float m = 1024.0f / k;
            saxis_r = (int)(xr * m);
            saxis_g = (int)(xg * m);
            saxis_b = (int)(xb * m);
        }

        int low_dot = INT_MAX, high_dot = INT_MIN;
        for (uint32_t i = 0; i < 16; i++)
        {
            int r = (int)pSrc_pixels[i].r, g = (int)pSrc_pixels[i].g, b = (int)pSrc_pixels[i].b;

            if ((r | g | b) < 4)
                continue;

            int dot = r * saxis_r + g * saxis_g + b * saxis_b;
            if (dot < low_dot)
            {
                low_dot = dot;
                low_c = i;
            }
            if (dot > high_dot)
            {
                high_dot = dot;
                high_c = i;
            }
        }

        int lr = to_5(pSrc_pixels[low_c].r);
        int lg = to_6(pSrc_pixels[low_c].g);
        int lb = to_5(pSrc_pixels[low_c].b);

        int hr = to_5(pSrc_pixels[high_c].r);
        int hg = to_6(pSrc_pixels[high_c].g);
        int hb = to_5(pSrc_pixels[high_c].b);

        uint8_t trial_sels[16];
        uint32_t trial_err = bc1_find_sels3_fullerr(true, pSrc_pixels, lr, lg, lb, hr, hg, hb, trial_sels, UINT32_MAX);

        if (trial_err)
        {
            const uint32_t total_ls_passes = flags & cEncodeBC1TwoLeastSquaresPasses ? 2 : 1;
            for (uint32_t trials = 0; trials < total_ls_passes; trials++)
            {
                vec3F xl, xh;
                int lr2, lg2, lb2, hr2, hg2, hb2;
                if (!compute_least_squares_endpoints3_rgb(true, pSrc_pixels, trial_sels, &xl, &xh))
                {
                    lr2 = g_bc1_match5_half[avg_r].m_hi;
                    lg2 = g_bc1_match6_half[avg_g].m_hi;
                    lb2 = g_bc1_match5_half[avg_b].m_hi;

                    hr2 = g_bc1_match5_half[avg_r].m_lo;
                    hg2 = g_bc1_match6_half[avg_g].m_lo;
                    hb2 = g_bc1_match5_half[avg_b].m_lo;
                }
                else
                {
                    precise_round_565(xl, xh, hr2, hg2, hb2, lr2, lg2, lb2);
                }

                if ((lr == lr2) && (lg == lg2) && (lb == lb2) && (hr == hr2) && (hg == hg2) && (hb == hb2))
                    break;

                uint8_t trial_sels2[16];
                uint32_t trial_err2 = bc1_find_sels3_fullerr(true, pSrc_pixels, lr2, lg2, lb2, hr2, hg2, hb2, trial_sels2, trial_err);

                if (trial_err2 < trial_err)
                {
                    trial_err = trial_err2;
                    lr = lr2; lg = lg2; lb = lb2;
                    hr = hr2; hg = hg2; hb = hb2;
                    memcpy(trial_sels, trial_sels2, sizeof(trial_sels));
                }
                else
                    break;
            }
        }

        if (trial_err < cur_err)
        {
            results.m_3color = true;
            results.lr = lr;
            results.lg = lg;
            results.lb = lb;
            results.hr = hr;
            results.hg = hg;
            results.hb = hb;
            memcpy(results.sels, trial_sels, 16);

            cur_err = trial_err;

            return true;
        }

        return false;
    }

    static bool try_3color_block(const color32* pSrc_pixels, uint32_t flags, uint32_t &cur_err,
        int avg_r, int avg_g, int avg_b, int lr, int lg, int lb, int hr, int hg, int hb, int total_r, int total_g, int total_b, uint32_t total_orderings_to_try,
        bc1_encode_results &results)
    {
        uint8_t trial_sels[16];
        uint32_t trial_err = bc1_find_sels3_fullerr(false, pSrc_pixels, lr, lg, lb, hr, hg, hb, trial_sels, UINT32_MAX);

        if (trial_err)
        {
            const uint32_t total_ls_passes = flags & cEncodeBC1TwoLeastSquaresPasses ? 2 : 1;
            for (uint32_t trials = 0; trials < total_ls_passes; trials++)
            {
                vec3F xl, xh;
                int lr2, lg2, lb2, hr2, hg2, hb2;
                if (!compute_least_squares_endpoints3_rgb(false, pSrc_pixels, trial_sels, &xl, &xh))
                {
                    lr2 = g_bc1_match5_half[avg_r].m_hi;
                    lg2 = g_bc1_match6_half[avg_g].m_hi;
                    lb2 = g_bc1_match5_half[avg_b].m_hi;

                    hr2 = g_bc1_match5_half[avg_r].m_lo;
                    hg2 = g_bc1_match6_half[avg_g].m_lo;
                    hb2 = g_bc1_match5_half[avg_b].m_lo;
                }
                else
                {
                    precise_round_565(xl, xh, hr2, hg2, hb2, lr2, lg2, lb2);
                }

                if ((lr == lr2) && (lg == lg2) && (lb == lb2) && (hr == hr2) && (hg == hg2) && (hb == hb2))
                    break;

                uint8_t trial_sels2[16];
                uint32_t trial_err2 = bc1_find_sels3_fullerr(false, pSrc_pixels, lr2, lg2, lb2, hr2, hg2, hb2, trial_sels2, trial_err);

                if (trial_err2 < trial_err)
                {
                    trial_err = trial_err2;
                    lr = lr2; lg = lg2; lb = lb2;
                    hr = hr2; hg = hg2; hb = hb2;
                    memcpy(trial_sels, trial_sels2, sizeof(trial_sels));
                }
                else
                    break;
            }
        }

        if ((trial_err) && (flags & cEncodeBC1UseLikelyTotalOrderings) && (total_orderings_to_try))
        {
            hist3 h;
            for (uint32_t i = 0; i < 16; i++)
            {
                assert(trial_sels[i] < 3);
                h.m_hist[trial_sels[i]]++;
            }

            const uint32_t orig_total_order_index = h.lookup_total_ordering_index();

            int r0, g0, b0, r3, g3, b3;
            r0 = (lr << 3) | (lr >> 2); g0 = (lg << 2) | (lg >> 4); b0 = (lb << 3) | (lb >> 2);
            r3 = (hr << 3) | (hr >> 2); g3 = (hg << 2) | (hg >> 4); b3 = (hb << 3) | (hb >> 2);

            int ar = r3 - r0, ag = g3 - g0, ab = b3 - b0;

            int dots[16];
            for (uint32_t i = 0; i < 16; i++)
            {
                int r = pSrc_pixels[i].r;
                int g = pSrc_pixels[i].g;
                int b = pSrc_pixels[i].b;
                int d = 0x1000000 + (r * ar + g * ag + b * ab);
                assert(d >= 0);
                dots[i] = (d << 4) + i;
            }

            std::sort(dots, dots + 16);

            uint32_t r_sum[17], g_sum[17], b_sum[17];
            uint32_t r = 0, g = 0, b = 0;
            for (uint32_t i = 0; i < 16; i++)
            {
                const uint32_t p = dots[i] & 15;

                r_sum[i] = r;
                g_sum[i] = g;
                b_sum[i] = b;

                r += pSrc_pixels[p].r;
                g += pSrc_pixels[p].g;
                b += pSrc_pixels[p].b;
            }

            r_sum[16] = total_r;
            g_sum[16] = total_g;
            b_sum[16] = total_b;

            const uint32_t q_total = (flags & cEncodeBC1Exhaustive) ? NUM_UNIQUE_TOTAL_ORDERINGS3 : std::min(total_orderings_to_try, MAX_TOTAL_ORDERINGS3);
            for (uint32_t q = 0; q < q_total; q++)
            {
                const uint32_t s = (flags & cEncodeBC1Exhaustive) ? q : g_best_total_orderings3[orig_total_order_index][q];

                int trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb;

                vec3F xl, xh;

                if ((s == TOTAL_ORDER_3_0_16) || (s == TOTAL_ORDER_3_1_16) || (s == TOTAL_ORDER_3_2_16))
                {
                    trial_lr = g_bc1_match5_half[avg_r].m_hi;
                    trial_lg = g_bc1_match6_half[avg_g].m_hi;
                    trial_lb = g_bc1_match5_half[avg_b].m_hi;

                    trial_hr = g_bc1_match5_half[avg_r].m_lo;
                    trial_hg = g_bc1_match6_half[avg_g].m_lo;
                    trial_hb = g_bc1_match5_half[avg_b].m_lo;
                }
                else
                {
                    compute_least_squares_endpoints3_rgb(&xl, &xh, total_r, total_g, total_b,
                        g_selector_factors3[s][0], g_selector_factors3[s][1], g_selector_factors3[s][2], s, r_sum, g_sum, b_sum);

                    precise_round_565(xl, xh, trial_hr, trial_hg, trial_hb, trial_lr, trial_lg, trial_lb);
                }

                uint8_t trial_sels2[16];
                uint32_t trial_err2 = bc1_find_sels3_fullerr(false, pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, trial_sels2, UINT32_MAX);

                if (trial_err2 < trial_err)
                {
                    trial_err = trial_err2;

                    lr = trial_lr;
                    lg = trial_lg;
                    lb = trial_lb;

                    hr = trial_hr;
                    hg = trial_hg;
                    hb = trial_hb;

                    memcpy(trial_sels, trial_sels2, sizeof(trial_sels));
                }

            } // s
        }

        if (trial_err < cur_err)
        {
            results.m_3color = true;
            results.lr = lr;
            results.lg = lg;
            results.lb = lb;
            results.hr = hr;
            results.hg = hg;
            results.hb = hb;
            memcpy(results.sels, trial_sels, 16);

            cur_err = trial_err;

            return true;
        }

        return false;
    }

    void encode_bc1(uint32_t level, void* pDst, const uint8_t* pPixels, bool allow_3color, bool allow_transparent_texels_for_black)
    {
        uint32_t flags = 0, total_orderings4 = 1, total_orderings3 = 1;

        static_assert(MAX_TOTAL_ORDERINGS3 >= 32, "MAX_TOTAL_ORDERINGS3 >= 32");
        static_assert(MAX_TOTAL_ORDERINGS4 >= 32, "MAX_TOTAL_ORDERINGS4 >= 32");

        switch (level)
        {
        case 0:
            // Faster/higher quality than stb_dxt default.
            flags = cEncodeBC1BoundingBoxInt;
            break;
        case 1:
            // Faster/higher quality than stb_dxt default. A bit higher average quality vs. mode 0.
            flags = cEncodeBC1Use2DLS;
            break;
        case 2:
            // On average mode 2 is a little weaker than modes 0/1, but it's stronger on outliers (very tough textures).
            // Slightly stronger than stb_dxt.
            flags = 0;
            break;
        case 3:
            // Slightly stronger than stb_dxt HIGHQUAL.
            flags = cEncodeBC1TwoLeastSquaresPasses;
            break;
        case 4:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1Use6PowerIters;
            break;
        default:
        case 5:
            // stb_dxt HIGHQUAL + permit 3 color (if it's enabled).
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFasterMSEEval;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            break;
        case 6:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFasterMSEEval | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            break;
        case 7:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFasterMSEEval | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 4;
            break;
        case 8:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFasterMSEEval | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 8;
            break;
        case 9:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 11;
            total_orderings3 = 3;
            break;
        case 10:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 20;
            total_orderings3 = 8;
            break;
        case 11:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 28;
            total_orderings3 = 16;
            break;
        case 12:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseLikelyTotalOrderings;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 32;
            total_orderings3 = 32;
            break;
        case 13:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | (20 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 32;
            total_orderings3 = 32;
            break;
        case 14:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | (32 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 32;
            total_orderings3 = 32;
            break;
        case 15:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | (32 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = ((((32 + MAX_TOTAL_ORDERINGS4) / 2) + 32) / 2);
            total_orderings3 = 32;
            break;
        case 16:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | (256 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = (32 + MAX_TOTAL_ORDERINGS4) / 2;
            total_orderings3 = 32;
            break;
        case 17:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | (256 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = MAX_TOTAL_ORDERINGS4;
            total_orderings3 = 32;
            break;
        case 18:
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | cEncodeBC1Iterative | (256 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = MAX_TOTAL_ORDERINGS4;
            total_orderings3 = 32;
            break;
        case 19:
            // This hidden mode is *extremely* slow and abuses the encoder. It's just for testing/training.
            flags = cEncodeBC1TwoLeastSquaresPasses | cEncodeBC1UseFullMSEEval | cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use6PowerIters | cEncodeBC1Exhaustive | cEncodeBC1Iterative | (256 << cEncodeBC1EndpointSearchRoundsShift) | cEncodeBC1TryAllInitialEndponts;
            flags |= (allow_3color ? cEncodeBC1Use3ColorBlocks : 0) | (allow_transparent_texels_for_black ? cEncodeBC1Use3ColorBlocksForBlackPixels : 0);
            total_orderings4 = 32;
            total_orderings3 = 32;
            break;
        }

        encode_bc1(pDst, pPixels, flags, total_orderings4, total_orderings3);
    }

    static inline void encode_bc1_pick_initial(const color32 *pSrc_pixels, uint32_t flags, bool grayscale_flag,
        int min_r, int min_g, int min_b, int max_r, int max_g, int max_b,
        int avg_r, int avg_g, int avg_b, int total_r, int total_g, int total_b,
        int &lr, int &lg, int &lb, int &hr, int &hg, int &hb)
    {
        if (grayscale_flag)
        {
            const int fr = pSrc_pixels[0].r;

            // Grayscale blocks are a common enough case to specialize.
            if ((max_r - min_r) < 2)
            {
                lr = lb = hr = hb = to_5(fr);
                lg = hg = to_6(fr);
            }
            else
            {
                lr = lb = to_5(min_r);
                lg = to_6(min_r);

                hr = hb = to_5(max_r);
                hg = to_6(max_r);
            }
        }
        else if (flags & cEncodeBC1Use2DLS)
        {
            //  2D Least Squares approach from Humus's example, with added inset and optimal rounding.
            int big_chan = 0, min_chan_val = min_r, max_chan_val = max_r;
            if ((max_g - min_g) > (max_chan_val - min_chan_val))
                big_chan = 1, min_chan_val = min_g, max_chan_val = max_g;

            if ((max_b - min_b) > (max_chan_val - min_chan_val))
                big_chan = 2, min_chan_val = min_b, max_chan_val = max_b;

            int sum_xy_r = 0, sum_xy_g = 0, sum_xy_b = 0;
            vec3F l, h;
            if (big_chan == 0)
            {
                for (uint32_t i = 0; i < 16; i++)
                {
                    const int r = pSrc_pixels[i].r, g = pSrc_pixels[i].g, b = pSrc_pixels[i].b;
                    sum_xy_r += r * r, sum_xy_g += r * g, sum_xy_b += r * b;
                }

                int sum_x = total_r;
                int sum_x2 = sum_xy_r;

                float div = (float)(16 * sum_x2 - sum_x * sum_x);
                float b_y = 0.0f, b_z = 0.0f;
                if (fabs(div) > 1e-8f)
                {
                    div = 1.0f / div;
                    b_y = (16 * sum_xy_g - sum_x * total_g) * div;
                    b_z = (16 * sum_xy_b - sum_x * total_b) * div;
                }

                float a_y = (total_g - b_y * sum_x) / 16.0f;
                float a_z = (total_b - b_z * sum_x) / 16.0f;

                l.c[1] = a_y + b_y * min_chan_val;
                l.c[2] = a_z + b_z * min_chan_val;

                h.c[1] = a_y + b_y * max_chan_val;
                h.c[2] = a_z + b_z * max_chan_val;

                float dg = (h.c[1] - l.c[1]);
                float db = (h.c[2] - l.c[2]);

                h.c[1] = l.c[1] + dg * (15.0f / 16.0f);
                h.c[2] = l.c[2] + db * (15.0f / 16.0f);

                l.c[1] = l.c[1] + dg * (1.0f / 16.0f);
                l.c[2] = l.c[2] + db * (1.0f / 16.0f);

                float d = (float)(max_chan_val - min_chan_val);
                float fmin_chan_val = min_chan_val + d * (1.0f / 16.0f);
                float fmax_chan_val = min_chan_val + d * (15.0f / 16.0f);

                l.c[0] = fmin_chan_val;
                h.c[0] = fmax_chan_val;
            }
            else if (big_chan == 1)
            {
                for (uint32_t i = 0; i < 16; i++)
                {
                    const int r = pSrc_pixels[i].r, g = pSrc_pixels[i].g, b = pSrc_pixels[i].b;
                    sum_xy_r += g * r, sum_xy_g += g * g, sum_xy_b += g * b;
                }

                int sum_x = total_g;
                int sum_x2 = sum_xy_g;

                float div = (float)(16 * sum_x2 - sum_x * sum_x);
                float b_x = 0.0f, b_z = 0.0f;
                if (fabs(div) > 1e-8f)
                {
                    div = 1.0f / div;
                    b_x = (16 * sum_xy_r - sum_x * total_r) * div;
                    b_z = (16 * sum_xy_b - sum_x * total_b) * div;
                }

                float a_x = (total_r - b_x * sum_x) / 16.0f;
                float a_z = (total_b - b_z * sum_x) / 16.0f;

                l.c[0] = a_x + b_x * min_chan_val;
                l.c[2] = a_z + b_z * min_chan_val;

                h.c[0] = a_x + b_x * max_chan_val;
                h.c[2] = a_z + b_z * max_chan_val;

                float dr = (h.c[0] - l.c[0]);
                float db = (h.c[2] - l.c[2]);

                h.c[0] = l.c[0] + dr * (15.0f / 16.0f);
                h.c[2] = l.c[2] + db * (15.0f / 16.0f);

                l.c[0] = l.c[0] + dr * (1.0f / 16.0f);
                l.c[2] = l.c[2] + db * (1.0f / 16.0f);

                float d = (float)(max_chan_val - min_chan_val);
                float fmin_chan_val = min_chan_val + d * (1.0f / 16.0f);
                float fmax_chan_val = min_chan_val + d * (15.0f / 16.0f);

                l.c[1] = fmin_chan_val;
                h.c[1] = fmax_chan_val;
            }
            else
            {
                for (uint32_t i = 0; i < 16; i++)
                {
                    const int r = pSrc_pixels[i].r, g = pSrc_pixels[i].g, b = pSrc_pixels[i].b;
                    sum_xy_r += b * r, sum_xy_g += b * g, sum_xy_b += b * b;
                }

                int sum_x = total_b;
                int sum_x2 = sum_xy_b;

                float div = (float)(16 * sum_x2 - sum_x * sum_x);
                float b_x = 0.0f, b_y = 0.0f;
                if (fabs(div) > 1e-8f)
                {
                    div = 1.0f / div;
                    b_x = (16 * sum_xy_r - sum_x * total_r) * div;
                    b_y = (16 * sum_xy_g - sum_x * total_g) * div;
                }

                float a_x = (total_r - b_x * sum_x) / 16.0f;
                float a_y = (total_g - b_y * sum_x) / 16.0f;

                l.c[0] = a_x + b_x * min_chan_val;
                l.c[1] = a_y + b_y * min_chan_val;

                h.c[0] = a_x + b_x * max_chan_val;
                h.c[1] = a_y + b_y * max_chan_val;

                float dr = (h.c[0] - l.c[0]);
                float dg = (h.c[1] - l.c[1]);

                h.c[0] = l.c[0] + dr * (15.0f / 16.0f);
                h.c[1] = l.c[1] + dg * (15.0f / 16.0f);

                l.c[0] = l.c[0] + dr * (1.0f / 16.0f);
                l.c[1] = l.c[1] + dg * (1.0f / 16.0f);

                float d = (float)(max_chan_val - min_chan_val);
                float fmin_chan_val = min_chan_val + d * (1.0f / 16.0f);
                float fmax_chan_val = min_chan_val + d * (15.0f / 16.0f);

                l.c[2] = fmin_chan_val;
                h.c[2] = fmax_chan_val;
            }

            precise_round_565_noscale(l, h, lr, lg, lb, hr, hg, hb);
        }
        else if (flags & cEncodeBC1BoundingBox)
        {
            // Algorithm from icbc.h compress_dxt1_fast()
            vec3F l, h;
            l.c[0] = min_r * (1.0f / 255.0f);
            l.c[1] = min_g * (1.0f / 255.0f);
            l.c[2] = min_b * (1.0f / 255.0f);

            h.c[0] = max_r * (1.0f / 255.0f);
            h.c[1] = max_g * (1.0f / 255.0f);
            h.c[2] = max_b * (1.0f / 255.0f);

            const float bias = 8.0f / 255.0f;
            float inset_r = (h.c[0] - l.c[0] - bias) * (1.0f / 16.0f);
            float inset_g = (h.c[1] - l.c[1] - bias) * (1.0f / 16.0f);
            float inset_b = (h.c[2] - l.c[2] - bias) * (1.0f / 16.0f);

            l.c[0] = clampf(l.c[0] + inset_r, 0.0f, 1.0f);
            l.c[1] = clampf(l.c[1] + inset_g, 0.0f, 1.0f);
            l.c[2] = clampf(l.c[2] + inset_b, 0.0f, 1.0f);

            h.c[0] = clampf(h.c[0] - inset_r, 0.0f, 1.0f);
            h.c[1] = clampf(h.c[1] - inset_g, 0.0f, 1.0f);
            h.c[2] = clampf(h.c[2] - inset_b, 0.0f, 1.0f);

            int icov_xz = 0, icov_yz = 0;
            for (uint32_t i = 0; i < 16; i++)
            {
                int r = (int)pSrc_pixels[i].r - avg_r;
                int g = (int)pSrc_pixels[i].g - avg_g;
                int b = (int)pSrc_pixels[i].b - avg_b;
                icov_xz += r * b;
                icov_yz += g * b;
            }

            if (icov_xz < 0)
                std::swap(l.c[0], h.c[0]);

            if (icov_yz < 0)
                std::swap(l.c[1], h.c[1]);

            precise_round_565(l, h, lr, lg, lb, hr, hg, hb);
        }
        else if (flags & cEncodeBC1BoundingBoxInt)
        {
            // Algorithm from icbc.h compress_dxt1_fast(), but converted to integer.
            int inset_r = (max_r - min_r - 8) >> 4;
            int inset_g = (max_g - min_g - 8) >> 4;
            int inset_b = (max_b - min_b - 8) >> 4;

            min_r += inset_r;
            min_g += inset_g;
            min_b += inset_b;
            if ((uint32_t)(min_r | min_g | min_b) > 255U)
            {
                min_r = clampi(min_r, 0, 255);
                min_g = clampi(min_g, 0, 255);
                min_b = clampi(min_b, 0, 255);
            }

            max_r -= inset_r;
            max_g -= inset_g;
            max_b -= inset_b;
            if ((uint32_t)(max_r | max_g | max_b) > 255U)
            {
                max_r = clampi(max_r, 0, 255);
                max_g = clampi(max_g, 0, 255);
                max_b = clampi(max_b, 0, 255);
            }

            int icov_xz = 0, icov_yz = 0;
            for (uint32_t i = 0; i < 16; i++)
            {
                int r = (int)pSrc_pixels[i].r - avg_r;
                int g = (int)pSrc_pixels[i].g - avg_g;
                int b = (int)pSrc_pixels[i].b - avg_b;
                icov_xz += r * b;
                icov_yz += g * b;
            }

            int x0 = min_r;
            int y0 = min_g;
            int x1 = max_r;
            int y1 = max_g;

            if (icov_xz < 0)
                std::swap(x0, x1);

            if (icov_yz < 0)
                std::swap(y0, y1);

            lr = to_5(x0);
            lg = to_6(y0);
            lb = to_5(min_b);

            hr = to_5(x1);
            hg = to_6(y1);
            hb = to_5(max_b);
        }
        else
        {
            // Select 2 colors along the principle axis. (There must be a faster/simpler way.)
            uint32_t low_c = 0, high_c = 0;

            int icov[6] = { 0, 0, 0, 0, 0, 0 };
            for (uint32_t i = 0; i < 16; i++)
            {
                int r = (int)pSrc_pixels[i].r - avg_r;
                int g = (int)pSrc_pixels[i].g - avg_g;
                int b = (int)pSrc_pixels[i].b - avg_b;
                icov[0] += r * r;
                icov[1] += r * g;
                icov[2] += r * b;
                icov[3] += g * g;
                icov[4] += g * b;
                icov[5] += b * b;
            }

            int saxis_r = 306, saxis_g = 601, saxis_b = 117;

            float xr = (float)(max_r - min_r);
            float xg = (float)(max_g - min_g);
            float xb = (float)(max_b - min_b);

            if (icov[2] < 0)
                xr = -xr;

            if (icov[4] < 0)
                xg = -xg;

            float cov[6];
            for (uint32_t i = 0; i < 6; i++)
                cov[i] = (float)(icov[i]) * (1.0f / 255.0f);

            const uint32_t total_power_iters = (flags & cEncodeBC1Use6PowerIters) ? 6 : 4;
            for (uint32_t power_iter = 0; power_iter < total_power_iters; power_iter++)
            {
                float r = xr * cov[0] + xg * cov[1] + xb * cov[2];
                float g = xr * cov[1] + xg * cov[3] + xb * cov[4];
                float b = xr * cov[2] + xg * cov[4] + xb * cov[5];
                xr = r; xg = g; xb = b;
            }

            float k = maximum(fabsf(xr), fabsf(xg), fabsf(xb));
            if (k >= 2)
            {
                float m = 2048.0f / k;
                saxis_r = (int)(xr * m);
                saxis_g = (int)(xg * m);
                saxis_b = (int)(xb * m);
            }

            int low_dot = INT_MAX, high_dot = INT_MIN;

            saxis_r = (int)((uint32_t)saxis_r << 4U);
            saxis_g = (int)((uint32_t)saxis_g << 4U);
            saxis_b = (int)((uint32_t)saxis_b << 4U);

            for (uint32_t i = 0; i < 16; i += 4)
            {
                int dot0 = ((pSrc_pixels[i].r * saxis_r + pSrc_pixels[i].g * saxis_g + pSrc_pixels[i].b * saxis_b) & ~0xF) + i;
                int dot1 = ((pSrc_pixels[i + 1].r * saxis_r + pSrc_pixels[i + 1].g * saxis_g + pSrc_pixels[i + 1].b * saxis_b) & ~0xF) + i + 1;
                int dot2 = ((pSrc_pixels[i + 2].r * saxis_r + pSrc_pixels[i + 2].g * saxis_g + pSrc_pixels[i + 2].b * saxis_b) & ~0xF) + i + 2;
                int dot3 = ((pSrc_pixels[i + 3].r * saxis_r + pSrc_pixels[i + 3].g * saxis_g + pSrc_pixels[i + 3].b * saxis_b) & ~0xF) + i + 3;

                int min_d01 = std::min(dot0, dot1);
                int max_d01 = std::max(dot0, dot1);

                int min_d23 = std::min(dot2, dot3);
                int max_d23 = std::max(dot2, dot3);

                int min_d = std::min(min_d01, min_d23);
                int max_d = std::max(max_d01, max_d23);

                low_dot = std::min(low_dot, min_d);
                high_dot = std::max(high_dot, max_d);
            }
            low_c = low_dot & 15;
            high_c = high_dot & 15;

            lr = to_5(pSrc_pixels[low_c].r);
            lg = to_6(pSrc_pixels[low_c].g);
            lb = to_5(pSrc_pixels[low_c].b);

            hr = to_5(pSrc_pixels[high_c].r);
            hg = to_6(pSrc_pixels[high_c].g);
            hb = to_5(pSrc_pixels[high_c].b);
        }
    }

    static const int8_t s_adjacent_voxels[16][4] =
    {
        { 1,0,0, 3 },   // 0
        { 0,1,0, 4 },   // 1
        { 0,0,1, 5 },   // 2
        { -1,0,0, 0 },  // 3
        { 0,-1,0, 1 },  // 4
        { 0,0,-1, 2 },  // 5
        { 1,1,0, 9 },   // 6
        { 1,0,1, 10 },  // 7
        { 0,1,1, 11 },  // 8
        { -1,-1,0, 6 }, // 9
        { -1,0,-1, 7 }, // 10
        { 0,-1,-1, 8 }, // 11
        { -1,1,0, 13 }, // 12
        { 1,-1,0, 12 }, // 13
        { 0,-1,1, 15 }, // 14
        { 0,1,-1, 14 }, // 15
    };

    // From icbc's high quality mode.
    static inline void encode_bc1_endpoint_search(const color32 *pSrc_pixels, bool any_black_pixels,
        uint32_t flags, bc1_encode_results &results, uint32_t cur_err)
    {
        int &lr = results.lr, &lg = results.lg, &lb = results.lb, &hr = results.hr, &hg = results.hg, &hb = results.hb;
        uint8_t *sels = results.sels;

        int prev_improvement_index = 0, forbidden_direction = -1;

        const int endpoint_search_rounds = (flags & cEncodeBC1EndpointSearchRoundsMask) >> cEncodeBC1EndpointSearchRoundsShift;
        for (int i = 0; i < endpoint_search_rounds; i++)
        {
            assert(s_adjacent_voxels[s_adjacent_voxels[i & 15][3]][3] == (i & 15));

            if (forbidden_direction == (i & 31))
                continue;

            const int8_t delta[3] = { s_adjacent_voxels[i & 15][0], s_adjacent_voxels[i & 15][1], s_adjacent_voxels[i & 15][2] };

            int trial_lr = lr, trial_lg = lg, trial_lb = lb, trial_hr = hr, trial_hg = hg, trial_hb = hb;

            if ((i >> 4) & 1)
            {
                trial_lr = clampi(trial_lr + delta[0], 0, 31);
                trial_lg = clampi(trial_lg + delta[1], 0, 63);
                trial_lb = clampi(trial_lb + delta[2], 0, 31);
            }
            else
            {
                trial_hr = clampi(trial_hr + delta[0], 0, 31);
                trial_hg = clampi(trial_hg + delta[1], 0, 63);
                trial_hb = clampi(trial_hb + delta[2], 0, 31);
            }

            uint8_t trial_sels[16];

            uint32_t trial_err;
            if (results.m_3color)
            {
                trial_err = bc1_find_sels3_fullerr(
                    ((any_black_pixels) && ((flags & cEncodeBC1Use3ColorBlocksForBlackPixels) != 0)),
                    pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, trial_sels, cur_err);
            }
            else
            {
                trial_err = bc1_find_sels4(flags, pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, trial_sels, cur_err);
            }

            if (trial_err < cur_err)
            {
                cur_err = trial_err;

                forbidden_direction = s_adjacent_voxels[i & 15][3] | (i & 16);

                lr = trial_lr, lg = trial_lg, lb = trial_lb, hr = trial_hr, hg = trial_hg, hb = trial_hb;

                memcpy(sels, trial_sels, 16);

                prev_improvement_index = i;
            }

            if (i - prev_improvement_index > 32)
                break;
        }
    }

    void encode_bc1(void* pDst, const uint8_t* pPixels, uint32_t flags, uint32_t total_orderings_to_try, uint32_t total_orderings_to_try3)
    {
        assert(g_initialized);

        const color32* pSrc_pixels = (const color32*)pPixels;
        bc1_block* pDst_block = static_cast<bc1_block*>(pDst);

        int avg_r, avg_g, avg_b, min_r, min_g, min_b, max_r, max_g, max_b;

        const uint32_t fr = pSrc_pixels[0].r, fg = pSrc_pixels[0].g, fb = pSrc_pixels[0].b;

        uint32_t j;
        for (j = 15; j >= 1; --j)
            if ((pSrc_pixels[j].r != fr) || (pSrc_pixels[j].g != fg) || (pSrc_pixels[j].b != fb))
                break;

        if (j == 0)
        {
            encode_bc1_solid_block(pDst, fr, fg, fb, (flags & (cEncodeBC1Use3ColorBlocks | cEncodeBC1Use3ColorBlocksForBlackPixels)) != 0);
            return;
        }

        int total_r = fr, total_g = fg, total_b = fb;

        max_r = fr, max_g = fg, max_b = fb;
        min_r = fr, min_g = fg, min_b = fb;

        uint32_t grayscale_flag = (fr == fg) && (fr == fb);
        uint32_t any_black_pixels = (fr | fg | fb) < 4;

        for (uint32_t i = 1; i < 16; i++)
        {
            const int r = pSrc_pixels[i].r, g = pSrc_pixels[i].g, b = pSrc_pixels[i].b;

            grayscale_flag &= ((r == g) && (r == b));
            any_black_pixels |= ((r | g | b) < 4);

            max_r = std::max(max_r, r); max_g = std::max(max_g, g); max_b = std::max(max_b, b);
            min_r = std::min(min_r, r); min_g = std::min(min_g, g); min_b = std::min(min_b, b);
            total_r += r; total_g += g; total_b += b;
        }

        avg_r = (total_r + 8) >> 4, avg_g = (total_g + 8) >> 4, avg_b = (total_b + 8) >> 4;

        bc1_encode_results results;
        results.m_3color = false;

        uint8_t *sels = results.sels;
        int &lr = results.lr, &lg = results.lg, &lb = results.lb, &hr = results.hr, &hg = results.hg, &hb = results.hb;
        int orig_lr = 0, orig_lg = 0, orig_lb = 0, orig_hr = 0, orig_hg = 0, orig_hb = 0;

        lr = 0, lg = 0, lb = 0, hr = 0, hg = 0, hb = 0;

        const bool needs_block_error = ((flags & (cEncodeBC1UseLikelyTotalOrderings | cEncodeBC1Use3ColorBlocks | cEncodeBC1UseFullMSEEval | cEncodeBC1EndpointSearchRoundsMask)) != 0) ||
            (any_black_pixels && ((flags & cEncodeBC1Use3ColorBlocksForBlackPixels) != 0));

        uint32_t cur_err = UINT32_MAX;

        if (!needs_block_error)
        {
            assert((flags & cEncodeBC1TryAllInitialEndponts) == 0);

            encode_bc1_pick_initial(pSrc_pixels, flags, grayscale_flag != 0,
                min_r, min_g, min_b, max_r, max_g, max_b,
                avg_r, avg_g, avg_b, total_r, total_g, total_b,
                lr, lg, lb, hr, hg, hb);

            orig_lr = lr, orig_lg = lg, orig_lb = lb, orig_hr = hr, orig_hg = hg, orig_hb = hb;

            bc1_find_sels4_noerr(pSrc_pixels, lr, lg, lb, hr, hg, hb, sels);

            const uint32_t total_ls_passes = flags & cEncodeBC1TwoLeastSquaresPasses ? 2 : 1;
            for (uint32_t ls_pass = 0; ls_pass < total_ls_passes; ls_pass++)
            {
                int trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb;

                vec3F xl, xh;
                if (!compute_least_squares_endpoints4_rgb(pSrc_pixels, sels, &xl, &xh, total_r, total_g, total_b))
                {
                    // All selectors equal - treat it as a solid block which should always be equal or better.
                    trial_lr = g_bc1_match5_equals_1[avg_r].m_hi;
                    trial_lg = g_bc1_match6_equals_1[avg_g].m_hi;
                    trial_lb = g_bc1_match5_equals_1[avg_b].m_hi;

                    trial_hr = g_bc1_match5_equals_1[avg_r].m_lo;
                    trial_hg = g_bc1_match6_equals_1[avg_g].m_lo;
                    trial_hb = g_bc1_match5_equals_1[avg_b].m_lo;

                    // In high/higher quality mode, let it try again in case the optimal tables have caused the sels to diverge.
                }
                else
                {
                    precise_round_565(xl, xh, trial_hr, trial_hg, trial_hb, trial_lr, trial_lg, trial_lb);
                }

                if ((lr == trial_lr) && (lg == trial_lg) && (lb == trial_lb) && (hr == trial_hr) && (hg == trial_hg) && (hb == trial_hb))
                    break;

                bc1_find_sels4_noerr(pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, sels);

                lr = trial_lr;
                lg = trial_lg;
                lb = trial_lb;
                hr = trial_hr;
                hg = trial_hg;
                hb = trial_hb;

            } // ls_pass
        }
        else
        {
            const uint32_t total_rounds = (flags & cEncodeBC1TryAllInitialEndponts) ? 2 : 1;
            for (uint32_t round = 0; round < total_rounds; round++)
            {
                uint32_t modified_flags = flags;
                if (round == 1)
                {
                    modified_flags &= ~(cEncodeBC1Use2DLS | cEncodeBC1BoundingBox);
                    modified_flags |= cEncodeBC1BoundingBox;
                }

                int round_lr, round_lg, round_lb, round_hr, round_hg, round_hb;
                uint8_t round_sels[16];

                encode_bc1_pick_initial(pSrc_pixels, modified_flags, grayscale_flag != 0,
                    min_r, min_g, min_b, max_r, max_g, max_b,
                    avg_r, avg_g, avg_b, total_r, total_g, total_b,
                    round_lr, round_lg, round_lb, round_hr, round_hg, round_hb);

                int orig_round_lr = round_lr, orig_round_lg = round_lg, orig_round_lb = round_lb, orig_round_hr = round_hr, orig_round_hg = round_hg, orig_round_hb = round_hb;

                uint32_t round_err = bc1_find_sels4(flags, pSrc_pixels, round_lr, round_lg, round_lb, round_hr, round_hg, round_hb, round_sels, UINT32_MAX);

                const uint32_t total_ls_passes = flags & cEncodeBC1TwoLeastSquaresPasses ? 2 : 1;
                for (uint32_t ls_pass = 0; ls_pass < total_ls_passes; ls_pass++)
                {
                    int trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb;

                    vec3F xl, xh;
                    if (!compute_least_squares_endpoints4_rgb(pSrc_pixels, round_sels, &xl, &xh, total_r, total_g, total_b))
                    {
                        // All selectors equal - treat it as a solid block which should always be equal or better.
                        trial_lr = g_bc1_match5_equals_1[avg_r].m_hi;
                        trial_lg = g_bc1_match6_equals_1[avg_g].m_hi;
                        trial_lb = g_bc1_match5_equals_1[avg_b].m_hi;

                        trial_hr = g_bc1_match5_equals_1[avg_r].m_lo;
                        trial_hg = g_bc1_match6_equals_1[avg_g].m_lo;
                        trial_hb = g_bc1_match5_equals_1[avg_b].m_lo;

                        // In high/higher quality mode, let it try again in case the optimal tables have caused the sels to diverge.
                    }
                    else
                    {
                        precise_round_565(xl, xh, trial_hr, trial_hg, trial_hb, trial_lr, trial_lg, trial_lb);
                    }

                    if ((round_lr == trial_lr) && (round_lg == trial_lg) && (round_lb == trial_lb) && (round_hr == trial_hr) && (round_hg == trial_hg) && (round_hb == trial_hb))
                        break;

                    uint8_t trial_sels[16];
                    uint32_t trial_err = bc1_find_sels4(flags, pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, trial_sels, round_err);

                    if (trial_err < round_err)
                    {
                        round_lr = trial_lr;
                        round_lg = trial_lg;
                        round_lb = trial_lb;

                        round_hr = trial_hr;
                        round_hg = trial_hg;
                        round_hb = trial_hb;

                        round_err = trial_err;
                        memcpy(round_sels, trial_sels, 16);
                    }
                    else
                        break;

                } // ls_pass

                if (round_err <= cur_err)
                {
                    cur_err = round_err;

                    lr = round_lr;
                    lg = round_lg;
                    lb = round_lb;
                    hr = round_hr;
                    hg = round_hg;
                    hb = round_hb;

                    orig_lr = orig_round_lr;
                    orig_lg = orig_round_lg;
                    orig_lb = orig_round_lb;
                    orig_hr = orig_round_hr;
                    orig_hg = orig_round_hg;
                    orig_hb = orig_round_hb;

                    memcpy(sels, round_sels, 16);
                }

            } // round
        }

        if ((cur_err) && (flags & cEncodeBC1UseLikelyTotalOrderings))
        {
            assert(needs_block_error);

            const uint32_t total_iters = (flags & cEncodeBC1Iterative) ? 2 : 1;
            for (uint32_t iter_index = 0; iter_index < total_iters; iter_index++)
            {
                const uint32_t orig_err = cur_err;

                hist4 h;
                for (uint32_t i = 0; i < 16; i++)
                {
                    assert(sels[i] < 4);
                    h.m_hist[sels[i]]++;
                }

                const uint32_t orig_total_order_index = h.lookup_total_ordering_index();

                int r0, g0, b0, r3, g3, b3;
                r0 = (lr << 3) | (lr >> 2); g0 = (lg << 2) | (lg >> 4); b0 = (lb << 3) | (lb >> 2);
                r3 = (hr << 3) | (hr >> 2); g3 = (hg << 2) | (hg >> 4); b3 = (hb << 3) | (hb >> 2);

                int ar = r3 - r0, ag = g3 - g0, ab = b3 - b0;

                int dots[16];
                for (uint32_t i = 0; i < 16; i++)
                {
                    int r = pSrc_pixels[i].r;
                    int g = pSrc_pixels[i].g;
                    int b = pSrc_pixels[i].b;
                    int d = 0x1000000 + (r * ar + g * ag + b * ab);
                    assert(d >= 0);
                    dots[i] = (d << 4) + i;
                }

                std::sort(dots, dots + 16);

                uint32_t r_sum[17], g_sum[17], b_sum[17];
                uint32_t r = 0, g = 0, b = 0;
                for (uint32_t i = 0; i < 16; i++)
                {
                    const uint32_t p = dots[i] & 15;

                    r_sum[i] = r;
                    g_sum[i] = g;
                    b_sum[i] = b;

                    r += pSrc_pixels[p].r;
                    g += pSrc_pixels[p].g;
                    b += pSrc_pixels[p].b;
                }

                r_sum[16] = total_r;
                g_sum[16] = total_g;
                b_sum[16] = total_b;

                const uint32_t q_total = (flags & cEncodeBC1Exhaustive) ? NUM_UNIQUE_TOTAL_ORDERINGS4 : clampi(total_orderings_to_try, MIN_TOTAL_ORDERINGS, MAX_TOTAL_ORDERINGS4);
                for (uint32_t q = 0; q < q_total; q++)
                {
                    const uint32_t s = (flags & cEncodeBC1Exhaustive) ? q : g_best_total_orderings4[orig_total_order_index][q];

                    int trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb;

                    vec3F xl, xh;

                    if ((s == TOTAL_ORDER_4_0_16) || (s == TOTAL_ORDER_4_1_16) || (s == TOTAL_ORDER_4_2_16) || (s == TOTAL_ORDER_4_3_16))
                    {
                        trial_lr = g_bc1_match5_equals_1[avg_r].m_hi;
                        trial_lg = g_bc1_match6_equals_1[avg_g].m_hi;
                        trial_lb = g_bc1_match5_equals_1[avg_b].m_hi;

                        trial_hr = g_bc1_match5_equals_1[avg_r].m_lo;
                        trial_hg = g_bc1_match6_equals_1[avg_g].m_lo;
                        trial_hb = g_bc1_match5_equals_1[avg_b].m_lo;
                    }
                    else
                    {
                        compute_least_squares_endpoints4_rgb(&xl, &xh, total_r, total_g, total_b,
                            g_selector_factors4[s][0], g_selector_factors4[s][1], g_selector_factors4[s][2], s, r_sum, g_sum, b_sum);

                        precise_round_565(xl, xh, trial_hr, trial_hg, trial_hb, trial_lr, trial_lg, trial_lb);
                    }

                    uint8_t trial_sels[16];

                    uint32_t trial_err = bc1_find_sels4(flags, pSrc_pixels, trial_lr, trial_lg, trial_lb, trial_hr, trial_hg, trial_hb, trial_sels, cur_err);

                    if (trial_err < cur_err)
                    {
                        cur_err = trial_err;

                        lr = trial_lr;
                        lg = trial_lg;
                        lb = trial_lb;

                        hr = trial_hr;
                        hg = trial_hg;
                        hb = trial_hb;

                        memcpy(sels, trial_sels, 16);
                    }

                } // s

                if ((!cur_err) || (cur_err == orig_err))
                    break;

            } // iter_index
        }

        if (((flags & (cEncodeBC1Use3ColorBlocks | cEncodeBC1Use3ColorBlocksForBlackPixels)) != 0) && (cur_err))
        {
            if (flags & cEncodeBC1Use3ColorBlocks)
            {
                assert(needs_block_error);
                try_3color_block(pSrc_pixels, flags, cur_err, avg_r, avg_g, avg_b, orig_lr, orig_lg, orig_lb, orig_hr, orig_hg, orig_hb, total_r, total_g, total_b, total_orderings_to_try3, results);
            }

            if ((any_black_pixels) && ((flags & cEncodeBC1Use3ColorBlocksForBlackPixels) != 0))
            {
                assert(needs_block_error);
                try_3color_block_useblack(pSrc_pixels, flags, cur_err, results);
            }
        }

        if ((flags & cEncodeBC1EndpointSearchRoundsMask) && (cur_err))
        {
            assert(needs_block_error);

            encode_bc1_endpoint_search(pSrc_pixels, any_black_pixels != 0, flags, results, cur_err);
        }

        if (results.m_3color)
            bc1_encode3(pDst_block, results.lr, results.lg, results.lb, results.hr, results.hg, results.hb, results.sels);
        else
            bc1_encode4(pDst_block, results.lr, results.lg, results.lb, results.hr, results.hg, results.hb, results.sels);
    }

    // BC3-5

    struct bc4_block
    {
        enum { cBC4SelectorBits = 3, cTotalSelectorBytes = 6, cMaxSelectorValues = 8 };
        uint8_t m_endpoints[2];

        uint8_t m_selectors[cTotalSelectorBytes];

        inline uint32_t get_low_alpha() const { return m_endpoints[0]; }
        inline uint32_t get_high_alpha() const { return m_endpoints[1]; }
        inline bool is_alpha6_block() const { return get_low_alpha() <= get_high_alpha(); }

        inline uint64_t get_selector_bits() const
        {
            return ((uint64_t)((uint32_t)m_selectors[0] | ((uint32_t)m_selectors[1] << 8U) | ((uint32_t)m_selectors[2] << 16U) | ((uint32_t)m_selectors[3] << 24U))) |
                (((uint64_t)m_selectors[4]) << 32U) |
                (((uint64_t)m_selectors[5]) << 40U);
        }

        inline uint32_t get_selector(uint32_t x, uint32_t y, uint64_t selector_bits) const
        {
            assert((x < 4U) && (y < 4U));
            return (selector_bits >> (((y * 4) + x) * cBC4SelectorBits))& (cMaxSelectorValues - 1);
        }

        static inline uint32_t get_block_values6(uint8_t* pDst, uint32_t l, uint32_t h)
        {
            pDst[0] = static_cast<uint8_t>(l);
            pDst[1] = static_cast<uint8_t>(h);
            pDst[2] = static_cast<uint8_t>((l * 4 + h) / 5);
            pDst[3] = static_cast<uint8_t>((l * 3 + h * 2) / 5);
            pDst[4] = static_cast<uint8_t>((l * 2 + h * 3) / 5);
            pDst[5] = static_cast<uint8_t>((l + h * 4) / 5);
            pDst[6] = 0;
            pDst[7] = 255;
            return 6;
        }

        static inline uint32_t get_block_values8(uint8_t* pDst, uint32_t l, uint32_t h)
        {
            pDst[0] = static_cast<uint8_t>(l);
            pDst[1] = static_cast<uint8_t>(h);
            pDst[2] = static_cast<uint8_t>((l * 6 + h) / 7);
            pDst[3] = static_cast<uint8_t>((l * 5 + h * 2) / 7);
            pDst[4] = static_cast<uint8_t>((l * 4 + h * 3) / 7);
            pDst[5] = static_cast<uint8_t>((l * 3 + h * 4) / 7);
            pDst[6] = static_cast<uint8_t>((l * 2 + h * 5) / 7);
            pDst[7] = static_cast<uint8_t>((l + h * 6) / 7);
            return 8;
        }

        static inline uint32_t get_block_values(uint8_t* pDst, uint32_t l, uint32_t h)
        {
            if (l > h)
                return get_block_values8(pDst, l, h);
            else
                return get_block_values6(pDst, l, h);
        }
    };

    void encode_bc4(void* pDst, const uint8_t* pPixels, uint32_t stride)
    {
        assert(g_initialized);

        uint32_t min0_v, max0_v, min1_v, max1_v, min2_v, max2_v, min3_v, max3_v;

        {
            min0_v = max0_v = pPixels[0 * stride];
            min1_v = max1_v = pPixels[1 * stride];
            min2_v = max2_v = pPixels[2 * stride];
            min3_v = max3_v = pPixels[3 * stride];
        }

        {
            uint32_t v0 = pPixels[4 * stride]; min0_v = std::min(min0_v, v0); max0_v = std::max(max0_v, v0);
            uint32_t v1 = pPixels[5 * stride]; min1_v = std::min(min1_v, v1); max1_v = std::max(max1_v, v1);
            uint32_t v2 = pPixels[6 * stride]; min2_v = std::min(min2_v, v2); max2_v = std::max(max2_v, v2);
            uint32_t v3 = pPixels[7 * stride]; min3_v = std::min(min3_v, v3); max3_v = std::max(max3_v, v3);
        }

        {
            uint32_t v0 = pPixels[8 * stride]; min0_v = std::min(min0_v, v0); max0_v = std::max(max0_v, v0);
            uint32_t v1 = pPixels[9 * stride]; min1_v = std::min(min1_v, v1); max1_v = std::max(max1_v, v1);
            uint32_t v2 = pPixels[10 * stride]; min2_v = std::min(min2_v, v2); max2_v = std::max(max2_v, v2);
            uint32_t v3 = pPixels[11 * stride]; min3_v = std::min(min3_v, v3); max3_v = std::max(max3_v, v3);
        }

        {
            uint32_t v0 = pPixels[12 * stride]; min0_v = std::min(min0_v, v0); max0_v = std::max(max0_v, v0);
            uint32_t v1 = pPixels[13 * stride]; min1_v = std::min(min1_v, v1); max1_v = std::max(max1_v, v1);
            uint32_t v2 = pPixels[14 * stride]; min2_v = std::min(min2_v, v2); max2_v = std::max(max2_v, v2);
            uint32_t v3 = pPixels[15 * stride]; min3_v = std::min(min3_v, v3); max3_v = std::max(max3_v, v3);
        }

        const uint32_t min_v = minimum(min0_v, min1_v, min2_v, min3_v);
        const uint32_t max_v = maximum(max0_v, max1_v, max2_v, max3_v);

        uint8_t* pDst_bytes = static_cast<uint8_t*>(pDst);
        pDst_bytes[0] = (uint8_t)max_v;
        pDst_bytes[1] = (uint8_t)min_v;

        if (max_v == min_v)
        {
            memset(pDst_bytes + 2, 0, 6);
            return;
        }

        const uint32_t delta = max_v - min_v;

        // min_v is now 0. Compute thresholds between values by scaling max_v. It's x14 because we're adding two x7 scale factors.
        const int t0 = delta * 13;
        const int t1 = delta * 11;
        const int t2 = delta * 9;
        const int t3 = delta * 7;
        const int t4 = delta * 5;
        const int t5 = delta * 3;
        const int t6 = delta * 1;

        // BC4 floors in its divisions, which we compensate for with the 4 bias.
        // This function is optimal for all possible inputs (i.e. it outputs the same results as checking all 8 values and choosing the closest one).
        const int bias = 4 - min_v * 14;

        static const uint32_t s_tran0[8] = { 1U      , 7U      , 6U      , 5U      , 4U      , 3U      , 2U      , 0U };
        static const uint32_t s_tran1[8] = { 1U << 3U, 7U << 3U, 6U << 3U, 5U << 3U, 4U << 3U, 3U << 3U, 2U << 3U, 0U << 3U };
        static const uint32_t s_tran2[8] = { 1U << 6U, 7U << 6U, 6U << 6U, 5U << 6U, 4U << 6U, 3U << 6U, 2U << 6U, 0U << 6U };
        static const uint32_t s_tran3[8] = { 1U << 9U, 7U << 9U, 6U << 9U, 5U << 9U, 4U << 9U, 3U << 9U, 2U << 9U, 0U << 9U };

        uint64_t a0, a1, a2, a3;
        {
            const int v0 = pPixels[0 * stride] * 14 + bias;
            const int v1 = pPixels[1 * stride] * 14 + bias;
            const int v2 = pPixels[2 * stride] * 14 + bias;
            const int v3 = pPixels[3 * stride] * 14 + bias;
            a0 = s_tran0[(v0 >= t0) + (v0 >= t1) + (v0 >= t2) + (v0 >= t3) + (v0 >= t4) + (v0 >= t5) + (v0 >= t6)];
            a1 = s_tran1[(v1 >= t0) + (v1 >= t1) + (v1 >= t2) + (v1 >= t3) + (v1 >= t4) + (v1 >= t5) + (v1 >= t6)];
            a2 = s_tran2[(v2 >= t0) + (v2 >= t1) + (v2 >= t2) + (v2 >= t3) + (v2 >= t4) + (v2 >= t5) + (v2 >= t6)];
            a3 = s_tran3[(v3 >= t0) + (v3 >= t1) + (v3 >= t2) + (v3 >= t3) + (v3 >= t4) + (v3 >= t5) + (v3 >= t6)];
        }

        {
            const int v0 = pPixels[4 * stride] * 14 + bias;
            const int v1 = pPixels[5 * stride] * 14 + bias;
            const int v2 = pPixels[6 * stride] * 14 + bias;
            const int v3 = pPixels[7 * stride] * 14 + bias;
            a0 |= (uint64_t)(s_tran0[(v0 >= t0) + (v0 >= t1) + (v0 >= t2) + (v0 >= t3) + (v0 >= t4) + (v0 >= t5) + (v0 >= t6)] << 12U);
            a1 |= (uint64_t)(s_tran1[(v1 >= t0) + (v1 >= t1) + (v1 >= t2) + (v1 >= t3) + (v1 >= t4) + (v1 >= t5) + (v1 >= t6)] << 12U);
            a2 |= (uint64_t)(s_tran2[(v2 >= t0) + (v2 >= t1) + (v2 >= t2) + (v2 >= t3) + (v2 >= t4) + (v2 >= t5) + (v2 >= t6)] << 12U);
            a3 |= (uint64_t)(s_tran3[(v3 >= t0) + (v3 >= t1) + (v3 >= t2) + (v3 >= t3) + (v3 >= t4) + (v3 >= t5) + (v3 >= t6)] << 12U);
        }

        {
            const int v0 = pPixels[8 * stride] * 14 + bias;
            const int v1 = pPixels[9 * stride] * 14 + bias;
            const int v2 = pPixels[10 * stride] * 14 + bias;
            const int v3 = pPixels[11 * stride] * 14 + bias;
            a0 |= (((uint64_t)s_tran0[(v0 >= t0) + (v0 >= t1) + (v0 >= t2) + (v0 >= t3) + (v0 >= t4) + (v0 >= t5) + (v0 >= t6)]) << 24U);
            a1 |= (((uint64_t)s_tran1[(v1 >= t0) + (v1 >= t1) + (v1 >= t2) + (v1 >= t3) + (v1 >= t4) + (v1 >= t5) + (v1 >= t6)]) << 24U);
            a2 |= (((uint64_t)s_tran2[(v2 >= t0) + (v2 >= t1) + (v2 >= t2) + (v2 >= t3) + (v2 >= t4) + (v2 >= t5) + (v2 >= t6)]) << 24U);
            a3 |= (((uint64_t)s_tran3[(v3 >= t0) + (v3 >= t1) + (v3 >= t2) + (v3 >= t3) + (v3 >= t4) + (v3 >= t5) + (v3 >= t6)]) << 24U);
        }

        {
            const int v0 = pPixels[12 * stride] * 14 + bias;
            const int v1 = pPixels[13 * stride] * 14 + bias;
            const int v2 = pPixels[14 * stride] * 14 + bias;
            const int v3 = pPixels[15 * stride] * 14 + bias;
            a0 |= (((uint64_t)s_tran0[(v0 >= t0) + (v0 >= t1) + (v0 >= t2) + (v0 >= t3) + (v0 >= t4) + (v0 >= t5) + (v0 >= t6)]) << 36U);
            a1 |= (((uint64_t)s_tran1[(v1 >= t0) + (v1 >= t1) + (v1 >= t2) + (v1 >= t3) + (v1 >= t4) + (v1 >= t5) + (v1 >= t6)]) << 36U);
            a2 |= (((uint64_t)s_tran2[(v2 >= t0) + (v2 >= t1) + (v2 >= t2) + (v2 >= t3) + (v2 >= t4) + (v2 >= t5) + (v2 >= t6)]) << 36U);
            a3 |= (((uint64_t)s_tran3[(v3 >= t0) + (v3 >= t1) + (v3 >= t2) + (v3 >= t3) + (v3 >= t4) + (v3 >= t5) + (v3 >= t6)]) << 36U);
        }

        const uint64_t f = a0 | a1 | a2 | a3;

        pDst_bytes[2] = (uint8_t)f;
        pDst_bytes[3] = (uint8_t)(f >> 8U);
        pDst_bytes[4] = (uint8_t)(f >> 16U);
        pDst_bytes[5] = (uint8_t)(f >> 24U);
        pDst_bytes[6] = (uint8_t)(f >> 32U);
        pDst_bytes[7] = (uint8_t)(f >> 40U);
    }

    void encode_bc3(void* pDst, const uint8_t* pPixels, uint32_t flags, uint32_t total_orderings_to_try)
    {
        assert(g_initialized);

        // 3-color blocks are not allowed with BC3 (on most GPU's).
        flags &= ~(cEncodeBC1Use3ColorBlocksForBlackPixels | cEncodeBC1Use3ColorBlocks);

        encode_bc4(pDst, pPixels + 3, 4);
        encode_bc1(static_cast<uint8_t*>(pDst) + 8, pPixels, flags, total_orderings_to_try);
    }

    void encode_bc3(uint32_t level, void* pDst, const uint8_t* pPixels)
    {
        assert(g_initialized);

        encode_bc4(pDst, pPixels + 3, 4);
        encode_bc1(level, static_cast<uint8_t*>(pDst) + 8, pPixels, false, false);
    }

    void encode_bc5(void* pDst, const uint8_t* pPixels, uint32_t chan0, uint32_t chan1, uint32_t stride)
    {
        assert(g_initialized);

        encode_bc4(pDst, pPixels + chan0, stride);
        encode_bc4(static_cast<uint8_t*>(pDst) + 8, pPixels + chan1, stride);
    }

    // Returns true if the block uses 3 color punchthrough alpha mode.
    bool unpack_bc1(const void* pBlock_bits, void* pPixels, bool set_alpha, bc1_approx_mode mode)
    {
        color32* pDst_pixels = static_cast<color32*>(pPixels);

        static_assert(sizeof(bc1_block) == 8, "sizeof(bc1_block) == 8");
        static_assert(sizeof(bc4_block) == 8, "sizeof(bc4_block) == 8");

        const bc1_block* pBlock = static_cast<const bc1_block*>(pBlock_bits);

        const uint32_t l = pBlock->get_low_color();
        const uint32_t h = pBlock->get_high_color();

        color32 c[4];

        const int cr0 = (l >> 11) & 31;
        const int cg0 = (l >> 5) & 63;
        const int cb0 = l & 31;
        const int r0 = (cr0 << 3) | (cr0 >> 2);
        const int g0 = (cg0 << 2) | (cg0 >> 4);
        const int b0 = (cb0 << 3) | (cb0 >> 2);

        const int cr1 = (h >> 11) & 31;
        const int cg1 = (h >> 5) & 63;
        const int cb1 = h & 31;
        const int r1 = (cr1 << 3) | (cr1 >> 2);
        const int g1 = (cg1 << 2) | (cg1 >> 4);
        const int b1 = (cb1 << 3) | (cb1 >> 2);

        bool used_punchthrough = false;

        if (l > h)
        {
            c[0].set_noclamp_rgba(r0, g0, b0, 255);
            c[1].set_noclamp_rgba(r1, g1, b1, 255);
            switch (mode)
            {
            case bc1_approx_mode::cBC1Ideal:
                c[2].set_noclamp_rgba((r0 * 2 + r1) / 3, (g0 * 2 + g1) / 3, (b0 * 2 + b1) / 3, 255);
                c[3].set_noclamp_rgba((r1 * 2 + r0) / 3, (g1 * 2 + g0) / 3, (b1 * 2 + b0) / 3, 255);
                break;
            case bc1_approx_mode::cBC1IdealRound4:
                c[2].set_noclamp_rgba((r0 * 2 + r1 + 1) / 3, (g0 * 2 + g1 + 1) / 3, (b0 * 2 + b1 + 1) / 3, 255);
                c[3].set_noclamp_rgba((r1 * 2 + r0 + 1) / 3, (g1 * 2 + g0 + 1) / 3, (b1 * 2 + b0 + 1) / 3, 255);
                break;
            case bc1_approx_mode::cBC1NVidia:
                c[2].set_noclamp_rgba(interp_5_nv(cr0, cr1), interp_6_nv(g0, g1), interp_5_nv(cb0, cb1), 255);
                c[3].set_noclamp_rgba(interp_5_nv(cr1, cr0), interp_6_nv(g1, g0), interp_5_nv(cb1, cb0), 255);
                break;
            case bc1_approx_mode::cBC1AMD:
                c[2].set_noclamp_rgba(interp_5_6_amd(r0, r1), interp_5_6_amd(g0, g1), interp_5_6_amd(b0, b1), 255);
                c[3].set_noclamp_rgba(interp_5_6_amd(r1, r0), interp_5_6_amd(g1, g0), interp_5_6_amd(b1, b0), 255);
                break;
            }
        }
        else
        {
            c[0].set_noclamp_rgba(r0, g0, b0, 255);
            c[1].set_noclamp_rgba(r1, g1, b1, 255);
            switch (mode)
            {
            case bc1_approx_mode::cBC1Ideal:
            case bc1_approx_mode::cBC1IdealRound4:
                c[2].set_noclamp_rgba((r0 + r1) / 2, (g0 + g1) / 2, (b0 + b1) / 2, 255);
                break;
            case bc1_approx_mode::cBC1NVidia:
                c[2].set_noclamp_rgba(interp_half_5_nv(cr0, cr1), interp_half_6_nv(g0, g1), interp_half_5_nv(cb0, cb1), 255);
                break;
            case bc1_approx_mode::cBC1AMD:
                c[2].set_noclamp_rgba(interp_half_5_6_amd(r0, r1), interp_half_5_6_amd(g0, g1), interp_half_5_6_amd(b0, b1), 255);
                break;
            }

            c[3].set_noclamp_rgba(0, 0, 0, 0);
            used_punchthrough = true;
        }

        if (set_alpha)
        {
            for (uint32_t y = 0; y < 4; y++, pDst_pixels += 4)
            {
                pDst_pixels[0] = c[pBlock->get_selector(0, y)];
                pDst_pixels[1] = c[pBlock->get_selector(1, y)];
                pDst_pixels[2] = c[pBlock->get_selector(2, y)];
                pDst_pixels[3] = c[pBlock->get_selector(3, y)];
            }
        }
        else
        {
            for (uint32_t y = 0; y < 4; y++, pDst_pixels += 4)
            {
                pDst_pixels[0].set_rgb(c[pBlock->get_selector(0, y)]);
                pDst_pixels[1].set_rgb(c[pBlock->get_selector(1, y)]);
                pDst_pixels[2].set_rgb(c[pBlock->get_selector(2, y)]);
                pDst_pixels[3].set_rgb(c[pBlock->get_selector(3, y)]);
            }
        }

        return used_punchthrough;
    }

    void unpack_bc4(const void* pBlock_bits, uint8_t* pPixels, uint32_t stride)
    {
        static_assert(sizeof(bc4_block) == 8, "sizeof(bc4_block) == 8");

        const bc4_block* pBlock = static_cast<const bc4_block*>(pBlock_bits);

        uint8_t sel_values[8];
        bc4_block::get_block_values(sel_values, pBlock->get_low_alpha(), pBlock->get_high_alpha());

        const uint64_t selector_bits = pBlock->get_selector_bits();

        for (uint32_t y = 0; y < 4; y++, pPixels += (stride * 4U))
        {
            pPixels[0] = sel_values[pBlock->get_selector(0, y, selector_bits)];
            pPixels[stride * 1] = sel_values[pBlock->get_selector(1, y, selector_bits)];
            pPixels[stride * 2] = sel_values[pBlock->get_selector(2, y, selector_bits)];
            pPixels[stride * 3] = sel_values[pBlock->get_selector(3, y, selector_bits)];
        }
    }

    // Returns false if the block uses 3-color punchthrough alpha mode, which isn't supported on some GPU's for BC3.
    bool unpack_bc3(const void* pBlock_bits, void* pPixels, bc1_approx_mode mode)
    {
        color32* pDst_pixels = static_cast<color32*>(pPixels);

        bool success = true;

        if (unpack_bc1((const uint8_t*)pBlock_bits + sizeof(bc4_block), pDst_pixels, true, mode))
            success = false;

        unpack_bc4(pBlock_bits, &pDst_pixels[0].a, sizeof(color32));

        return success;
    }

    // writes RG
    void unpack_bc5(const void* pBlock_bits, void* pPixels, uint32_t chan0, uint32_t chan1, uint32_t stride)
    {
        unpack_bc4(pBlock_bits, (uint8_t *)pPixels + chan0, stride);
        unpack_bc4((const uint8_t*)pBlock_bits + sizeof(bc4_block), (uint8_t *)pPixels + chan1, stride);
    }

} // namespace rgbcx

#endif //#ifdef RGBCX_IMPLEMENTATION

/*
------------------------------------------------------------------------------
This software is available under 2 licenses -- choose whichever you prefer.
------------------------------------------------------------------------------
ALTERNATIVE A - MIT License
Copyright(c) 2020 Richard Geldreich, Jr.
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files(the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and / or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions :
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
------------------------------------------------------------------------------
ALTERNATIVE B - Public Domain(www.unlicense.org)
This is free and unencumbered software released into the public domain.
Anyone is free to copy, modify, publish, use, compile, sell, or distribute this
software, either in source code form or as a compiled binary, for any purpose,
commercial or non - commercial, and by any means.
In jurisdictions that recognize copyright laws, the author or authors of this
software dedicate any and all copyright interest in the software to the public
domain.We make this dedication for the benefit of the public at large and to
the detriment of our heirs and successors.We intend this dedication to be an
overt act of relinquishment in perpetuity of all present and future rights to
this software under copyright law.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
------------------------------------------------------------------------------
*/