init

[convexer.git] / src / nbvtf / 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 1
#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  },
                { 9,0,180,217,237,101,141,352,88,100,230,64,175,317,115,498,68,39,30,1,702,83,213,36,365,208,752,13,252,321,952,546  },
                { 28,9,22,1,49,0,109,39,83,95,86,30,13,105,128,55,141,168,158,67,31,159,208,12,96,5,185,2,160,64,137,23  },
                { 72,4,38,12,51,89,477,11,57,76,401,308,23,474,99,148,413,179,59,13,431,152,54,569,17,3,205,629,197,421,405,15  },
                { 457,13,23,961,15,51,515,700,165,12,753,629,11,1,719,117,0,3,2,37,569,197,40,328,33,5,153,134,99,64,38,196  },
                { 254,100,310,9,30,1,39,625,166,265,190,0,272,557,131,731,31,98,578,688,404,93,101,88,49,21,127,264,44,36,252,478  },
                { 51,23,12,13,15,128,99,120,10,202,515,153,64,82,700,33,165,2,5,117,403,1,141,0,3,196,37,453,753,197,260,93  },
                { 38,99,542,139,453,117,196,23,457,13,328,111,37,134,961,11,12,51,40,775,587,401,474,54,153,477,41,629,33,475,14,277  },
                { 6,85,25,233,343,91,26,63,138,29,19,65,283,4,81,235,42,122,605,64,648,256,174,370,74,389,718,59,45,194,445,416  },
                { 49,5,97,20,197,21,18,193,0,64,408,729,173,350,43,422,165,7,14,104,61,32,509,713,523,102,120,95,125,397,35,232  },
                { 144,116,268,434,384,489,367,206,93,855,940,44,98,332,617,127,959,911,137,282,203,31,22,219,141,9,131,276,417,0,1,120  },
                { 17,106,64,62,32,255,136,292,476,162,129,241,123,141,41,237,720,214,209,352,519,211,186,148,752,247,507,90,21,77,197,119  },
                { 2,29,52,50,5,58,14,6,27,1,366,357,45,53,17,19,171,151,26,181,133,38,218,764,287,583,61,113,3,487,600,281  },
                { 130,59,196,412,381,730,711,236,77,210,202,402,453,99,401,108,361,803,291,283,153,4,57,51,128,183,14,719,503,117,23,11  },
                { 13,23,51,141,77,4,33,64,115,0,217,10,180,202,2,102,11,9,15,165,40,21,128,352,22,7,197,3,317,515,269,1  },
                { 23,13,202,51,120,15,21,5,141,1,128,269,137,515,64,102,125,48,98,33,260,523,318,93,700,165,450,77,2,12,403,82  },
                { 1,2,14,46,29,67,38,52,5,171,58,24,103,69,96,70,83,181,54,75,163,223,16,45,112,309,155,0,186,35,18,108  },
                { 15,515,700,753,13,0,1,2,153,5,23,10,117,3,9,7,134,165,12,6,341,33,4,14,77,457,115,21,719,180,217,82  },
                { 197,165,509,13,391,180,308,115,23,546,5,498,2,29,3,401,901,61,34,80,14,457,250,569,237,873,38,297,45,15,468,386  },
                { 19,73,27,250,200,714,444,472,26,53,34,17,813,322,283,390,128,297,78,123,432,14,436,136,106,690,57,122,389,80,503,3  },
                { 3,17,21,45,62,32,38,12,155,14,2,328,5,99,401,536,828,13,227,488,106,51,719,119,540,76,165,221,115,629,209,41  },
                { 115,341,873,197,365,13,901,180,569,752,317,1,10,498,143,634,261,0,509,15,943,237,44,31,116,601,165,127,282,23,141,64  },
                { 453,51,23,403,33,421,475,102,15,153,196,515,13,700,117,523,12,40,753,21,4,134,0,494,670,899,22,801,730,10,11,401  },
                { 23,13,51,33,12,117,153,134,453,196,15,99,515,40,14,700,128,102,11,753,77,64,403,202,0,401,475,37,65,2,3,38  },
                { 2,7,5,14,70,1,29,61,52,45,6,112,66,16,21,32,592,46,38,135,87,58,186,315,290,128,113,0,64,48,227,23  },
                { 33,23,102,51,128,13,64,202,141,1,77,10,153,40,196,117,2,3,0,5,15,269,403,12,137,134,318,165,120,6,453,99  },
                { 16,92,7,20,43,35,126,71,60,14,107,18,68,97,0,121,279,149,24,246,191,48,118,575,55,140,362,783,230,150,375,566  },
                { 13,23,4,33,77,64,51,102,141,128,32,10,0,202,40,115,59,22,90,11,177,21,291,6,7,318,180,117,137,2,95,165  },
                { 507,162,129,41,4,211,62,38,123,59,57,248,183,130,99,11,3,361,202,17,402,556,266,305,803,210,128,184,152,136,313,117  },
                { 643,123,193,650,802,18,25,389,718,256,65,289,84,91,619,511,415,90,235,63,57,510,324,216,862,102,6,183,108,397,217,736  },
                { 13,23,15,1,515,51,0,2,700,5,753,165,141,115,12,3,4,180,21,197,457,7,6,10,120,9,33,202,77,32,8,11  },
                { 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  },
                { 35,0,68,69,24,9,1,16,65,103,149,133,18,114,28,50,83,2,189,7,46,14,101,336,175,124,251,55,71,218,38,238  },
                { 16,101,0,118,9,18,24,68,35,154,71,124,60,212,191,520,55,806,694,167,28,39,364,375,1,346,252,65,604,302,22,21  },
                { 0,9,16,35,1,24,68,18,65,21,103,67,13,149,28,189,71,23,101,238,114,7,335,133,486,141,22,212,48,50,30,118  },
                { 13,202,23,77,33,51,128,5,21,141,115,32,102,64,4,0,318,269,10,15,291,2,494,177,11,217,3,515,22,137,6,700  },
                { 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  },
                { 76,90,21,179,316,148,205,32,464,288,184,257,245,1,89,2,460,57,152,45,38,358,645,5,12,449,350,48,37,17,4,14  },
                { 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  },
                { 6,26,235,138,19,145,112,70,331,262,25,42,52,624,27,453,122,47,500,78,648,85,29,2,630,632,409,113,50,226,108,75  },
                { 7,16,14,24,92,35,18,2,46,9,60,140,0,87,50,5,54,13,12,38,171,23,126,21,58,64,1,70,128,71,220,163  },
                { 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  },
                { 15,515,700,753,4,5,11,141,13,1,33,3,0,128,202,23,180,21,2,64,269,32,117,134,120,40,102,318,153,17,137,352  },
                { 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  },
                { 214,90,289,6,874,64,25,65,235,42,751,249,256,312,194,85,746,875,174,32,525,288,519,835,247,348,233,544,217,524,437,352  },
                { 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  },
                { 89,79,468,179,358,205,94,405,115,498,72,180,365,431,37,111,341,734,188,317,482,217,11,4,245,152,413,216,12,474,490,752  },
                { 24,16,35,68,18,71,7,92,0,108,9,14,118,101,336,175,375,302,28,124,154,55,149,60,398,1,65,2,140,273,345,230  },
                { 51,730,421,801,453,386,23,523,13,475,719,401,670,365,899,403,115,457,758,165,33,494,450,6,423,805,629,56,569,514,958,388  },
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                { 4,339,188,471,11,59,79,12,377,94,99,33,77,102,51,111,37,152,13,961,474,542,40,342,3,23,128,403,202,177,184,57  },
                { 15,4,515,11,700,33,82,40,0,120,753,10,8,110,13,93,23,165,77,260,64,31,22,51,44,102,351,1,125,9,197,21  },
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                { 17,45,227,21,106,3,2,243,209,5,48,32,221,62,207,50,29,186,290,270,263,52,14,496,400,119,46,255,54,430,38,721  },
                { 340,354,586,658,156,195,698,668,1,296,9,18,883,363,447,379,303,98,411,13,31,163,51,5,371,48,919,846,121,21,360,70  },
                { 277,153,111,12,23,51,474,99,38,37,139,117,41,457,79,453,542,13,11,33,134,157,629,188,961,14,196,401,102,569,15,94  },
                { 0,18,16,159,49,24,9,105,35,68,7,28,22,1,60,344,55,101,109,2,14,158,13,23,71,118,455,286,272,424,5,327  },
                { 0,105,9,49,16,18,158,28,518,24,101,320,1,68,170,301,272,127,7,286,35,890,109,39,159,98,21,344,31,55,371,23  },
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                { 4,23,51,33,19,17,102,153,485,880,40,403,196,26,300,453,27,117,78,0,12,200,47,5,11,14,342,99,53,77,475,2  },
                { 62,184,56,440,130,229,183,3,556,152,99,162,12,266,17,548,136,57,305,161,123,14,452,4,383,403,257,34,40,84,33,139  },
                { 13,23,77,141,64,202,33,51,269,115,0,102,21,4,217,128,5,32,318,137,291,9,15,2,180,10,3,317,177,515,7,6  },
                { 1,22,36,105,170,0,86,2,31,28,239,64,55,5,10,98,9,44,127,95,654,67,301,143,13,12,49,23,320,141,83,21  },
                { 15,515,700,753,0,1,13,2,23,901,5,8,51,82,9,180,457,4,7,12,3,6,10,120,341,141,22,898,197,351,115,260  },
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                { 24,28,22,0,7,1,2,16,14,65,35,49,158,95,109,159,55,105,10,18,124,9,67,5,239,149,12,289,108,68,21,424  },
                { 105,22,131,272,286,98,55,239,1,31,320,9,127,327,36,185,28,374,86,219,0,64,187,44,578,164,224,913,535,115,601,13  },
                { 22,31,28,301,127,98,44,0,105,1,512,395,9,293,109,299,95,338,239,125,242,116,36,320,55,841,900,685,599,23,13,763  },
                { 2,1,58,29,5,14,52,46,186,334,45,155,151,50,400,75,38,69,502,61,48,227,223,7,163,17,262,67,549,21,70,113  },
                { 7,107,135,232,97,14,2,92,66,16,172,192,278,387,298,356,38,35,448,52,46,43,60,29,20,126,324,526,357,359,64,5  },
                { 20,43,104,426,173,7,560,414,707,784,319,81,0,861,422,819,38,74,715,52,376,97,879,32,330,22,49,64,66,95,192,526  },
                { 104,74,636,66,204,0,355,81,222,25,29,319,145,784,20,65,90,4,174,194,7,64,6,746,138,173,750,715,91,43,192,32  },
                { 0,9,101,35,68,39,65,28,252,124,67,154,364,336,100,166,30,1,289,55,149,346,16,114,158,88,439,24,429,22,570,194  },
                { 57,14,4,231,236,585,176,59,369,23,361,13,719,51,300,342,12,457,56,3,62,38,202,401,34,46,2,322,11,215,210,507  },
                { 1,2,15,3,141,0,515,5,33,700,13,64,77,180,6,128,753,10,4,269,102,202,11,7,134,197,352,120,117,318,12,291  },
                { 5,1,21,202,13,32,48,23,0,61,259,22,494,120,70,49,51,18,137,128,465,12,178,115,2,453,403,141,58,3,90,450  },
                { 141,205,4,72,59,79,245,11,352,94,152,76,247,216,21,188,452,217,497,12,89,37,111,339,588,77,64,875,864,115,358,464  },
                { 15,515,700,753,0,1,2,13,5,4,23,3,8,341,365,51,115,10,120,457,6,141,77,197,31,7,165,9,202,450,961,260  },
                { 5,2,50,14,58,38,171,46,29,1,45,186,17,52,155,218,48,281,61,487,54,36,67,21,328,334,151,227,760,114,400,133  },
                { 457,120,70,125,318,64,23,48,795,291,202,761,751,415,77,846,269,758,21,237,96,260,391,165,87,1,128,5,221,13,137,763  },
                { 13,23,51,33,4,40,117,102,453,64,153,196,0,77,15,11,12,475,1,65,134,10,515,22,21,14,700,59,403,141,2,753  },
                { 229,152,57,266,452,381,432,12,313,184,99,471,17,4,62,339,157,3,129,59,128,11,369,37,77,38,40,123,5,497,188,257  },
                { 49,28,109,22,159,9,272,95,105,131,55,35,254,168,39,327,169,0,1,286,175,374,347,158,420,67,36,194,312,424,627,346  },
                { 5,2,61,29,45,58,80,311,1,17,209,227,52,243,106,869,454,151,592,496,48,334,14,155,6,186,46,171,75,21,255,667  },
                { 244,44,110,141,260,30,269,352,839,131,574,228,373,276,1,406,219,717,217,137,253,224,120,93,36,31,567,116,661,187,341,88  },
                { 12,99,79,139,11,453,196,51,277,474,111,23,542,37,94,188,33,13,401,775,40,961,313,102,4,339,153,485,629,134,300,431  },
                { 16,35,9,0,68,24,149,69,67,18,1,114,65,230,71,7,103,133,50,167,212,118,101,191,140,64,399,28,124,283,55,565  },
                { 88,30,274,435,131,613,190,100,93,829,166,1,187,795,530,127,382,957,960,160,31,137,466,264,39,800,406,254,28,473,521,219  },
                { 167,16,18,118,212,24,60,71,101,68,191,9,375,411,363,35,0,1,589,199,302,21,447,55,146,126,92,271,647,121,562,48  },
                { 64,141,86,177,77,128,147,597,304,95,269,102,275,4,352,49,120,5,372,194,465,13,588,237,947,216,202,180,612,751,107,534  },
                { 18,65,90,403,523,289,240,214,194,102,701,475,202,217,283,862,389,51,33,0,494,421,453,817,84,64,847,899,352,13,23,437  },
                { 13,51,23,202,5,12,21,128,15,115,0,1,141,120,64,32,4,2,515,403,165,457,3,10,700,99,453,318,719,450,308,401  },
                { 98,223,393,31,1,271,834,791,167,44,202,64,93,697,5,116,77,125,450,446,212,18,541,293,51,120,195,132,284,13,807,765  },
                { 15,515,700,753,4,11,23,13,40,51,82,165,0,110,93,33,141,64,120,5,10,77,3,102,180,32,202,125,8,197,31,21  },
                { 15,515,700,753,0,1,13,2,901,23,5,341,3,51,82,8,4,180,961,9,115,10,12,6,898,7,351,141,134,22,31,120  },
                { 234,416,77,5,315,639,325,202,147,198,113,49,450,61,455,142,0,21,22,342,329,494,178,58,102,427,318,230,13,120,43,470  },
                { 60,146,16,18,156,126,121,271,199,360,132,24,167,0,640,10,71,522,21,92,5,340,107,354,118,150,22,195,446,35,28,212  },
                { 4,361,11,14,56,368,377,161,27,12,300,77,59,200,17,554,202,33,40,494,495,21,210,80,757,25,128,23,19,38,444,53  },
                { 141,82,217,351,15,352,120,1,180,260,515,64,854,36,700,317,752,372,13,269,77,753,922,21,349,23,202,110,93,137,51,373  },
                { 15,515,700,753,77,13,0,1,23,33,102,2,51,4,3,5,291,217,10,9,450,120,341,7,317,6,11,117,115,8,260,180  },
                { 15,515,120,13,700,23,77,141,1,260,0,753,180,51,137,202,115,365,110,291,217,5,128,9,21,341,197,269,2,450,317,165  },
                { 174,6,348,85,138,74,280,204,66,233,192,355,289,65,81,580,636,353,25,91,104,343,673,214,64,95,42,712,792,32,194,90  },
                { 152,497,452,59,4,216,11,79,94,77,128,188,269,339,588,33,76,529,318,32,141,471,12,202,111,21,5,51,37,90,72,177  },
                { 417,499,10,141,253,244,110,559,8,564,180,260,728,120,352,638,642,341,951,206,143,752,901,93,137,661,922,373,44,31,811,197  },
                { 13,77,23,33,4,51,0,102,128,59,141,40,64,115,177,10,137,22,202,2,7,11,90,1,117,180,269,14,49,6,134,3  },
                { 1,2,22,0,36,5,67,50,14,28,12,86,38,46,83,168,194,65,103,114,49,7,10,95,21,69,23,24,128,51,55,13  },
                { 17,106,119,207,255,306,742,378,84,62,136,45,3,5,240,80,61,56,209,383,311,790,655,32,2,440,76,151,58,29,179,263  },
                { 3,128,1,141,2,202,33,5,64,15,0,515,102,13,269,10,700,180,134,51,120,6,77,318,23,137,17,117,753,197,82,153  },
                { 514,38,377,328,11,57,41,248,880,266,556,4,152,361,471,757,485,403,305,102,3,211,313,99,457,130,12,14,157,40,23,54  },
                { 68,0,167,101,9,118,264,520,16,18,21,478,562,1,124,212,100,936,664,777,191,88,806,154,48,24,759,604,35,252,265,65  },
                { 230,689,699,213,466,352,217,831,30,443,418,144,854,201,840,855,1,251,203,317,530,957,96,93,822,539,36,752,351,137,83,800  },
                { 33,77,102,117,15,82,13,134,23,64,0,515,120,153,51,4,40,128,700,260,202,141,196,22,753,11,351,10,1,326,95,269  },
                { 11,40,33,51,117,13,542,328,14,134,38,153,23,12,485,231,102,54,775,37,3,377,111,139,211,4,457,403,369,475,99,719  },
                { 33,64,77,128,141,2,1,202,102,13,23,117,0,15,3,153,51,134,10,40,6,5,515,269,137,180,318,165,700,7,196,753  },
                { 15,515,700,753,4,1,5,11,13,21,33,180,93,141,64,2,23,77,82,3,0,102,32,40,352,341,10,197,98,110,117,901  },
                { 1,2,14,67,50,46,38,24,103,83,0,5,36,28,29,133,114,96,65,52,18,75,54,108,22,7,238,58,160,9,361,69  },
                { 258,201,276,137,160,860,116,261,295,843,567,144,131,44,187,268,943,219,284,31,202,935,141,98,662,203,127,96,36,93,224,1  },
                { 7,2,14,16,46,87,75,52,92,278,29,38,140,70,1,5,35,294,24,262,135,69,171,172,58,409,112,60,50,66,97,12  },
                { 13,23,0,2,51,1,33,4,115,10,15,141,77,3,5,180,217,515,9,7,64,11,700,6,102,40,197,22,317,753,165,202  },
                { 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  },
                { 187,219,258,871,44,442,160,574,137,224,908,116,839,131,36,926,276,201,93,228,202,860,31,613,144,531,406,1,902,30,190,318  },
                { 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  },
                { 13,23,77,33,51,4,64,141,115,102,0,2,128,177,40,11,202,10,6,180,7,15,269,1,32,217,59,22,291,3,137,515  },
                { 340,897,691,478,658,264,914,382,100,812,363,1,724,156,166,698,88,521,39,404,682,447,296,96,303,411,30,909,9,274,656,772  },
                { 9,18,310,101,265,159,326,120,105,158,33,363,77,195,51,55,13,39,354,132,23,7,28,639,16,137,98,1,252,272,709,49  },
                { 57,313,471,12,99,369,157,339,266,152,38,37,475,453,328,775,11,40,59,188,77,514,401,403,342,4,139,33,377,51,229,14  },
                { 16,7,24,14,35,140,60,92,18,69,71,2,189,1,46,230,108,388,150,38,21,172,278,67,246,267,50,309,236,135,451,0  },
                { 206,417,93,940,959,473,499,203,8,137,559,728,31,202,44,120,450,141,10,260,116,564,22,326,269,318,268,244,0,1,253,638  },
                { 15,515,700,753,1,0,13,2,23,4,3,51,5,217,7,77,341,115,8,9,10,33,6,180,317,349,291,120,11,165,457,901  },
                { 1,2,5,14,48,21,290,32,50,45,38,46,263,207,155,72,76,29,17,408,425,171,89,52,7,0,292,449,3,227,513,428  },
                { 121,132,354,167,271,223,146,98,18,463,1,668,446,195,407,60,212,447,781,48,360,363,411,522,156,393,807,9,21,16,293,13  },
                { 131,578,105,371,219,224,716,616,187,49,9,254,737,159,385,98,258,127,272,761,0,916,623,910,28,286,39,31,22,518,924,242  },
                { 302,467,97,6,273,1,24,484,124,51,36,18,2,398,453,421,523,69,7,23,13,403,386,150,66,0,298,65,426,165,22,158  },
                { 30,190,530,88,1,100,778,539,625,274,382,410,96,731,960,39,795,321,9,131,264,144,840,748,44,166,669,957,36,31,435,228  },
                { 141,1,2,128,64,33,15,202,3,0,180,5,13,77,515,134,269,102,197,700,10,137,318,6,120,165,753,352,4,82,23,117  },
                { 44,201,567,116,131,224,295,662,489,268,219,31,434,144,187,276,110,384,93,261,699,137,36,442,120,1,613,30,228,64,141,244  },
                { 12,15,51,23,515,37,99,13,700,0,10,117,753,38,165,82,134,120,11,453,197,64,115,569,1,629,401,22,457,474,110,153  },
                { 7,135,2,92,172,14,66,140,38,52,97,46,29,74,16,324,278,226,6,87,1,571,262,5,357,232,35,380,69,314,24,330  },
                { 125,386,23,963,949,60,51,391,165,221,13,197,118,21,719,193,541,421,517,150,393,7,401,453,308,5,791,551,326,558,48,173  },
                { 6,85,42,25,138,222,174,235,280,256,525,289,26,214,64,746,90,32,544,65,204,19,66,337,355,95,348,415,74,29,5,312  },
                { 1,14,5,50,2,67,24,0,46,69,48,21,58,103,16,12,18,38,54,96,83,7,502,45,36,181,35,9,430,28,10,155  },
                { 811,351,642,180,951,752,110,638,253,10,82,352,197,341,365,564,499,854,873,55,9,417,282,901,244,22,559,143,206,141,28,898  },
                { 23,13,51,15,12,453,403,165,4,515,115,719,475,457,700,523,2,21,0,99,202,197,14,5,386,753,128,401,37,308,33,117  },
                { 120,13,23,77,141,1,15,93,217,82,260,51,137,202,110,515,21,180,165,5,128,102,64,351,291,700,269,352,326,203,177,0  },
                { 1,5,0,22,12,2,36,21,10,23,86,13,28,51,9,128,48,14,32,50,7,3,96,137,54,4,202,49,37,65,208,323  },
                { 219,98,23,127,301,51,258,308,170,910,13,165,22,105,293,616,125,242,276,401,201,395,964,115,55,284,31,374,327,206,512,900  },
                { 64,180,80,165,5,237,2,250,34,58,297,61,197,17,22,29,186,498,231,445,247,3,752,311,95,32,483,153,27,45,115,469  },
                { 13,77,23,33,0,2,1,64,141,51,102,10,15,3,115,40,180,6,515,128,7,22,269,202,4,217,700,5,177,117,14,165  },
                { 15,120,51,515,13,450,23,700,202,153,196,753,260,64,128,141,730,4,326,386,21,523,33,318,5,457,95,32,403,1,77,269  },
                { 2,1,5,29,32,45,207,263,14,425,58,72,76,21,7,408,48,46,52,186,17,292,38,6,61,89,476,50,155,720,119,3  },
                { 15,515,700,753,4,13,11,5,1,23,33,21,3,141,32,2,40,180,117,64,269,202,102,197,0,165,120,51,341,352,153,12  },
                { 76,5,214,129,2,123,45,710,17,249,618,460,179,32,1,257,205,519,90,207,245,184,162,61,769,209,292,106,6,29,14,128  },
                { 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  },
                { 7,2,135,14,29,87,66,52,97,172,70,112,5,58,46,337,92,16,20,43,1,38,232,155,74,294,6,461,409,151,262,32  },
                { 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  },
                { 250,80,34,472,17,495,176,469,33,194,64,483,4,297,141,14,161,27,53,667,56,833,73,527,585,231,106,51,84,814,2,59  },
                { 97,7,81,140,66,92,172,192,24,298,43,6,74,69,314,426,462,14,501,16,21,508,60,189,267,232,230,104,48,20,135,330  },
                { 31,44,116,144,268,393,492,434,367,489,127,98,918,0,384,9,22,206,948,105,93,203,1,456,332,940,299,28,137,49,293,125  },
                { 15,128,33,3,13,51,141,1,202,64,23,2,515,120,102,0,5,82,10,700,165,197,269,153,403,110,753,137,196,318,117,12  },
                { 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  },
                { 7,24,124,1,6,97,2,69,14,18,23,92,21,67,66,16,5,484,43,20,118,65,36,22,28,0,51,140,13,71,29,150  },
                { 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  },
                { 1,15,2,141,515,0,700,13,3,180,10,753,5,64,77,33,4,6,7,197,102,269,165,23,134,11,352,341,291,349,22,120  },
                { 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  },
                { 15,515,700,753,4,11,1,93,13,5,180,110,82,21,120,23,2,33,10,141,3,165,197,102,901,0,32,341,117,40,153,12  },
                { 15,515,700,753,1,13,0,2,23,4,77,51,3,5,341,291,7,33,6,115,10,9,8,217,11,177,120,180,102,165,197,365  },
                { 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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                { 0,68,9,35,65,101,189,212,114,67,124,69,1,154,149,39,230,64,252,16,88,702,103,100,18,336,28,329,520,83,30,755  },
                { 5,2,186,29,61,45,17,1,52,48,58,171,155,227,80,209,311,21,14,46,50,106,243,513,334,502,496,38,3,6,32,592  },
                { 15,515,700,753,13,1,2,0,3,4,5,23,341,11,10,33,6,51,165,117,153,7,180,12,365,901,77,569,197,115,64,9  },
                { 13,15,23,515,0,51,1,700,4,2,753,10,3,5,12,77,33,961,165,457,197,11,115,9,22,102,40,403,202,21,14,59  },
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                { 166,39,30,274,190,100,333,438,530,310,88,252,0,9,539,265,1,656,404,101,625,131,778,254,31,455,676,329,724,158,21,23  },
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                { 539,228,224,219,816,190,30,258,871,840,669,93,406,530,957,187,160,531,748,137,131,88,863,36,728,839,44,213,352,116,202,466  },
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                { 2,29,7,70,52,14,1,58,112,46,75,5,171,163,87,220,307,151,186,334,38,66,155,16,69,135,278,45,262,97,6,21  },
                { 88,321,213,100,230,435,689,466,1,382,30,352,217,699,410,96,795,36,921,752,190,141,144,180,44,831,317,83,443,31,840,251  },
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                { 13,23,51,730,12,719,453,457,401,475,5,21,403,2,0,1,15,4,3,899,99,32,165,11,515,308,197,115,6,961,700,523  },
                { 72,76,89,12,37,4,308,179,38,528,90,431,54,205,148,184,401,57,152,474,23,59,51,245,428,11,32,99,405,316,257,21  },
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                { 202,141,269,494,318,137,51,128,403,4,217,96,77,5,64,177,291,180,15,352,102,10,33,349,2,317,0,341,120,515,21,453  },
                { 77,202,33,128,102,318,494,269,13,0,117,23,342,291,403,15,134,51,153,141,177,515,82,137,196,700,203,64,22,351,753,4  },
                { 253,110,951,352,499,811,10,854,180,638,244,559,642,752,564,8,141,143,417,341,901,260,206,197,922,661,93,15,498,373,165,911  },
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                { 28,109,9,39,0,158,49,22,168,35,55,175,1,65,67,185,194,159,289,95,272,114,30,105,86,584,36,169,254,2,83,24  },
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                { 173,693,104,422,5,18,61,32,102,0,20,13,784,560,33,66,397,526,49,207,29,25,510,707,65,6,11,344,21,263,81,77  },
                { 23,13,386,51,308,801,719,221,401,949,21,730,165,421,102,115,125,33,341,670,468,117,770,1,120,6,197,14,403,97,67,958  },
                { 0,49,105,16,28,24,159,9,158,320,1,68,35,239,170,18,109,7,55,65,2,95,301,124,347,14,21,154,22,127,286,31  },
                { 2,5,1,207,45,29,32,58,76,61,6,263,292,655,72,14,17,476,7,119,52,306,70,64,21,90,186,214,106,38,3,790  },
                { 21,6,125,49,13,64,715,66,115,95,197,33,22,32,204,165,56,278,0,408,241,120,4,808,681,350,263,85,81,571,135,509  },
                { 612,427,325,107,202,5,376,49,64,392,403,470,21,147,31,788,494,14,362,465,858,98,20,804,518,43,845,318,125,97,725,534  },
                { 32,21,76,72,2,1,14,5,241,449,89,38,350,221,155,48,50,292,37,46,45,90,270,54,17,179,214,12,148,430,476,413  },
                { 24,0,28,16,7,124,35,154,14,149,65,18,9,68,55,108,175,71,2,1,22,109,92,67,484,336,118,69,302,398,570,420  },
                { 1,5,14,2,48,50,38,67,46,21,0,54,45,270,281,12,24,32,155,96,513,103,290,83,61,58,36,17,37,72,69,181  },
                { 13,961,569,197,37,15,23,474,515,94,148,111,12,165,629,341,700,79,901,401,51,405,753,10,134,4,115,734,873,11,89,117  },
                { 33,23,102,51,13,40,77,128,64,202,141,15,4,12,0,1,2,117,22,11,10,403,153,515,99,318,137,269,139,196,700,134  },
                { 0,1,24,67,9,16,18,35,28,69,103,50,5,2,65,12,83,68,7,96,14,22,21,149,75,114,13,133,23,71,218,54  },
                { 384,617,940,332,855,911,206,959,434,282,141,10,93,253,244,110,144,268,120,36,352,137,417,203,116,31,44,269,160,201,143,951  },
                { 30,93,473,137,31,704,450,652,190,203,800,254,166,274,326,144,269,160,127,303,120,625,88,848,110,435,77,521,349,131,340,744  },
                { 53,27,73,26,19,250,297,200,25,630,17,6,611,122,34,42,714,235,472,65,436,14,80,684,690,106,45,113,680,108,64,4  },
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                { 254,530,39,613,688,221,30,31,438,190,228,960,1,44,141,21,180,406,23,166,9,202,13,96,137,48,131,829,317,269,393,51  },
                { 9,39,28,35,30,166,158,36,0,175,101,346,364,67,49,68,168,420,88,1,194,131,100,352,55,83,190,64,137,570,86,65  },
                { 62,56,3,548,555,507,440,161,34,4,215,136,162,514,361,527,17,14,211,130,328,11,383,123,84,183,38,57,184,152,205,494  },
                { 92,126,107,7,356,493,97,279,359,298,16,246,35,60,14,441,362,121,43,423,5,132,392,20,508,230,199,146,232,173,150,414  },
                { 15,82,141,515,291,922,349,700,217,260,372,120,351,93,77,753,318,352,373,854,1,326,269,21,13,102,144,202,64,23,203,137  },
                { 141,217,352,115,180,13,269,317,752,77,23,21,341,197,5,372,244,291,9,64,51,102,4,1,365,2,165,33,3,48,237,351  },
                { 78,47,390,19,130,453,108,27,711,813,730,444,412,283,196,690,123,14,128,26,250,389,650,236,200,65,51,4,34,183,297,73  },
                { 34,250,297,80,472,64,495,17,311,3,148,45,667,61,176,53,243,27,90,161,469,141,483,151,62,128,29,4,58,56,5,231  },
                { 51,23,33,13,551,77,102,326,421,21,523,120,5,899,453,692,202,153,308,615,115,958,450,401,791,68,221,93,475,18,403,4  },
                { 98,223,393,363,411,1,478,834,664,156,284,691,447,791,914,293,354,724,697,9,807,541,759,51,18,421,48,264,948,586,195,848  },
                { 7,14,107,232,16,92,2,60,46,5,359,121,24,526,220,620,135,1,172,21,126,314,132,77,18,75,32,278,12,23,52,38  },
                { 32,76,2,1,21,72,241,14,5,48,292,89,476,45,720,270,179,90,17,214,148,38,50,29,129,155,350,46,290,227,123,464  },
                { 15,515,700,753,13,23,33,77,51,4,102,0,32,202,1,11,128,82,117,141,40,5,110,8,3,90,137,21,10,318,403,165  },
                { 66,6,69,2,1,74,14,135,278,267,380,24,29,97,67,38,103,75,7,388,324,25,52,150,87,83,189,357,335,108,204,172  },
                { 152,4,339,59,79,471,188,11,77,94,128,33,529,377,12,111,102,202,452,402,216,99,13,542,51,40,474,37,64,291,23,961  },
                { 15,515,700,753,1,0,196,13,33,2,77,5,23,102,3,10,9,7,217,4,6,153,117,177,14,457,115,12,40,730,11,134  },
                { 17,209,45,106,207,5,255,119,62,2,61,3,263,742,306,655,425,378,32,56,29,136,84,80,311,58,186,240,243,383,14,21  },
                { 120,260,450,15,1,23,817,13,515,523,326,5,700,51,82,31,202,64,21,753,318,93,32,269,98,33,351,77,102,125,457,165  },
                { 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  },
                { 15,515,700,753,165,13,0,1,197,23,4,82,120,2,180,12,260,719,8,3,386,117,5,523,901,11,341,51,10,9,141,351  },
                { 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  },
                { 7,14,16,2,46,5,70,107,87,13,58,307,92,32,38,23,202,0,172,24,18,21,60,128,77,35,20,10,9,4,171,112  },
                { 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  },
                { 15,1,13,515,0,2,700,5,23,753,4,3,341,317,10,115,180,11,33,64,217,77,117,165,197,7,6,365,9,141,102,134  },
                { 19,4,119,40,33,202,27,84,102,56,77,73,504,485,26,494,757,63,862,59,23,300,25,12,128,11,5,13,342,880,469,6  },
                { 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  },
                { 15,515,13,700,1,217,141,120,23,180,753,115,365,51,317,341,77,260,0,291,110,137,202,5,21,269,64,36,349,2,4,10  },
                { 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  },
                { 107,126,132,612,362,279,20,146,259,493,199,121,590,43,660,147,35,376,939,60,941,534,683,5,0,953,16,7,49,649,595,470  },
                { 15,515,700,753,13,1,0,23,2,33,77,4,3,51,5,102,115,10,9,341,6,7,11,342,217,12,120,180,40,317,141,8  },
                { 53,27,17,161,469,378,73,527,19,136,383,250,495,56,862,26,62,84,80,106,200,4,34,14,440,297,3,128,585,5,129,123  },
                { 17,45,209,106,5,207,243,454,119,255,2,263,186,290,29,3,21,62,425,61,84,32,58,56,48,408,655,136,306,14,742,227  },
                { 4,152,59,452,128,79,216,11,339,471,529,188,94,77,202,12,291,33,318,377,99,51,23,5,402,349,32,474,102,13,205,111  },
                { 15,515,700,753,1,0,2,13,3,5,23,4,180,51,115,9,6,12,7,8,197,33,10,961,901,77,141,752,110,22,120,341  },
                { 951,752,638,811,351,642,180,253,10,341,197,901,110,873,8,244,15,352,165,898,143,515,564,762,499,55,365,700,82,753,141,854  },
                { 6,262,197,350,74,26,115,509,841,583,165,38,21,13,47,50,235,19,33,324,453,4,308,196,138,99,64,903,675,1,223,130  },
                { 125,165,391,23,386,221,21,13,558,457,51,867,197,115,401,758,77,97,308,791,7,180,48,120,963,451,743,89,603,134,403,450  },
                { 1,14,2,5,16,46,7,38,58,24,50,0,69,48,35,67,54,18,12,75,21,45,513,155,430,37,270,9,61,163,223,32  },
                { 23,13,51,0,12,15,4,1,115,2,515,453,10,457,5,3,202,21,165,700,403,11,37,64,77,401,9,197,753,59,475,99  },
                { 129,84,17,56,27,495,19,548,80,123,162,378,3,504,161,469,618,73,40,53,4,26,205,184,106,183,62,6,257,128,862,12  },
                { 28,9,22,49,109,1,67,0,39,55,168,158,83,36,35,86,420,194,185,159,95,105,69,208,272,103,50,114,2,254,169,30  },
                { 242,391,8,456,116,13,23,492,341,165,867,51,499,457,479,638,338,509,719,10,1,642,417,762,401,93,206,268,901,569,22,197  },
                { 211,162,248,130,57,4,41,556,507,266,183,152,305,361,11,129,62,229,38,471,514,313,157,300,377,3,440,128,123,328,339,59  },
                { 7,92,97,16,298,140,60,126,14,35,279,314,232,246,43,230,508,173,71,107,423,24,150,779,20,189,66,18,607,21,0,653  },
                { 15,515,700,753,1,0,2,13,23,5,3,180,51,901,6,4,7,12,9,115,8,457,165,82,120,197,10,64,141,341,22,117  },
                { 0,18,403,25,523,74,6,24,42,91,22,102,13,51,49,193,475,681,95,85,730,64,899,397,273,750,247,673,32,805,757,288  },
                { 56,0,18,65,33,554,84,343,64,6,90,561,22,19,899,108,27,63,289,475,240,467,370,32,233,214,24,123,95,287,28,194  },
                { 31,98,127,9,0,44,293,105,395,299,49,242,28,22,599,116,1,284,276,125,456,685,763,159,272,623,23,935,393,144,201,137  },
                { 1,5,2,14,38,46,50,48,21,7,58,45,270,61,155,171,0,290,69,32,29,54,67,16,24,666,663,17,37,75,502,52  },
                { 23,51,13,453,457,12,719,4,15,99,401,2,961,3,11,730,475,515,0,1,165,115,629,700,14,17,403,40,5,33,37,64  },
                { 968,967,966,965,964,963,962,961,960,959,958,957,956,955,954,953,952,951,950,949,948,947,946,945,944,943,942,941,940,939,938,937  },
                { 2,1,14,29,67,103,6,46,52,75,24,133,38,218,83,309,36,108,70,114,96,5,238,74,25,26,220,236,65,50,69,87  },
                { 7,71,16,92,24,60,14,97,150,140,35,189,149,298,18,230,43,508,2,423,69,0,38,314,66,279,399,517,251,20,232,273  },
                { 23,1,120,51,13,202,77,141,260,21,15,5,128,82,2,450,269,165,102,318,48,32,137,515,125,64,12,115,351,180,33,7  },
                { 77,13,33,23,64,51,4,102,141,128,40,1,2,202,0,6,177,115,137,15,59,10,11,7,269,22,515,180,318,3,700,95  },
                { 101,9,18,363,264,520,411,604,676,682,905,271,16,821,167,0,621,364,39,100,121,118,166,781,647,252,1,848,447,265,404,60  },
                { 144,203,326,382,166,418,93,88,96,822,1,141,859,77,744,438,110,269,921,367,521,274,100,39,494,120,403,473,217,576,13,291  },
                { 13,21,180,125,5,23,191,32,18,16,146,199,115,24,165,118,0,225,22,1,60,197,64,901,375,241,48,12,408,71,522,818  },
                { 15,515,700,753,13,0,23,8,1,51,82,102,2,33,4,9,180,165,5,77,10,110,12,197,120,260,18,326,351,403,22,457  },
                { 33,77,102,64,13,23,128,51,141,202,1,40,0,2,117,10,15,4,6,318,269,134,22,515,180,115,177,153,137,196,3,700  },
                { 174,544,104,525,74,0,151,25,6,624,29,66,2,636,81,45,204,177,64,416,7,644,5,138,222,319,355,77,22,122,789,216  },
                { 141,304,372,352,291,947,177,269,128,954,77,349,217,202,64,318,498,437,102,864,86,13,115,180,137,5,210,197,32,950,678,7  },
                { 161,200,53,17,714,27,34,73,472,62,585,56,440,383,136,78,527,19,4,3,106,361,14,250,80,514,377,84,322,390,862,548  },
                { 32,76,72,21,38,14,89,54,12,37,2,241,5,428,17,1,181,221,350,45,3,4,449,90,148,179,99,292,794,770,477,46  },
                { 33,23,128,64,141,13,77,51,102,202,2,15,1,3,40,10,5,153,269,515,165,0,117,196,180,318,6,700,137,134,120,22  },
                { 96,137,30,0,9,39,840,202,669,406,141,530,613,1,180,88,22,160,679,576,28,403,31,219,49,228,829,100,36,15,10,856  },
                { 180,141,352,1,15,752,115,0,217,365,2,515,13,901,341,317,23,4,197,700,269,5,3,31,753,244,21,165,253,202,51,44  },
                { 1,2,67,0,28,50,83,65,14,46,103,114,24,38,36,9,69,5,18,7,22,133,55,218,16,124,29,54,96,160,12,480  },
                { 180,115,352,317,365,217,752,901,141,15,341,1,515,253,700,0,753,873,2,197,31,137,165,244,4,120,160,44,98,5,202,3  },
                { 5,32,347,49,13,21,95,713,23,1,77,33,60,64,107,4,126,928,296,850,0,241,197,102,652,195,180,534,165,153,379,10  },
                { 341,180,365,901,317,115,15,752,515,700,217,873,753,82,0,110,197,141,951,165,1,564,13,351,253,12,10,3,2,4,308,244  },
                { 17,45,21,3,106,5,155,38,227,32,2,209,62,54,12,243,14,181,552,587,46,540,207,794,37,48,430,119,255,221,770,29  },
                { 16,24,35,18,7,0,50,1,9,14,75,69,2,5,12,21,60,13,67,71,23,48,10,108,223,181,189,103,46,64,92,51  },
                { 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  },
                { 15,515,1,700,0,2,753,13,23,5,180,3,51,4,165,457,12,197,115,6,7,21,9,141,8,901,33,82,120,77,10,110  },
                { 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  },
                { 15,515,700,13,23,0,1,120,753,51,180,2,260,202,5,141,77,102,9,450,115,21,197,165,7,137,110,33,12,269,901,4  },
                { 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  },
                { 113,61,198,904,43,0,5,37,899,325,20,59,33,523,204,725,817,389,470,329,222,40,174,58,22,453,690,848,122,104,788,105  },
                { 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  },
                { 13,15,1,515,23,2,0,700,4,115,3,51,5,10,753,180,33,341,217,11,165,317,365,197,6,77,40,64,22,9,7,117  },
                { 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.
------------------------------------------------------------------------------
*/