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Note: This is a preliminary and in-progress specification, and is subject to change.

XUASTC LDR Specification

Copyright (C) 2025-2026 Binomial LLC. All rights reserved except as granted under the Apache 2.0 LICENSE. Also see our NOTICE file. If you modify the Basis Universal source code, specifications, or wiki documents and redistribute the files, you must cause any modified files to carry prominent notices stating that you changed the files (see Apache 2.0 §4(b)).

Table of Contents

• Intro: XUASTC LDR, or "JPEG for ASTC"
• Why ASTC?
• High-Level Features
• Unused ASTC LDR Features
• Internal References
• External References
• High Level Format Technical Description
• XUASTC LDR Profiles
• XUASTC LDR Byte Stream
• ZStd Profile Details
  • System Header
  • Temporary Per-Block Transcoding State
  • Block Decoding
  • Command Decoding Rules
  • RUN Command
  • SOLID Command
    • Solid Color Prediction
  • RAW Command
    • Raw Commands - Endpoint DPCM Decoding
  • REUSE_CFG_ENDPOINTS Commands
  • Weight Decoding - DPCM
  • Weight Decoding - DCT
• Appendix 1: Unique 2-3 Subset Partition Pattern Index Tables
• Appendix 2: Encoded XUASTC LDR Block Configuration Table
• Appendix 3: Reuse XY Delta Table

Intro: XUASTC LDR, or "JPEG for ASTC"

This document describes the format of XUASTC ("Supercompressed Universal ASTC") LDR, a supercompressed GPU texture/image format designed for rapid direct transcoding to ASTC LDR, BC7, and other compressed GPU texture or uncompressed pixel formats.

XUASTC LDR combines the strengths of ASTC with modern image compression approaches, resulting in highly compressed intermediate files that are directly transcodable to ASTC, and in many or all cases, depending on the block size and features exploited, directly to BC7 with no intermediate pixel processing.

XUASTC LDR uses the same fundamental ingredients as a modern transform or predictive codec:

• Transform coding: DCT applied directly in the ASTC weight grid domain
• Adaptive quantization (AQ), for per-block adaption of the DCT coefficient matrix to each block's ASTC parameters
• Spatial prediction via a command based architecture
• Cross-domain prediction: luma/color/alpha ASTC endpoint DPCM, with deterministic ASTC CEM domain conversion
• Multiple entropy coding profiles: Zstd, arithmetic, or a mixture
• Optional adaptive deblocking while transcoding to other formats, or shader-based deblocking when sampling from transcoded ASTC textures

In this design, XUASTC LDR provides the distribution-time codec, while its transcoded ASTC LDR output serves as the hardware playback codec, enabling fast, reliable, and driver- and API-independent transcoding with minimal memory, energy, and compute cost across billions of deployed ASTC capable devices.

---

Why ASTC?

ASTC LDR/HDR is now the most widely deployed hardware GPU compressed texture and image format in the world. A high speed hardware ASTC decoder is almost certainly in your pocket - or sitting nearby. Since its standardization by Khronos, it has shipped on virtually every modern mobile SoC: from Apple, Qualcomm, ARM Mali, Samsung, MediaTek, and others - representing many billions of devices across phones, tablets, VR headsets, smart TVs, laptops, and embedded systems.

ASTC’s impact on memory footprint is profound, especially for HDR content: LDR textures and images shrink from 24 or 32 bpp down to 0.89–8.0 bpp depending on block size, while modern ASTC HDR encoders can compress FP16 scene‑or display‑referenced HDR images and textures - typically 48–64 bpp - to just 3.56 bpp with 6×6 blocks, maintaining visually lossless quality.

This combination of pervasive universal hardware support, extreme scalability, efficiency, and quality is precisely why XUASTC LDR targets ASTC as its internal block format representation. Beyond hardware, ASTC is natively supported in major graphics APIs (Vulkan, OpenGL, OpenGL ES, Metal, WebGL, and WebGPU), web browsers (Chrome, Firefox, Safari), and many game engines, enabling seamless integration for developers across platforms.

---

XUASTC LDR: High-Level Features

• All 14 standard ASTC block sizes: 4x4 (8 bpp in memory) to 12x12 (.89 bpp in memory):
  • 4x4, 5x4, 5x5, 6x5, 6x6, 8x5, 8x6, 10x5, 10x6, 8x8, 10x8, 10x10, 12x10, 12x12
• Lossless or lossy supercompression of near-full ASTC LDR. Supports 13,659 total ASTC LDR mode configurations at the largest (12x12) block size.
• Extreme scalability: ~.25 bits/pixel (12x12, full arithmetic coding profile, weight grid DCT, windowed RDO) up to ~5.7 bits/pixel (4x4, no DCT, lossless supercompression of the XUASTC LDR data).
• Rapid transcoding directly to ASTC LDR, with simple direct BC7 transcoding from most 4x4, 6x6 and 8x6 XUASTC LDR blocks (or, for other block sizes, direct encoding to full-featured BC7 using bounded time O(1) analytical encoding techniques).
• Three profiles:
  • Full Zstd: Fastest, lowest compression, simplest decoding
  • Full arithmetic: Slowest, highest compression, lowest per-mipmap level header overhead
  • Hybrid: A mixture of arithmetic coding for metadata/endpoints and Zstd for weights
• ASTC LDR features included:
  • Weight grid upsampling: all valid ASTC weight grid dimensions for each block size/configuration
  • Nearly all LDR CEM's: L/LA/RGB/RGBA, Base+Offset and RGB+Scale, with or without Blue Contraction encoding.
  • Eight ASTC LDR CEM's: 0,4,6,8,9,10,12,13
  • Single plane: 1-3 subsets, all unique ASTC partition patterns
  • Dual plane: 1 subset, all CCS channel values
  • All valid ASTC BISE endpoint/weight levels for each configuration
• Two weight grid compression methods, selectable per-block:
  • Optional lossy weight grid domain DCT transform with per-block AQ (Adaptive Quantization)
    • Weight grid DCT can be applied to any XUASTC LDR block configuration: 1-2 planes, 1-3 subsets, any CEM's, any endpoint/weight BISE levels
  • Weight DPCM - typically lossless, but can be lossy
• ASTC endpoint BISE value DPCM compression which works across any combination of CEM's
  • Can reuse endpoints from nearby blocks, or DPCM code relative to nearby block endpoint values, independent of source/target CEMs
• ASTC block mode configuration compression, for efficient reuse of configurations used on nearby blocks
• Correct decompression guaranteed even when floating point IDCT is used during transcoding
• ASTC sRGB or linear 8-bit decode profiles
• Optional lossy Lagrangian or windowed/bounded Rate-Distortion Optimization (RDO) during compression
• New for Basis Universal v2.50: In-loop deblocking - The encoder now supports globally optimizing the generated ASTC/XUASTC texture blocks taking into account a 5-tap deblocking filter, which can be applied either in a small GPU pixel shader used during sampling, or during CPU transcoding. The deblocking pixel shader is compatible with bilinear/trilinear filtering and mipmapping. Note this feature was added without modifying the XUASTC LDR file format.

---

XUASTC LDR: Unused ASTC LDR Features

XUASTC LDR does not include these specific (and only these specific) ASTC LDR features, in order to reduce encoder and transcoder complexity, reduce transcoder memory consumption, reduce file format complexity, and increase rate-distortion performance:

• Dual Plane modes: 1 subset only
  The extra weight plane places too much pressure on the other block metadata, and these low-utility configs are not supported by any popular or strong encoder.
• CEM's 1 and 5 unused: L base+offset, L+A base+offset
  The L/L+A base+offset variants don't add enough PSNR gain to justify the added complexity and increased tanscoder size. All other LDR CEM's are included, including CEM's 0 (L direct) and 4 (L+A direct). Note, as far as we can tell, ARM's astcenc encoder doesn't utilize the L base+offset CEM. (See this PR.)
• 1-3 subsets included, but 4 subsets excluded
  Most encoders very rarely use 4 subsets (less than ~.4% of blocks), because 4 individual endpoint pairs place high pressure on the other block metadata.
• For 2-3 subsets, all CEM indices must be equal
  The CEM (Color Endpoint Mode) used for each subset must use the same CEM indices. This is the strongest constraint, but also the most valuable from a rate distortion, implementation complexity, and reduced transcoder memory size perspective.
• CEM 0 (LDR Luminance, direct) must always use a single plane. For CEM 4 (LDR Luminance+Alpha, direct), both single and dual plane is supported but for dual plane mode the CCS index must always be 3.

In practice the "no unequal CEM" constraint barely matters for 4x4, impacts 6x6 very little (a low fraction of a RGBA dB PSNR), and on larger block sizes the PSNR drop vs. full ASTC LDR is negligible (a low fraction of a RGBA dB PSNR with a strong encoder at 12x12). A strong encoder can work around this constraint by targeting the other configs with more effective encoding approaches.

Every other ASTC LDR feature not listed in this section is included in XUASTC LDR.

---

Internal References

• JPEG for ASTC
• XUASTC LDR - Weight Grid DCT
• XUASTC LDR - Endpoint Conversion for DPCM Prediction
• XUASTC LDR - log_astc_block structure
• XUASTC LDR - Arithmetic Profile
• XUASTC LDR - Arithmetic/Range Coding
• UASTC LDR 4x4 Texture Specification
• UASTC HDR 4x4 Texture Specification - Standard ASTC ISE Range Table Reference

External References

• Khronos ASTC Texture Format
• Khronos Data Format Specification v1.4.0 - ASTC Compressed Texture Image Formats
• JPEG: Still Image Data Compression Standard (1993), 3rd Edition, by William B. Pennebaker, Joan L. Mitchell
• CCITT T.81: Baseline JPEG Standard - IDCT, zig-zag scanning, quantization tables
• Zstd
• Discrete Cosine Transform
• Range Coding/Arithmetic Coding
• FastAC Library, Amir Said and William A. Pearlman
• Truncated Binary Encoding
• DPCM

---

High-Level Format Technical Description

1. XUASTC LDR is a supercompressed representation of ASTC LDR blocks.

Instead of storing texels or physical ASTC texture block data, XUASTC LDR stores a highly compressed stream of ASTC logical block parameters: color endpoint mode indices, unique partition pattern indices, endpoint values, weight grids, and all other fields required to synthesize valid physical ASTC LDR blocks. Logical ASTC blocks can be quickly, and always losslessly, packed to standard physical ASTC blocks during transcoding, directly converted to other GPU texture formats such as BC7, or immediately decompressed to texels and encoded to other GPU texture formats in real-time using modern analytical GPU texture encoding techniques.

The decoder (or transcoder) does not perform endpoint fitting, rate-distortion search, or color reconstruction - it simply rebuilds the ASTC block structure directly. This enables fast transcoding, since the decoder’s job is to reassemble ASTC data rather than re-encode colors.

2. Spatial coherence in ASTC metadata is exploited aggressively.

Adjacent ASTC blocks in typical images and textures commonly reuse the same partition patterns, CEMs, ISE ranges, and general endpoint structure. XUASTC LDR taps into this structure using a small set of block-local prediction modes: RUN, SOLID, and REUSE_CFG_ENDPOINTS from left/up/diagonal neighbors. These modes suppress redundant metadata and promote zero-residual coding. The effect is similar to intra-prediction in video codecs or how RDO GPU texture encoders (such as crunch's) reuse previous block configurations. Entire portions of ASTC metadata can be skipped when neighboring blocks share the same patterns and modes.

Strong XUASTC LDR encoders can use Rate-Distortion Optimization (RDO) approaches to further exploit this spatial coherence.

3. Endpoint prediction uses a deterministic cross-CEM conversion pipeline.

Block endpoint values are one of the heaviest components of ASTC texture metadata. XUASTC LDR uses a detailed cross-CEM endpoint conversion path so that endpoint DPCM residuals can be predicted from neighboring ASTC blocks, even when their color encoding modes differ (e.g., RGB direct → base+offset → luma+alpha). This is done by converting the neighbor’s endpoints into a canonical 8-bit RGBA form, deterministically re-encoding them using the current block’s CEM, and then coding only the residual differences. The residual precision automatically matches the endpoint’s ISE bit depth. A set of carefully designed, MSB-preserving integer adjustments ensures that ASTC endpoint encoding rules - such as Blue Contraction behavior and endpoint ordering - remain valid after prediction.

This approach is conceptually similar to the DC prediction used in JPEG, where blocks first convert to a common domain and then encode only the difference from a spatial neighbor; XUASTC applies the same idea specialized to encoded ASTC endpoint parameters instead of DC luminance/chrominance values.

4. Weight grids use either DPCM or a DCT transform with Adaptive Quantization (AQ).

ASTC interpolation weights live on small 2D weight grids of many possible potentially non-square sizes, which can be bilinearly upsampled to the ASTC block resolution in a standard way. XUASTC LDR supports two compressed representations, which can be selected by every block:

• Weight Grid DPCM: A simple delta-coding scheme that stores each weight value as the difference from the preceding weight in the same block, in a fixed traversal order. Because many ASTC weight grids tend to be relatively smooth and low-frequency, these deltas usually have low magnitudes, allowing efficient encoding. This representation is lossless with the current reference encoder, but it can also be applied in a controlled lossy fashion.

• Weight Grid DCT: A baseline JPEG-like 2D DCT optimized for any standard ASTC grid dimension, supporting non-square grids and all ASTC weight grid BISE quantization levels. The DCT/IDCT stage is applied directly to ASTC weight grid data (never texels).

The DCT path uses Adaptive Quantization (AQ - unlike baseline JPEG): each block’s DCT coefficients are quantized differently depending on perceptual importance, a single global DCT quality setting between [1,100], and the weight BISE quantization level chosen for that block. The current shipping reference decoder performs floating-point IDCT to recover each ASTC plane's weights; an integer IDCT is also possible.

5. Data streams are entropy-coded with Zstandard or context-based arithmetic/range coding

In the "Full Zstd" profile, each logical stream: mode bytes, endpoint delta values, BC flags, DCT coefficient packing symbols, etc., is Zstd-compressed separately into 18 individual sections per mipmap level. This maintains decoder simplicity, fast random access, and excellent compression ratios. The alternate full arithmetic profile merges all streams into a single adaptive arithmetic-coded bitstream for maximal size reduction and lower overhead on smaller mipmap levels, though with slower decode complexity. There is also an intermediate hybrid profile that uses arithmetic coding for metadata and endpoints, and Zstd for all weight data. The arithmetic profile results in files roughly 3-15% smaller than the full Zstd profile.

Regardless of profile, the decoding process (excluding the AQ+IDCT stages, which may be floating point or integer) is deterministic. In the Zstd profile blocks read exactly one mode byte, then fetch the matching data from the pre-decompressed streams.

6. XUASTC LDR scales from extremely low bitrates to near-lossless quality.

Because XUASTC LDR compresses ASTC metadata and not pixels, its bitrate range is unusually wide. At the low end (~0.25 bpp), 12×12 blocks with DCT+AQ are useable on very large (4k-8k) images/textures, especially with adaptive deblocking (either applied in a pixel shader or while transcoding to other formats such as BC7). XUASTC LDR in lossless (non-DCT) supercompression mode (relative to plain ASTC) is ~5.7bpp at 4x4.

The typical system bitrate with DCT for the smaller block sizes (6x6-8x6) is .4-2.0 bpp, while for 4x4 the typical bitrate with DCT is around 2-3.5 bpp.

---

XUASTC LDR Profiles (Syntaxes)

One XUASTC LDR bitstream represents one mipmap level. The first byte indicates which profile was used to encode the stream:

enum xuastc_ldr_syntax
{
    cFullArith = 0,
    cHybridArithZstd = 1,
    cFullZStd = 2
};

A single .KTX2 or .basis file can use a mixture of different profiles (or "syntaxes" in the reference code) for each mipmap level. For example, the largest mipmap levels can use the Zstd profile, while the smallest levels can use the full arithmetic profile (which has much lower header overhead).

If the syntax byte is cHybridArithZstd (1) or cFullArith (0), the mipmap level uses the arithmetic profile which is separately documented here. The cFullZStd (2) profile is documented next.

---

XUASTC LDR Byte Stream - Full Zstd Profile

The Full Zstd profile uses:

• 2 uncompressed sections
  • raw_bits
  • sign_bits
• 18 Zstd‑compressed sections
• 20 total sections, where each section is always stored into the mipmap level's output data in the same order

Top-Level Layout:

+----------------------------------------+
| xuastc_ldr_full_zstd_header (85 bytes) |
+----------------------------------------+
| raw_bits (uncompressed)                |
| mode_bytes (Zstd)                      |
+----------------------------------------+
| solid_dpcm (Zstd)                      |
| endpoint_dpcm_reuse_indices (Zstd)     |
| use_bc_bits (Zstd)                     |
| endpoint_dpcm_3bit (Zstd)              |
| endpoint_dpcm_4bit (Zstd)              |
| endpoint_dpcm_5bit (Zstd)              |
| endpoint_dpcm_6bit (Zstd)              |
| endpoint_dpcm_7bit (Zstd)              |
| endpoint_dpcm_8bit (Zstd)              |
+----------------------------------------+
| mean0_bits (Zstd)                      |
| mean1_bytes (Zstd)                     |
| run_bytes (Zstd)                       |
| coeff_bytes (Zstd)                     |
| sign_bits (uncompressed)               |
+----------------------------------------+
| weight2_bits (Zstd)                    |
| weight3_bits (Zstd)                    |
| weight4_bits (Zstd)                    |
| weight8_bytes (Zstd)                   |
+----------------------------------------+

If a section has length 0, it is omitted. A decoder must reject streams whose actual data is smaller than the total lengths specified in the header.

Some sections, after decoding, have multiple packed values stored within in each uncompressed byte. The values are always packed LSB first. Packed values never cross between bytes, i.e. all packed values are completely contained within each uncompressed byte. This means that packed value are always packed into each uncompressed byte using 1, 2, 4, or 8 bits.

---

Zstd Profile Details

The Zstd profile starts with the 85 byte little endian header xuastc_ldr_full_zstd_header. The first byte (m_flags) is also the syntax byte, documented above. The rest of the values in this header indicate the sizes in bytes of each each section of data, most of which are Zstd compressed. There are up to 20 sections of section data stored directly after this header:

#pragma pack(push, 1)
struct xuastc_ldr_full_zstd_header
{
    uint8_t m_flags; // syntax byte (cFullZStd, or 2)

    // Commands/control
    uint32_t m_raw_bits_len; // uncompressed, cannot be 0, variable length "raw" bits
    uint32_t m_mode_bytes_len; // Zstd compressed, cannot be 0, mode/command bytes

    // Solid/void extent DPCM bytes
    uint32_t m_solid_dpcm_bytes_len; // Zstd, void extent/solid DPCM bytes
	
    // Endpoint DPCM
    uint32_t m_endpoint_dpcm_reuse_indices_len; // Zstd
    uint32_t m_use_bc_bits_len; // Zstd, blue contraction flags, lowest bit is 1st value
    uint32_t m_endpoint_dpcm_3bit_len; // Zstd, 4-bits each (2 per byte), lowest 4 bits is 1st value
    uint32_t m_endpoint_dpcm_4bit_len; // Zstd, 4-bits each (2 per byte), lowest 4 bits is 1st value
    uint32_t m_endpoint_dpcm_5bit_len; // Zstd, 8-bits each
    uint32_t m_endpoint_dpcm_6bit_len; // Zstd, 8-bits each
    uint32_t m_endpoint_dpcm_7bit_len; // Zstd, 8-bits each
    uint32_t m_endpoint_dpcm_8bit_len; // Zstd, 8-bits each

    // Weight grid DCT
    uint32_t m_mean0_bits_len;   // Zstd, DC values: 4-bits each (2 per byte), lowest 4 bits is 1st value
    uint32_t m_mean1_bytes_len;  // Zstd, DC values: 8-bits each
    uint32_t m_run_bytes_len;    // Zstd, Zero AC coefficient run lengths: 8-bits each
    uint32_t m_coeff_bytes_len;  // Zstd, AC coefficient magnitudes: 8-bits each
    uint32_t m_sign_bits_len;    // uncompressed, AC coefficient sign bits: 1-bit each, lowest bit is 1st value
	
    // Weight grid DPCM
    uint32_t m_weight2_bits_len;  // Zstd, 2-bit weights (4 per byte), used for weight BISE ranges up to BISE_4_LEVELS
    uint32_t m_weight3_bits_len;  // Zstd, 3-bit weights (2 per byte), up to BISE_8_LEVELS
    uint32_t m_weight4_bits_len;  // Zstd, 4-bit weights (2 per byte), up to BISE_16_LEVELS
    uint32_t m_weight8_bytes_len; // Zstd, 8-bit weights (1 per byte), up to BISE_32_LEVELS

    uint32_t m_unused; // Future expansion
};
#pragma pack(pop)

If a section doesn't have any data, its corresponding "len" value in the stream header will be 0. The data for each section immediately follows the header in this specific order, sequentially one after the other, with no padding or other data in between each section:

1. raw_bits (always uncompressed/raw, must always exist)
2. mode_bytes (compressed)
3. solid_dpcm (compressed)
4. endpoint_dpcm (compressed)
5. use_bc (compressed)
6. endpoint_dpcm_3bit (compressed)
7. endpoint_dpcm_4bit (compressed)
8. endpoint_dpcm_5bit (compressed)
9. endpoint_dpcm_6bit (compressed)
10. endpoint_dpcm_7bit (compressed)
11. endpoint_dpcm_8bit (compressed)
12. mean0_bits (compressed)
13. mean1_bytes (compressed)
14. run_bytes (compressed)
15. coeff_bytes (compressed)
16. sign_bits (always uncompressed/raw)
17. weight2_bits (compressed)
18. weight3_bits (compressed)
19. weight4_bits (compressed)
20. weight8_bytes (compressed)

The total size of the stream header and each section's size must not exceed the total size of the compressed data for each mipmap level. It is not an error if there is extra unused data after the last section (this space may be used for future expansion). It is an error if the decoder, while processing commands, attempts to read from an empty section, or read beyond the end of a non-empty section's uncompressed (or raw) data.

A transcoder must Zstd decompress (using an API such as ZSTD_decompress) each compressed section individually, before proceeding to block decompression. The block decompression stage either consumes Zstd decompressed uncompressed data or (in a couple sections) raw data.

System Header

The raw bits section (which must always exist and cannot be empty) always starts with these system header fields, which must be read and processed before block processing.

Field	Bits
Stream Version	5
ASTC Block Size Index	4
sRGB Decode Flag	1
Actual Width	16
Actual Height	16
Has Alpha	1
Use DCT	1
DCT Q (dct_q)×2	8 (optional)

1. 5 bits: The value 1, indicating the stream version.
2. 4 bits: The ASTC block size index, which is an index into this table:

const uint32_t NUM_ASTC_BLOCK_SIZES = 14;
const uint8_t g_astc_block_sizes[NUM_ASTC_BLOCK_SIZES][2] = { 
	{ 4, 4 }, { 5, 4 }, { 5, 5 }, { 6, 5 }, 
	{ 6, 6 }, { 8, 5 }, { 8, 6 }, { 10, 5 }, 
	{ 10, 6 }, { 8, 8 }, { 10, 8 }, { 10, 10 }, 
	{ 12, 10 }, { 12, 12 } 
};

3. 1 bit: 1=sRGB ASTC decode profile, 0=linear ASTC decode profile (this matches the decode profile used during encoding)
4. 16 bits: Actual width in texels (cannot be 0)
5. 16 bits: Actual height in texels (cannot be 0)
6. 1 bit: 1 if any block has alpha < 255
7. 1 bit: UseDCT flag - 1 if weight grid DCT was used on any block in this level
8. 8-bits (only present if UseDCT was 1): The weight grid DCT base quality level multiplied by 2. Valid field values are [1,200]

The number of logical ASTC blocks to be decoded is computed as floor((actual_width+block_width-1)/block_width) and floor((actual_height+block_height-1)/block_height).

Temporary Per-Block Transcoding State

• Transcoders need to store, for each emitted logical/physical block on the current row and previous row, which XUASTC LDR mode configuration index (or "trial mode" index, or "tm_index" in the reference code) was used on that block. This is an integer index into a table of valid XUASTC LDR configurations, which is defined below in Appendix 2. If this index is -1, the block used a solid (void extent) encoding.

• Similarly, transcoders need to store the ASTC logical block configuration for at least the previously decoded 5 rows of blocks (i.e. the current row and 4 rows above it), because they may be referenced by REUSE commands.

• Transcoders also need 3 small hash tables, which are updated and referenced by various commands:

uint32_t PART_HASH_BITS = 6u;
uint32_t PART_HASH_SIZE = 1u << PART_HASH_BITS;

uint32_t TM_HASH_BITS = 7u;
uint32_t TM_HASH_SIZE = 1u << TM_HASH_BITS;

int part2_hash[PART_HASH_SIZE];
int part3_hash[PART_HASH_SIZE];
int tm_hash[TM_HASH_SIZE];

These hash tables are initialized to -1 before transcoding.

Block Decoding

XUASTC LDR blocks are always processed in raster order, from top to bottom and left to right:

for (by = 0 .. num_blocks_y-1)
  for (bx = 0 .. num_blocks_x-1)
    decode block

A transcoder outputs an ASTC logical block for each decoded block, which can be losslessly converted to a 128-bit ASTC physical block.

The decoder reads one byte from the previously uncompressed mode_bytes section and interprets the lower order bits as a command, with optional flag or other values stored in the higher bits of the mode byte.

The supported commands are:

• RAW: 0b0 (1 bit)
• RUN: 0b01 (2 bits)
• SOLID: 0b0011 (4 bits)
• REUSE_CFG_ENDPOINTS_LEFT: 0b0111 (4 bits)
• REUSE_CFG_ENDPOINTS_UP: 0b1011 (4 bits)
• REUSE_CFG_ENDPOINTS_DIAG: 0b1111 (4 bits)

Command Decoding Rules

Pattern	Meaning
(mode_byte & 3) == 1	RUN
(mode_byte & 15) == 0b0011	SOLID
(mode_byte & 1) == 0	RAW
(mode_byte & 15) in {0b0111, 0b1011, 0b1111}	REUSE

---

mode_byte bit flag constants:

const uint32_t XUASTC_LDR_MODE_BYTE_IS_BASE_OFS_FLAG = 1 << 3;
const uint32_t XUASTC_LDR_MODE_BYTE_PART_HASH_HIT = 1 << 4;
const uint32_t XUASTC_LDR_MODE_BYTE_DPCM_ENDPOINTS_FLAG = 1 << 5;
const uint32_t XUASTC_LDR_MODE_BYTE_TM_HASH_HIT_FLAG = 1 << 6;
const uint32_t XUASTC_LDR_MODE_BYTE_USE_DCT = 1 << 7;

---

RUN Command

run_len = 1 + (mode_byte >> 2)

RUN commands repeat a previously emitted block, either the previous block on the current row (i.e. to the left), or on the first block of a row the block directly above.

RUN commands cannot be used on the first block. Runs cannot cross rows. Run lengths which would cause the decoder to issue blocks beyond the end of the row are an error.

---

SOLID Command

A SOLID command encodes a block whose output color is a single uniform RGBA value (a void-extent ASTC block).
The mode byte for a solid block matches:

(mode_byte & 15) == 0b0011

SOLID blocks always store their color in the output ASTC logical/physical block in 16-bit replicated form:

solid_color[c] = (byte_value | (byte_value << 8))

The decoder must first determine the predicted solid color, then apply the delta values read from the solid_dpcm section.

---

SOLID Color Prediction

A SOLID block predicts its base color from the nearest available previously-decoded neighbor, chosen in this order (where bx=the current block's X coordinate and by=block Y coordinate):

1. Left block (if bx > 0)
2. Up block (if bx == 0 and by > 0)

It is an error for a SOLID block to appear at block (0,0) because there is no valid predictor.

Let P be the chosen predictor block.

Case 1 - Predictor block was also SOLID

If P was encoded using a SOLID command:

pred_r = P.solid_color[0] >> 8
pred_g = P.solid_color[1] >> 8
pred_b = P.solid_color[2] >> 8
pred_a = P.solid_color[3] >> 8    // only if has_alpha = 1

Case 2 - Predictor block was NOT SOLID

If the predictor block P is not a SOLID block, prediction falls back to using its first endpoint pair, which corresponds to its first subset and first CEM:

1. Decode P’s first subset “low” endpoint → prev_l
2. Decode P’s first subset “high” endpoint → prev_h
3. Predict each channel as the rounded midpoint:

pred_c = (prev_l[c] + prev_h[c] + 1) >> 1

The first endpoint pair must be decoded to 8-bits/component, by dequantizing the first endpoint's BISE endpoint values to 8-bits (256 levels), then following the CEM decoding functions in the ASTC specification. prev_l[] is the decoded "low" endpoint, and prev_h[] is the decoded "high" endpoint (as RGBA).

---

Applying SOLID DPCM Deltas

Once the predicted color (pred_r, pred_g, pred_b, pred_a) is computed:

1. Read three bytes for RGB deltas:

delta_r = solid_dpcm_section.get_next_bits8()
delta_g = solid_dpcm_section.get_next_bits8()
delta_b = solid_dpcm_section.get_next_bits8()

2. Read alpha delta only if the image uses alpha:

delta_a = solid_dpcm_section.get_next_bits8()

3. Compute final byte values (mod 256):

r = (pred_r + delta_r) & 0xFF
g = (pred_g + delta_g) & 0xFF
b = (pred_b + delta_b) & 0xFF
a = has_alpha ? ((pred_a + delta_a) & 0xFF) : 255

4. Convert to 16-bit replicated form:

solid_color[0] = r | (r << 8)
solid_color[1] = g | (g << 8)
solid_color[2] = b | (b << 8)
solid_color[3] = a | (a << 8)

---

RAW Command

A RAW command specifies either:

1. A configuration reuse (reusing ASTC block mode configuration but NOT endpoints),
   or
2. A fully specified new configuration (trial mode, CEM, partitions, endpoint ranges, grid sizes, CCS, endpoints).

A RAW command is selected when:

(mode_byte & 1) == 0

The RAW path always clears the current block structure (except its weight buffer) and rebuilds the ASTC LDR configuration from predictors or section data.

---

RAW Case 1 - Configuration Reuse (config_reuse_index < 3)

The lower bits of the mode byte define a 2-bit reuse selector:

config_reuse_index = (mode_byte >> 1) & 3

When this value is < 3, the RAW command reuses configuration only from a neighbor:

config_reuse_index	Neighbor	Δx	Δy
0	left	-1	0
1	up	0	-1
2	diagonal	-1	-1

If the required neighbor does not exist (e.g. left on bx=0, up on by=0), the stream is invalid.

Let P be the chosen neighbor block and S its previous-state struct.

Validation:

• S.m_tm_index must be ≥ 0 (trial mode must have been defined)
• Neighbor coordinates must be in-bounds
• Neighbor block must not be SOLID (SOLID has no configuration to reuse)

The block copies the following fields directly from the neighbor:

• tm_index
• num_partitions
• partition_id
• color_endpoint_modes[]
• dual_plane flag
• color_component_selector (CCS index)
• endpoint_ise_range
• weight_ise_range
• grid_width, grid_height

Endpoints are not reused here - RAW reuse of configuration is followed by endpoint decoding (direct or DPCM) as specified by the rest of the RAW logic.

The decoder then proceeds to the endpoint decode section (direct BISE or endpoint DPCM) exactly as with a freshly-specified RAW block.

The current block's previous-state structure is then updated:

new_prev_state.m_tm_index = tm_index is updated for future reuse.

---

RAW Case 2 - Fully Specified New Configuration (config_reuse_index == 3)

If:

(mode_byte >> 1) & 3 == 3

then no configuration is reused, and the block’s full ASTC configuration must be decoded from the bitstream.

The decoder performs the following steps in order.

---

Step 1 - Trial Mode (TM) Selection

The trial mode defines all key ASTC parameters:

• Subset count (1–3)
• ASTC CEM
• Dual-plane vs. single-plane
• CCS index (if dual-plane)
• Endpoint ISE range
• Weight ISE range
• Weight grid width/height

There are two TM (trial mode) selection mechanisms.

1. TM Hash Hit

If:

mode_byte & XUASTC_LDR_MODE_BYTE_TM_HASH_HIT_FLAG

then:

tm_hash_index = raw_bits.get_bits(TM_HASH_BITS)
tm_index = tm_hash[tm_hash_index]

This index must be valid, or the stream is invalid. See Appendix 2: Encoded XUASTC LDR Configuration Table below for the encoded trial mode table.

2. Direct TM Decode

Otherwise:

tm_index = raw_bits.decode_truncated_binary(num_trial_modes)

The TM index must be < num_trial_modes. num_trial_modes is the number of valid XUASTC LDR configurations for the mipmap level's block size (see Appendix 2).

After selection, the TM index is stored for reuse, and the TM hash table is updated:

new_prev_state.m_tm_index = tm_index

// Full ZStd syntax only
uint32_t tm_hash_index(uint32_t x)
{
	// fib hash
	return (x * 2654435769u) & (TM_HASH_SIZE - 1);
}

tm_hash[tm_hash_index(tm_index)] = tm_index;

---

Step 2 - Apply Base+Offset CEM flag

If TM’s CEM is one of:

• CEM_LDR_RGB_DIRECT
• CEM_LDR_RGBA_DIRECT

the mode byte may request a base+offset variant:

if (mode_byte & XUASTC_LDR_MODE_BYTE_IS_BASE_OFS_FLAG)

The CEM is converted accordingly to:

• CEM_LDR_RGB_BASE_PLUS_OFFSET
• CEM_LDR_RGBA_BASE_PLUS_OFFSET

This establishes the actual CEM for this block. (The encoded trial mode table does not include base+offset CEM variants, only direct CEM's.)

---

Step 3 - Partition Pattern (if subsets > 1)

If tm.m_num_parts > 1, the block must specify a non-redundant ASTC partition pattern via a unique pattern index (see the unique partition pattern tables in Appendix 1).

Two mechanisms exist:

1. Partition Hash Hit

If:

mode_byte & XUASTC_LDR_MODE_BYTE_PART_HASH_HIT

then:

h = raw_bits.get_bits(PART_HASH_BITS)
unique_pat_index = part_hash_table[h]

2. Direct Decode

Otherwise:

unique_pat_index = raw_bits.decode_truncated_binary(total_unique_indices)

The index must be < total_unique_indices.
The partition seed is recovered with:

partition_id = unique_pat_index_to_part_seed(block_size_index, subset_count, unique_pat_index)

The hash table is then updated with this index.

uint32_t part_hash_index(uint32_t x)
{
	// fib hash
	return (x * 2654435769u) & (PART_HASH_SIZE - 1);
}

pPart_hash[part_hash_index(unique_pat_index)] = unique_pat_index;

---

Step 4 - Set All ASTC Configuration Fields

The decoder fills:

• num_partitions = tm.m_num_parts
• color_endpoint_modes[] = actual_cem (for each subset)
• dual_plane, color_component_selector
• endpoint_ise_range, weight_ise_range
• grid_width, grid_height

At this point, the only values missing are endpoints and weights.

---

Step 5 - Endpoint Decoding (Direct vs. DPCM)

If:

mode_byte & XUASTC_LDR_MODE_BYTE_DPCM_ENDPOINTS_FLAG

then endpoint DPCM prediction is used (reuse-delta index, convert_endpoints_across_cems(), DPCM residual decode). See the section below, RAW Commands: Endpoint DPCM Decoding, for details on endpoint DPCM decoding.

Otherwise, endpoints are decoded, from the raw bits section, using direct BISE decoding:

decode_values(raw_bits, subset_count * values_per_cem, endpoint_ise_range, endpoints[])

This uses the same BISE value decoding logic as UASTC LDR 4×4. This is a slightly more efficient simplification of ASTC's BISE encoding.

---

Summary of RAW Behavior

1. If (mode_byte >> 1) & 3 < 3:

   • Reuse configuration from neighbor, then decode endpoints normally.

2. Otherwise (== 3):

   • Decode TM (hash or direct)
   • Apply base+offset CEM flag
   • Decode partition (hash or direct)
   • Fill all ASTC configuration fields
   • Decode endpoints (direct or DPCM)

After RAW handling completes, weight decoding (DPCM or DCT) is performed for the block as usual.

---

RAW Commands: Endpoint DPCM Decoding

If a RAW command specifies endpoint DPCM, indicated by:

(mode_byte & XUASTC_LDR_MODE_BYTE_DPCM_ENDPOINTS_FLAG) != 0

then all endpoint values for the block are reconstructed using spatial prediction from a previously‑decoded block, followed by DPCM residual decoding. This replaces direct BISE endpoint decoding.

Endpoint DPCM works for all supported CEM’s, including modes with Blue Contraction or base+offset variants.

---

1. Determine Number of Endpoint Levels

The number of representable endpoint values is determined by the block’s endpoint ISE range:

num_endpoint_levels = get_ise_levels(endpoint_ise_range)

The following lookup tables are used:

• endpoint_rank_to_ise[] - maps rank → ISE endpoint code
• endpoint_ise_to_rank[] - maps ISE endpoint code → rank

All residual arithmetic is done in rank space (NOT directly on BISE indices, because they are not always monotonic), modulo num_endpoint_levels.

---

2. Read Reuse‑Delta Index and Select Predictor Block

The DPCM predictor block is selected using an index read from the endpoint_dpcm_reuse_indices section:

reuse_delta_index = endpoint_dpcm_reuse_indices_section.get_next_bits8()

This index must be < NUM_REUSE_XY_DELTAS.

The predictor block coordinate is:

reuse_bx = bx + g_reuse_xy_deltas[reuse_delta_index].m_x
reuse_by = by + g_reuse_xy_deltas[reuse_delta_index].m_y

See Appendix 3 (Reuse XY Delta Table) for the g_reuse_xy_deltas[] table.

The predictor must satisfy:

• (reuse_bx, reuse_by) lies inside the image’s block grid
• The referenced block is already decoded
• The referenced block is not a SOLID block (SOLID has no valid endpoints)

If any condition fails, the bitstream is invalid.

Let P be the predictor block.

---

3. Determine BC (Blue‑Contraction) Usage Per Subset

For CEM modes that support Blue Contraction, the use of BC is signaled in the use_bc_bits section:

endpoints_use_bc[subset] = use_bc_bits_section.get_next_bits1()

This is read once per subset if the current block’s CEM supports BC.

---

4. Convert Predictor Endpoints to the Target CEM

Before DPCM residuals can be applied, predictor endpoints must be converted into the current block’s:

• CEM
• ISE endpoint range
• BC usage

This is performed by:

convert_endpoints_across_cems(
    predictor_cem,
    predictor_endpoint_ise_range,
    predictor_endpoints,
    target_cem,
    target_endpoint_ise_range,
    out_predicted_endpoints[],
    endpoints_use_bc[subset]
)

convert_endpoints_across_cems() performs:

• Endpoint value dequantization
• CEM domain transformation (RGB ↔ Base+Offset, RGB+Scale, etc.)
• Optional Blue Contraction clamping
• Repacking into the target ISE range
• Producing a valid predicted endpoint vector for each subset

If the function returns failure, the bitstream is invalid. For each subset, the result is an array:

predicted_endpoints[subset][value_index]

---

5. Apply DPCM Residuals

DPCM residuals are encoded in one of several bitstreams based on num_endpoint_levels.

Endpoint Levels	Residual Section	Bits per residual
≤ 8	endpoint_dpcm_3bit	3 (read as 4 bits)
≤ 16	endpoint_dpcm_4bit	4
≤ 32	endpoint_dpcm_5bit	8
≤ 64	endpoint_dpcm_6bit	8
≤ 128	endpoint_dpcm_7bit	8
> 128	endpoint_dpcm_8bit	8

For each subset and each endpoint value:

pred_rank = endpoint_ise_to_rank[predicted_endpoints[subset][value_index]]
delta     = read_residual_from_correct_stream()

new_rank  = (pred_rank + delta) % num_endpoint_levels
new_ise   = endpoint_rank_to_ise[new_rank]

The decoder writes:

log_blk.endpoints[subset * total_endpoint_vals_for_block_actual_cem + value_index] = new_ise

---

6. Summary of RAW Endpoint DPCM Behavior

1. Read reuse_delta_index → choose predictor block.
2. Validate predictor exists and is not SOLID.
3. Determine BC usage per subset (if applicable).
4. Convert predictor endpoints across CEM/ISE domains using convert_endpoints_across_cems().
5. Decode DPCM residuals from the appropriate bitstream.
6. Reconstruct each endpoint via modular rank arithmetic.
7. Store all endpoints for the block.

Endpoint DPCM fully replaces direct BISE endpoint decoding whenever the DPCM flag is set.

---

REUSE_CFG_ENDPOINTS Commands

A REUSE command reuses the entire ASTC block configuration (trial mode, partition pattern, CEM, ISE ranges, grid size, CCS index, number of subsets) and all endpoint values from a previously-decoded neighboring block. The weight values are not reused and must always be decoded after the reuse step.

A REUSE command matches one of these 4-bit patterns:

0b0111  → reuse from left
0b1011  → reuse from above
0b1111  → reuse from diagonal (up-left)

The exact neighbor source is determined by:

reuse_index = ((mode_byte >> 2) & 3) - 1

which yields:

reuse_index	Meaning
0	left
1	up
2	diagonal

Any other value is invalid.

The decoder must ensure the referenced neighbor block exists. For example, a REUSE_UP command on the first row, or REUSE_LEFT on column 0, is an error.

---

Fields Reused

The following ASTC logical block fields from the predictor block P are copied directly into the current block:

• num_partitions
• partition_id (10-bit ASTC seed)
• color_endpoint_modes[] (all subsets)
• endpoint_ise_range
• weight_ise_range
• grid_width, grid_height
• dual_plane flag
• color_component_selector (CCS index)
• All endpoint values (for all subsets)

Additionally, the trial mode index (see the table of valid trial modes in Appendix 2, below) used by the predictor is reused:

tm_index = P.tm_index

This value is stored into the current block’s previous-state buffer for potential future reuse.

---

Endpoint Values

All BISE endpoint values from the predictor block, for all subsets, are copied verbatim. No endpoint DPCM, direct BISE decode, or CEM conversion is performed for REUSE commands.

---

Weight Decoding Still Occurs

REUSE only copies configuration + endpoints.
The decoder must still decode block weights for this block using the appropriate weight mode (DPCM or DCT).

---

Neighbor Rules / Error Conditions

A REUSE command is only valid if:

• The referenced neighbor exists
• The referenced neighbor’s tm_index is ≥ 0 (i.e. it cannot be a solid block)
• The referenced neighbor has already been fully decoded
• The reuse does not cross image boundaries

Specifically:

REUSE_LEFT:     bx > 0
REUSE_UP:       by > 0
REUSE_DIAGONAL: bx > 0 and by > 0

If any of these conditions are violated, the stream is invalid.

---

Summary of REUSE behavior

1. Determine reuse_index ∈ {0=left, 1=up, 2=diag}.
2. Validate the neighbor exists.
3. Copy the neighbor block’s entire ASTC configuration:
   • partition pattern
   • CEM
   • CCS
   • ISE ranges
   • subsets
   • grid dims
   • endpoints
4. Copy tm_index.
5. Decode weights normally for this block.

REUSE_CFG_ENDPOINTS performs no endpoint decoding of its own and does not modify endpoints or configuration in any way.

---

Weight Decoding (DPCM)

When an ASTC block does not use DCT-based weight compression mode, the decoder falls back to a simple, deterministic DPCM-style delta coding scheme for reconstructing the ASTC weight grid. In this mode, weights are decoded directly from the bitstream using a differential pattern: each weight is determined by adding a small coded delta r to the previous weight prev_w, wrapping or masking according to the number of allowed weight levels.

This method is intentionally simple, fast, and completely local to the block: no cross-block dependencies and no transforms. The DPCM path is therefore used for blocks where DCT encoding was unhelpful or too costly, or for encoders that do not choose DCT mode. The current reference encoder always uses lossless DPCM, but lossy implementations are possible.

#-------------------------------------------------------------
# Determine whether the current ASTC block uses DCT-based
# weight compression or the traditional DPCM weight path.
#
# The global flag 'use_dct' is read from the XUASTC LDR
# system header. If it is enabled, then each block's
# mode byte contains a per-block bit that selects DCT.
#-------------------------------------------------------------
block_used_dct = false

if use_dct == true then
    # The mode byte contains a single bit indicating that this
    # block uses DCT for weight-grid compression.
    if (mode_byte & XUASTC_LDR_MODE_BYTE_USE_DCT) != 0 then
        block_used_dct = true
    end if
end if

#---------------------------------------------------------------------
# DPCM Weight Decoding Path (executed when block_used_dct == false)
#
# Each ASTC block has 1 or 2 interpolation planes.
#
# For each plane, weights are decoded via a small-delta DPCM scheme:
#    new_weight = (prev_weight + delta) mod num_weight_levels
#
# The bit width of the delta (2-bit, 4-bit, or 8-bit) depends on the
# ASTC weight ISE range for this block.
#
# After decoding, each weight is mapped through the ASTC "rank_to_ISE"
# lookup table, giving the final BISE-coded weight stored in the block.
#---------------------------------------------------------------------

# "tm" is the XUASTC LDR "trial mode" configuration selected for this block (see the table generator in Appendix 2)
total_planes  = (tm.ccs_index >= 0) ? 2 : 1
total_weights = tm.grid_width * tm.grid_height

# Lookup the total number of ASTC weight levels for this block.
num_weight_levels = astc_helpers::get_ise_levels(log_blk.weight_ise_range)

# Lookup table that maps decoded rank index to an ASTC BISE-encoded weight value.
rank_to_ise = astc_helpers::g_dequant_tables.weight_tab(log_blk.weight_ise_range).rank_to_ISE

#=====================================================================
# Loop over each weight plane in the block (1 for single, 2 for dual plane)
#=====================================================================
for plane_iter in 0 .. total_planes-1:

    #-------------------------------------------------------------
    # Initial predictor: midpoint of available ISE levels
    # Example: 4-level weights → prev_w starts at 2.
    #-------------------------------------------------------------
    prev_w = floor(num_weight_levels / 2)


    #-------------------------------------------------------------
    # Case 1: Very small weight precision (ISE levels < 4)
    # Delta is stored with 2 bits (values 0–3), read from the 
    # uncompressed weight2_bits section
    #-------------------------------------------------------------
    if num_weight_levels <= 4:

        for weight_iter in 0 .. total_weights-1:

            r = weight2_bits.read_bits(2)     # 2-bit delta, read LSB first from each uncompressed byte in the section
            w = (prev_w + r) mod num_weight_levels

            prev_w = w
            
            out_index = plane_iter + weight_iter * total_planes
            log_blk.weights[out_index] = rank_to_ise[w]

    #-------------------------------------------------------------
    # Case 3: 5–7 weight levels (ISE range < 8)
    # 4-bit deltas are used (0–15), mod by num_levels
    #-------------------------------------------------------------
    else if num_weight_levels <= 8:

        for weight_iter in 0 .. total_weights-1:

            r = weight3_bits.read_bits(4)     # 4-bit delta
            w = (prev_w + r) mod num_weight_levels

            prev_w = w

            out_index = plane_iter + weight_iter * total_planes
            log_blk.weights[out_index] = rank_to_ise[w]


    #-------------------------------------------------------------
    # Case 5: 9–15 weight levels (ISE < 16)
    # 4-bit deltas, modulo the weight level count
    #-------------------------------------------------------------
    else if num_weight_levels <= 16:

        for weight_iter in 0 .. total_weights-1:

            r = weight4_bits.read_bits(4)
            w = (prev_w + r) mod num_weight_levels

            prev_w = w

            out_index = plane_iter + weight_iter * total_planes
            log_blk.weights[out_index] = rank_to_ise[w]

    #-------------------------------------------------------------
    # Case 7: 17–32 weight levels (maximum ASTC range)
    # 8-bit deltas are used (0–255), modded by level count.
    #-------------------------------------------------------------
    else:

        for weight_iter in 0 .. total_weights-1:

            r = weight8_bytes.read_bits(8)    # 8-bit delta
            w = (prev_w + r) mod num_weight_levels

            prev_w = w

            out_index = plane_iter + weight_iter * total_planes
            log_blk.weights[out_index] = rank_to_ise[w]

# End of DPCM decoding path.

---

Weight Decoding (DCT)

See the Wiki page Weight Grid DCT.

---

Appendix 1: Unique 2-3 Subset Partition Pattern Index to ASTC Partition 10-bit Seed Index Tables

These tables define, for each XUASTC LDR block size, and for each unique 2/3 subset index selecting a unique partition pattern, which 10-bit ASTC seed value that unique partition pattern corresponds to. (These tables are needed because the ASTC procedural pattern generator outputs many redundant patterns.) These tables are used when transcoding or decoding XUASTC LDR to ASTC.

const uint16_t g_unique_to_seed_4x4_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,20,21,23,24,25,26,27,28,29,30,33,36,37,39,42,43,44,45,47,48,49,50,51,53,54,55,56,58,59,61,62,63,65,66,68,69,70,71,72,73,74,75,76,78,83,87,89,90,91,94,95,98,99,100,101,107,108,109,110,111,113,114,115,116,119,121,122,124,125,128,129,130,131,134,135,137,138,139,142,143,144,146,147,149,150,151,156,158,159,161,165,167,168,169,170,171,172,174,175,177,181,183,184,191,194,195,196,198,199,203,204,206,207,208,210,211,213,214,215,216,218,220,222,226,227,230,231,232,235,236,239,245,246,247,248,249,250,252,253,254,255,257,258,260,262,264,270,271,273,277,278,279,280,281,284,291,293,299,302,304,305,306,307,309,314,319,324,325,326,327,329,330,335,337,339,341,343,344,347,348,351,352,354,355,359,362,368,370,373,374,375,376,380,386,387,388,389,394,395,399,404,409,411,412,418,419,422,423,426,430,432,438,441,443,445,447,453,455,463,471,474,475,476,478,479,484,487,488,489,490,491,495,496,498,500,504,510,511,513,517,518,523,524,526,527,529,530,531,534,539,542,546,547,549,553,558,567,578,581,583,586,587,591,593,594,595,598,600,601,602,605,607,611,612,614,615,619,622,625,627,631,633,634,638,639,643,647,649,655,658,661,662,663,664,666,672,673,674,681,683,684,686,690,693,694,695,696,700,703,705,707,713,716,719,720,724,726,727,730,731,732,736,742,751,754,756,762,764,766,769,770,773,774,778,780,789,791,796,798,799,801,802,804,807,810,811,812,818,819,821,826,828,831,833,834,836,839,840,842,847,849,852,868,872,873,877,881,886,887,888,890,895,897,898,899,902,903,906,911,914,915,919,923,924,930,934,937,938,943,945,947,948,950,951,954,958,959,963,964,966,967,971,976,983,987,988,993,994,995,998,999,1006,1007,1009,1013,1014,1015,1016,1019,1022,1023 } ;
const uint16_t g_unique_to_seed_5x4_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,20,21,23,24,25,26,27,28,29,30,31,33,36,37,39,42,43,44,45,47,48,49,50,51,53,54,55,56,58,59,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,78,83,87,88,89,90,91,94,95,97,98,99,100,101,107,108,109,110,111,113,114,115,116,119,121,122,124,125,128,129,130,131,132,134,135,137,138,139,142,143,144,145,146,147,149,150,151,153,154,156,157,158,159,161,165,167,168,169,170,171,172,174,175,177,181,183,184,185,188,190,191,194,195,196,198,199,200,203,204,206,207,208,210,211,213,214,215,216,217,218,220,222,225,226,227,229,230,231,232,235,236,239,245,246,247,248,249,250,252,253,254,255,257,258,260,261,262,264,265,267,270,271,273,275,277,278,279,280,281,282,284,287,291,293,295,296,299,300,302,304,305,306,307,309,314,317,319,323,324,325,326,327,329,330,332,335,337,339,341,342,343,344,347,348,349,350,351,352,354,355,359,361,362,365,368,370,373,374,375,376,380,381,386,387,388,389,391,394,395,399,404,405,407,409,410,411,412,418,419,420,422,423,426,430,432,438,439,441,443,445,447,449,453,454,455,462,463,465,471,473,474,475,476,478,479,482,484,486,487,488,489,490,491,495,496,498,500,501,503,504,505,508,510,511,513,516,517,518,519,521,523,524,526,527,529,530,531,533,534,538,539,542,546,547,549,550,551,553,554,558,563,567,569,572,575,578,579,581,583,586,587,591,593,594,595,598,600,601,602,605,606,607,608,611,612,614,615,616,619,622,623,625,627,631,633,634,636,638,639,643,645,647,649,652,655,658,661,662,663,664,665,666,668,672,673,674,675,681,683,684,686,687,690,692,693,694,695,696,697,700,702,703,705,707,709,711,713,716,719,720,724,725,726,727,730,731,732,736,739,742,748,751,754,756,758,762,763,764,766,768,769,770,772,773,774,776,778,780,782,786,789,791,792,796,798,799,801,802,804,807,810,811,812,814,818,819,821,823,826,828,830,831,833,834,835,836,839,840,842,845,847,849,852,858,861,866,868,870,871,872,873,876,877,878,881,886,887,888,890,891,895,897,898,899,901,902,903,906,909,911,914,915,919,923,924,927,929,930,933,934,935,936,937,938,941,942,943,945,947,948,950,951,954,955,958,959,963,964,966,967,970,971,975,976,980,983,986,987,988,993,994,995,997,998,999,1001,1006,1007,1009,1010,1013,1014,1015,1016,1019,1020,1022,1023 };
const uint16_t g_unique_to_seed_5x5_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,20,21,23,24,25,26,27,28,29,30,31,33,34,36,37,39,42,43,44,45,47,48,49,50,51,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,81,82,83,87,88,89,90,91,92,94,95,97,98,99,100,101,105,107,108,109,110,111,113,114,115,116,119,120,121,122,124,125,128,129,130,131,132,134,135,137,138,139,142,143,144,145,146,147,148,149,150,151,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,176,177,181,182,183,184,185,188,190,191,193,194,195,196,198,199,200,203,204,206,207,208,209,210,211,213,214,215,216,217,218,220,222,224,225,226,227,229,230,231,232,235,236,239,240,242,245,246,247,248,249,250,252,253,254,255,256,257,258,260,261,262,264,265,267,270,271,273,275,276,277,278,279,280,281,282,283,284,286,287,289,291,293,294,295,296,298,299,300,302,303,304,305,306,307,309,313,314,317,318,319,323,324,325,326,327,329,330,331,332,335,337,338,339,341,342,343,344,347,348,349,350,351,352,354,355,356,359,361,362,365,368,370,373,374,375,376,377,378,380,381,386,387,388,389,390,391,392,393,394,395,399,403,404,405,407,409,410,411,412,415,418,419,420,421,422,423,424,426,430,432,433,437,438,439,440,441,443,444,445,446,447,449,453,454,455,458,462,463,465,466,469,470,471,473,474,475,476,478,479,481,482,484,486,487,488,489,490,491,492,495,496,498,500,501,502,503,504,505,506,508,509,510,511,513,516,517,518,519,521,523,524,526,527,529,530,531,533,534,538,539,542,546,547,548,549,550,551,553,554,558,559,561,562,563,567,569,572,575,578,579,580,581,583,585,586,587,590,591,593,594,595,596,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,619,620,621,622,623,625,627,631,633,634,636,638,639,643,645,646,647,648,649,652,654,655,658,661,662,663,664,665,666,668,672,673,674,675,681,683,684,686,687,688,690,692,693,694,695,696,697,699,700,701,702,703,705,707,709,711,713,714,716,719,720,722,724,725,726,727,730,731,732,736,738,739,742,748,751,753,754,756,758,760,762,763,764,766,768,769,770,772,773,774,776,778,780,782,783,786,789,791,792,796,798,799,801,802,804,806,807,808,810,811,812,813,814,818,819,821,823,826,828,830,831,833,834,835,836,839,840,841,842,845,847,849,851,852,858,861,866,868,869,870,871,872,873,874,876,877,878,879,881,886,887,888,890,891,893,894,895,897,898,899,901,902,903,906,909,910,911,912,914,915,917,919,920,921,923,924,927,929,930,933,934,935,936,937,938,941,942,943,945,947,948,950,951,954,955,958,959,961,962,963,964,966,967,968,970,971,975,976,977,980,983,986,987,988,993,994,995,996,997,998,999,1001,1006,1007,1009,1010,1013,1014,1015,1016,1018,1019,1020,1022,1023 };
const uint16_t g_unique_to_seed_6x5_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,20,21,23,24,25,26,27,28,29,30,31,33,34,36,37,39,42,43,44,45,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,86,87,88,89,90,91,92,94,95,97,98,99,100,101,105,107,108,109,110,111,112,113,114,115,116,117,119,120,121,122,123,124,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,176,177,178,181,182,183,184,185,188,190,191,193,194,195,196,198,199,200,201,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,220,222,223,224,225,226,227,229,230,231,232,235,236,239,240,242,243,245,246,247,248,249,250,252,253,254,255,256,257,258,260,261,262,264,265,266,267,270,271,273,275,276,277,278,279,280,281,282,283,284,286,287,289,291,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,313,314,317,318,319,323,324,325,326,327,329,330,331,332,335,337,338,339,341,342,343,344,347,348,349,350,351,352,354,355,356,357,359,360,361,362,363,365,367,368,370,371,373,374,375,376,377,378,380,381,383,386,387,388,389,390,391,392,393,394,395,399,402,403,404,405,407,409,410,411,412,415,418,419,420,421,422,423,424,426,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,453,454,455,458,461,462,463,465,466,469,470,471,473,474,475,476,478,479,481,482,484,486,487,488,489,490,491,492,493,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,516,517,518,519,521,523,524,526,527,529,530,531,532,533,534,536,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,561,562,563,564,567,569,570,572,575,578,579,580,581,583,584,585,586,587,590,591,593,594,595,596,597,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,619,620,621,622,623,624,625,627,628,629,631,633,634,636,638,639,643,645,646,647,648,649,651,652,654,655,657,658,661,662,663,664,665,666,668,672,673,674,675,681,683,684,686,687,688,690,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,719,720,722,723,724,725,726,727,730,731,732,736,738,739,742,745,747,748,751,753,754,756,758,760,762,763,764,766,768,769,770,772,773,774,776,778,780,782,783,784,786,788,789,791,792,795,796,798,799,801,802,804,806,807,808,810,811,812,813,814,818,819,820,821,823,826,828,830,831,833,834,835,836,839,840,841,842,845,847,849,851,852,856,858,861,866,868,869,870,871,872,873,874,875,876,877,878,879,881,883,886,887,888,890,891,893,894,895,896,897,898,899,901,902,903,906,908,909,910,911,912,914,915,917,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,941,942,943,945,947,948,950,951,954,955,956,958,959,960,961,962,963,964,966,967,968,970,971,972,975,976,977,979,980,982,983,986,987,988,993,994,995,996,997,998,999,1001,1004,1006,1007,1009,1010,1013,1014,1015,1016,1017,1018,1019,1020,1022,1023 };
const uint16_t g_unique_to_seed_6x6_p2[] = { 1,2,3,4,5,7,8,9,10,11,14,15,16,17,18,19,21,23,24,25,26,27,28,29,31,33,36,37,39,42,43,44,45,46,47,48,49,50,51,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,83,86,87,88,89,90,91,94,95,98,99,100,101,103,107,108,109,110,112,114,115,116,119,121,122,125,128,129,130,131,132,134,135,136,137,138,139,142,144,146,147,148,149,151,153,154,156,158,159,167,168,169,170,171,172,174,175,177,178,181,183,190,191,193,194,195,196,198,199,203,206,207,210,211,213,214,215,216,217,218,220,222,223,225,226,227,229,230,231,232,235,236,237,240,247,249,250,252,254,255,257,258,260,262,264,266,267,270,271,272,273,277,278,279,281,283,284,286,289,291,292,293,295,298,299,302,303,305,306,307,309,314,316,318,319,323,324,326,327,329,335,339,341,343,347,348,351,352,353,354,355,361,362,363,366,367,368,370,373,374,376,380,386,387,388,389,390,392,393,394,395,402,403,404,407,409,411,414,415,418,419,422,423,426,430,432,433,436,437,438,439,440,441,445,447,450,452,453,455,458,461,463,470,471,474,475,476,478,480,482,486,487,488,490,495,496,498,499,500,504,506,508,510,513,517,518,519,521,523,524,526,527,529,530,531,533,534,538,539,543,545,546,547,549,550,551,553,554,558,562,567,569,572,578,581,583,585,586,587,591,593,594,595,596,598,600,601,602,606,607,608,610,611,612,614,615,616,619,621,622,623,625,627,631,633,634,638,639,643,645,646,647,648,649,652,655,658,661,662,663,664,665,670,672,673,674,675,681,683,684,685,686,687,688,690,691,693,694,695,696,697,700,702,703,705,713,714,716,719,720,722,724,726,727,730,731,732,736,740,742,751,753,754,756,758,760,762,763,764,766,769,770,774,778,780,786,789,791,794,797,798,799,801,802,804,805,807,808,810,811,812,817,819,821,822,826,828,831,834,835,836,839,842,847,852,854,858,862,868,869,870,872,874,876,877,878,886,887,890,891,893,895,897,898,899,902,903,906,909,910,911,912,914,919,929,930,934,936,937,938,942,943,945,947,948,950,951,954,955,958,959,963,964,966,967,968,976,980,983,987,988,993,994,995,998,999,1001,1006,1007,1008,1009,1013,1014,1015,1016,1019,1022,1023 };
const uint16_t g_unique_to_seed_8x5_p2[] = { 1,2,3,4,5,7,8,9,10,11,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,36,37,39,42,43,45,46,47,48,49,50,51,53,54,55,56,58,59,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,86,87,88,89,90,91,94,95,98,99,100,101,103,107,108,109,110,112,114,115,116,119,121,122,123,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,146,147,148,149,150,151,154,156,158,159,165,167,168,169,170,171,172,174,175,177,178,181,183,184,191,193,194,195,196,198,199,203,204,206,207,209,210,211,213,214,215,216,217,218,220,222,225,226,227,229,230,231,232,235,236,237,240,247,248,249,250,252,253,254,255,257,258,260,261,262,264,266,267,270,271,272,273,277,278,279,281,284,286,287,289,291,292,293,295,296,298,299,300,302,303,304,305,306,307,309,314,316,317,318,319,323,324,325,326,327,329,330,335,337,339,341,342,343,344,347,348,351,352,353,354,355,359,361,362,363,366,367,368,370,371,374,375,376,380,381,386,387,388,389,390,391,392,393,394,395,399,402,403,404,405,407,409,410,411,412,415,418,419,422,423,424,426,430,432,433,436,437,438,439,440,441,444,445,446,447,450,451,452,453,454,455,458,461,462,463,465,470,471,473,474,475,476,478,479,482,484,486,487,488,490,491,495,496,498,499,500,501,502,504,505,506,508,510,511,513,517,518,519,521,523,524,526,527,530,531,533,534,535,538,539,543,545,546,547,550,551,554,558,559,562,567,569,572,578,579,581,583,585,586,587,591,593,594,595,598,600,601,602,606,607,608,610,611,612,614,615,618,619,621,622,623,625,627,631,633,636,638,639,643,645,646,647,648,649,650,651,652,655,658,659,661,662,663,664,665,666,668,672,673,674,675,683,684,685,686,687,688,690,691,692,693,694,695,696,697,700,701,702,703,705,707,711,713,716,719,720,722,724,725,726,727,730,731,732,736,739,740,742,748,751,753,754,756,758,760,762,763,764,766,768,770,774,775,778,780,786,789,791,794,796,798,799,801,802,804,805,807,808,810,811,812,813,817,819,821,825,826,831,834,836,839,841,842,845,847,849,851,852,854,856,862,868,869,870,871,872,874,876,877,879,881,886,887,890,891,893,895,897,898,899,902,903,906,909,910,911,914,915,918,919,921,923,924,927,929,930,934,936,937,938,942,943,945,947,948,951,954,955,958,959,962,963,964,966,967,968,970,971,976,977,979,983,987,988,989,993,994,995,997,998,999,1001,1006,1007,1008,1009,1013,1015,1016,1018,1019,1022,1023 };
const uint16_t g_unique_to_seed_8x6_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,36,37,39,42,43,44,45,46,47,48,49,50,51,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,86,87,88,89,90,91,94,95,98,99,100,101,103,107,108,109,110,112,113,114,115,116,119,121,122,123,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,146,147,148,149,150,151,153,154,156,158,159,165,167,168,169,170,171,172,174,175,177,178,181,183,184,190,191,193,194,195,196,198,199,200,203,204,206,207,208,209,210,211,213,214,215,216,217,218,220,222,223,225,226,227,229,230,231,232,235,236,237,240,245,246,247,248,249,250,252,253,254,255,257,258,260,261,262,264,266,267,270,271,272,273,277,278,279,281,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,314,316,317,318,319,323,324,325,326,327,329,330,335,337,339,341,342,343,344,347,348,349,350,351,352,353,354,355,359,361,362,363,365,366,367,368,370,371,373,374,375,376,380,381,386,387,388,389,390,391,392,393,394,395,399,402,403,404,405,407,409,410,411,412,414,415,418,419,422,423,424,426,430,432,433,436,437,438,439,440,441,443,444,445,446,447,450,451,452,453,454,455,458,461,462,463,465,470,471,473,474,475,476,478,479,480,482,484,486,487,488,489,490,491,495,496,498,499,500,501,502,504,505,506,508,510,511,513,517,518,519,521,523,524,526,527,529,530,531,533,534,535,538,539,543,545,546,547,549,550,551,553,554,558,559,562,567,569,572,575,578,579,581,583,585,586,587,591,593,594,595,596,598,600,601,602,606,607,608,610,611,612,614,615,616,618,619,621,622,623,625,627,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,655,658,659,661,662,663,664,665,666,668,670,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,700,701,702,703,705,707,711,713,714,716,719,720,722,724,725,726,727,730,731,732,736,739,740,742,748,751,753,754,756,758,760,762,763,764,766,768,769,770,773,774,775,776,778,780,786,789,791,792,794,796,797,798,799,801,802,804,805,807,808,810,811,812,813,817,818,819,821,822,825,826,828,830,831,833,834,835,836,839,841,842,845,847,849,851,852,854,856,858,861,862,868,869,870,871,872,873,874,876,877,878,879,881,886,887,888,890,891,893,895,897,898,899,902,903,906,909,910,911,912,914,915,918,919,921,923,924,927,929,930,933,934,935,936,937,938,940,942,943,945,947,948,950,951,954,955,958,959,962,963,964,966,967,968,970,971,976,977,979,980,983,986,987,988,989,993,994,995,997,998,999,1001,1006,1007,1008,1009,1013,1014,1015,1016,1018,1019,1021,1022,1023 };
const uint16_t g_unique_to_seed_10x5_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,84,85,86,87,88,89,90,91,94,95,97,98,99,100,101,103,107,108,109,110,112,113,114,115,116,119,121,122,123,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,153,154,155,156,157,158,159,165,167,168,169,170,171,172,174,175,177,178,181,183,184,185,188,191,193,194,195,196,198,199,200,203,204,206,207,208,209,210,211,213,214,215,216,217,218,219,220,222,223,225,226,227,229,230,231,232,235,236,237,238,239,240,247,248,249,250,252,253,254,255,257,258,260,261,262,263,264,265,266,267,270,271,272,273,275,277,278,279,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,314,316,317,318,319,323,324,325,326,327,329,330,332,335,337,339,341,342,343,344,347,348,349,350,351,352,353,354,355,358,359,361,362,363,365,366,367,368,370,371,374,375,376,380,381,386,387,388,389,390,391,392,393,394,395,399,402,403,404,405,407,409,410,411,412,415,418,419,422,423,424,426,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,458,461,462,463,465,470,471,473,474,475,476,478,479,481,482,484,486,487,488,489,490,491,492,495,496,498,499,500,501,502,503,504,505,506,508,510,511,513,517,518,519,521,523,524,526,527,529,530,531,533,534,535,538,539,542,543,545,546,547,548,550,551,554,558,559,562,567,569,570,571,572,575,578,579,580,581,583,585,586,587,591,593,594,595,597,598,600,601,602,606,607,608,609,610,611,612,614,615,616,617,618,619,621,622,623,624,625,627,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,655,657,658,659,661,662,663,664,665,666,668,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,711,713,716,719,720,722,723,724,725,726,727,730,731,732,736,739,740,742,748,751,753,754,755,756,757,758,760,762,763,764,766,768,770,773,774,775,776,778,780,786,789,791,794,795,796,798,799,801,802,804,805,807,808,810,811,812,813,814,817,818,819,821,822,823,825,826,828,830,831,834,835,836,839,841,842,845,847,849,851,852,854,856,862,868,869,870,871,872,873,874,876,877,878,879,881,883,886,887,888,890,891,893,895,897,898,899,901,902,903,906,909,910,911,914,915,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,941,942,943,945,947,948,950,951,954,955,956,958,959,961,962,963,964,966,967,968,969,970,971,975,976,977,979,980,983,986,987,988,989,993,994,995,996,997,998,999,1001,1006,1007,1008,1009,1013,1014,1015,1016,1017,1018,1019,1020,1022,1023 };
const uint16_t g_unique_to_seed_10x6_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,84,85,86,87,88,89,90,91,94,95,97,98,99,100,101,103,107,108,109,110,112,113,114,115,116,119,121,122,123,124,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,153,154,155,156,157,158,159,165,167,168,169,170,171,172,174,175,177,178,181,183,184,185,188,190,191,193,194,195,196,198,199,200,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,225,226,227,229,230,231,232,235,236,237,238,239,240,245,246,247,248,249,250,252,253,254,255,257,258,260,261,262,263,264,265,266,267,270,271,272,273,274,275,277,278,279,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,314,316,317,318,319,323,324,325,326,327,329,330,332,335,337,338,339,341,342,343,344,347,348,349,350,351,352,353,354,355,358,359,361,362,363,365,366,367,368,370,371,373,374,375,376,380,381,386,387,388,389,390,391,392,393,394,395,399,402,403,404,405,407,409,410,411,412,414,415,418,419,422,423,424,426,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,458,461,462,463,465,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,492,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,516,517,518,519,521,523,524,526,527,529,530,531,533,534,535,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,562,567,569,570,571,572,575,578,579,580,581,583,585,586,587,590,591,593,594,595,596,597,598,600,601,602,606,607,608,609,610,611,612,614,615,616,617,618,619,621,622,623,624,625,627,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,655,657,658,659,661,662,663,664,665,666,668,670,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,719,720,722,723,724,725,726,727,730,731,732,736,739,740,742,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,772,773,774,775,776,778,780,782,783,786,788,789,791,792,794,795,796,797,798,799,801,802,804,805,807,808,810,811,812,813,814,817,818,819,821,822,823,825,826,828,830,831,833,834,835,836,839,841,842,845,847,849,851,852,854,856,858,861,862,868,869,870,871,872,873,874,876,877,878,879,881,883,886,887,888,890,891,893,895,897,898,899,901,902,903,906,908,909,910,911,912,914,915,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,940,941,942,943,945,947,948,949,950,951,954,955,956,958,959,961,962,963,964,966,967,968,969,970,971,975,976,977,979,980,983,986,987,988,989,993,994,995,996,997,998,999,1001,1004,1006,1007,1008,1009,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_8x8_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,36,37,39,42,43,44,45,46,47,48,49,50,51,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,86,87,88,89,90,91,94,95,97,98,99,100,101,102,103,107,108,109,110,111,112,113,114,115,116,118,119,120,121,122,123,124,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,146,147,148,149,150,151,152,153,154,155,156,158,159,161,165,167,168,169,170,171,172,174,175,177,178,181,182,183,184,188,190,191,193,194,195,196,198,199,200,201,203,204,206,207,208,209,210,211,213,214,215,216,217,218,220,222,223,224,225,226,227,229,230,231,232,235,236,237,239,240,242,245,246,247,248,249,250,252,253,254,255,257,258,260,261,262,264,265,266,267,270,271,272,273,276,277,278,279,280,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,314,316,317,318,319,323,324,325,326,327,329,330,331,332,333,335,337,338,339,341,342,343,344,347,348,349,350,351,352,353,354,355,359,361,362,363,365,366,367,368,370,371,373,374,375,376,380,381,386,387,388,389,390,391,392,393,394,395,399,400,402,403,404,405,407,409,410,411,412,414,415,418,419,420,422,423,424,426,430,432,433,436,437,438,439,440,441,443,444,445,446,447,450,451,452,453,454,455,458,461,462,463,465,466,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,495,496,498,499,500,501,502,503,504,505,506,508,510,511,513,516,517,518,519,521,523,524,526,527,529,530,531,533,534,535,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,562,563,567,569,572,575,578,579,580,581,583,585,586,587,590,591,593,594,595,596,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,618,619,620,621,622,623,625,627,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,655,658,659,661,662,663,664,665,666,668,670,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,700,701,702,703,705,707,709,711,713,714,716,719,720,722,724,725,726,727,730,731,732,736,739,740,742,743,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,772,773,774,775,776,778,780,782,783,786,789,791,792,793,794,796,797,798,799,801,802,804,805,806,807,808,810,811,812,813,814,817,818,819,821,822,825,826,828,830,831,833,834,835,836,839,840,841,842,845,847,849,851,852,854,856,858,861,862,866,868,869,870,871,872,873,874,876,877,878,879,881,886,887,888,890,891,893,894,895,897,898,899,901,902,903,906,908,909,910,911,912,914,915,916,917,918,919,921,923,924,927,929,930,933,934,935,936,937,938,940,942,943,945,947,948,949,950,951,954,955,956,958,959,962,963,964,966,967,968,969,970,971,975,976,977,979,980,983,986,987,988,989,993,994,995,997,998,999,1001,1006,1007,1008,1009,1010,1013,1014,1015,1016,1018,1019,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_10x8_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,83,84,85,86,87,88,89,90,91,92,94,95,97,98,99,100,101,102,103,105,107,108,109,110,111,112,113,114,115,116,118,119,120,121,122,123,124,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,177,178,179,180,181,182,183,184,185,188,190,191,193,194,195,196,198,199,200,201,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,229,230,231,232,235,236,237,238,239,240,242,245,246,247,248,249,250,252,253,254,255,257,258,260,261,262,263,264,265,266,267,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,314,316,317,318,319,321,323,324,325,326,327,329,330,331,332,333,335,337,338,339,341,342,343,344,347,348,349,350,351,352,353,354,355,358,359,361,362,363,365,366,367,368,370,371,373,374,375,376,378,380,381,385,386,387,388,389,390,391,392,393,394,395,399,400,402,403,404,405,407,409,410,411,412,414,415,418,419,420,422,423,424,426,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,458,461,462,463,465,466,469,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,492,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,516,517,518,519,520,521,523,524,526,527,529,530,531,533,534,535,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,562,563,567,569,570,571,572,575,578,579,580,581,583,584,585,586,587,590,591,593,594,595,596,597,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,618,619,620,621,622,623,624,625,627,628,629,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,655,657,658,659,661,662,663,664,665,666,668,670,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,719,720,722,723,724,725,726,727,730,731,732,736,739,740,742,743,745,747,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,772,773,774,775,776,778,780,781,782,783,786,788,789,791,792,793,794,795,796,797,798,799,801,802,804,805,806,807,808,810,811,812,813,814,817,818,819,821,822,823,825,826,828,830,831,833,834,835,836,839,840,841,842,845,847,849,851,852,854,856,858,861,862,866,868,869,870,871,872,873,874,876,877,878,879,880,881,883,886,887,888,890,891,893,894,895,897,898,899,901,902,903,906,908,909,910,911,912,914,915,916,917,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,940,941,942,943,945,947,948,949,950,951,954,955,956,958,959,960,961,962,963,964,966,967,968,969,970,971,975,976,977,979,980,982,983,986,987,988,989,993,994,995,996,997,998,999,1001,1004,1006,1007,1008,1009,1010,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_10x10_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83,84,85,86,87,88,89,90,91,92,94,95,97,98,99,100,101,102,103,105,107,108,109,110,111,112,113,114,115,116,118,119,120,121,122,123,124,125,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,176,177,178,179,180,181,182,183,184,185,188,190,191,193,194,195,196,198,199,200,201,202,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,229,230,231,232,235,236,237,238,239,240,242,245,246,247,248,249,250,252,253,254,255,256,257,258,260,261,262,263,264,265,266,267,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,313,314,316,317,318,319,321,323,324,325,326,327,329,330,331,332,333,335,337,338,339,341,342,343,344,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,365,366,367,368,370,371,373,374,375,376,377,378,380,381,385,386,387,388,389,390,391,392,393,394,395,399,400,402,403,404,405,407,409,410,411,412,414,415,417,418,419,420,421,422,423,424,425,426,427,428,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,458,459,461,462,463,465,466,469,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,492,493,494,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,514,516,517,518,519,520,521,522,523,524,526,527,528,529,530,531,532,533,534,535,536,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,561,562,563,566,567,569,570,571,572,575,578,579,580,581,583,584,585,586,587,590,591,593,594,595,596,597,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,618,619,620,621,622,623,624,625,627,628,629,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,654,655,657,658,659,661,662,663,664,665,666,667,668,670,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,719,720,722,723,724,725,726,727,730,731,732,736,738,739,740,742,743,745,747,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,771,772,773,774,775,776,778,780,781,782,783,784,786,788,789,791,792,793,794,795,796,797,798,799,801,802,803,804,805,806,807,808,810,811,812,813,814,817,818,819,820,821,822,823,825,826,828,829,830,831,833,834,835,836,839,840,841,842,845,846,847,848,849,851,852,854,855,856,858,861,862,866,867,868,869,870,871,872,873,874,876,877,878,879,880,881,883,886,887,888,890,891,893,894,895,896,897,898,899,901,902,903,904,906,908,909,910,911,912,914,915,916,917,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,940,941,942,943,945,947,948,949,950,951,954,955,956,958,959,960,961,962,963,964,966,967,968,969,970,971,972,975,976,977,979,980,982,983,986,987,988,989,993,994,995,996,997,998,999,1001,1004,1006,1007,1008,1009,1010,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_12x10_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,94,95,97,98,99,100,101,102,103,104,105,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,176,177,178,179,180,181,182,183,184,185,188,190,191,193,194,195,196,198,199,200,201,202,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,229,230,231,232,235,236,237,238,239,240,242,243,244,245,246,247,248,249,250,252,253,254,255,256,257,258,260,261,262,263,264,265,266,267,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,286,287,289,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,313,314,316,317,318,319,321,323,324,325,326,327,329,330,331,332,333,335,337,338,339,341,342,343,344,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,365,366,367,368,370,371,373,374,375,376,377,378,380,381,383,385,386,387,388,389,390,391,392,393,394,395,399,400,402,403,404,405,407,409,410,411,412,414,415,417,418,419,420,421,422,423,424,425,426,427,428,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,458,459,461,462,463,465,466,469,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,492,493,494,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,514,515,516,517,518,519,520,521,522,523,524,526,527,528,529,530,531,532,533,534,535,536,537,538,539,542,543,545,546,547,548,549,550,551,553,554,558,559,561,562,563,564,566,567,569,570,571,572,575,578,579,580,581,583,584,585,586,587,589,590,591,593,594,595,596,597,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,618,619,620,621,622,623,624,625,627,628,629,631,633,634,636,638,639,643,645,646,647,648,649,650,651,652,654,655,657,658,659,661,662,663,664,665,666,667,668,670,671,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,719,720,722,723,724,725,726,727,730,731,732,736,738,739,740,742,743,745,747,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,771,772,773,774,775,776,778,780,781,782,783,784,785,786,787,788,789,791,792,793,794,795,796,797,798,799,801,802,803,804,805,806,807,808,810,811,812,813,814,817,818,819,820,821,822,823,825,826,828,829,830,831,833,834,835,836,839,840,841,842,845,846,847,848,849,851,852,854,855,856,857,858,861,862,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,883,886,887,888,890,891,893,894,895,896,897,898,899,901,902,903,904,906,908,909,910,911,912,913,914,915,916,917,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,940,941,942,943,944,945,947,948,949,950,951,954,955,956,958,959,960,961,962,963,964,966,967,968,969,970,971,972,975,976,977,979,980,982,983,986,987,988,989,993,994,995,996,997,998,999,1001,1004,1006,1007,1008,1009,1010,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_12x12_p2[] = { 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,36,37,39,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,94,95,97,98,99,100,101,102,103,104,105,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,128,129,130,131,132,134,135,136,137,138,139,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,161,165,167,168,169,170,171,172,174,175,176,177,178,179,180,181,182,183,184,185,186,188,190,191,193,194,195,196,198,199,200,201,202,203,204,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,229,230,231,232,235,236,237,238,239,240,242,243,244,245,246,247,248,249,250,252,253,254,255,256,257,258,260,261,262,263,264,265,266,267,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,286,287,289,290,291,292,293,294,295,296,298,299,300,302,303,304,305,306,307,309,310,313,314,316,317,318,319,321,323,324,325,326,327,329,330,331,332,333,335,337,338,339,340,341,342,343,344,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,365,366,367,368,370,371,373,374,375,376,377,378,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,399,400,402,403,404,405,407,409,410,411,412,414,415,417,418,419,420,421,422,423,424,425,426,427,428,429,430,432,433,436,437,438,439,440,441,443,444,445,446,447,449,450,451,452,453,454,455,456,458,459,461,462,463,465,466,469,470,471,473,474,475,476,478,479,480,481,482,484,486,487,488,489,490,491,492,493,494,495,496,498,499,500,501,502,503,504,505,506,508,509,510,511,513,514,515,516,517,518,519,520,521,522,523,524,526,527,528,529,530,531,532,533,534,535,536,537,538,539,542,543,545,546,547,548,549,550,551,553,554,557,558,559,561,562,563,564,566,567,569,570,571,572,575,576,578,579,580,581,583,584,585,586,587,589,590,591,593,594,595,596,597,598,599,600,601,602,605,606,607,608,609,610,611,612,614,615,616,617,618,619,620,621,622,623,624,625,627,628,629,631,633,634,636,638,639,640,643,644,645,646,647,648,649,650,651,652,654,655,657,658,659,660,661,662,663,664,665,666,667,668,670,671,672,673,674,675,681,683,684,685,686,687,688,690,691,692,693,694,695,696,697,699,700,701,702,703,705,706,707,709,711,713,714,716,717,719,720,721,722,723,724,725,726,727,730,731,732,736,738,739,740,742,743,745,747,748,751,753,754,755,756,757,758,760,762,763,764,766,768,769,770,771,772,773,774,775,776,778,780,781,782,783,784,785,786,787,788,789,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,810,811,812,813,814,815,817,818,819,820,821,822,823,825,826,828,829,830,831,833,834,835,836,837,839,840,841,842,844,845,846,847,848,849,851,852,854,855,856,857,858,861,862,863,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,883,886,887,888,890,891,893,894,895,896,897,898,899,901,902,903,904,906,908,909,910,911,912,913,914,915,916,917,918,919,920,921,923,924,927,929,930,932,933,934,935,936,937,938,940,941,942,943,944,945,947,948,949,950,951,954,955,956,958,959,960,961,962,963,964,966,967,968,969,970,971,972,975,976,977,979,980,982,983,986,987,988,989,993,994,995,996,997,998,999,1001,1004,1006,1007,1008,1009,1010,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023 };

const uint16_t g_unique_to_seed_4x4_p3[] = { 0,3,8,11,14,15,17,26,29,30,31,32,33,36,38,43,44,47,49,51,55,56,57,59,67,70,74,76,79,81,82,88,89,90,100,104,108,110,111,117,122,126,127,132,133,134,135,139,147,150,151,152,156,157,163,166,167,168,171,175,176,179,181,182,183,186,189,192,199,203,205,207,210,214,216,230,236,247,249,250,252,254,260,262,263,266,272,273,276,291,292,294,297,302,309,310,313,314,318,319,324,327,328,330,331,335,337,346,355,356,357,358,363,365,368,378,381,384,386,388,390,391,392,397,398,401,410,411,417,419,427,431,437,439,440,446,451,455,457,458,459,460,462,464,467,468,471,472,474,475,477,479,483,487,488,493,495,496,497,502,503,504,511,512,516,518,519,523,525,530,532,538,543,544,546,547,549,550,551,553,554,562,567,568,570,571,578,579,581,582,588,589,590,593,594,600,601,606,611,613,623,624,625,630,637,638,645,646,648,650,651,658,659,662,666,669,670,678,683,686,688,691,694,696,699,700,701,703,704,707,713,715,717,719,722,724,725,727,730,731,735,738,739,745,750,751,758,759,760,766,775,776,779,783,784,785,786,787,788,798,799,802,804,805,807,808,809,812,821,822,823,825,827,831,835,837,838,842,844,845,846,848,853,854,858,859,860,866,884,888,892,894,898,902,906,907,915,918,922,923,925,927,931,932,937,938,940,943,945,953,955,958,959,963,971,974,977,979,989,990,998,1005,1006,1007,1011,1012,1015,1020,1023 };
const uint16_t g_unique_to_seed_5x4_p3[] = { 0,3,7,8,11,12,14,15,17,18,26,29,30,31,32,33,34,36,38,39,43,44,47,49,51,55,56,57,59,62,63,67,70,74,76,79,81,82,88,89,90,91,100,103,104,108,110,111,117,122,123,126,127,132,133,134,135,136,139,144,147,150,151,152,156,157,158,163,166,167,168,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,210,214,216,222,230,236,246,247,249,250,252,254,259,260,262,263,266,269,272,273,274,275,276,291,292,293,294,297,302,306,309,310,311,313,314,315,318,319,324,327,328,330,331,335,337,346,355,356,357,358,359,363,365,368,377,378,381,384,386,388,390,391,392,394,397,398,401,407,410,411,417,419,427,430,431,437,439,440,446,451,455,457,458,459,460,462,464,467,468,470,471,472,474,475,477,478,479,483,485,487,488,493,495,496,497,501,502,503,504,506,508,510,511,512,515,516,518,519,521,523,524,525,530,532,538,541,543,544,546,547,549,550,551,552,553,554,562,567,568,570,571,577,578,579,581,582,588,589,590,593,594,595,600,601,603,606,609,611,613,623,624,625,630,632,637,638,639,645,646,648,650,651,654,658,659,662,666,669,670,678,679,683,685,686,688,691,694,696,699,700,701,703,704,707,713,715,717,719,722,724,725,727,730,731,732,735,738,739,742,745,746,749,750,751,758,759,760,766,769,773,775,776,779,783,784,785,786,787,788,791,793,798,799,802,804,805,806,807,808,809,812,813,821,822,823,825,827,831,835,837,838,839,842,844,845,846,848,853,854,858,859,860,866,873,876,877,884,887,888,892,894,898,902,906,907,914,915,918,919,922,923,925,927,931,932,937,938,940,943,944,945,951,953,955,958,959,963,971,972,974,977,979,982,983,989,990,991,998,999,1005,1006,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_5x5_p3[] = { 0,3,7,8,10,11,12,14,15,17,18,26,27,29,30,31,32,33,34,36,38,39,43,44,47,48,49,50,51,55,56,57,59,60,61,62,63,67,70,72,74,76,79,81,82,88,89,90,91,94,100,103,104,106,108,110,111,115,117,122,123,126,127,128,130,132,133,134,135,136,139,144,147,150,151,152,156,157,158,162,163,166,167,168,169,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,209,210,214,216,220,222,227,230,235,236,246,247,249,250,252,254,257,259,260,262,263,266,269,272,273,274,275,276,279,282,291,292,293,294,295,297,302,306,309,310,311,313,314,315,318,319,324,326,327,328,330,331,335,337,342,345,346,353,355,356,357,358,359,363,364,365,368,371,374,377,378,381,384,386,387,388,390,391,392,394,397,398,399,401,407,410,411,417,419,427,430,431,437,438,439,440,443,446,451,455,456,457,458,459,460,462,463,464,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,501,502,503,504,506,508,510,511,512,515,516,518,519,521,522,523,524,525,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,555,562,567,568,570,571,577,578,579,581,582,586,588,589,590,593,594,595,600,601,602,603,606,609,610,611,613,618,623,624,625,626,630,632,637,638,639,645,646,648,650,651,654,658,659,662,666,667,668,669,670,671,678,679,683,685,686,687,688,691,694,696,698,699,700,701,703,704,707,708,713,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,745,746,747,748,749,750,751,753,758,759,760,764,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,791,793,794,798,799,800,802,804,805,806,807,808,809,811,812,813,821,822,823,825,827,831,835,837,838,839,840,842,843,844,845,846,847,848,850,852,853,854,858,859,860,866,869,873,874,876,877,881,884,886,887,888,892,894,897,898,902,905,906,907,914,915,918,919,920,922,923,925,927,931,932,937,938,940,943,944,945,951,953,954,955,958,959,963,971,972,973,974,977,978,979,982,983,989,990,991,992,998,999,1004,1005,1006,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_6x5_p3[] = { 0,3,7,8,10,11,12,14,15,17,18,21,23,26,27,29,30,31,32,33,34,35,36,38,39,42,43,44,47,48,49,50,51,55,56,57,59,60,61,62,63,67,70,72,74,76,79,81,82,88,89,90,91,94,100,102,103,104,106,108,110,111,114,115,117,120,122,123,126,127,128,130,132,133,134,135,136,139,140,144,147,150,151,152,153,156,157,158,162,163,166,167,168,169,171,173,175,176,179,181,182,183,186,189,192,198,199,200,203,205,207,209,210,214,216,220,222,227,230,231,235,236,245,246,247,249,250,252,254,257,259,260,262,263,266,269,272,273,274,275,276,279,281,282,288,291,292,293,294,295,297,300,302,306,309,310,311,313,314,315,318,319,324,326,327,328,330,331,335,337,342,345,346,348,353,355,356,357,358,359,363,364,365,368,371,372,374,377,378,379,381,384,386,387,388,390,391,392,394,395,397,398,399,401,407,410,411,412,413,417,419,427,430,431,437,438,439,440,443,446,450,451,455,456,457,458,459,460,461,462,463,464,465,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,500,501,502,503,504,505,506,508,510,511,512,513,515,516,518,519,521,522,523,524,525,527,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,555,557,558,562,566,567,568,570,571,577,578,579,580,581,582,584,586,588,589,590,593,594,595,600,601,602,603,606,609,610,611,613,614,618,623,624,625,626,630,632,637,638,639,644,645,646,648,650,651,654,658,659,662,666,667,668,669,670,671,678,679,683,685,686,687,688,689,691,694,696,698,699,700,701,703,704,707,708,711,713,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,746,747,748,749,750,751,753,758,759,760,764,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,791,793,794,798,799,800,802,804,805,806,807,808,809,810,811,812,813,821,822,823,824,825,827,831,835,836,837,838,839,840,841,842,843,844,845,846,847,848,850,852,853,854,858,859,860,866,869,873,874,876,877,881,884,886,887,888,892,894,897,898,900,902,905,906,907,914,915,918,919,920,922,923,925,927,931,932,937,938,940,943,944,945,951,953,954,955,957,958,959,963,967,971,972,973,974,977,978,979,982,983,986,989,990,991,992,998,999,1003,1004,1005,1006,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_6x6_p3[] = { 0,8,11,14,15,17,18,19,26,31,34,35,36,38,44,47,48,49,51,56,59,61,70,74,76,82,88,90,96,100,103,104,108,110,111,117,122,123,126,127,132,133,135,139,147,150,151,152,156,157,163,166,168,171,175,176,179,181,182,183,186,189,192,199,203,205,207,210,214,216,222,247,249,250,252,254,260,261,262,263,266,272,273,275,276,288,291,292,293,294,297,302,309,310,313,314,318,327,328,331,335,337,346,356,357,358,363,365,368,378,381,384,386,390,391,392,396,397,398,399,401,410,411,419,427,430,431,437,439,440,451,455,457,458,459,460,462,468,470,471,472,474,475,477,479,482,483,488,493,495,496,502,503,504,507,510,511,512,515,516,518,519,522,523,525,526,527,538,543,544,546,547,549,550,552,553,554,562,570,578,579,581,582,588,589,590,593,595,600,606,611,613,618,623,625,632,637,638,645,646,650,651,658,659,662,666,667,669,670,678,679,685,686,687,688,691,694,696,698,699,700,701,703,704,707,713,714,715,717,719,722,724,727,730,731,734,738,739,743,747,748,750,751,753,758,760,764,766,769,775,776,783,784,785,787,791,793,798,799,802,804,805,806,807,808,809,810,813,822,823,825,831,835,837,838,839,840,842,845,846,848,853,854,858,859,860,866,874,882,884,887,888,892,894,898,902,907,914,915,918,919,922,923,925,927,931,932,937,938,940,943,944,945,953,955,958,959,963,966,971,974,979,990,991,998,999,1007,1010,1011,1012,1015,1020,1023 };
const uint16_t g_unique_to_seed_8x5_p3[] = { 0,3,8,11,14,15,17,18,19,23,26,27,29,31,33,34,35,36,38,43,44,47,48,49,51,55,56,59,61,67,70,76,79,81,82,88,89,90,96,100,103,104,108,110,111,117,122,123,126,127,132,133,134,135,139,147,150,151,152,156,157,163,166,167,168,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,210,214,216,227,230,247,249,250,254,260,261,262,263,266,272,273,275,276,279,288,291,292,293,294,297,302,307,309,310,313,314,315,318,319,327,328,331,335,337,346,355,356,357,358,359,363,365,377,378,381,384,386,390,391,392,394,396,397,398,399,401,407,410,411,419,424,427,430,431,437,439,440,450,451,455,457,458,459,460,462,464,467,468,470,471,472,474,475,477,478,479,482,483,487,488,493,495,496,502,503,504,507,508,511,512,515,516,518,519,522,523,524,526,527,538,543,544,547,549,550,552,553,554,557,562,568,570,578,579,581,582,588,589,590,593,595,600,602,603,606,609,611,613,614,624,625,632,637,638,639,645,646,650,651,658,659,662,666,667,669,670,678,679,685,686,687,688,689,691,694,696,699,700,701,703,704,707,712,713,715,717,719,722,724,727,730,731,734,738,739,743,745,747,750,751,758,759,760,763,764,766,769,771,775,776,779,781,783,784,785,787,791,793,798,799,802,804,805,806,807,809,810,812,813,822,823,825,831,835,837,838,840,842,844,845,846,848,853,854,858,859,860,866,873,876,882,884,887,888,892,894,895,898,902,906,907,914,915,918,919,922,923,925,927,931,932,937,938,940,943,944,945,947,951,953,955,958,959,963,966,971,974,977,979,983,989,990,991,998,999,1005,1007,1010,1011,1012,1015,1023 };
const uint16_t g_unique_to_seed_8x6_p3[] = { 0,3,8,11,14,15,17,18,19,23,26,27,29,31,33,34,35,36,38,43,44,47,48,49,51,55,56,59,61,67,70,74,76,79,81,82,88,89,90,96,100,103,104,108,110,111,117,122,123,126,127,131,132,133,134,135,139,147,150,151,152,156,157,163,166,167,168,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,210,214,216,222,227,230,236,247,249,250,252,254,260,261,262,263,266,272,273,275,276,279,288,291,292,293,294,297,302,307,309,310,313,314,315,318,319,324,327,328,331,335,337,338,346,355,356,357,358,359,363,365,368,377,378,381,384,386,390,391,392,394,396,397,398,399,401,407,410,411,419,424,427,430,431,437,439,440,450,451,455,457,458,459,460,462,464,467,468,470,471,472,474,475,477,478,479,482,483,485,487,488,493,495,496,502,503,504,507,508,510,511,512,515,516,518,519,522,523,524,525,526,527,538,541,543,544,546,547,549,550,552,553,554,557,562,566,567,568,570,578,579,581,582,588,589,590,593,595,600,601,602,603,606,609,611,613,614,618,623,624,625,632,637,638,639,645,646,650,651,658,659,662,666,667,669,670,678,679,685,686,687,688,689,691,694,696,698,699,700,701,703,704,707,708,712,713,714,715,717,719,722,724,725,727,730,731,732,734,738,739,743,745,747,748,750,751,753,758,759,760,763,764,766,769,771,775,776,779,781,783,784,785,786,787,791,793,798,799,802,804,805,806,807,808,809,810,812,813,822,823,825,831,835,837,838,839,840,842,844,845,846,848,850,853,854,858,859,860,866,873,874,876,882,884,887,888,892,894,895,898,900,902,906,907,914,915,918,919,922,923,925,927,931,932,937,938,940,943,944,945,947,951,953,955,958,959,963,966,971,974,977,979,983,989,990,991,998,999,1005,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_10x5_p3[] = { 0,3,7,8,11,14,15,17,18,19,23,26,27,29,31,33,34,35,36,38,43,44,47,48,49,51,55,56,59,61,62,67,70,72,76,79,81,82,88,89,90,91,95,96,100,103,104,108,110,111,114,117,122,123,126,127,131,132,133,134,135,139,140,147,150,151,152,156,157,158,163,166,167,168,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,210,213,214,216,227,230,245,247,249,250,254,259,260,261,262,263,266,269,272,273,274,275,276,279,281,288,291,292,293,294,295,297,302,307,309,310,313,314,315,318,319,327,328,331,335,337,346,355,356,357,358,359,363,365,377,378,381,384,386,390,391,392,394,396,397,398,399,401,407,410,411,412,413,419,424,427,430,431,437,439,440,450,451,455,457,458,459,460,462,464,467,468,470,471,472,474,475,477,478,479,482,483,487,488,493,495,496,500,501,502,503,504,506,507,508,510,511,512,515,516,518,519,521,522,523,524,526,527,530,538,541,543,544,547,549,550,552,553,554,555,557,562,565,568,570,577,578,579,581,582,588,589,590,593,595,600,601,602,603,606,609,611,613,614,618,624,625,632,637,638,639,645,646,650,651,654,658,659,662,666,667,669,670,678,679,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,712,713,715,717,719,722,724,725,727,730,731,732,734,738,739,742,743,745,747,749,750,751,758,759,760,763,764,765,766,769,771,773,775,776,779,781,783,784,785,786,787,791,793,798,799,802,804,805,806,807,809,810,812,813,821,822,823,825,827,831,835,836,837,838,839,840,841,842,844,845,846,848,853,854,858,859,860,866,869,873,876,877,882,884,887,888,891,892,894,895,898,900,902,905,906,907,909,914,915,918,919,922,923,925,927,931,932,937,938,939,940,943,944,945,947,951,953,954,955,957,958,959,961,963,966,967,971,974,975,977,978,979,983,989,990,991,993,998,999,1005,1007,1010,1011,1012,1015,1023 };
const uint16_t g_unique_to_seed_10x6_p3[] = { 0,3,7,8,11,12,14,15,17,18,19,23,26,27,29,31,33,34,35,36,38,43,44,47,48,49,51,55,56,59,61,62,67,70,72,74,76,79,81,82,88,89,90,91,95,96,100,103,104,108,110,111,114,117,122,123,126,127,131,132,133,134,135,139,140,147,150,151,152,156,157,158,163,166,167,168,171,173,175,176,179,181,182,183,186,189,192,199,203,205,207,210,213,214,216,222,227,230,236,245,246,247,249,250,252,254,259,260,261,262,263,266,269,272,273,274,275,276,279,281,288,291,292,293,294,295,297,302,306,307,309,310,311,313,314,315,318,319,324,327,328,330,331,335,337,338,346,355,356,357,358,359,363,364,365,368,377,378,381,384,386,390,391,392,394,396,397,398,399,401,407,410,411,412,413,419,424,427,430,431,437,439,440,450,451,455,457,458,459,460,462,464,467,468,470,471,472,474,475,477,478,479,482,483,485,487,488,493,495,496,500,501,502,503,504,506,507,508,510,511,512,515,516,518,519,521,522,523,524,525,526,527,530,538,539,541,543,544,546,547,549,550,552,553,554,555,557,562,565,566,567,568,570,577,578,579,581,582,588,589,590,593,595,600,601,602,603,606,609,611,613,614,618,623,624,625,632,637,638,639,645,646,648,650,651,654,658,659,662,666,667,669,670,678,679,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,708,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,747,748,749,750,751,753,758,759,760,763,764,765,766,769,771,773,775,776,779,781,783,784,785,786,787,791,793,798,799,802,804,805,806,807,808,809,810,812,813,821,822,823,825,827,831,835,836,837,838,839,840,841,842,844,845,846,848,850,853,854,858,859,860,866,869,873,874,876,877,882,884,887,888,891,892,894,895,898,900,902,905,906,907,909,914,915,918,919,922,923,925,927,931,932,937,938,939,940,943,944,945,947,951,953,954,955,957,958,959,961,963,966,967,971,974,975,977,978,979,982,983,989,990,991,993,998,999,1005,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_8x8_p3[] = { 0,3,7,8,11,12,14,15,17,18,19,23,26,27,29,30,31,32,33,34,35,36,38,39,43,44,47,48,49,50,51,55,56,57,59,60,61,63,67,70,72,74,76,79,81,82,88,89,90,96,100,103,104,106,108,110,111,117,122,123,126,127,131,132,133,134,135,136,139,144,147,150,151,152,156,157,158,163,166,167,168,171,173,175,176,178,179,181,182,183,186,189,192,199,203,205,207,210,214,216,222,227,230,235,236,246,247,249,250,252,254,260,261,262,263,266,269,272,273,275,276,279,288,291,292,293,294,295,297,302,306,307,309,310,311,313,314,315,318,319,324,327,328,330,331,335,337,338,342,345,346,355,356,357,358,359,363,365,368,371,377,378,381,384,386,388,390,391,392,394,396,397,398,399,401,407,410,411,417,419,424,427,430,431,437,439,440,446,450,451,455,457,458,459,460,462,464,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,502,503,504,507,508,510,511,512,515,516,518,519,521,522,523,524,525,526,527,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,557,562,566,567,568,570,571,577,578,579,581,582,586,588,589,590,592,593,594,595,600,601,602,603,606,609,610,611,613,614,618,623,624,625,630,632,637,638,639,645,646,648,650,651,658,659,662,666,667,669,670,671,678,679,683,685,686,687,688,689,691,694,696,698,699,700,701,703,704,707,708,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,743,745,746,747,748,750,751,753,758,759,760,763,764,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,791,793,794,798,799,802,804,805,806,807,808,809,810,811,812,813,821,822,823,825,827,831,835,837,838,839,840,842,844,845,846,847,848,850,852,853,854,858,859,860,866,873,874,876,877,882,884,886,887,888,892,894,895,897,898,900,902,906,907,914,915,918,919,920,922,923,925,927,931,932,937,938,940,943,944,945,947,951,953,954,955,958,959,963,966,971,972,974,977,979,982,983,989,990,991,998,999,1005,1006,1007,1010,1011,1012,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_10x8_p3[] = { 0,3,7,8,11,12,14,15,17,18,19,23,26,27,29,30,31,32,33,34,35,36,38,39,43,44,47,48,49,50,51,55,56,57,59,60,61,62,63,67,70,72,74,76,79,81,82,88,89,90,91,94,95,96,100,103,104,106,108,110,111,114,115,117,122,123,126,127,131,132,133,134,135,136,139,140,144,147,150,151,152,153,156,157,158,163,166,167,168,171,173,175,176,178,179,181,182,183,186,189,192,198,199,203,205,207,210,213,214,216,220,222,227,230,235,236,245,246,247,249,250,252,254,259,260,261,262,263,266,269,272,273,274,275,276,279,281,288,291,292,293,294,295,297,302,306,307,309,310,311,313,314,315,318,319,324,327,328,330,331,335,337,338,342,345,346,355,356,357,358,359,363,364,365,368,371,374,377,378,379,381,384,386,387,388,390,391,392,394,395,396,397,398,399,401,407,410,411,412,413,417,419,424,427,430,431,437,438,439,440,443,446,450,451,455,457,458,459,460,462,464,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,500,501,502,503,504,505,506,507,508,510,511,512,515,516,518,519,521,522,523,524,525,526,527,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,555,557,562,565,566,567,568,570,571,577,578,579,581,582,586,588,589,590,592,593,594,595,600,601,602,603,606,609,610,611,613,614,618,623,624,625,630,632,637,638,639,644,645,646,648,650,651,654,658,659,662,666,667,669,670,671,678,679,683,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,708,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,746,747,748,749,750,751,753,758,759,760,763,764,765,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,791,793,794,798,799,800,802,804,805,806,807,808,809,810,811,812,813,821,822,823,825,827,831,835,836,837,838,839,840,841,842,844,845,846,847,848,850,852,853,854,858,859,860,866,869,873,874,876,877,882,884,886,887,888,891,892,894,895,897,898,900,902,905,906,907,909,914,915,918,919,920,922,923,925,927,931,932,937,938,939,940,943,944,945,947,951,953,954,955,957,958,959,961,963,966,967,971,972,973,974,975,977,978,979,982,983,986,989,990,991,993,998,999,1005,1006,1007,1010,1011,1012,1015,1020,1022,1023};
const uint16_t g_unique_to_seed_10x10_p3[] = { 0,3,7,8,10,11,12,14,15,17,18,19,23,26,27,29,30,31,32,33,34,35,36,38,39,40,43,44,47,48,49,50,51,55,56,57,59,60,61,62,63,67,70,72,74,75,76,79,81,82,88,89,90,91,94,95,96,100,103,104,106,108,110,111,114,115,117,120,122,123,126,127,128,130,131,132,133,134,135,136,139,140,144,147,150,151,152,153,156,157,158,162,163,166,167,168,169,171,173,175,176,178,179,181,182,183,186,189,192,198,199,200,203,205,207,209,210,213,214,216,218,220,222,227,230,235,236,238,242,245,246,247,249,250,252,254,257,259,260,261,262,263,266,269,272,273,274,275,276,279,281,282,288,291,292,293,294,295,297,302,306,307,308,309,310,311,313,314,315,318,319,324,326,327,328,330,331,335,337,338,342,345,346,347,350,353,355,356,357,358,359,363,364,365,368,371,372,374,377,378,379,381,384,386,387,388,390,391,392,394,395,396,397,398,399,401,407,408,410,411,412,413,417,419,424,427,430,431,435,437,438,439,440,443,446,450,451,455,456,457,458,459,460,462,463,464,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,500,501,502,503,504,505,506,507,508,510,511,512,513,515,516,518,519,521,522,523,524,525,526,527,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,555,557,562,565,566,567,568,570,571,577,578,579,580,581,582,586,588,589,590,592,593,594,595,600,601,602,603,606,609,610,611,613,614,618,623,624,625,626,630,632,634,637,638,639,644,645,646,648,650,651,654,658,659,662,666,667,668,669,670,671,678,679,683,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,708,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,746,747,748,749,750,751,753,758,759,760,763,764,765,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,789,790,791,793,794,798,799,800,802,804,805,806,807,808,809,810,811,812,813,821,822,823,825,827,831,835,836,837,838,839,840,841,842,843,844,845,846,847,848,850,852,853,854,858,859,860,866,869,873,874,876,877,881,882,884,886,887,888,891,892,894,895,897,898,900,902,905,906,907,909,914,915,918,919,920,922,923,925,927,931,932,937,938,939,940,943,944,945,947,951,952,953,954,955,957,958,959,961,963,966,967,971,972,973,974,975,977,978,979,980,982,983,986,989,990,991,992,993,998,999,1003,1004,1005,1006,1007,1010,1011,1012,1014,1015,1020,1022,1023 };
const uint16_t g_unique_to_seed_12x10_p3[] = { 0,3,7,8,10,11,12,14,15,16,17,18,19,21,23,26,27,29,30,31,32,33,34,35,36,38,39,40,42,43,44,45,47,48,49,50,51,55,56,57,59,60,61,62,63,67,70,72,74,75,76,79,81,82,88,89,90,91,94,95,96,100,102,103,104,106,108,110,111,114,115,117,120,122,123,126,127,128,129,130,131,132,133,134,135,136,139,140,144,147,150,151,152,153,156,157,158,161,162,163,166,167,168,169,171,173,175,176,178,179,181,182,183,185,186,189,192,195,198,199,200,203,205,207,209,210,213,214,216,218,220,222,227,230,231,235,236,238,242,245,246,247,249,250,251,252,254,257,259,260,261,262,263,266,269,272,273,274,275,276,279,281,282,283,288,291,292,293,294,295,297,300,302,306,307,308,309,310,311,313,314,315,318,319,324,326,327,328,330,331,335,337,338,342,345,346,347,348,350,353,355,356,357,358,359,363,364,365,368,371,372,374,377,378,379,381,384,386,387,388,390,391,392,394,395,396,397,398,399,401,407,408,410,411,412,413,415,417,419,424,427,430,431,435,437,438,439,440,443,446,450,451,455,456,457,458,459,460,461,462,463,464,465,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,500,501,502,503,504,505,506,507,508,510,511,512,513,515,516,518,519,521,522,523,524,525,526,527,530,532,538,539,541,543,544,546,547,549,550,551,552,553,554,555,557,558,562,563,565,566,567,568,570,571,577,578,579,580,581,582,584,586,588,589,590,592,593,594,595,600,601,602,603,604,606,609,610,611,613,614,618,623,624,625,626,630,632,634,637,638,639,643,644,645,646,648,650,651,654,658,659,662,666,667,668,669,670,671,673,678,679,683,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,708,711,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,746,747,748,749,750,751,753,758,759,760,763,764,765,766,767,769,771,773,775,776,779,780,781,783,784,785,786,787,788,789,790,791,793,794,798,799,800,802,804,805,806,807,808,809,810,811,812,813,821,822,823,824,825,827,828,831,835,836,837,838,839,840,841,842,843,844,845,846,847,848,850,852,853,854,858,859,860,866,869,873,874,876,877,881,882,884,886,887,888,891,892,894,895,897,898,900,902,905,906,907,909,914,915,918,919,920,922,923,925,927,931,932,937,938,939,940,943,944,945,947,951,952,953,954,955,957,958,959,961,963,966,967,971,972,973,974,975,977,978,979,980,982,983,986,989,990,991,992,993,995,998,999,1002,1003,1004,1005,1006,1007,1010,1011,1012,1014,1015,1020,1021,1022,1023 };
const uint16_t g_unique_to_seed_12x12_p3[] = { 0,3,4,7,8,10,11,12,14,15,16,17,18,19,21,23,26,27,29,30,31,32,33,34,35,36,38,39,40,42,43,44,45,47,48,49,50,51,53,55,56,57,58,59,60,61,62,63,67,70,72,74,75,76,79,81,82,83,88,89,90,91,94,95,96,100,102,103,104,106,108,110,111,114,115,117,120,122,123,126,127,128,129,130,131,132,133,134,135,136,138,139,140,144,147,150,151,152,153,156,157,158,159,160,161,162,163,166,167,168,169,171,173,175,176,177,178,179,181,182,183,185,186,189,192,195,196,198,199,200,203,205,207,208,209,210,213,214,216,218,220,222,227,230,231,235,236,238,242,245,246,247,249,250,251,252,254,257,259,260,261,262,263,266,269,272,273,274,275,276,279,281,282,283,288,291,292,293,294,295,297,300,302,306,307,308,309,310,311,313,314,315,318,319,324,326,327,328,330,331,335,337,338,342,345,346,347,348,350,353,355,356,357,358,359,363,364,365,368,371,372,374,377,378,379,381,384,386,387,388,390,391,392,394,395,396,397,398,399,401,407,408,410,411,412,413,415,417,419,424,426,427,430,431,432,435,437,438,439,440,443,444,446,450,451,455,456,457,458,459,460,461,462,463,464,465,466,467,468,470,471,472,474,475,477,478,479,480,482,483,485,487,488,493,495,496,497,500,501,502,503,504,505,506,507,508,510,511,512,513,515,516,518,519,521,522,523,524,525,526,527,530,532,535,538,539,540,541,543,544,546,547,549,550,551,552,553,554,555,557,558,562,563,565,566,567,568,569,570,571,577,578,579,580,581,582,584,586,588,589,590,592,593,594,595,600,601,602,603,604,606,609,610,611,613,614,618,623,624,625,626,628,630,631,632,634,636,637,638,639,640,643,644,645,646,648,650,651,654,658,659,662,666,667,668,669,670,671,673,678,679,683,685,686,687,688,689,691,694,695,696,698,699,700,701,703,704,707,708,711,712,713,714,715,717,719,722,724,725,727,730,731,732,734,735,738,739,742,743,745,746,747,748,749,750,751,753,758,759,760,763,764,765,766,767,768,769,771,773,774,775,776,778,779,780,781,783,784,785,786,787,788,789,790,791,793,794,798,799,800,802,804,805,806,807,808,809,810,811,812,813,821,822,823,824,825,827,828,831,835,836,837,838,839,840,841,842,843,844,845,846,847,848,850,852,853,854,858,859,860,863,866,869,873,874,876,877,881,882,884,886,887,888,891,892,894,895,897,898,900,902,905,906,907,909,911,912,914,915,918,919,920,922,923,925,927,929,930,931,932,937,938,939,940,943,944,945,947,951,952,953,954,955,957,958,959,961,963,966,967,971,972,973,974,975,977,978,979,980,982,983,986,989,990,991,992,993,995,998,999,1000,1002,1003,1004,1005,1006,1007,1010,1011,1012,1014,1015,1020,1021,1022,1023 };

The total number of 2 subset and 3 subset unique partition pattern indices, for each of the 14 ASTC block sizes:

const uint16_t g_total_unique_patterns[astc_helpers::NUM_ASTC_BLOCK_SIZES][2] =
{
	{ 437, 329 }, { 559, 405 }, { 659, 486 }, { 720, 534 },
	{ 521, 333 }, { 584, 377 }, { 640, 410 }, { 672, 436 },
	{ 710, 468 }, { 701, 476 }, { 759, 528 }, { 799, 568 },
	{ 818, 597 }, { 838, 626 }
};

Appendix 2: Encoded XUASTC LDR Configuration Table

The following "trial mode" table, needed by a XUASTC LDR transcoder, defines 10,311 "base" XUASTC LDR configurations. Each configuration is defined by a little endian 24-bit unsigned integer containing several bitfields. Each 24-bit integer is stored as 3 bytes in the byte table, one after the other with no padding or alignment. This table can be used for any of the XUASTC LDR block sizes, by ignoring any weight grid dimensions larger than the ASTC block size. The configurations in this table are sorted by the grid width.

Some configurations have base+offset variants (specifically CEM_LDR_RGB_DIRECT and CEM_LDR_RGBA_DIRECT), which aren't included in this table because they are trivially derived from the non-base-offset CEM variants. The total number of valid XUASTC LDR configurations at 12x12, once the base-offset variants are included, is 13,659. Smaller block sizes have lower total valid configurations.

Each configuration field is tightly bit packed into 24-bit value, in this order from LSB to MSB:

uint32_t CFG_PACK_EISE_BITS = 5; // LSB of 24-bit value, endpoint BISE range index minus 4, at bit 0
uint32_t CFG_PACK_WISE_BITS = 4; // weight BISE range index, at bit 5
uint32_t CFG_PACK_CCS_BITS = 3; // 0 for single plane, or 1+ for dual plane, at bit 9
uint32_t CFG_PACK_SUBSETS_BITS = 2; // number of subsets minus 1, at bit 12
uint32_t CFG_PACK_CEM_BITS = 3; // unique CEM index, see s_unique_ldr_index_to_astc_cem[] table below, at bit 14
uint32_t CFG_PACK_GRID_BITS = 7; // at MSB of 24-bit value, encoded weight grid res, at bit 17

To unpack each configuration, first read the little endian 24-bit integer value from the table, then extract each field one at a time starting at the LSB.

• The first field (at bit position 0) containing 5 bits is the endpoint ISE range index minus 4 (BISE_6_LEVELS, the lowest valid BISE endpoint range for endpoints). See the BISE range table in the UASTC HDR 4x4 Specification - Standard ASTC ISE Range Table Reference.

• The second field, at bit position 5, contains 4 bits and defines the weight ISE range index.

• The third field, at bit position 9, is 3 bits. If the value is 0, it's a single plane mode, otherwise it's a dual plane mode with a CCS (Color Component Selector) index of this field minus 1.

• The fourth field, at bit position 12, is 2 bits, defines the number of subsets minus one. XUASTC LDR only supports 1-3 subsets.

• The fifth field, at bit position 14, is 3 bits, defines the unique CEM index. The unique CEM indices can be converted to standard ASTC CEM indices using this table:

int s_unique_ldr_index_to_astc_cem[6] =
{
  0, // CEM_LDR_LUM_DIRECT
  4, // CEM_LDR_LUM_ALPHA_DIRECT
  6, // CEM_LDR_RGB_BASE_SCALE
  8, // CEM_LDR_RGB_DIRECT
  10, // CEM_LDR_RGB_BASE_SCALE_PLUS_TWO_A
  12 // CEM_LDR_RGBA_DIRECT
};

• The final sixth field, at bit position 17, defines the weight grid's weight and height as a single integer. The grid dimensions can be computed like this:

const uint32_t grid_width = (grid_wh / 11) + 2;
const uint32_t grid_height = (grid_wh % 11) + 2;

Here's the XUASTC LDR mode configuration table:

const uint32_t BU_TOTAL_ASTC_CFGS = 10311;
const uint8_t s_astc_cfg_table[BU_TOTAL_ASTC_CFGS*3] = {
176,72,0,208,72,0,240,72,0,16,73,0,48,73,0,80,73,0,112,73,0,176,130,0,208,130,0,240,130,0,16,131,0,48,131,0,80,131,0,112,131,0,176,132,0,208,132,0,
240,132,0,16,133,0,48,133,0,80,133,0,112,133,0,176,134,0,208,134,0,240,134,0,16,135,0,48,135,0,80,135,0,112,135,0,176,194,0,208,194,0,240,194,0,16,195,0,
48,195,0,80,195,0,112,195,0,176,196,0,208,196,0,240,196,0,16,197,0,48,197,0,80,197,0,112,197,0,176,198,0,208,198,0,240,198,0,16,199,0,48,199,0,80,199,0,
112,199,0,176,2,1,208,2,1,240,2,1,16,3,1,48,3,1,80,3,1,112,3,1,176,4,1,208,4,1,240,4,1,16,5,1,48,5,1,80,5,1,112,5,1,176,6,1,
208,6,1,240,6,1,16,7,1,48,7,1,80,7,1,112,7,1,176,8,1,208,8,1,240,8,1,16,9,1,48,9,1,80,9,1,112,9,1,176,66,1,208,66,1,240,66,1,
16,67,1,48,67,1,80,67,1,112,67,1,176,68,1,208,68,1,240,68,1,16,69,1,48,69,1,80,69,1,112,69,1,176,70,1,208,70,1,240,70,1,16,71,1,48,71,1,
80,71,1,112,71,1,176,72,1,208,72,1,240,72,1,16,73,1,48,73,1,80,73,1,112,73,1,16,1,2,48,1,2,80,1,2,112,1,2,16,17,2,48,17,2,80,17,2,
112,17,2,16,33,2,48,33,2,80,33,2,112,33,2,16,65,2,48,65,2,80,65,2,112,65,2,80,72,2,112,72,2,144,72,2,176,72,2,208,72,2,240,72,2,16,73,2,
48,73,2,80,73,2,112,73,2,16,81,2,48,81,2,80,81,2,112,81,2,10,97,2,42,97,2,73,97,2,105,97,2,16,129,2,48,129,2,80,129,2,112,129,2,80,130,2,
112,130,2,144,130,2,176,130,2,208,130,2,240,130,2,16,131,2,48,131,2,80,131,2,112,131,2,80,132,2,112,132,2,144,132,2,176,132,2,208,132,2,240,132,2,16,133,2,
48,133,2,80,133,2,112,133,2,80,134,2,112,134,2,144,134,2,176,134,2,208,134,2,240,134,2,16,135,2,48,135,2,80,135,2,112,135,2,16,145,2,48,145,2,80,145,2,
112,145,2,10,161,2,42,161,2,73,161,2,105,161,2,16,193,2,48,193,2,80,193,2,112,193,2,80,194,2,112,194,2,144,194,2,176,194,2,208,194,2,240,194,2,16,195,2,
48,195,2,80,195,2,112,195,2,80,196,2,112,196,2,144,196,2,176,196,2,208,196,2,240,196,2,16,197,2,48,197,2,80,197,2,112,197,2,80,198,2,112,198,2,144,198,2,
176,198,2,208,198,2,240,198,2,16,199,2,48,199,2,80,199,2,112,199,2,10,209,2,42,209,2,73,209,2,105,209,2,4,225,2,36,225,2,67,225,2,99,225,2,16,1,3,
48,1,3,80,1,3,112,1,3,80,2,3,112,2,3,144,2,3,176,2,3,208,2,3,240,2,3,16,3,3,48,3,3,80,3,3,112,3,3,80,4,3,112,4,3,144,4,3,
176,4,3,208,4,3,240,4,3,16,5,3,48,5,3,80,5,3,112,5,3,80,6,3,112,6,3,144,6,3,176,6,3,208,6,3,240,6,3,16,7,3,48,7,3,80,7,3,
112,7,3,80,8,3,112,8,3,144,8,3,176,8,3,208,8,3,240,8,3,16,9,3,48,9,3,80,9,3,112,9,3,10,17,3,42,17,3,73,17,3,105,17,3,4,33,3,
36,33,3,67,33,3,99,33,3,16,65,3,48,65,3,80,65,3,112,65,3,80,66,3,112,66,3,144,66,3,176,66,3,208,66,3,240,66,3,15,67,3,45,67,3,76,67,3,
106,67,3,80,68,3,112,68,3,144,68,3,176,68,3,208,68,3,240,68,3,15,69,3,45,69,3,76,69,3,106,69,3,80,70,3,112,70,3,144,70,3,176,70,3,208,70,3,
240,70,3,15,71,3,45,71,3,76,71,3,106,71,3,80,72,3,112,72,3,144,72,3,176,72,3,208,72,3,240,72,3,15,73,3,45,73,3,76,73,3,106,73,3,6,81,3,
37,81,3,69,81,3,100,81,3,176,0,4,208,0,4,240,0,4,16,1,4,48,1,4,80,1,4,112,1,4,176,16,4,208,16,4,240,16,4,16,17,4,48,17,4,80,17,4,
112,17,4,176,32,4,208,32,4,240,32,4,16,33,4,48,33,4,80,33,4,112,33,4,176,64,4,208,64,4,240,64,4,16,65,4,48,65,4,80,65,4,112,65,4,48,72,4,
80,72,4,112,72,4,144,72,4,176,72,4,208,72,4,240,72,4,16,73,4,48,73,4,80,73,4,109,73,4,176,80,4,208,80,4,240,80,4,16,81,4,48,81,4,79,81,4,
110,81,4,170,96,4,202,96,4,233,96,4,8,97,4,40,97,4,71,97,4,102,97,4,176,128,4,208,128,4,240,128,4,16,129,4,48,129,4,80,129,4,112,129,4,48,130,4,
80,130,4,112,130,4,144,130,4,176,130,4,208,130,4,240,130,4,16,131,4,48,131,4,80,131,4,109,131,4,48,132,4,80,132,4,112,132,4,144,132,4,176,132,4,208,132,4,
240,132,4,16,133,4,48,133,4,80,133,4,109,133,4,48,134,4,80,134,4,112,134,4,144,134,4,176,134,4,208,134,4,240,134,4,16,135,4,48,135,4,80,135,4,109,135,4,
176,144,4,208,144,4,240,144,4,16,145,4,48,145,4,79,145,4,110,145,4,170,160,4,202,160,4,233,160,4,8,161,4,40,161,4,71,161,4,102,161,4,176,192,4,208,192,4,
240,192,4,16,193,4,48,193,4,80,193,4,112,193,4,48,194,4,80,194,4,112,194,4,144,194,4,176,194,4,208,194,4,240,194,4,14,195,4,43,195,4,73,195,4,102,195,4,
48,196,4,80,196,4,112,196,4,144,196,4,176,196,4,208,196,4,240,196,4,14,197,4,43,197,4,73,197,4,102,197,4,48,198,4,80,198,4,112,198,4,144,198,4,176,198,4,
208,198,4,240,198,4,14,199,4,43,199,4,73,199,4,102,199,4,170,208,4,202,208,4,233,208,4,8,209,4,40,209,4,71,209,4,102,209,4,164,224,4,196,224,4,227,224,4,
3,225,4,34,225,4,66,225,4,97,225,4,176,0,5,208,0,5,240,0,5,16,1,5,48,1,5,80,1,5,112,1,5,48,2,5,80,2,5,112,2,5,144,2,5,176,2,5,
208,2,5,240,2,5,14,3,5,43,3,5,73,3,5,102,3,5,48,4,5,80,4,5,112,4,5,144,4,5,176,4,5,208,4,5,240,4,5,14,5,5,43,5,5,73,5,5,
102,5,5,48,6,5,80,6,5,112,6,5,144,6,5,176,6,5,208,6,5,240,6,5,14,7,5,43,7,5,73,7,5,102,7,5,48,8,5,80,8,5,112,8,5,144,8,5,
176,8,5,208,8,5,240,8,5,14,9,5,43,9,5,73,9,5,102,9,5,170,16,5,202,16,5,233,16,5,8,17,5,40,17,5,71,17,5,102,17,5,164,32,5,196,32,5,
227,32,5,3,33,5,34,33,5,66,33,5,97,33,5,176,64,5,208,64,5,240,64,5,16,65,5,48,65,5,80,65,5,112,65,5,48,66,5,80,66,5,112,66,5,144,66,5,
175,66,5,204,66,5,235,66,5,9,67,5,38,67,5,69,67,5,99,67,5,48,68,5,80,68,5,112,68,5,144,68,5,175,68,5,204,68,5,235,68,5,9,69,5,38,69,5,
69,69,5,99,69,5,48,70,5,80,70,5,112,70,5,144,70,5,175,70,5,204,70,5,235,70,5,9,71,5,38,71,5,69,71,5,99,71,5,48,72,5,80,72,5,112,72,5,
144,72,5,175,72,5,204,72,5,235,72,5,9,73,5,38,73,5,69,73,5,99,73,5,166,80,5,197,80,5,229,80,5,4,81,5,36,81,5,67,81,5,99,81,5,112,0,6,
144,0,6,176,0,6,208,0,6,240,0,6,16,1,6,48,1,6,80,1,6,112,1,6,112,16,6,144,16,6,176,16,6,208,16,6,240,16,6,16,17,6,48,17,6,80,17,6,
112,17,6,112,32,6,144,32,6,176,32,6,208,32,6,240,32,6,16,33,6,48,33,6,80,33,6,112,33,6,112,64,6,144,64,6,176,64,6,208,64,6,240,64,6,16,65,6,
48,65,6,80,65,6,112,65,6,48,72,6,80,72,6,112,72,6,144,72,6,176,72,6,208,72,6,240,72,6,13,73,6,40,73,6,68,73,6,112,80,6,144,80,6,176,80,6,
208,80,6,239,80,6,14,81,6,44,81,6,76,81,6,106,81,6,106,96,6,138,96,6,169,96,6,200,96,6,231,96,6,6,97,6,37,97,6,69,97,6,100,97,6,112,128,6,
144,128,6,176,128,6,208,128,6,240,128,6,16,129,6,48,129,6,80,129,6,112,129,6,48,130,6,80,130,6,112,130,6,144,130,6,176,130,6,208,130,6,240,130,6,13,131,6,
40,131,6,68,131,6,48,132,6,80,132,6,112,132,6,144,132,6,176,132,6,208,132,6,240,132,6,13,133,6,40,133,6,68,133,6,48,134,6,80,134,6,112,134,6,144,134,6,
176,134,6,208,134,6,240,134,6,13,135,6,40,135,6,68,135,6,112,144,6,144,144,6,176,144,6,208,144,6,239,144,6,14,145,6,44,145,6,76,145,6,106,145,6,106,160,6,
138,160,6,169,160,6,200,160,6,231,160,6,6,161,6,37,161,6,69,161,6,100,161,6,112,192,6,144,192,6,176,192,6,208,192,6,240,192,6,16,193,6,48,193,6,80,193,6,
112,193,6,48,194,6,80,194,6,112,194,6,144,194,6,176,194,6,205,194,6,234,194,6,6,195,6,35,195,6,64,195,6,48,196,6,80,196,6,112,196,6,144,196,6,176,196,6,
205,196,6,234,196,6,6,197,6,35,197,6,64,197,6,48,198,6,80,198,6,112,198,6,144,198,6,176,198,6,205,198,6,234,198,6,6,199,6,35,199,6,64,199,6,106,208,6,
138,208,6,169,208,6,200,208,6,231,208,6,6,209,6,37,209,6,69,209,6,100,209,6,100,224,6,132,224,6,163,224,6,195,224,6,226,224,6,1,225,6,33,225,6,64,225,6,
96,225,6,112,0,7,144,0,7,176,0,7,208,0,7,240,0,7,16,1,7,48,1,7,80,1,7,112,1,7,48,2,7,80,2,7,112,2,7,144,2,7,176,2,7,205,2,7,
234,2,7,6,3,7,35,3,7,64,3,7,48,4,7,80,4,7,112,4,7,144,4,7,176,4,7,205,4,7,234,4,7,6,5,7,35,5,7,64,5,7,48,6,7,80,6,7,
112,6,7,144,6,7,176,6,7,205,6,7,234,6,7,6,7,7,35,7,7,64,7,7,48,8,7,80,8,7,112,8,7,144,8,7,176,8,7,205,8,7,234,8,7,6,9,7,
35,9,7,64,9,7,106,16,7,138,16,7,169,16,7,200,16,7,231,16,7,6,17,7,37,17,7,69,17,7,100,17,7,100,32,7,132,32,7,163,32,7,195,32,7,226,32,7,
1,33,7,33,33,7,64,33,7,96,33,7,112,64,7,144,64,7,176,64,7,208,64,7,240,64,7,16,65,7,48,65,7,80,65,7,111,65,7,48,66,7,80,66,7,111,66,7,
141,66,7,170,66,7,199,66,7,230,66,7,3,67,7,32,67,7,48,68,7,80,68,7,111,68,7,141,68,7,170,68,7,199,68,7,230,68,7,3,69,7,32,69,7,48,70,7,
80,70,7,111,70,7,141,70,7,170,70,7,199,70,7,230,70,7,3,71,7,32,71,7,48,72,7,80,72,7,111,72,7,141,72,7,170,72,7,199,72,7,230,72,7,3,73,7,
32,73,7,102,80,7,133,80,7,164,80,7,196,80,7,227,80,7,3,81,7,34,81,7,65,81,7,97,81,7,80,0,8,112,0,8,144,0,8,176,0,8,208,0,8,240,0,8,
16,1,8,48,1,8,80,1,8,112,1,8,80,16,8,112,16,8,144,16,8,176,16,8,208,16,8,240,16,8,16,17,8,48,17,8,80,17,8,112,17,8,80,32,8,112,32,8,
144,32,8,176,32,8,208,32,8,240,32,8,16,33,8,47,33,8,77,33,8,107,33,8,80,64,8,112,64,8,144,64,8,176,64,8,208,64,8,240,64,8,16,65,8,48,65,8,
80,65,8,112,65,8,16,72,8,48,72,8,80,72,8,112,72,8,144,72,8,176,72,8,205,72,8,232,72,8,1,73,8,80,80,8,112,80,8,144,80,8,175,80,8,206,80,8,
236,80,8,11,81,8,41,81,8,72,81,8,102,81,8,74,96,8,105,96,8,136,96,8,167,96,8,198,96,8,229,96,8,4,97,8,35,97,8,66,97,8,97,97,8,80,128,8,
112,128,8,144,128,8,176,128,8,208,128,8,240,128,8,16,129,8,48,129,8,80,129,8,112,129,8,16,130,8,48,130,8,80,130,8,112,130,8,144,130,8,176,130,8,205,130,8,
232,130,8,1,131,8,16,132,8,48,132,8,80,132,8,112,132,8,144,132,8,176,132,8,205,132,8,232,132,8,1,133,8,16,134,8,48,134,8,80,134,8,112,134,8,144,134,8,
176,134,8,205,134,8,232,134,8,1,135,8,80,144,8,112,144,8,144,144,8,175,144,8,206,144,8,236,144,8,11,145,8,41,145,8,72,145,8,102,145,8,74,160,8,105,160,8,
136,160,8,167,160,8,198,160,8,229,160,8,4,161,8,35,161,8,66,161,8,97,161,8,80,192,8,112,192,8,144,192,8,176,192,8,208,192,8,240,192,8,16,193,8,48,193,8,
80,193,8,112,193,8,16,194,8,48,194,8,80,194,8,112,194,8,143,194,8,170,194,8,198,194,8,227,194,8,16,196,8,48,196,8,80,196,8,112,196,8,143,196,8,170,196,8,
198,196,8,227,196,8,16,198,8,48,198,8,80,198,8,112,198,8,143,198,8,170,198,8,198,198,8,227,198,8,74,208,8,105,208,8,136,208,8,167,208,8,198,208,8,229,208,8,
4,209,8,35,209,8,66,209,8,97,209,8,68,224,8,99,224,8,131,224,8,162,224,8,193,224,8,225,224,8,0,225,8,32,225,8,80,0,9,112,0,9,144,0,9,176,0,9,
208,0,9,240,0,9,16,1,9,48,1,9,80,1,9,112,1,9,16,2,9,48,2,9,80,2,9,112,2,9,143,2,9,170,2,9,198,2,9,227,2,9,16,4,9,48,4,9,
80,4,9,112,4,9,143,4,9,170,4,9,198,4,9,227,4,9,16,6,9,48,6,9,80,6,9,112,6,9,143,6,9,170,6,9,198,6,9,227,6,9,16,8,9,48,8,9,
80,8,9,112,8,9,143,8,9,170,8,9,198,8,9,227,8,9,74,16,9,105,16,9,136,16,9,167,16,9,198,16,9,229,16,9,4,17,9,35,17,9,66,17,9,97,17,9,
68,32,9,99,32,9,131,32,9,162,32,9,193,32,9,225,32,9,0,33,9,32,33,9,80,64,9,112,64,9,144,64,9,176,64,9,208,64,9,240,64,9,15,65,9,46,65,9,
76,65,9,107,65,9,16,66,9,48,66,9,79,66,9,108,66,9,137,66,9,166,66,9,195,66,9,224,66,9,16,68,9,48,68,9,79,68,9,108,68,9,137,68,9,166,68,9,
195,68,9,224,68,9,16,70,9,48,70,9,79,70,9,108,70,9,137,70,9,166,70,9,195,70,9,224,70,9,16,72,9,48,72,9,79,72,9,108,72,9,137,72,9,166,72,9,
195,72,9,224,72,9,70,80,9,101,80,9,132,80,9,163,80,9,195,80,9,226,80,9,1,81,9,32,81,9,64,81,9,80,0,10,112,0,10,144,0,10,176,0,10,208,0,10,
240,0,10,16,1,10,48,1,10,80,1,10,112,1,10,80,16,10,112,16,10,144,16,10,176,16,10,208,16,10,240,16,10,16,17,10,48,17,10,80,17,10,109,17,10,80,32,10,
112,32,10,144,32,10,176,32,10,208,32,10,240,32,10,13,33,10,43,33,10,73,33,10,102,33,10,80,64,10,112,64,10,144,64,10,176,64,10,208,64,10,240,64,10,16,65,10,
48,65,10,80,65,10,112,65,10,16,72,10,48,72,10,80,72,10,112,72,10,144,72,10,170,72,10,195,72,10,80,80,10,112,80,10,143,80,10,173,80,10,203,80,10,234,80,10,
8,81,10,38,81,10,68,81,10,99,81,10,73,96,10,104,96,10,135,96,10,166,96,10,197,96,10,228,96,10,2,97,10,33,97,10,64,97,10,80,128,10,112,128,10,144,128,10,
176,128,10,208,128,10,240,128,10,16,129,10,48,129,10,80,129,10,112,129,10,16,130,10,48,130,10,80,130,10,112,130,10,144,130,10,170,130,10,195,130,10,16,132,10,48,132,10,
80,132,10,112,132,10,144,132,10,170,132,10,195,132,10,16,134,10,48,134,10,80,134,10,112,134,10,144,134,10,170,134,10,195,134,10,80,144,10,112,144,10,143,144,10,173,144,10,
203,144,10,234,144,10,8,145,10,38,145,10,68,145,10,99,145,10,73,160,10,104,160,10,135,160,10,166,160,10,197,160,10,228,160,10,2,161,10,33,161,10,64,161,10,80,192,10,
112,192,10,144,192,10,176,192,10,208,192,10,240,192,10,16,193,10,48,193,10,79,193,10,108,193,10,16,194,10,48,194,10,80,194,10,109,194,10,138,194,10,164,194,10,16,196,10,
48,196,10,80,196,10,109,196,10,138,196,10,164,196,10,16,198,10,48,198,10,80,198,10,109,198,10,138,198,10,164,198,10,73,208,10,104,208,10,135,208,10,166,208,10,197,208,10,
228,208,10,2,209,10,33,209,10,64,209,10,67,224,10,99,224,10,130,224,10,161,224,10,192,224,10,224,224,10,80,0,11,112,0,11,144,0,11,176,0,11,208,0,11,240,0,11,
16,1,11,48,1,11,79,1,11,108,1,11,16,2,11,48,2,11,80,2,11,109,2,11,138,2,11,164,2,11,16,4,11,48,4,11,80,4,11,109,4,11,138,4,11,164,4,11,
16,6,11,48,6,11,80,6,11,109,6,11,138,6,11,164,6,11,16,8,11,48,8,11,80,8,11,109,8,11,138,8,11,164,8,11,73,16,11,104,16,11,135,16,11,166,16,11,
197,16,11,228,16,11,2,17,11,33,17,11,64,17,11,67,32,11,99,32,11,130,32,11,161,32,11,192,32,11,224,32,11,80,64,11,112,64,11,144,64,11,176,64,11,208,64,11,
238,64,11,12,65,11,42,65,11,73,65,11,103,65,11,16,66,11,48,66,11,76,66,11,104,66,11,133,66,11,161,66,11,16,68,11,48,68,11,76,68,11,104,68,11,133,68,11,
161,68,11,16,70,11,48,70,11,76,70,11,104,70,11,133,70,11,161,70,11,16,72,11,48,72,11,76,72,11,104,72,11,133,72,11,161,72,11,69,80,11,100,80,11,131,80,11,
162,80,11,193,80,11,225,80,11,0,81,11,48,0,12,80,0,12,112,0,12,144,0,12,176,0,12,208,0,12,240,0,12,16,1,12,48,1,12,80,1,12,112,1,12,48,16,12,
80,16,12,112,16,12,144,16,12,176,16,12,208,16,12,240,16,12,16,17,12,45,17,12,74,17,12,102,17,12,48,32,12,80,32,12,112,32,12,144,32,12,176,32,12,206,32,12,
236,32,12,9,33,12,38,33,12,68,33,12,97,33,12,48,64,12,80,64,12,112,64,12,144,64,12,176,64,12,208,64,12,240,64,12,16,65,12,48,65,12,80,65,12,111,65,12,
16,72,12,48,72,12,80,72,12,112,72,12,138,72,12,161,72,12,48,80,12,80,80,12,111,80,12,141,80,12,171,80,12,201,80,12,231,80,12,5,81,12,35,81,12,65,81,12,
42,96,12,72,96,12,103,96,12,134,96,12,164,96,12,195,96,12,226,96,12,0,97,12,48,128,12,80,128,12,112,128,12,144,128,12,176,128,12,208,128,12,240,128,12,16,129,12,
48,129,12,80,129,12,111,129,12,16,130,12,48,130,12,80,130,12,112,130,12,138,130,12,161,130,12,16,132,12,48,132,12,80,132,12,112,132,12,138,132,12,161,132,12,16,134,12,
48,134,12,80,134,12,112,134,12,138,134,12,161,134,12,48,144,12,80,144,12,111,144,12,141,144,12,171,144,12,201,144,12,231,144,12,5,145,12,35,145,12,65,145,12,42,160,12,
72,160,12,103,160,12,134,160,12,164,160,12,195,160,12,226,160,12,0,161,12,48,192,12,80,192,12,112,192,12,144,192,12,176,192,12,208,192,12,240,192,12,15,193,12,44,193,12,
74,193,12,103,193,12,16,194,12,48,194,12,78,194,12,105,194,12,132,194,12,16,196,12,48,196,12,78,196,12,105,196,12,132,196,12,16,198,12,48,198,12,78,198,12,105,198,12,
132,198,12,42,208,12,72,208,12,103,208,12,134,208,12,164,208,12,195,208,12,226,208,12,0,209,12,36,224,12,67,224,12,98,224,12,129,224,12,160,224,12,48,0,13,80,0,13,
112,0,13,144,0,13,176,0,13,208,0,13,240,0,13,15,1,13,44,1,13,74,1,13,103,1,13,16,2,13,48,2,13,78,2,13,105,2,13,132,2,13,16,4,13,48,4,13,
78,4,13,105,4,13,132,4,13,16,6,13,48,6,13,78,6,13,105,6,13,132,6,13,16,8,13,48,8,13,78,8,13,105,8,13,132,8,13,42,16,13,72,16,13,103,16,13,
134,16,13,164,16,13,195,16,13,226,16,13,0,17,13,36,32,13,67,32,13,98,32,13,129,32,13,160,32,13,48,64,13,80,64,13,112,64,13,144,64,13,175,64,13,205,64,13,
236,64,13,9,65,13,39,65,13,70,65,13,99,65,13,16,66,13,45,66,13,73,66,13,100,66,13,129,66,13,16,68,13,45,68,13,73,68,13,100,68,13,129,68,13,16,70,13,
45,70,13,73,70,13,100,70,13,129,70,13,16,72,13,45,72,13,73,72,13,100,72,13,129,72,13,37,80,13,68,80,13,99,80,13,130,80,13,161,80,13,192,80,13,48,0,14,
80,0,14,112,0,14,144,0,14,176,0,14,208,0,14,240,0,14,16,1,14,48,1,14,80,1,14,112,1,14,48,16,14,80,16,14,112,16,14,144,16,14,176,16,14,208,16,14,
240,16,14,12,17,14,39,17,14,68,17,14,48,32,14,80,32,14,112,32,14,144,32,14,174,32,14,203,32,14,233,32,14,5,33,14,34,33,14,64,33,14,48,64,14,80,64,14,
112,64,14,144,64,14,176,64,14,208,64,14,240,64,14,16,65,14,48,65,14,77,65,14,103,65,14,16,72,14,48,72,14,80,72,14,106,72,14,131,72,14,48,80,14,79,80,14,
109,80,14,139,80,14,169,80,14,198,80,14,228,80,14,2,81,14,32,81,14,41,96,14,71,96,14,102,96,14,133,96,14,163,96,14,193,96,14,224,96,14,48,128,14,80,128,14,
112,128,14,144,128,14,176,128,14,208,128,14,240,128,14,16,129,14,48,129,14,77,129,14,103,129,14,16,130,14,48,130,14,80,130,14,106,130,14,131,130,14,16,132,14,48,132,14,
80,132,14,106,132,14,131,132,14,16,134,14,48,134,14,80,134,14,106,134,14,131,134,14,48,144,14,79,144,14,109,144,14,139,144,14,169,144,14,198,144,14,228,144,14,2,145,14,
32,145,14,41,160,14,71,160,14,102,160,14,133,160,14,163,160,14,193,160,14,224,160,14,48,192,14,80,192,14,112,192,14,144,192,14,176,192,14,208,192,14,239,192,14,11,193,14,
40,193,14,70,193,14,98,193,14,16,194,14,48,194,14,74,194,14,100,194,14,16,196,14,48,196,14,74,196,14,100,196,14,16,198,14,48,198,14,74,198,14,100,198,14,41,208,14,
71,208,14,102,208,14,133,208,14,163,208,14,193,208,14,224,208,14,35,224,14,66,224,14,97,224,14,128,224,14,48,0,15,80,0,15,112,0,15,144,0,15,176,0,15,208,0,15,
239,0,15,11,1,15,40,1,15,70,1,15,98,1,15,16,2,15,48,2,15,74,2,15,100,2,15,16,4,15,48,4,15,74,4,15,100,4,15,16,6,15,48,6,15,74,6,15,
100,6,15,16,8,15,48,8,15,74,8,15,100,8,15,41,16,15,71,16,15,102,16,15,133,16,15,163,16,15,193,16,15,224,16,15,35,32,15,66,32,15,97,32,15,128,32,15,
48,64,15,80,64,15,112,64,15,144,64,15,173,64,15,203,64,15,233,64,15,6,65,15,36,65,15,66,65,15,96,65,15,16,66,15,43,66,15,70,66,15,97,66,15,16,68,15,
43,68,15,70,68,15,97,68,15,16,70,15,43,70,15,70,70,15,97,70,15,16,72,15,43,72,15,70,72,15,97,72,15,37,80,15,67,80,15,98,80,15,129,80,15,160,80,15,
48,0,16,80,0,16,112,0,16,144,0,16,176,0,16,208,0,16,240,0,16,16,1,16,48,1,16,80,1,16,48,16,16,80,16,16,112,16,16,144,16,16,176,16,16,208,16,16,
236,16,16,6,17,16,33,17,16,48,32,16,80,32,16,112,32,16,143,32,16,171,32,16,200,32,16,229,32,16,1,33,16,48,64,16,80,64,16,112,64,16,144,64,16,176,64,16,
208,64,16,240,64,16,15,65,16,42,65,16,70,65,16,16,72,16,48,72,16,77,72,16,99,72,16,48,80,16,78,80,16,107,80,16,137,80,16,166,80,16,196,80,16,226,80,16,
40,96,16,70,96,16,101,96,16,131,96,16,161,96,16,192,96,16,48,128,16,80,128,16,112,128,16,144,128,16,176,128,16,208,128,16,240,128,16,15,129,16,42,129,16,70,129,16,
16,130,16,48,130,16,77,130,16,99,130,16,16,132,16,48,132,16,77,132,16,99,132,16,16,134,16,48,134,16,77,134,16,99,134,16,48,144,16,78,144,16,107,144,16,137,144,16,
166,144,16,196,144,16,226,144,16,40,160,16,70,160,16,101,160,16,131,160,16,161,160,16,192,160,16,48,192,16,80,192,16,112,192,16,144,192,16,176,192,16,206,192,16,235,192,16,
7,193,16,36,193,16,65,193,16,16,194,16,46,194,16,70,194,16,16,196,16,46,196,16,70,196,16,16,198,16,46,198,16,70,198,16,40,208,16,70,208,16,101,208,16,131,208,16,
161,208,16,192,208,16,35,224,16,65,224,16,96,224,16,128,224,16,48,0,17,80,0,17,112,0,17,144,0,17,176,0,17,206,0,17,235,0,17,7,1,17,36,1,17,65,1,17,
16,2,17,46,2,17,70,2,17,16,4,17,46,4,17,70,4,17,16,6,17,46,6,17,70,6,17,16,8,17,46,8,17,70,8,17,40,16,17,70,16,17,101,16,17,131,16,17,
161,16,17,192,16,17,35,32,17,65,32,17,96,32,17,128,32,17,48,64,17,80,64,17,112,64,17,142,64,17,171,64,17,200,64,17,230,64,17,3,65,17,33,65,17,16,66,17,
41,66,17,67,66,17,16,68,17,41,68,17,67,68,17,16,70,17,41,70,17,67,70,17,16,72,17,41,72,17,67,72,17,36,80,17,67,80,17,97,80,17,128,80,17,48,0,18,
80,0,18,112,0,18,144,0,18,176,0,18,208,0,18,240,0,18,16,1,18,46,1,18,48,16,18,80,16,18,112,16,18,144,16,18,176,16,18,202,16,18,230,16,18,0,17,18,
48,32,18,80,32,18,111,32,18,140,32,18,168,32,18,196,32,18,225,32,18,48,64,18,80,64,18,112,64,18,144,64,18,176,64,18,208,64,18,239,64,18,9,65,18,35,65,18,
16,72,18,48,72,18,71,72,18,47,80,18,76,80,18,105,80,18,135,80,18,164,80,18,193,80,18,39,96,18,69,96,18,99,96,18,130,96,18,160,96,18,48,128,18,80,128,18,
112,128,18,144,128,18,176,128,18,208,128,18,239,128,18,9,129,18,35,129,18,16,130,18,48,130,18,71,130,18,16,132,18,48,132,18,71,132,18,16,134,18,48,134,18,71,134,18,
47,144,18,76,144,18,105,144,18,135,144,18,164,144,18,193,144,18,39,160,18,69,160,18,99,160,18,130,160,18,160,160,18,48,192,18,80,192,18,112,192,18,144,192,18,174,192,18,
202,192,18,231,192,18,3,193,18,16,194,18,43,194,18,66,194,18,16,196,18,43,196,18,66,196,18,16,198,18,43,198,18,66,198,18,39,208,18,69,208,18,99,208,18,130,208,18,
160,208,18,34,224,18,65,224,18,96,224,18,48,0,19,80,0,19,112,0,19,144,0,19,174,0,19,202,0,19,231,0,19,3,1,19,16,2,19,43,2,19,66,2,19,16,4,19,
43,4,19,66,4,19,16,6,19,43,6,19,66,6,19,16,8,19,43,8,19,66,8,19,39,16,19,69,16,19,99,16,19,130,16,19,160,16,19,34,32,19,65,32,19,96,32,19,
48,64,19,80,64,19,110,64,19,140,64,19,169,64,19,198,64,19,227,64,19,0,65,19,16,66,19,38,66,19,64,66,19,16,68,19,38,68,19,64,68,19,16,70,19,38,70,19,
64,70,19,16,72,19,38,72,19,64,72,19,35,80,19,66,80,19,96,80,19,16,0,20,48,0,20,80,0,20,112,0,20,144,0,20,176,0,20,208,0,20,240,0,20,14,1,20,
16,16,20,48,16,20,80,16,20,112,16,20,144,16,20,172,16,20,198,16,20,225,16,20,16,32,20,48,32,20,80,32,20,109,32,20,138,32,20,165,32,20,193,32,20,16,64,20,
48,64,20,80,64,20,112,64,20,144,64,20,176,64,20,207,64,20,234,64,20,3,65,20,16,72,20,48,72,20,65,72,20,16,80,20,46,80,20,75,80,20,104,80,20,133,80,20,
162,80,20,10,96,20,39,96,20,68,96,20,98,96,20,129,96,20,16,128,20,48,128,20,80,128,20,112,128,20,144,128,20,176,128,20,207,128,20,234,128,20,3,129,20,16,130,20,
48,130,20,65,130,20,16,132,20,48,132,20,65,132,20,16,134,20,48,134,20,65,134,20,16,144,20,46,144,20,75,144,20,104,144,20,133,144,20,162,144,20,10,160,20,39,160,20,
68,160,20,98,160,20,129,160,20,16,192,20,48,192,20,80,192,20,112,192,20,144,192,20,171,192,20,199,192,20,228,192,20,16,194,20,40,194,20,16,196,20,40,196,20,16,198,20,
40,198,20,10,208,20,39,208,20,68,208,20,98,208,20,129,208,20,4,224,20,34,224,20,64,224,20,16,0,21,48,0,21,80,0,21,112,0,21,144,0,21,171,0,21,199,0,21,
228,0,21,16,2,21,40,2,21,16,4,21,40,4,21,16,6,21,40,6,21,16,8,21,40,8,21,10,16,21,39,16,21,68,16,21,98,16,21,129,16,21,4,32,21,34,32,21,
64,32,21,16,64,21,48,64,21,79,64,21,108,64,21,138,64,21,166,64,21,195,64,21,225,64,21,15,66,21,36,66,21,15,68,21,36,68,21,15,70,21,36,70,21,15,72,21,
36,72,21,6,80,21,35,80,21,65,80,21,96,80,21,16,1,22,48,1,22,80,1,22,112,1,22,16,17,22,48,17,22,80,17,22,112,17,22,16,33,22,48,33,22,80,33,22,
112,33,22,16,65,22,48,65,22,80,65,22,112,65,22,80,72,22,112,72,22,144,72,22,176,72,22,208,72,22,240,72,22,16,73,22,48,73,22,80,73,22,112,73,22,16,81,22,
48,81,22,80,81,22,112,81,22,10,97,22,42,97,22,73,97,22,105,97,22,16,129,22,48,129,22,80,129,22,112,129,22,80,130,22,112,130,22,144,130,22,176,130,22,208,130,22,
240,130,22,16,131,22,48,131,22,80,131,22,112,131,22,80,132,22,112,132,22,144,132,22,176,132,22,208,132,22,240,132,22,16,133,22,48,133,22,80,133,22,112,133,22,80,134,22,
112,134,22,144,134,22,176,134,22,208,134,22,240,134,22,16,135,22,48,135,22,80,135,22,112,135,22,16,145,22,48,145,22,80,145,22,112,145,22,10,161,22,42,161,22,73,161,22,
105,161,22,16,193,22,48,193,22,80,193,22,112,193,22,80,194,22,112,194,22,144,194,22,176,194,22,208,194,22,240,194,22,16,195,22,48,195,22,80,195,22,112,195,22,80,196,22,
112,196,22,144,196,22,176,196,22,208,196,22,240,196,22,16,197,22,48,197,22,80,197,22,112,197,22,80,198,22,112,198,22,144,198,22,176,198,22,208,198,22,240,198,22,16,199,22,
48,199,22,80,199,22,112,199,22,10,209,22,42,209,22,73,209,22,105,209,22,4,225,22,36,225,22,67,225,22,99,225,22,16,1,23,48,1,23,80,1,23,112,1,23,80,2,23,
112,2,23,144,2,23,176,2,23,208,2,23,240,2,23,16,3,23,48,3,23,80,3,23,112,3,23,80,4,23,112,4,23,144,4,23,176,4,23,208,4,23,240,4,23,16,5,23,
48,5,23,80,5,23,112,5,23,80,6,23,112,6,23,144,6,23,176,6,23,208,6,23,240,6,23,16,7,23,48,7,23,80,7,23,112,7,23,80,8,23,112,8,23,144,8,23,
176,8,23,208,8,23,240,8,23,16,9,23,48,9,23,80,9,23,112,9,23,10,17,23,42,17,23,73,17,23,105,17,23,4,33,23,36,33,23,67,33,23,99,33,23,16,65,23,
48,65,23,80,65,23,112,65,23,80,66,23,112,66,23,144,66,23,176,66,23,208,66,23,240,66,23,15,67,23,45,67,23,76,67,23,106,67,23,80,68,23,112,68,23,144,68,23,
176,68,23,208,68,23,240,68,23,15,69,23,45,69,23,76,69,23,106,69,23,80,70,23,112,70,23,144,70,23,176,70,23,208,70,23,240,70,23,15,71,23,45,71,23,76,71,23,
106,71,23,80,72,23,112,72,23,144,72,23,176,72,23,208,72,23,240,72,23,15,73,23,45,73,23,76,73,23,106,73,23,6,81,23,37,81,23,69,81,23,100,81,23,144,0,24,
176,0,24,208,0,24,240,0,24,16,1,24,48,1,24,80,1,24,112,1,24,144,16,24,176,16,24,208,16,24,240,16,24,16,17,24,48,17,24,80,17,24,112,17,24,144,32,24,
176,32,24,208,32,24,240,32,24,16,33,24,48,33,24,80,33,24,112,33,24,144,64,24,176,64,24,208,64,24,240,64,24,16,65,24,48,65,24,80,65,24,112,65,24,48,72,24,
80,72,24,112,72,24,144,72,24,176,72,24,208,72,24,240,72,24,16,73,24,47,73,24,75,73,24,102,73,24,144,80,24,176,80,24,208,80,24,240,80,24,15,81,24,46,81,24,
77,81,24,108,81,24,138,96,24,170,96,24,201,96,24,232,96,24,7,97,24,39,97,24,70,97,24,101,97,24,144,128,24,176,128,24,208,128,24,240,128,24,16,129,24,48,129,24,
80,129,24,112,129,24,48,130,24,80,130,24,112,130,24,144,130,24,176,130,24,208,130,24,240,130,24,16,131,24,47,131,24,75,131,24,102,131,24,48,132,24,80,132,24,112,132,24,
144,132,24,176,132,24,208,132,24,240,132,24,16,133,24,47,133,24,75,133,24,102,133,24,48,134,24,80,134,24,112,134,24,144,134,24,176,134,24,208,134,24,240,134,24,16,135,24,
47,135,24,75,135,24,102,135,24,144,144,24,176,144,24,208,144,24,240,144,24,15,145,24,46,145,24,77,145,24,108,145,24,138,160,24,170,160,24,201,160,24,232,160,24,7,161,24,
39,161,24,70,161,24,101,161,24,144,192,24,176,192,24,208,192,24,240,192,24,16,193,24,48,193,24,80,193,24,112,193,24,48,194,24,80,194,24,112,194,24,144,194,24,176,194,24,
208,194,24,238,194,24,10,195,24,39,195,24,69,195,24,97,195,24,48,196,24,80,196,24,112,196,24,144,196,24,176,196,24,208,196,24,238,196,24,10,197,24,39,197,24,69,197,24,
97,197,24,48,198,24,80,198,24,112,198,24,144,198,24,176,198,24,208,198,24,238,198,24,10,199,24,39,199,24,69,199,24,97,199,24,138,208,24,170,208,24,201,208,24,232,208,24,
7,209,24,39,209,24,70,209,24,101,209,24,132,224,24,164,224,24,195,224,24,227,224,24,2,225,24,34,225,24,65,225,24,97,225,24,144,0,25,176,0,25,208,0,25,240,0,25,
16,1,25,48,1,25,80,1,25,112,1,25,48,2,25,80,2,25,112,2,25,144,2,25,176,2,25,208,2,25,238,2,25,10,3,25,39,3,25,69,3,25,97,3,25,48,4,25,
80,4,25,112,4,25,144,4,25,176,4,25,208,4,25,238,4,25,10,5,25,39,5,25,69,5,25,97,5,25,48,6,25,80,6,25,112,6,25,144,6,25,176,6,25,208,6,25,
238,6,25,10,7,25,39,7,25,69,7,25,97,7,25,48,8,25,80,8,25,112,8,25,144,8,25,176,8,25,208,8,25,238,8,25,10,9,25,39,9,25,69,9,25,97,9,25,
138,16,25,170,16,25,201,16,25,232,16,25,7,17,25,39,17,25,70,17,25,101,17,25,132,32,25,164,32,25,195,32,25,227,32,25,2,33,25,34,33,25,65,33,25,97,33,25,
144,64,25,176,64,25,208,64,25,240,64,25,16,65,25,48,65,25,80,65,25,112,65,25,48,66,25,80,66,25,112,66,25,143,66,25,172,66,25,202,66,25,232,66,25,6,67,25,
35,67,25,65,67,25,48,68,25,80,68,25,112,68,25,143,68,25,172,68,25,202,68,25,232,68,25,6,69,25,35,69,25,65,69,25,48,70,25,80,70,25,112,70,25,143,70,25,
172,70,25,202,70,25,232,70,25,6,71,25,35,71,25,65,71,25,48,72,25,80,72,25,112,72,25,143,72,25,172,72,25,202,72,25,232,72,25,6,73,25,35,73,25,65,73,25,
134,80,25,165,80,25,196,80,25,228,80,25,3,81,25,35,81,25,66,81,25,98,81,25,80,0,26,112,0,26,144,0,26,176,0,26,208,0,26,240,0,26,16,1,26,48,1,26,
80,1,26,112,1,26,80,16,26,112,16,26,144,16,26,176,16,26,208,16,26,240,16,26,16,17,26,48,17,26,80,17,26,112,17,26,80,32,26,112,32,26,144,32,26,176,32,26,
208,32,26,240,32,26,16,33,26,47,33,26,77,33,26,107,33,26,80,64,26,112,64,26,144,64,26,176,64,26,208,64,26,240,64,26,16,65,26,48,65,26,80,65,26,112,65,26,
16,72,26,48,72,26,80,72,26,112,72,26,144,72,26,176,72,26,205,72,26,232,72,26,1,73,26,80,80,26,112,80,26,144,80,26,175,80,26,206,80,26,236,80,26,11,81,26,
41,81,26,72,81,26,102,81,26,74,96,26,105,96,26,136,96,26,167,96,26,198,96,26,229,96,26,4,97,26,35,97,26,66,97,26,97,97,26,80,128,26,112,128,26,144,128,26,
176,128,26,208,128,26,240,128,26,16,129,26,48,129,26,80,129,26,112,129,26,16,130,26,48,130,26,80,130,26,112,130,26,144,130,26,176,130,26,205,130,26,232,130,26,1,131,26,
16,132,26,48,132,26,80,132,26,112,132,26,144,132,26,176,132,26,205,132,26,232,132,26,1,133,26,16,134,26,48,134,26,80,134,26,112,134,26,144,134,26,176,134,26,205,134,26,
232,134,26,1,135,26,80,144,26,112,144,26,144,144,26,175,144,26,206,144,26,236,144,26,11,145,26,41,145,26,72,145,26,102,145,26,74,160,26,105,160,26,136,160,26,167,160,26,
198,160,26,229,160,26,4,161,26,35,161,26,66,161,26,97,161,26,80,192,26,112,192,26,144,192,26,176,192,26,208,192,26,240,192,26,16,193,26,48,193,26,80,193,26,112,193,26,
16,194,26,48,194,26,80,194,26,112,194,26,143,194,26,170,194,26,198,194,26,227,194,26,16,196,26,48,196,26,80,196,26,112,196,26,143,196,26,170,196,26,198,196,26,227,196,26,
16,198,26,48,198,26,80,198,26,112,198,26,143,198,26,170,198,26,198,198,26,227,198,26,74,208,26,105,208,26,136,208,26,167,208,26,198,208,26,229,208,26,4,209,26,35,209,26,
66,209,26,97,209,26,68,224,26,99,224,26,131,224,26,162,224,26,193,224,26,225,224,26,0,225,26,32,225,26,80,0,27,112,0,27,144,0,27,176,0,27,208,0,27,240,0,27,
16,1,27,48,1,27,80,1,27,112,1,27,16,2,27,48,2,27,80,2,27,112,2,27,143,2,27,170,2,27,198,2,27,227,2,27,16,4,27,48,4,27,80,4,27,112,4,27,
143,4,27,170,4,27,198,4,27,227,4,27,16,6,27,48,6,27,80,6,27,112,6,27,143,6,27,170,6,27,198,6,27,227,6,27,16,8,27,48,8,27,80,8,27,112,8,27,
143,8,27,170,8,27,198,8,27,227,8,27,74,16,27,105,16,27,136,16,27,167,16,27,198,16,27,229,16,27,4,17,27,35,17,27,66,17,27,97,17,27,68,32,27,99,32,27,
131,32,27,162,32,27,193,32,27,225,32,27,0,33,27,32,33,27,80,64,27,112,64,27,144,64,27,176,64,27,208,64,27,240,64,27,15,65,27,46,65,27,76,65,27,107,65,27,
16,66,27,48,66,27,79,66,27,108,66,27,137,66,27,166,66,27,195,66,27,224,66,27,16,68,27,48,68,27,79,68,27,108,68,27,137,68,27,166,68,27,195,68,27,224,68,27,
16,70,27,48,70,27,79,70,27,108,70,27,137,70,27,166,70,27,195,70,27,224,70,27,16,72,27,48,72,27,79,72,27,108,72,27,137,72,27,166,72,27,195,72,27,224,72,27,
70,80,27,101,80,27,132,80,27,163,80,27,195,80,27,226,80,27,1,81,27,32,81,27,64,81,27,48,0,28,80,0,28,112,0,28,144,0,28,176,0,28,208,0,28,240,0,28,
16,1,28,48,1,28,80,1,28,112,1,28,48,16,28,80,16,28,112,16,28,144,16,28,176,16,28,208,16,28,240,16,28,16,17,28,48,17,28,78,17,28,106,17,28,48,32,28,
80,32,28,112,32,28,144,32,28,176,32,28,208,32,28,238,32,28,11,33,28,41,33,28,71,33,28,100,33,28,48,64,28,80,64,28,112,64,28,144,64,28,176,64,28,208,64,28,
240,64,28,16,65,28,48,65,28,80,65,28,112,65,28,16,72,28,48,72,28,80,72,28,112,72,28,143,72,28,166,72,28,48,80,28,80,80,28,112,80,28,142,80,28,172,80,28,
202,80,28,233,80,28,6,81,28,36,81,28,67,81,28,97,81,28,42,96,28,73,96,28,104,96,28,135,96,28,165,96,28,196,96,28,227,96,28,1,97,28,32,97,28,48,128,28,
80,128,28,112,128,28,144,128,28,176,128,28,208,128,28,240,128,28,16,129,28,48,129,28,80,129,28,112,129,28,16,130,28,48,130,28,80,130,28,112,130,28,143,130,28,166,130,28,
16,132,28,48,132,28,80,132,28,112,132,28,143,132,28,166,132,28,16,134,28,48,134,28,80,134,28,112,134,28,143,134,28,166,134,28,48,144,28,80,144,28,112,144,28,142,144,28,
172,144,28,202,144,28,233,144,28,6,145,28,36,145,28,67,145,28,97,145,28,42,160,28,73,160,28,104,160,28,135,160,28,165,160,28,196,160,28,227,160,28,1,161,28,32,161,28,
48,192,28,80,192,28,112,192,28,144,192,28,176,192,28,208,192,28,240,192,28,16,193,28,47,193,28,77,193,28,106,193,28,16,194,28,48,194,28,80,194,28,107,194,28,135,194,28,
161,194,28,16,196,28,48,196,28,80,196,28,107,196,28,135,196,28,161,196,28,16,198,28,48,198,28,80,198,28,107,198,28,135,198,28,161,198,28,42,208,28,73,208,28,104,208,28,
135,208,28,165,208,28,196,208,28,227,208,28,1,209,28,32,209,28,36,224,28,67,224,28,98,224,28,130,224,28,161,224,28,192,224,28,48,0,29,80,0,29,112,0,29,144,0,29,
176,0,29,208,0,29,240,0,29,16,1,29,47,1,29,77,1,29,106,1,29,16,2,29,48,2,29,80,2,29,107,2,29,135,2,29,161,2,29,16,4,29,48,4,29,80,4,29,
107,4,29,135,4,29,161,4,29,16,6,29,48,6,29,80,6,29,107,6,29,135,6,29,161,6,29,16,8,29,48,8,29,80,8,29,107,8,29,135,8,29,161,8,29,42,16,29,
73,16,29,104,16,29,135,16,29,165,16,29,196,16,29,227,16,29,1,17,29,32,17,29,36,32,29,67,32,29,98,32,29,130,32,29,161,32,29,192,32,29,48,64,29,80,64,29,
112,64,29,144,64,29,176,64,29,207,64,29,237,64,29,11,65,29,41,65,29,71,65,29,101,65,29,16,66,29,47,66,29,74,66,29,102,66,29,131,66,29,16,68,29,47,68,29,
74,68,29,102,68,29,131,68,29,16,70,29,47,70,29,74,70,29,102,70,29,131,70,29,16,72,29,47,72,29,74,72,29,102,72,29,131,72,29,38,80,29,68,80,29,100,80,29,
131,80,29,162,80,29,193,80,29,224,80,29,48,0,30,80,0,30,112,0,30,144,0,30,176,0,30,208,0,30,240,0,30,16,1,30,48,1,30,80,1,30,112,1,30,48,16,30,
80,16,30,112,16,30,144,16,30,176,16,30,208,16,30,240,16,30,12,17,30,39,17,30,68,17,30,48,32,30,80,32,30,112,32,30,144,32,30,174,32,30,203,32,30,233,32,30,
5,33,30,34,33,30,64,33,30,48,64,30,80,64,30,112,64,30,144,64,30,176,64,30,208,64,30,240,64,30,16,65,30,48,65,30,77,65,30,103,65,30,16,72,30,48,72,30,
80,72,30,106,72,30,131,72,30,48,80,30,79,80,30,109,80,30,139,80,30,169,80,30,198,80,30,228,80,30,2,81,30,32,81,30,41,96,30,71,96,30,102,96,30,133,96,30,
163,96,30,193,96,30,224,96,30,48,128,30,80,128,30,112,128,30,144,128,30,176,128,30,208,128,30,240,128,30,16,129,30,48,129,30,77,129,30,103,129,30,16,130,30,48,130,30,
80,130,30,106,130,30,131,130,30,16,132,30,48,132,30,80,132,30,106,132,30,131,132,30,16,134,30,48,134,30,80,134,30,106,134,30,131,134,30,48,144,30,79,144,30,109,144,30,
139,144,30,169,144,30,198,144,30,228,144,30,2,145,30,32,145,30,41,160,30,71,160,30,102,160,30,133,160,30,163,160,30,193,160,30,224,160,30,48,192,30,80,192,30,112,192,30,
144,192,30,176,192,30,208,192,30,239,192,30,11,193,30,40,193,30,70,193,30,98,193,30,16,194,30,48,194,30,74,194,30,100,194,30,16,196,30,48,196,30,74,196,30,100,196,30,
16,198,30,48,198,30,74,198,30,100,198,30,41,208,30,71,208,30,102,208,30,133,208,30,163,208,30,193,208,30,224,208,30,35,224,30,66,224,30,97,224,30,128,224,30,48,0,31,
80,0,31,112,0,31,144,0,31,176,0,31,208,0,31,239,0,31,11,1,31,40,1,31,70,1,31,98,1,31,16,2,31,48,2,31,74,2,31,100,2,31,16,4,31,48,4,31,
74,4,31,100,4,31,16,6,31,48,6,31,74,6,31,100,6,31,16,8,31,48,8,31,74,8,31,100,8,31,41,16,31,71,16,31,102,16,31,133,16,31,163,16,31,193,16,31,
224,16,31,35,32,31,66,32,31,97,32,31,128,32,31,48,64,31,80,64,31,112,64,31,144,64,31,173,64,31,203,64,31,233,64,31,6,65,31,36,65,31,66,65,31,96,65,31,
16,66,31,43,66,31,70,66,31,97,66,31,16,68,31,43,68,31,70,68,31,97,68,31,16,70,31,43,70,31,70,70,31,97,70,31,16,72,31,43,72,31,70,72,31,97,72,31,
37,80,31,67,80,31,98,80,31,129,80,31,160,80,31,48,0,32,80,0,32,112,0,32,144,0,32,176,0,32,208,0,32,240,0,32,16,1,32,48,1,32,48,16,32,80,16,32,
112,16,32,144,16,32,176,16,32,205,16,32,233,16,32,3,17,32,48,32,32,80,32,32,112,32,32,142,32,32,170,32,32,198,32,32,227,32,32,48,64,32,80,64,32,112,64,32,
144,64,32,176,64,32,208,64,32,240,64,32,12,65,32,39,65,32,16,72,32,48,72,32,74,72,32,48,80,32,77,80,32,106,80,32,136,80,32,165,80,32,195,80,32,224,80,32,
40,96,32,70,96,32,100,96,32,131,96,32,161,96,32,48,128,32,80,128,32,112,128,32,144,128,32,176,128,32,208,128,32,240,128,32,12,129,32,39,129,32,16,130,32,48,130,32,
74,130,32,16,132,32,48,132,32,74,132,32,16,134,32,48,134,32,74,134,32,48,144,32,77,144,32,106,144,32,136,144,32,165,144,32,195,144,32,224,144,32,40,160,32,70,160,32,
100,160,32,131,160,32,161,160,32,48,192,32,80,192,32,112,192,32,144,192,32,176,192,32,204,192,32,233,192,32,5,193,32,34,193,32,16,194,32,44,194,32,68,194,32,16,196,32,
44,196,32,68,196,32,16,198,32,44,198,32,68,198,32,40,208,32,70,208,32,100,208,32,131,208,32,161,208,32,35,224,32,65,224,32,96,224,32,48,0,33,80,0,33,112,0,33,
144,0,33,176,0,33,204,0,33,233,0,33,5,1,33,34,1,33,16,2,33,44,2,33,68,2,33,16,4,33,44,4,33,68,4,33,16,6,33,44,6,33,68,6,33,16,8,33,
44,8,33,68,8,33,40,16,33,70,16,33,100,16,33,131,16,33,161,16,33,35,32,33,65,32,33,96,32,33,48,64,33,80,64,33,111,64,33,141,64,33,170,64,33,199,64,33,
229,64,33,2,65,33,16,66,33,39,66,33,65,66,33,16,68,33,39,68,33,65,68,33,16,70,33,39,70,33,65,70,33,16,72,33,39,72,33,65,72,33,36,80,33,66,80,33,
97,80,33,128,80,33,16,0,34,48,0,34,80,0,34,112,0,34,144,0,34,176,0,34,208,0,34,240,0,34,14,1,34,16,16,34,48,16,34,80,16,34,112,16,34,144,16,34,
172,16,34,198,16,34,225,16,34,16,32,34,48,32,34,80,32,34,109,32,34,138,32,34,165,32,34,193,32,34,16,64,34,48,64,34,80,64,34,112,64,34,144,64,34,176,64,34,
207,64,34,234,64,34,3,65,34,16,72,34,48,72,34,65,72,34,16,80,34,46,80,34,75,80,34,104,80,34,133,80,34,162,80,34,10,96,34,39,96,34,68,96,34,98,96,34,
129,96,34,16,128,34,48,128,34,80,128,34,112,128,34,144,128,34,176,128,34,207,128,34,234,128,34,3,129,34,16,130,34,48,130,34,65,130,34,16,132,34,48,132,34,65,132,34,
16,134,34,48,134,34,65,134,34,16,144,34,46,144,34,75,144,34,104,144,34,133,144,34,162,144,34,10,160,34,39,160,34,68,160,34,98,160,34,129,160,34,16,192,34,48,192,34,
80,192,34,112,192,34,144,192,34,171,192,34,199,192,34,228,192,34,16,194,34,40,194,34,16,196,34,40,196,34,16,198,34,40,198,34,10,208,34,39,208,34,68,208,34,98,208,34,
129,208,34,4,224,34,34,224,34,64,224,34,16,0,35,48,0,35,80,0,35,112,0,35,144,0,35,171,0,35,199,0,35,228,0,35,16,2,35,40,2,35,16,4,35,40,4,35,
16,6,35,40,6,35,16,8,35,40,8,35,10,16,35,39,16,35,68,16,35,98,16,35,129,16,35,4,32,35,34,32,35,64,32,35,16,64,35,48,64,35,79,64,35,108,64,35,
138,64,35,166,64,35,195,64,35,225,64,35,15,66,35,36,66,35,15,68,35,36,68,35,15,70,35,36,70,35,15,72,35,36,72,35,6,80,35,35,80,35,65,80,35,96,80,35,
16,0,36,48,0,36,80,0,36,112,0,36,144,0,36,176,0,36,208,0,36,16,16,36,48,16,36,80,16,36,112,16,36,141,16,36,165,16,36,16,32,36,48,32,36,78,32,36,
106,32,36,134,32,36,161,32,36,16,64,36,48,64,36,80,64,36,112,64,36,144,64,36,174,64,36,199,64,36,16,72,36,40,72,36,16,80,36,44,80,36,73,80,36,101,80,36,
130,80,36,10,96,36,37,96,36,67,96,36,97,96,36,16,128,36,48,128,36,80,128,36,112,128,36,144,128,36,174,128,36,199,128,36,16,130,36,40,130,36,16,132,36,40,132,36,
16,134,36,40,134,36,16,144,36,44,144,36,73,144,36,101,144,36,130,144,36,10,160,36,37,160,36,67,160,36,97,160,36,16,192,36,48,192,36,80,192,36,112,192,36,140,192,36,
167,192,36,194,192,36,16,194,36,35,194,36,16,196,36,35,196,36,16,198,36,35,198,36,10,208,36,37,208,36,67,208,36,97,208,36,4,224,36,33,224,36,16,0,37,48,0,37,
80,0,37,112,0,37,140,0,37,167,0,37,194,0,37,16,2,37,35,2,37,16,4,37,35,4,37,16,6,37,35,6,37,16,8,37,35,8,37,10,16,37,37,16,37,67,16,37,
97,16,37,4,32,37,33,32,37,16,64,37,48,64,37,77,64,37,106,64,37,135,64,37,163,64,37,192,64,37,12,66,37,32,66,37,12,68,37,32,68,37,12,70,37,32,70,37,
12,72,37,32,72,37,5,80,37,34,80,37,64,80,37,16,0,38,48,0,38,80,0,38,112,0,38,144,0,38,176,0,38,16,16,38,48,16,38,80,16,38,109,16,38,135,16,38,
16,32,38,48,32,38,75,32,38,102,32,38,130,32,38,16,64,38,48,64,38,80,64,38,112,64,38,144,64,38,167,64,38,16,72,38,33,72,38,16,80,38,43,80,38,70,80,38,
99,80,38,128,80,38,9,96,38,36,96,38,65,96,38,16,128,38,48,128,38,80,128,38,112,128,38,144,128,38,167,128,38,16,130,38,33,130,38,16,132,38,33,132,38,16,134,38,
33,134,38,16,144,38,43,144,38,70,144,38,99,144,38,128,144,38,9,160,38,36,160,38,65,160,38,16,192,38,48,192,38,80,192,38,108,192,38,136,192,38,162,192,38,16,194,38,
16,196,38,16,198,38,9,208,38,36,208,38,65,208,38,3,224,38,32,224,38,16,0,39,48,0,39,80,0,39,108,0,39,136,0,39,162,0,39,16,2,39,16,4,39,16,6,39,
16,8,39,9,16,39,36,16,39,65,16,39,3,32,39,32,32,39,16,64,39,47,64,39,75,64,39,103,64,39,132,64,39,160,64,39,10,66,39,10,68,39,10,70,39,10,72,39,
4,80,39,33,80,39,16,0,40,48,0,40,80,0,40,112,0,40,144,0,40,16,16,40,48,16,40,80,16,40,104,16,40,129,16,40,16,32,40,47,32,40,72,32,40,99,32,40,
16,64,40,48,64,40,80,64,40,112,64,40,138,64,40,16,80,40,41,80,40,68,80,40,96,80,40,8,96,40,35,96,40,64,96,40,16,128,40,48,128,40,80,128,40,112,128,40,
138,128,40,16,144,40,41,144,40,68,144,40,96,144,40,8,160,40,35,160,40,64,160,40,16,192,40,48,192,40,78,192,40,105,192,40,132,192,40,8,208,40,35,208,40,64,208,40,
3,224,40,16,0,41,48,0,41,78,0,41,105,0,41,132,0,41,8,16,41,35,16,41,64,16,41,3,32,41,16,64,41,45,64,41,73,64,41,100,64,41,129,64,41,4,80,41,
32,80,41,16,0,42,48,0,42,80,0,42,112,0,42,144,0,42,16,16,42,48,16,42,76,16,42,99,16,42,16,32,42,44,32,42,69,32,42,16,64,42,48,64,42,80,64,42,
108,64,42,132,64,42,15,80,42,39,80,42,66,80,42,7,96,42,34,96,42,16,128,42,48,128,42,80,128,42,108,128,42,132,128,42,15,144,42,39,144,42,66,144,42,7,160,42,
34,160,42,16,192,42,48,192,42,75,192,42,101,192,42,128,192,42,7,208,42,34,208,42,2,224,42,16,0,43,48,0,43,75,0,43,101,0,43,128,0,43,7,16,43,34,16,43,
2,32,43,16,64,43,44,64,43,70,64,43,98,64,43,3,80,43,176,0,44,208,0,44,240,0,44,16,1,44,48,1,44,80,1,44,112,1,44,176,16,44,208,16,44,240,16,44,
16,17,44,48,17,44,80,17,44,112,17,44,176,32,44,208,32,44,240,32,44,16,33,44,48,33,44,80,33,44,112,33,44,176,64,44,208,64,44,240,64,44,16,65,44,48,65,44,
80,65,44,112,65,44,48,72,44,80,72,44,112,72,44,144,72,44,176,72,44,208,72,44,240,72,44,16,73,44,48,73,44,80,73,44,109,73,44,176,80,44,208,80,44,240,80,44,
16,81,44,48,81,44,79,81,44,110,81,44,170,96,44,202,96,44,233,96,44,8,97,44,40,97,44,71,97,44,102,97,44,176,128,44,208,128,44,240,128,44,16,129,44,48,129,44,
80,129,44,112,129,44,48,130,44,80,130,44,112,130,44,144,130,44,176,130,44,208,130,44,240,130,44,16,131,44,48,131,44,80,131,44,109,131,44,48,132,44,80,132,44,112,132,44,
144,132,44,176,132,44,208,132,44,240,132,44,16,133,44,48,133,44,80,133,44,109,133,44,48,134,44,80,134,44,112,134,44,144,134,44,176,134,44,208,134,44,240,134,44,16,135,44,
48,135,44,80,135,44,109,135,44,176,144,44,208,144,44,240,144,44,16,145,44,48,145,44,79,145,44,110,145,44,170,160,44,202,160,44,233,160,44,8,161,44,40,161,44,71,161,44,
102,161,44,176,192,44,208,192,44,240,192,44,16,193,44,48,193,44,80,193,44,112,193,44,48,194,44,80,194,44,112,194,44,144,194,44,176,194,44,208,194,44,240,194,44,14,195,44,
43,195,44,73,195,44,102,195,44,48,196,44,80,196,44,112,196,44,144,196,44,176,196,44,208,196,44,240,196,44,14,197,44,43,197,44,73,197,44,102,197,44,48,198,44,80,198,44,
112,198,44,144,198,44,176,198,44,208,198,44,240,198,44,14,199,44,43,199,44,73,199,44,102,199,44,170,208,44,202,208,44,233,208,44,8,209,44,40,209,44,71,209,44,102,209,44,
164,224,44,196,224,44,227,224,44,3,225,44,34,225,44,66,225,44,97,225,44,176,0,45,208,0,45,240,0,45,16,1,45,48,1,45,80,1,45,112,1,45,48,2,45,80,2,45,
112,2,45,144,2,45,176,2,45,208,2,45,240,2,45,14,3,45,43,3,45,73,3,45,102,3,45,48,4,45,80,4,45,112,4,45,144,4,45,176,4,45,208,4,45,240,4,45,
14,5,45,43,5,45,73,5,45,102,5,45,48,6,45,80,6,45,112,6,45,144,6,45,176,6,45,208,6,45,240,6,45,14,7,45,43,7,45,73,7,45,102,7,45,48,8,45,
80,8,45,112,8,45,144,8,45,176,8,45,208,8,45,240,8,45,14,9,45,43,9,45,73,9,45,102,9,45,170,16,45,202,16,45,233,16,45,8,17,45,40,17,45,71,17,45,
102,17,45,164,32,45,196,32,45,227,32,45,3,33,45,34,33,45,66,33,45,97,33,45,176,64,45,208,64,45,240,64,45,16,65,45,48,65,45,80,65,45,112,65,45,48,66,45,
80,66,45,112,66,45,144,66,45,175,66,45,204,66,45,235,66,45,9,67,45,38,67,45,69,67,45,99,67,45,48,68,45,80,68,45,112,68,45,144,68,45,175,68,45,204,68,45,
235,68,45,9,69,45,38,69,45,69,69,45,99,69,45,48,70,45,80,70,45,112,70,45,144,70,45,175,70,45,204,70,45,235,70,45,9,71,45,38,71,45,69,71,45,99,71,45,
48,72,45,80,72,45,112,72,45,144,72,45,175,72,45,204,72,45,235,72,45,9,73,45,38,73,45,69,73,45,99,73,45,166,80,45,197,80,45,229,80,45,4,81,45,36,81,45,
67,81,45,99,81,45,80,0,46,112,0,46,144,0,46,176,0,46,208,0,46,240,0,46,16,1,46,48,1,46,80,1,46,112,1,46,80,16,46,112,16,46,144,16,46,176,16,46,
208,16,46,240,16,46,16,17,46,48,17,46,80,17,46,112,17,46,80,32,46,112,32,46,144,32,46,176,32,46,208,32,46,240,32,46,16,33,46,47,33,46,77,33,46,107,33,46,
80,64,46,112,64,46,144,64,46,176,64,46,208,64,46,240,64,46,16,65,46,48,65,46,80,65,46,112,65,46,16,72,46,48,72,46,80,72,46,112,72,46,144,72,46,176,72,46,
205,72,46,232,72,46,1,73,46,80,80,46,112,80,46,144,80,46,175,80,46,206,80,46,236,80,46,11,81,46,41,81,46,72,81,46,102,81,46,74,96,46,105,96,46,136,96,46,
167,96,46,198,96,46,229,96,46,4,97,46,35,97,46,66,97,46,97,97,46,80,128,46,112,128,46,144,128,46,176,128,46,208,128,46,240,128,46,16,129,46,48,129,46,80,129,46,
112,129,46,16,130,46,48,130,46,80,130,46,112,130,46,144,130,46,176,130,46,205,130,46,232,130,46,1,131,46,16,132,46,48,132,46,80,132,46,112,132,46,144,132,46,176,132,46,
205,132,46,232,132,46,1,133,46,16,134,46,48,134,46,80,134,46,112,134,46,144,134,46,176,134,46,205,134,46,232,134,46,1,135,46,80,144,46,112,144,46,144,144,46,175,144,46,
206,144,46,236,144,46,11,145,46,41,145,46,72,145,46,102,145,46,74,160,46,105,160,46,136,160,46,167,160,46,198,160,46,229,160,46,4,161,46,35,161,46,66,161,46,97,161,46,
80,192,46,112,192,46,144,192,46,176,192,46,208,192,46,240,192,46,16,193,46,48,193,46,80,193,46,112,193,46,16,194,46,48,194,46,80,194,46,112,194,46,143,194,46,170,194,46,
198,194,46,227,194,46,16,196,46,48,196,46,80,196,46,112,196,46,143,196,46,170,196,46,198,196,46,227,196,46,16,198,46,48,198,46,80,198,46,112,198,46,143,198,46,170,198,46,
198,198,46,227,198,46,74,208,46,105,208,46,136,208,46,167,208,46,198,208,46,229,208,46,4,209,46,35,209,46,66,209,46,97,209,46,68,224,46,99,224,46,131,224,46,162,224,46,
193,224,46,225,224,46,0,225,46,32,225,46,80,0,47,112,0,47,144,0,47,176,0,47,208,0,47,240,0,47,16,1,47,48,1,47,80,1,47,112,1,47,16,2,47,48,2,47,
80,2,47,112,2,47,143,2,47,170,2,47,198,2,47,227,2,47,16,4,47,48,4,47,80,4,47,112,4,47,143,4,47,170,4,47,198,4,47,227,4,47,16,6,47,48,6,47,
80,6,47,112,6,47,143,6,47,170,6,47,198,6,47,227,6,47,16,8,47,48,8,47,80,8,47,112,8,47,143,8,47,170,8,47,198,8,47,227,8,47,74,16,47,105,16,47,
136,16,47,167,16,47,198,16,47,229,16,47,4,17,47,35,17,47,66,17,47,97,17,47,68,32,47,99,32,47,131,32,47,162,32,47,193,32,47,225,32,47,0,33,47,32,33,47,
80,64,47,112,64,47,144,64,47,176,64,47,208,64,47,240,64,47,15,65,47,46,65,47,76,65,47,107,65,47,16,66,47,48,66,47,79,66,47,108,66,47,137,66,47,166,66,47,
195,66,47,224,66,47,16,68,47,48,68,47,79,68,47,108,68,47,137,68,47,166,68,47,195,68,47,224,68,47,16,70,47,48,70,47,79,70,47,108,70,47,137,70,47,166,70,47,
195,70,47,224,70,47,16,72,47,48,72,47,79,72,47,108,72,47,137,72,47,166,72,47,195,72,47,224,72,47,70,80,47,101,80,47,132,80,47,163,80,47,195,80,47,226,80,47,
1,81,47,32,81,47,64,81,47,48,0,48,80,0,48,112,0,48,144,0,48,176,0,48,208,0,48,240,0,48,16,1,48,48,1,48,80,1,48,112,1,48,48,16,48,80,16,48,
112,16,48,144,16,48,176,16,48,208,16,48,240,16,48,16,17,48,45,17,48,74,17,48,102,17,48,48,32,48,80,32,48,112,32,48,144,32,48,176,32,48,206,32,48,236,32,48,
9,33,48,38,33,48,68,33,48,97,33,48,48,64,48,80,64,48,112,64,48,144,64,48,176,64,48,208,64,48,240,64,48,16,65,48,48,65,48,80,65,48,111,65,48,16,72,48,
48,72,48,80,72,48,112,72,48,138,72,48,161,72,48,48,80,48,80,80,48,111,80,48,141,80,48,171,80,48,201,80,48,231,80,48,5,81,48,35,81,48,65,81,48,42,96,48,
72,96,48,103,96,48,134,96,48,164,96,48,195,96,48,226,96,48,0,97,48,48,128,48,80,128,48,112,128,48,144,128,48,176,128,48,208,128,48,240,128,48,16,129,48,48,129,48,
80,129,48,111,129,48,16,130,48,48,130,48,80,130,48,112,130,48,138,130,48,161,130,48,16,132,48,48,132,48,80,132,48,112,132,48,138,132,48,161,132,48,16,134,48,48,134,48,
80,134,48,112,134,48,138,134,48,161,134,48,48,144,48,80,144,48,111,144,48,141,144,48,171,144,48,201,144,48,231,144,48,5,145,48,35,145,48,65,145,48,42,160,48,72,160,48,
103,160,48,134,160,48,164,160,48,195,160,48,226,160,48,0,161,48,48,192,48,80,192,48,112,192,48,144,192,48,176,192,48,208,192,48,240,192,48,15,193,48,44,193,48,74,193,48,
103,193,48,16,194,48,48,194,48,78,194,48,105,194,48,132,194,48,16,196,48,48,196,48,78,196,48,105,196,48,132,196,48,16,198,48,48,198,48,78,198,48,105,198,48,132,198,48,
42,208,48,72,208,48,103,208,48,134,208,48,164,208,48,195,208,48,226,208,48,0,209,48,36,224,48,67,224,48,98,224,48,129,224,48,160,224,48,48,0,49,80,0,49,112,0,49,
144,0,49,176,0,49,208,0,49,240,0,49,15,1,49,44,1,49,74,1,49,103,1,49,16,2,49,48,2,49,78,2,49,105,2,49,132,2,49,16,4,49,48,4,49,78,4,49,
105,4,49,132,4,49,16,6,49,48,6,49,78,6,49,105,6,49,132,6,49,16,8,49,48,8,49,78,8,49,105,8,49,132,8,49,42,16,49,72,16,49,103,16,49,134,16,49,
164,16,49,195,16,49,226,16,49,0,17,49,36,32,49,67,32,49,98,32,49,129,32,49,160,32,49,48,64,49,80,64,49,112,64,49,144,64,49,175,64,49,205,64,49,236,64,49,
9,65,49,39,65,49,70,65,49,99,65,49,16,66,49,45,66,49,73,66,49,100,66,49,129,66,49,16,68,49,45,68,49,73,68,49,100,68,49,129,68,49,16,70,49,45,70,49,
73,70,49,100,70,49,129,70,49,16,72,49,45,72,49,73,72,49,100,72,49,129,72,49,37,80,49,68,80,49,99,80,49,130,80,49,161,80,49,192,80,49,48,0,50,80,0,50,
112,0,50,144,0,50,176,0,50,208,0,50,240,0,50,16,1,50,48,1,50,80,1,50,48,16,50,80,16,50,112,16,50,144,16,50,176,16,50,208,16,50,236,16,50,6,17,50,
33,17,50,48,32,50,80,32,50,112,32,50,143,32,50,171,32,50,200,32,50,229,32,50,1,33,50,48,64,50,80,64,50,112,64,50,144,64,50,176,64,50,208,64,50,240,64,50,
15,65,50,42,65,50,70,65,50,16,72,50,48,72,50,77,72,50,99,72,50,48,80,50,78,80,50,107,80,50,137,80,50,166,80,50,196,80,50,226,80,50,40,96,50,70,96,50,
101,96,50,131,96,50,161,96,50,192,96,50,48,128,50,80,128,50,112,128,50,144,128,50,176,128,50,208,128,50,240,128,50,15,129,50,42,129,50,70,129,50,16,130,50,48,130,50,
77,130,50,99,130,50,16,132,50,48,132,50,77,132,50,99,132,50,16,134,50,48,134,50,77,134,50,99,134,50,48,144,50,78,144,50,107,144,50,137,144,50,166,144,50,196,144,50,
226,144,50,40,160,50,70,160,50,101,160,50,131,160,50,161,160,50,192,160,50,48,192,50,80,192,50,112,192,50,144,192,50,176,192,50,206,192,50,235,192,50,7,193,50,36,193,50,
65,193,50,16,194,50,46,194,50,70,194,50,16,196,50,46,196,50,70,196,50,16,198,50,46,198,50,70,198,50,40,208,50,70,208,50,101,208,50,131,208,50,161,208,50,192,208,50,
35,224,50,65,224,50,96,224,50,128,224,50,48,0,51,80,0,51,112,0,51,144,0,51,176,0,51,206,0,51,235,0,51,7,1,51,36,1,51,65,1,51,16,2,51,46,2,51,
70,2,51,16,4,51,46,4,51,70,4,51,16,6,51,46,6,51,70,6,51,16,8,51,46,8,51,70,8,51,40,16,51,70,16,51,101,16,51,131,16,51,161,16,51,192,16,51,
35,32,51,65,32,51,96,32,51,128,32,51,48,64,51,80,64,51,112,64,51,142,64,51,171,64,51,200,64,51,230,64,51,3,65,51,33,65,51,16,66,51,41,66,51,67,66,51,
16,68,51,41,68,51,67,68,51,16,70,51,41,70,51,67,70,51,16,72,51,41,72,51,67,72,51,36,80,51,67,80,51,97,80,51,128,80,51,16,0,52,48,0,52,80,0,52,
112,0,52,144,0,52,176,0,52,208,0,52,240,0,52,14,1,52,16,16,52,48,16,52,80,16,52,112,16,52,144,16,52,172,16,52,198,16,52,225,16,52,16,32,52,48,32,52,
80,32,52,109,32,52,138,32,52,165,32,52,193,32,52,16,64,52,48,64,52,80,64,52,112,64,52,144,64,52,176,64,52,207,64,52,234,64,52,3,65,52,16,72,52,48,72,52,
65,72,52,16,80,52,46,80,52,75,80,52,104,80,52,133,80,52,162,80,52,10,96,52,39,96,52,68,96,52,98,96,52,129,96,52,16,128,52,48,128,52,80,128,52,112,128,52,
144,128,52,176,128,52,207,128,52,234,128,52,3,129,52,16,130,52,48,130,52,65,130,52,16,132,52,48,132,52,65,132,52,16,134,52,48,134,52,65,134,52,16,144,52,46,144,52,
75,144,52,104,144,52,133,144,52,162,144,52,10,160,52,39,160,52,68,160,52,98,160,52,129,160,52,16,192,52,48,192,52,80,192,52,112,192,52,144,192,52,171,192,52,199,192,52,
228,192,52,16,194,52,40,194,52,16,196,52,40,196,52,16,198,52,40,198,52,10,208,52,39,208,52,68,208,52,98,208,52,129,208,52,4,224,52,34,224,52,64,224,52,16,0,53,
48,0,53,80,0,53,112,0,53,144,0,53,171,0,53,199,0,53,228,0,53,16,2,53,40,2,53,16,4,53,40,4,53,16,6,53,40,6,53,16,8,53,40,8,53,10,16,53,
39,16,53,68,16,53,98,16,53,129,16,53,4,32,53,34,32,53,64,32,53,16,64,53,48,64,53,79,64,53,108,64,53,138,64,53,166,64,53,195,64,53,225,64,53,15,66,53,
36,66,53,15,68,53,36,68,53,15,70,53,36,70,53,15,72,53,36,72,53,6,80,53,35,80,53,65,80,53,96,80,53,16,0,54,48,0,54,80,0,54,112,0,54,144,0,54,
176,0,54,208,0,54,16,16,54,48,16,54,80,16,54,112,16,54,139,16,54,163,16,54,16,32,54,48,32,54,77,32,54,104,32,54,133,32,54,16,64,54,48,64,54,80,64,54,
112,64,54,144,64,54,172,64,54,196,64,54,16,72,54,38,72,54,16,80,54,44,80,54,72,80,54,100,80,54,129,80,54,9,96,54,37,96,54,66,96,54,96,96,54,16,128,54,
48,128,54,80,128,54,112,128,54,144,128,54,172,128,54,196,128,54,16,130,54,38,130,54,16,132,54,38,132,54,16,134,54,38,134,54,16,144,54,44,144,54,72,144,54,100,144,54,
129,144,54,9,160,54,37,160,54,66,160,54,96,160,54,16,192,54,48,192,54,80,192,54,110,192,54,139,192,54,165,192,54,192,192,54,16,194,54,33,194,54,16,196,54,33,196,54,
16,198,54,33,198,54,9,208,54,37,208,54,66,208,54,96,208,54,3,224,54,33,224,54,16,0,55,48,0,55,80,0,55,110,0,55,139,0,55,165,0,55,192,0,55,16,2,55,
33,2,55,16,4,55,33,4,55,16,6,55,33,6,55,16,8,55,33,8,55,9,16,55,37,16,55,66,16,55,96,16,55,3,32,55,33,32,55,16,64,55,48,64,55,76,64,55,
105,64,55,134,64,55,162,64,55,12,66,55,12,68,55,12,70,55,12,72,55,5,80,55,34,80,55,64,80,55,16,0,56,48,0,56,80,0,56,112,0,56,144,0,56,174,0,56,
16,16,56,48,16,56,80,16,56,106,16,56,131,16,56,16,32,56,47,32,56,73,32,56,100,32,56,16,64,56,48,64,56,80,64,56,112,64,56,140,64,56,163,64,56,16,72,56,
16,80,56,41,80,56,69,80,56,97,80,56,8,96,56,35,96,56,64,96,56,16,128,56,48,128,56,80,128,56,112,128,56,140,128,56,163,128,56,16,130,56,16,132,56,16,134,56,
16,144,56,41,144,56,69,144,56,97,144,56,8,160,56,35,160,56,64,160,56,16,192,56,48,192,56,79,192,56,106,192,56,133,192,56,14,194,56,14,196,56,14,198,56,8,208,56,
35,208,56,64,208,56,3,224,56,32,224,56,16,0,57,48,0,57,79,0,57,106,0,57,133,0,57,14,2,57,14,4,57,14,6,57,14,8,57,8,16,57,35,16,57,64,16,57,
3,32,57,32,32,57,16,64,57,46,64,57,73,64,57,101,64,57,130,64,57,9,66,57,9,68,57,9,70,57,9,72,57,4,80,57,32,80,57,16,0,58,48,0,58,80,0,58,
112,0,58,144,0,58,16,16,58,48,16,58,76,16,58,99,16,58,16,32,58,44,32,58,69,32,58,16,64,58,48,64,58,80,64,58,108,64,58,132,64,58,15,80,58,39,80,58,
66,80,58,7,96,58,34,96,58,16,128,58,48,128,58,80,128,58,108,128,58,132,128,58,15,144,58,39,144,58,66,144,58,7,160,58,34,160,58,16,192,58,48,192,58,75,192,58,
101,192,58,128,192,58,7,208,58,34,208,58,2,224,58,16,0,59,48,0,59,75,0,59,101,0,59,128,0,59,7,16,59,34,16,59,2,32,59,16,64,59,44,64,59,70,64,59,
98,64,59,3,80,59,16,0,60,48,0,60,80,0,60,112,0,60,16,16,60,48,16,60,70,16,60,16,32,60,41,32,60,65,32,60,16,64,60,48,64,60,79,64,60,100,64,60,
14,80,60,37,80,60,6,96,60,32,96,60,16,128,60,48,128,60,79,128,60,100,128,60,14,144,60,37,144,60,6,160,60,32,160,60,16,192,60,47,192,60,71,192,60,96,192,60,
6,208,60,32,208,60,1,224,60,16,0,61,47,0,61,71,0,61,96,0,61,6,16,61,32,16,61,1,32,61,16,64,61,41,64,61,67,64,61,3,80,61,16,0,62,48,0,62,
80,0,62,16,16,62,45,16,62,64,16,62,16,32,62,38,32,62,16,64,62,48,64,62,73,64,62,12,80,62,34,80,62,5,96,62,16,128,62,48,128,62,73,128,62,12,144,62,
34,144,62,5,160,62,16,192,62,44,192,62,67,192,62,5,208,62,1,224,62,16,0,63,44,0,63,67,0,63,5,16,63,1,32,63,16,64,63,39,64,63,64,64,63,2,80,63,
16,0,64,48,0,64,78,0,64,16,16,64,40,16,64,16,32,64,35,32,64,16,64,64,48,64,64,67,64,64,11,80,64,32,80,64,4,96,64,16,128,64,48,128,64,67,128,64,
11,144,64,32,144,64,4,160,64,16,192,64,41,192,64,4,208,64,0,224,64,16,0,65,41,0,65,4,16,65,0,32,65,15,64,65,36,64,65,1,80,65,112,0,66,144,0,66,
176,0,66,208,0,66,240,0,66,16,1,66,48,1,66,80,1,66,112,1,66,112,16,66,144,16,66,176,16,66,208,16,66,240,16,66,16,17,66,48,17,66,80,17,66,112,17,66,
112,32,66,144,32,66,176,32,66,208,32,66,240,32,66,16,33,66,48,33,66,80,33,66,112,33,66,112,64,66,144,64,66,176,64,66,208,64,66,240,64,66,16,65,66,48,65,66,
80,65,66,112,65,66,48,72,66,80,72,66,112,72,66,144,72,66,176,72,66,208,72,66,240,72,66,13,73,66,40,73,66,68,73,66,112,80,66,144,80,66,176,80,66,208,80,66,
239,80,66,14,81,66,44,81,66,76,81,66,106,81,66,106,96,66,138,96,66,169,96,66,200,96,66,231,96,66,6,97,66,37,97,66,69,97,66,100,97,66,112,128,66,144,128,66,
176,128,66,208,128,66,240,128,66,16,129,66,48,129,66,80,129,66,112,129,66,48,130,66,80,130,66,112,130,66,144,130,66,176,130,66,208,130,66,240,130,66,13,131,66,40,131,66,
68,131,66,48,132,66,80,132,66,112,132,66,144,132,66,176,132,66,208,132,66,240,132,66,13,133,66,40,133,66,68,133,66,48,134,66,80,134,66,112,134,66,144,134,66,176,134,66,
208,134,66,240,134,66,13,135,66,40,135,66,68,135,66,112,144,66,144,144,66,176,144,66,208,144,66,239,144,66,14,145,66,44,145,66,76,145,66,106,145,66,106,160,66,138,160,66,
169,160,66,200,160,66,231,160,66,6,161,66,37,161,66,69,161,66,100,161,66,112,192,66,144,192,66,176,192,66,208,192,66,240,192,66,16,193,66,48,193,66,80,193,66,112,193,66,
48,194,66,80,194,66,112,194,66,144,194,66,176,194,66,205,194,66,234,194,66,6,195,66,35,195,66,64,195,66,48,196,66,80,196,66,112,196,66,144,196,66,176,196,66,205,196,66,
234,196,66,6,197,66,35,197,66,64,197,66,48,198,66,80,198,66,112,198,66,144,198,66,176,198,66,205,198,66,234,198,66,6,199,66,35,199,66,64,199,66,106,208,66,138,208,66,
169,208,66,200,208,66,231,208,66,6,209,66,37,209,66,69,209,66,100,209,66,100,224,66,132,224,66,163,224,66,195,224,66,226,224,66,1,225,66,33,225,66,64,225,66,96,225,66,
112,0,67,144,0,67,176,0,67,208,0,67,240,0,67,16,1,67,48,1,67,80,1,67,112,1,67,48,2,67,80,2,67,112,2,67,144,2,67,176,2,67,205,2,67,234,2,67,
6,3,67,35,3,67,64,3,67,48,4,67,80,4,67,112,4,67,144,4,67,176,4,67,205,4,67,234,4,67,6,5,67,35,5,67,64,5,67,48,6,67,80,6,67,112,6,67,
144,6,67,176,6,67,205,6,67,234,6,67,6,7,67,35,7,67,64,7,67,48,8,67,80,8,67,112,8,67,144,8,67,176,8,67,205,8,67,234,8,67,6,9,67,35,9,67,
64,9,67,106,16,67,138,16,67,169,16,67,200,16,67,231,16,67,6,17,67,37,17,67,69,17,67,100,17,67,100,32,67,132,32,67,163,32,67,195,32,67,226,32,67,1,33,67,
33,33,67,64,33,67,96,33,67,112,64,67,144,64,67,176,64,67,208,64,67,240,64,67,16,65,67,48,65,67,80,65,67,111,65,67,48,66,67,80,66,67,111,66,67,141,66,67,
170,66,67,199,66,67,230,66,67,3,67,67,32,67,67,48,68,67,80,68,67,111,68,67,141,68,67,170,68,67,199,68,67,230,68,67,3,69,67,32,69,67,48,70,67,80,70,67,
111,70,67,141,70,67,170,70,67,199,70,67,230,70,67,3,71,67,32,71,67,48,72,67,80,72,67,111,72,67,141,72,67,170,72,67,199,72,67,230,72,67,3,73,67,32,73,67,
102,80,67,133,80,67,164,80,67,196,80,67,227,80,67,3,81,67,34,81,67,65,81,67,97,81,67,48,0,68,80,0,68,112,0,68,144,0,68,176,0,68,208,0,68,240,0,68,
16,1,68,48,1,68,80,1,68,112,1,68,48,16,68,80,16,68,112,16,68,144,16,68,176,16,68,208,16,68,240,16,68,16,17,68,48,17,68,78,17,68,106,17,68,48,32,68,
80,32,68,112,32,68,144,32,68,176,32,68,208,32,68,238,32,68,11,33,68,41,33,68,71,33,68,100,33,68,48,64,68,80,64,68,112,64,68,144,64,68,176,64,68,208,64,68,
240,64,68,16,65,68,48,65,68,80,65,68,112,65,68,16,72,68,48,72,68,80,72,68,112,72,68,143,72,68,166,72,68,48,80,68,80,80,68,112,80,68,142,80,68,172,80,68,
202,80,68,233,80,68,6,81,68,36,81,68,67,81,68,97,81,68,42,96,68,73,96,68,104,96,68,135,96,68,165,96,68,196,96,68,227,96,68,1,97,68,32,97,68,48,128,68,
80,128,68,112,128,68,144,128,68,176,128,68,208,128,68,240,128,68,16,129,68,48,129,68,80,129,68,112,129,68,16,130,68,48,130,68,80,130,68,112,130,68,143,130,68,166,130,68,
16,132,68,48,132,68,80,132,68,112,132,68,143,132,68,166,132,68,16,134,68,48,134,68,80,134,68,112,134,68,143,134,68,166,134,68,48,144,68,80,144,68,112,144,68,142,144,68,
172,144,68,202,144,68,233,144,68,6,145,68,36,145,68,67,145,68,97,145,68,42,160,68,73,160,68,104,160,68,135,160,68,165,160,68,196,160,68,227,160,68,1,161,68,32,161,68,
48,192,68,80,192,68,112,192,68,144,192,68,176,192,68,208,192,68,240,192,68,16,193,68,47,193,68,77,193,68,106,193,68,16,194,68,48,194,68,80,194,68,107,194,68,135,194,68,
161,194,68,16,196,68,48,196,68,80,196,68,107,196,68,135,196,68,161,196,68,16,198,68,48,198,68,80,198,68,107,198,68,135,198,68,161,198,68,42,208,68,73,208,68,104,208,68,
135,208,68,165,208,68,196,208,68,227,208,68,1,209,68,32,209,68,36,224,68,67,224,68,98,224,68,130,224,68,161,224,68,192,224,68,48,0,69,80,0,69,112,0,69,144,0,69,
176,0,69,208,0,69,240,0,69,16,1,69,47,1,69,77,1,69,106,1,69,16,2,69,48,2,69,80,2,69,107,2,69,135,2,69,161,2,69,16,4,69,48,4,69,80,4,69,
107,4,69,135,4,69,161,4,69,16,6,69,48,6,69,80,6,69,107,6,69,135,6,69,161,6,69,16,8,69,48,8,69,80,8,69,107,8,69,135,8,69,161,8,69,42,16,69,
73,16,69,104,16,69,135,16,69,165,16,69,196,16,69,227,16,69,1,17,69,32,17,69,36,32,69,67,32,69,98,32,69,130,32,69,161,32,69,192,32,69,48,64,69,80,64,69,
112,64,69,144,64,69,176,64,69,207,64,69,237,64,69,11,65,69,41,65,69,71,65,69,101,65,69,16,66,69,47,66,69,74,66,69,102,66,69,131,66,69,16,68,69,47,68,69,
74,68,69,102,68,69,131,68,69,16,70,69,47,70,69,74,70,69,102,70,69,131,70,69,16,72,69,47,72,69,74,72,69,102,72,69,131,72,69,38,80,69,68,80,69,100,80,69,
131,80,69,162,80,69,193,80,69,224,80,69,48,0,70,80,0,70,112,0,70,144,0,70,176,0,70,208,0,70,240,0,70,16,1,70,48,1,70,80,1,70,48,16,70,80,16,70,
112,16,70,144,16,70,176,16,70,208,16,70,236,16,70,6,17,70,33,17,70,48,32,70,80,32,70,112,32,70,143,32,70,171,32,70,200,32,70,229,32,70,1,33,70,48,64,70,
80,64,70,112,64,70,144,64,70,176,64,70,208,64,70,240,64,70,15,65,70,42,65,70,70,65,70,16,72,70,48,72,70,77,72,70,99,72,70,48,80,70,78,80,70,107,80,70,
137,80,70,166,80,70,196,80,70,226,80,70,40,96,70,70,96,70,101,96,70,131,96,70,161,96,70,192,96,70,48,128,70,80,128,70,112,128,70,144,128,70,176,128,70,208,128,70,
240,128,70,15,129,70,42,129,70,70,129,70,16,130,70,48,130,70,77,130,70,99,130,70,16,132,70,48,132,70,77,132,70,99,132,70,16,134,70,48,134,70,77,134,70,99,134,70,
48,144,70,78,144,70,107,144,70,137,144,70,166,144,70,196,144,70,226,144,70,40,160,70,70,160,70,101,160,70,131,160,70,161,160,70,192,160,70,48,192,70,80,192,70,112,192,70,
144,192,70,176,192,70,206,192,70,235,192,70,7,193,70,36,193,70,65,193,70,16,194,70,46,194,70,70,194,70,16,196,70,46,196,70,70,196,70,16,198,70,46,198,70,70,198,70,
40,208,70,70,208,70,101,208,70,131,208,70,161,208,70,192,208,70,35,224,70,65,224,70,96,224,70,128,224,70,48,0,71,80,0,71,112,0,71,144,0,71,176,0,71,206,0,71,
235,0,71,7,1,71,36,1,71,65,1,71,16,2,71,46,2,71,70,2,71,16,4,71,46,4,71,70,4,71,16,6,71,46,6,71,70,6,71,16,8,71,46,8,71,70,8,71,
40,16,71,70,16,71,101,16,71,131,16,71,161,16,71,192,16,71,35,32,71,65,32,71,96,32,71,128,32,71,48,64,71,80,64,71,112,64,71,142,64,71,171,64,71,200,64,71,
230,64,71,3,65,71,33,65,71,16,66,71,41,66,71,67,66,71,16,68,71,41,68,71,67,68,71,16,70,71,41,70,71,67,70,71,16,72,71,41,72,71,67,72,71,36,80,71,
67,80,71,97,80,71,128,80,71,16,0,72,48,0,72,80,0,72,112,0,72,144,0,72,176,0,72,208,0,72,240,0,72,16,16,72,48,16,72,80,16,72,112,16,72,144,16,72,
170,16,72,195,16,72,16,32,72,48,32,72,80,32,72,108,32,72,137,32,72,164,32,72,16,64,72,48,64,72,80,64,72,112,64,72,144,64,72,176,64,72,204,64,72,231,64,72,
16,72,72,45,72,72,16,80,72,46,80,72,74,80,72,103,80,72,132,80,72,161,80,72,10,96,72,38,96,72,68,96,72,98,96,72,128,96,72,16,128,72,48,128,72,80,128,72,
112,128,72,144,128,72,176,128,72,204,128,72,231,128,72,16,130,72,45,130,72,16,132,72,45,132,72,16,134,72,45,134,72,16,144,72,46,144,72,74,144,72,103,144,72,132,144,72,
161,144,72,10,160,72,38,160,72,68,160,72,98,160,72,128,160,72,16,192,72,48,192,72,80,192,72,112,192,72,143,192,72,170,192,72,197,192,72,226,192,72,16,194,72,38,194,72,
16,196,72,38,196,72,16,198,72,38,198,72,10,208,72,38,208,72,68,208,72,98,208,72,128,208,72,4,224,72,33,224,72,64,224,72,16,0,73,48,0,73,80,0,73,112,0,73,
143,0,73,170,0,73,197,0,73,226,0,73,16,2,73,38,2,73,16,4,73,38,4,73,16,6,73,38,6,73,16,8,73,38,8,73,10,16,73,38,16,73,68,16,73,98,16,73,
128,16,73,4,32,73,33,32,73,64,32,73,16,64,73,48,64,73,79,64,73,107,64,73,137,64,73,165,64,73,194,64,73,224,64,73,14,66,73,35,66,73,14,68,73,35,68,73,
14,70,73,35,70,73,14,72,73,35,72,73,6,80,73,35,80,73,65,80,73,16,0,74,48,0,74,80,0,74,112,0,74,144,0,74,176,0,74,16,16,74,48,16,74,80,16,74,
109,16,74,135,16,74,16,32,74,48,32,74,75,32,74,102,32,74,130,32,74,16,64,74,48,64,74,80,64,74,112,64,74,144,64,74,167,64,74,16,72,74,33,72,74,16,80,74,
43,80,74,70,80,74,99,80,74,128,80,74,9,96,74,36,96,74,65,96,74,16,128,74,48,128,74,80,128,74,112,128,74,144,128,74,167,128,74,16,130,74,33,130,74,16,132,74,
33,132,74,16,134,74,33,134,74,16,144,74,43,144,74,70,144,74,99,144,74,128,144,74,9,160,74,36,160,74,65,160,74,16,192,74,48,192,74,80,192,74,108,192,74,136,192,74,
162,192,74,16,194,74,16,196,74,16,198,74,9,208,74,36,208,74,65,208,74,3,224,74,32,224,74,16,0,75,48,0,75,80,0,75,108,0,75,136,0,75,162,0,75,16,2,75,
16,4,75,16,6,75,16,8,75,9,16,75,36,16,75,65,16,75,3,32,75,32,32,75,16,64,75,47,64,75,75,64,75,103,64,75,132,64,75,160,64,75,10,66,75,10,68,75,
10,70,75,10,72,75,4,80,75,33,80,75,16,0,76,48,0,76,80,0,76,112,0,76,144,0,76,16,16,76,48,16,76,77,16,76,100,16,76,16,32,76,45,32,76,70,32,76,
96,32,76,16,64,76,48,64,76,80,64,76,109,64,76,135,64,76,16,80,76,40,80,76,67,80,76,8,96,76,34,96,76,16,128,76,48,128,76,80,128,76,109,128,76,135,128,76,
16,144,76,40,144,76,67,144,76,8,160,76,34,160,76,16,192,76,48,192,76,76,192,76,102,192,76,130,192,76,8,208,76,34,208,76,2,224,76,16,0,77,48,0,77,76,0,77,
102,0,77,130,0,77,8,16,77,34,16,77,2,32,77,16,64,77,44,64,77,71,64,77,99,64,77,4,80,77,32,80,77,16,0,78,48,0,78,80,0,78,112,0,78,16,16,78,
48,16,78,70,16,78,16,32,78,41,32,78,65,32,78,16,64,78,48,64,78,79,64,78,100,64,78,14,80,78,37,80,78,6,96,78,32,96,78,16,128,78,48,128,78,79,128,78,
100,128,78,14,144,78,37,144,78,6,160,78,32,160,78,16,192,78,47,192,78,71,192,78,96,192,78,6,208,78,32,208,78,1,224,78,16,0,79,47,0,79,71,0,79,96,0,79,
6,16,79,32,16,79,1,32,79,16,64,79,41,64,79,67,64,79,3,80,79,16,0,80,48,0,80,80,0,80,16,16,80,44,16,80,16,32,80,37,32,80,16,64,80,48,64,80,
71,64,80,12,80,80,34,80,80,5,96,80,16,128,80,48,128,80,71,128,80,12,144,80,34,144,80,5,160,80,16,192,80,43,192,80,66,192,80,5,208,80,1,224,80,16,0,81,
43,0,81,66,0,81,5,16,81,1,32,81,16,64,81,38,64,81,64,64,81,2,80,81,16,0,82,48,0,82,16,16,82,38,16,82,16,32,82,33,32,82,16,64,82,47,64,82,
10,80,82,4,96,82,16,128,82,47,128,82,10,144,82,4,160,82,16,192,82,39,192,82,4,208,82,0,224,82,16,0,83,39,0,83,4,16,83,0,32,83,15,64,83,35,64,83,
1,80,83,16,0,84,48,0,84,16,16,84,32,16,84,14,32,84,16,64,84,41,64,84,8,80,84,3,96,84,16,128,84,41,128,84,8,144,84,3,160,84,16,192,84,35,192,84,
3,208,84,16,0,85,35,0,85,3,16,85,13,64,85,32,64,85,0,80,85,16,0,86,46,0,86,16,16,86,11,32,86,16,64,86,35,64,86,6,80,86,1,96,86,16,128,86,
35,128,86,6,144,86,1,160,86,16,192,86,1,208,86,16,0,87,1,16,87,11,64,87,80,0,88,112,0,88,144,0,88,176,0,88,208,0,88,240,0,88,16,1,88,48,1,88,
80,1,88,112,1,88,80,16,88,112,16,88,144,16,88,176,16,88,208,16,88,240,16,88,16,17,88,48,17,88,80,17,88,112,17,88,80,32,88,112,32,88,144,32,88,176,32,88,
208,32,88,240,32,88,16,33,88,47,33,88,77,33,88,107,33,88,80,64,88,112,64,88,144,64,88,176,64,88,208,64,88,240,64,88,16,65,88,48,65,88,80,65,88,112,65,88,
16,72,88,48,72,88,80,72,88,112,72,88,144,72,88,176,72,88,205,72,88,232,72,88,1,73,88,80,80,88,112,80,88,144,80,88,175,80,88,206,80,88,236,80,88,11,81,88,
41,81,88,72,81,88,102,81,88,74,96,88,105,96,88,136,96,88,167,96,88,198,96,88,229,96,88,4,97,88,35,97,88,66,97,88,97,97,88,80,128,88,112,128,88,144,128,88,
176,128,88,208,128,88,240,128,88,16,129,88,48,129,88,80,129,88,112,129,88,16,130,88,48,130,88,80,130,88,112,130,88,144,130,88,176,130,88,205,130,88,232,130,88,1,131,88,
16,132,88,48,132,88,80,132,88,112,132,88,144,132,88,176,132,88,205,132,88,232,132,88,1,133,88,16,134,88,48,134,88,80,134,88,112,134,88,144,134,88,176,134,88,205,134,88,
232,134,88,1,135,88,80,144,88,112,144,88,144,144,88,175,144,88,206,144,88,236,144,88,11,145,88,41,145,88,72,145,88,102,145,88,74,160,88,105,160,88,136,160,88,167,160,88,
198,160,88,229,160,88,4,161,88,35,161,88,66,161,88,97,161,88,80,192,88,112,192,88,144,192,88,176,192,88,208,192,88,240,192,88,16,193,88,48,193,88,80,193,88,112,193,88,
16,194,88,48,194,88,80,194,88,112,194,88,143,194,88,170,194,88,198,194,88,227,194,88,16,196,88,48,196,88,80,196,88,112,196,88,143,196,88,170,196,88,198,196,88,227,196,88,
16,198,88,48,198,88,80,198,88,112,198,88,143,198,88,170,198,88,198,198,88,227,198,88,74,208,88,105,208,88,136,208,88,167,208,88,198,208,88,229,208,88,4,209,88,35,209,88,
66,209,88,97,209,88,68,224,88,99,224,88,131,224,88,162,224,88,193,224,88,225,224,88,0,225,88,32,225,88,80,0,89,112,0,89,144,0,89,176,0,89,208,0,89,240,0,89,
16,1,89,48,1,89,80,1,89,112,1,89,16,2,89,48,2,89,80,2,89,112,2,89,143,2,89,170,2,89,198,2,89,227,2,89,16,4,89,48,4,89,80,4,89,112,4,89,
143,4,89,170,4,89,198,4,89,227,4,89,16,6,89,48,6,89,80,6,89,112,6,89,143,6,89,170,6,89,198,6,89,227,6,89,16,8,89,48,8,89,80,8,89,112,8,89,
143,8,89,170,8,89,198,8,89,227,8,89,74,16,89,105,16,89,136,16,89,167,16,89,198,16,89,229,16,89,4,17,89,35,17,89,66,17,89,97,17,89,68,32,89,99,32,89,
131,32,89,162,32,89,193,32,89,225,32,89,0,33,89,32,33,89,80,64,89,112,64,89,144,64,89,176,64,89,208,64,89,240,64,89,15,65,89,46,65,89,76,65,89,107,65,89,
16,66,89,48,66,89,79,66,89,108,66,89,137,66,89,166,66,89,195,66,89,224,66,89,16,68,89,48,68,89,79,68,89,108,68,89,137,68,89,166,68,89,195,68,89,224,68,89,
16,70,89,48,70,89,79,70,89,108,70,89,137,70,89,166,70,89,195,70,89,224,70,89,16,72,89,48,72,89,79,72,89,108,72,89,137,72,89,166,72,89,195,72,89,224,72,89,
70,80,89,101,80,89,132,80,89,163,80,89,195,80,89,226,80,89,1,81,89,32,81,89,64,81,89,48,0,90,80,0,90,112,0,90,144,0,90,176,0,90,208,0,90,240,0,90,
16,1,90,48,1,90,80,1,90,112,1,90,48,16,90,80,16,90,112,16,90,144,16,90,176,16,90,208,16,90,240,16,90,12,17,90,39,17,90,68,17,90,48,32,90,80,32,90,
112,32,90,144,32,90,174,32,90,203,32,90,233,32,90,5,33,90,34,33,90,64,33,90,48,64,90,80,64,90,112,64,90,144,64,90,176,64,90,208,64,90,240,64,90,16,65,90,
48,65,90,77,65,90,103,65,90,16,72,90,48,72,90,80,72,90,106,72,90,131,72,90,48,80,90,79,80,90,109,80,90,139,80,90,169,80,90,198,80,90,228,80,90,2,81,90,
32,81,90,41,96,90,71,96,90,102,96,90,133,96,90,163,96,90,193,96,90,224,96,90,48,128,90,80,128,90,112,128,90,144,128,90,176,128,90,208,128,90,240,128,90,16,129,90,
48,129,90,77,129,90,103,129,90,16,130,90,48,130,90,80,130,90,106,130,90,131,130,90,16,132,90,48,132,90,80,132,90,106,132,90,131,132,90,16,134,90,48,134,90,80,134,90,
106,134,90,131,134,90,48,144,90,79,144,90,109,144,90,139,144,90,169,144,90,198,144,90,228,144,90,2,145,90,32,145,90,41,160,90,71,160,90,102,160,90,133,160,90,163,160,90,
193,160,90,224,160,90,48,192,90,80,192,90,112,192,90,144,192,90,176,192,90,208,192,90,239,192,90,11,193,90,40,193,90,70,193,90,98,193,90,16,194,90,48,194,90,74,194,90,
100,194,90,16,196,90,48,196,90,74,196,90,100,196,90,16,198,90,48,198,90,74,198,90,100,198,90,41,208,90,71,208,90,102,208,90,133,208,90,163,208,90,193,208,90,224,208,90,
35,224,90,66,224,90,97,224,90,128,224,90,48,0,91,80,0,91,112,0,91,144,0,91,176,0,91,208,0,91,239,0,91,11,1,91,40,1,91,70,1,91,98,1,91,16,2,91,
48,2,91,74,2,91,100,2,91,16,4,91,48,4,91,74,4,91,100,4,91,16,6,91,48,6,91,74,6,91,100,6,91,16,8,91,48,8,91,74,8,91,100,8,91,41,16,91,
71,16,91,102,16,91,133,16,91,163,16,91,193,16,91,224,16,91,35,32,91,66,32,91,97,32,91,128,32,91,48,64,91,80,64,91,112,64,91,144,64,91,173,64,91,203,64,91,
233,64,91,6,65,91,36,65,91,66,65,91,96,65,91,16,66,91,43,66,91,70,66,91,97,66,91,16,68,91,43,68,91,70,68,91,97,68,91,16,70,91,43,70,91,70,70,91,
97,70,91,16,72,91,43,72,91,70,72,91,97,72,91,37,80,91,67,80,91,98,80,91,129,80,91,160,80,91,16,0,92,48,0,92,80,0,92,112,0,92,144,0,92,176,0,92,
208,0,92,240,0,92,14,1,92,16,16,92,48,16,92,80,16,92,112,16,92,144,16,92,172,16,92,198,16,92,225,16,92,16,32,92,48,32,92,80,32,92,109,32,92,138,32,92,
165,32,92,193,32,92,16,64,92,48,64,92,80,64,92,112,64,92,144,64,92,176,64,92,207,64,92,234,64,92,3,65,92,16,72,92,48,72,92,65,72,92,16,80,92,46,80,92,
75,80,92,104,80,92,133,80,92,162,80,92,10,96,92,39,96,92,68,96,92,98,96,92,129,96,92,16,128,92,48,128,92,80,128,92,112,128,92,144,128,92,176,128,92,207,128,92,
234,128,92,3,129,92,16,130,92,48,130,92,65,130,92,16,132,92,48,132,92,65,132,92,16,134,92,48,134,92,65,134,92,16,144,92,46,144,92,75,144,92,104,144,92,133,144,92,
162,144,92,10,160,92,39,160,92,68,160,92,98,160,92,129,160,92,16,192,92,48,192,92,80,192,92,112,192,92,144,192,92,171,192,92,199,192,92,228,192,92,16,194,92,40,194,92,
16,196,92,40,196,92,16,198,92,40,198,92,10,208,92,39,208,92,68,208,92,98,208,92,129,208,92,4,224,92,34,224,92,64,224,92,16,0,93,48,0,93,80,0,93,112,0,93,
144,0,93,171,0,93,199,0,93,228,0,93,16,2,93,40,2,93,16,4,93,40,4,93,16,6,93,40,6,93,16,8,93,40,8,93,10,16,93,39,16,93,68,16,93,98,16,93,
129,16,93,4,32,93,34,32,93,64,32,93,16,64,93,48,64,93,79,64,93,108,64,93,138,64,93,166,64,93,195,64,93,225,64,93,15,66,93,36,66,93,15,68,93,36,68,93,
15,70,93,36,70,93,15,72,93,36,72,93,6,80,93,35,80,93,65,80,93,96,80,93,16,0,94,48,0,94,80,0,94,112,0,94,144,0,94,176,0,94,16,16,94,48,16,94,
80,16,94,109,16,94,135,16,94,16,32,94,48,32,94,75,32,94,102,32,94,130,32,94,16,64,94,48,64,94,80,64,94,112,64,94,144,64,94,167,64,94,16,72,94,33,72,94,
16,80,94,43,80,94,70,80,94,99,80,94,128,80,94,9,96,94,36,96,94,65,96,94,16,128,94,48,128,94,80,128,94,112,128,94,144,128,94,167,128,94,16,130,94,33,130,94,
16,132,94,33,132,94,16,134,94,33,134,94,16,144,94,43,144,94,70,144,94,99,144,94,128,144,94,9,160,94,36,160,94,65,160,94,16,192,94,48,192,94,80,192,94,108,192,94,
136,192,94,162,192,94,16,194,94,16,196,94,16,198,94,9,208,94,36,208,94,65,208,94,3,224,94,32,224,94,16,0,95,48,0,95,80,0,95,108,0,95,136,0,95,162,0,95,
16,2,95,16,4,95,16,6,95,16,8,95,9,16,95,36,16,95,65,16,95,3,32,95,32,32,95,16,64,95,47,64,95,75,64,95,103,64,95,132,64,95,160,64,95,10,66,95,
10,68,95,10,70,95,10,72,95,4,80,95,33,80,95,16,0,96,48,0,96,80,0,96,112,0,96,144,0,96,16,16,96,48,16,96,76,16,96,99,16,96,16,32,96,44,32,96,
69,32,96,16,64,96,48,64,96,80,64,96,108,64,96,132,64,96,15,80,96,39,80,96,66,80,96,7,96,96,34,96,96,16,128,96,48,128,96,80,128,96,108,128,96,132,128,96,
15,144,96,39,144,96,66,144,96,7,160,96,34,160,96,16,192,96,48,192,96,75,192,96,101,192,96,128,192,96,7,208,96,34,208,96,2,224,96,16,0,97,48,0,97,75,0,97,
101,0,97,128,0,97,7,16,97,34,16,97,2,32,97,16,64,97,44,64,97,70,64,97,98,64,97,3,80,97,16,0,98,48,0,98,80,0,98,16,16,98,47,16,98,67,16,98,
16,32,98,39,32,98,16,64,98,48,64,98,76,64,98,13,80,98,35,80,98,6,96,98,16,128,98,48,128,98,76,128,98,13,144,98,35,144,98,6,160,98,16,192,98,45,192,98,
69,192,98,6,208,98,1,224,98,16,0,99,45,0,99,69,0,99,6,16,99,1,32,99,16,64,99,40,64,99,66,64,99,2,80,99,16,0,100,48,0,100,78,0,100,16,16,100,
40,16,100,16,32,100,35,32,100,16,64,100,48,64,100,67,64,100,11,80,100,32,80,100,4,96,100,16,128,100,48,128,100,67,128,100,11,144,100,32,144,100,4,160,100,16,192,100,
41,192,100,4,208,100,0,224,100,16,0,101,41,0,101,4,16,101,0,32,101,15,64,101,36,64,101,1,80,101,16,0,102,48,0,102,16,16,102,33,16,102,14,32,102,16,64,102,
42,64,102,9,80,102,3,96,102,16,128,102,42,128,102,9,144,102,3,160,102,16,192,102,36,192,102,3,208,102,16,0,103,36,0,103,3,16,103,13,64,103,33,64,103,0,80,103,
16,0,104,46,0,104,16,16,104,11,32,104,16,64,104,35,64,104,6,80,104,1,96,104,16,128,104,35,128,104,6,144,104,1,160,104,16,192,104,1,208,104,16,0,105,1,16,105,
11,64,105,80,0,110,112,0,110,144,0,110,176,0,110,208,0,110,240,0,110,16,1,110,48,1,110,80,1,110,112,1,110,80,16,110,112,16,110,144,16,110,176,16,110,208,16,110,
240,16,110,16,17,110,48,17,110,80,17,110,109,17,110,80,32,110,112,32,110,144,32,110,176,32,110,208,32,110,240,32,110,13,33,110,43,33,110,73,33,110,102,33,110,80,64,110,
112,64,110,144,64,110,176,64,110,208,64,110,240,64,110,16,65,110,48,65,110,80,65,110,112,65,110,16,72,110,48,72,110,80,72,110,112,72,110,144,72,110,170,72,110,195,72,110,
80,80,110,112,80,110,143,80,110,173,80,110,203,80,110,234,80,110,8,81,110,38,81,110,68,81,110,99,81,110,73,96,110,104,96,110,135,96,110,166,96,110,197,96,110,228,96,110,
2,97,110,33,97,110,64,97,110,80,128,110,112,128,110,144,128,110,176,128,110,208,128,110,240,128,110,16,129,110,48,129,110,80,129,110,112,129,110,16,130,110,48,130,110,80,130,110,
112,130,110,144,130,110,170,130,110,195,130,110,16,132,110,48,132,110,80,132,110,112,132,110,144,132,110,170,132,110,195,132,110,16,134,110,48,134,110,80,134,110,112,134,110,144,134,110,
170,134,110,195,134,110,80,144,110,112,144,110,143,144,110,173,144,110,203,144,110,234,144,110,8,145,110,38,145,110,68,145,110,99,145,110,73,160,110,104,160,110,135,160,110,166,160,110,
197,160,110,228,160,110,2,161,110,33,161,110,64,161,110,80,192,110,112,192,110,144,192,110,176,192,110,208,192,110,240,192,110,16,193,110,48,193,110,79,193,110,108,193,110,16,194,110,
48,194,110,80,194,110,109,194,110,138,194,110,164,194,110,16,196,110,48,196,110,80,196,110,109,196,110,138,196,110,164,196,110,16,198,110,48,198,110,80,198,110,109,198,110,138,198,110,
164,198,110,73,208,110,104,208,110,135,208,110,166,208,110,197,208,110,228,208,110,2,209,110,33,209,110,64,209,110,67,224,110,99,224,110,130,224,110,161,224,110,192,224,110,224,224,110,
80,0,111,112,0,111,144,0,111,176,0,111,208,0,111,240,0,111,16,1,111,48,1,111,79,1,111,108,1,111,16,2,111,48,2,111,80,2,111,109,2,111,138,2,111,164,2,111,
16,4,111,48,4,111,80,4,111,109,4,111,138,4,111,164,4,111,16,6,111,48,6,111,80,6,111,109,6,111,138,6,111,164,6,111,16,8,111,48,8,111,80,8,111,109,8,111,
138,8,111,164,8,111,73,16,111,104,16,111,135,16,111,166,16,111,197,16,111,228,16,111,2,17,111,33,17,111,64,17,111,67,32,111,99,32,111,130,32,111,161,32,111,192,32,111,
224,32,111,80,64,111,112,64,111,144,64,111,176,64,111,208,64,111,238,64,111,12,65,111,42,65,111,73,65,111,103,65,111,16,66,111,48,66,111,76,66,111,104,66,111,133,66,111,
161,66,111,16,68,111,48,68,111,76,68,111,104,68,111,133,68,111,161,68,111,16,70,111,48,70,111,76,70,111,104,70,111,133,70,111,161,70,111,16,72,111,48,72,111,76,72,111,
104,72,111,133,72,111,161,72,111,69,80,111,100,80,111,131,80,111,162,80,111,193,80,111,225,80,111,0,81,111,48,0,112,80,0,112,112,0,112,144,0,112,176,0,112,208,0,112,
240,0,112,16,1,112,48,1,112,48,16,112,80,16,112,112,16,112,144,16,112,176,16,112,205,16,112,233,16,112,3,17,112,48,32,112,80,32,112,112,32,112,142,32,112,170,32,112,
198,32,112,227,32,112,48,64,112,80,64,112,112,64,112,144,64,112,176,64,112,208,64,112,240,64,112,12,65,112,39,65,112,16,72,112,48,72,112,74,72,112,48,80,112,77,80,112,
106,80,112,136,80,112,165,80,112,195,80,112,224,80,112,40,96,112,70,96,112,100,96,112,131,96,112,161,96,112,48,128,112,80,128,112,112,128,112,144,128,112,176,128,112,208,128,112,
240,128,112,12,129,112,39,129,112,16,130,112,48,130,112,74,130,112,16,132,112,48,132,112,74,132,112,16,134,112,48,134,112,74,134,112,48,144,112,77,144,112,106,144,112,136,144,112,
165,144,112,195,144,112,224,144,112,40,160,112,70,160,112,100,160,112,131,160,112,161,160,112,48,192,112,80,192,112,112,192,112,144,192,112,176,192,112,204,192,112,233,192,112,5,193,112,
34,193,112,16,194,112,44,194,112,68,194,112,16,196,112,44,196,112,68,196,112,16,198,112,44,198,112,68,198,112,40,208,112,70,208,112,100,208,112,131,208,112,161,208,112,35,224,112,
65,224,112,96,224,112,48,0,113,80,0,113,112,0,113,144,0,113,176,0,113,204,0,113,233,0,113,5,1,113,34,1,113,16,2,113,44,2,113,68,2,113,16,4,113,44,4,113,
68,4,113,16,6,113,44,6,113,68,6,113,16,8,113,44,8,113,68,8,113,40,16,113,70,16,113,100,16,113,131,16,113,161,16,113,35,32,113,65,32,113,96,32,113,48,64,113,
80,64,113,111,64,113,141,64,113,170,64,113,199,64,113,229,64,113,2,65,113,16,66,113,39,66,113,65,66,113,16,68,113,39,68,113,65,68,113,16,70,113,39,70,113,65,70,113,
16,72,113,39,72,113,65,72,113,36,80,113,66,80,113,97,80,113,128,80,113,16,0,114,48,0,114,80,0,114,112,0,114,144,0,114,176,0,114,208,0,114,16,16,114,48,16,114,
80,16,114,112,16,114,139,16,114,163,16,114,16,32,114,48,32,114,77,32,114,104,32,114,133,32,114,16,64,114,48,64,114,80,64,114,112,64,114,144,64,114,172,64,114,196,64,114,
16,72,114,38,72,114,16,80,114,44,80,114,72,80,114,100,80,114,129,80,114,9,96,114,37,96,114,66,96,114,96,96,114,16,128,114,48,128,114,80,128,114,112,128,114,144,128,114,
172,128,114,196,128,114,16,130,114,38,130,114,16,132,114,38,132,114,16,134,114,38,134,114,16,144,114,44,144,114,72,144,114,100,144,114,129,144,114,9,160,114,37,160,114,66,160,114,
96,160,114,16,192,114,48,192,114,80,192,114,110,192,114,139,192,114,165,192,114,192,192,114,16,194,114,33,194,114,16,196,114,33,196,114,16,198,114,33,198,114,9,208,114,37,208,114,
66,208,114,96,208,114,3,224,114,33,224,114,16,0,115,48,0,115,80,0,115,110,0,115,139,0,115,165,0,115,192,0,115,16,2,115,33,2,115,16,4,115,33,4,115,16,6,115,
33,6,115,16,8,115,33,8,115,9,16,115,37,16,115,66,16,115,96,16,115,3,32,115,33,32,115,16,64,115,48,64,115,76,64,115,105,64,115,134,64,115,162,64,115,12,66,115,
12,68,115,12,70,115,12,72,115,5,80,115,34,80,115,64,80,115,16,0,116,48,0,116,80,0,116,112,0,116,144,0,116,16,16,116,48,16,116,77,16,116,100,16,116,16,32,116,
45,32,116,70,32,116,96,32,116,16,64,116,48,64,116,80,64,116,109,64,116,135,64,116,16,80,116,40,80,116,67,80,116,8,96,116,34,96,116,16,128,116,48,128,116,80,128,116,
109,128,116,135,128,116,16,144,116,40,144,116,67,144,116,8,160,116,34,160,116,16,192,116,48,192,116,76,192,116,102,192,116,130,192,116,8,208,116,34,208,116,2,224,116,16,0,117,
48,0,117,76,0,117,102,0,117,130,0,117,8,16,117,34,16,117,2,32,117,16,64,117,44,64,117,71,64,117,99,64,117,4,80,117,32,80,117,16,0,118,48,0,118,80,0,118,
16,16,118,47,16,118,67,16,118,16,32,118,39,32,118,16,64,118,48,64,118,76,64,118,13,80,118,35,80,118,6,96,118,16,128,118,48,128,118,76,128,118,13,144,118,35,144,118,
6,160,118,16,192,118,45,192,118,69,192,118,6,208,118,1,224,118,16,0,119,45,0,119,69,0,119,6,16,119,1,32,119,16,64,119,40,64,119,66,64,119,2,80,119,16,0,120,
48,0,120,16,16,120,39,16,120,16,32,120,34,32,120,16,64,120,48,64,120,10,80,120,4,96,120,16,128,120,48,128,120,10,144,120,4,160,120,16,192,120,40,192,120,4,208,120,
0,224,120,16,0,121,40,0,121,4,16,121,0,32,121,15,64,121,36,64,121,1,80,121,16,0,122,48,0,122,16,16,122,13,32,122,16,64,122,39,64,122,8,80,122,2,96,122,
16,128,122,39,128,122,8,144,122,2,160,122,16,192,122,34,192,122,2,208,122,16,0,123,34,0,123,2,16,123,12,64,123,32,64,123,0,80,123,16,0,124,16,16,124,10,32,124,
16,64,124,5,80,124,1,96,124,16,128,124,5,144,124,1,160,124,16,192,124,1,208,124,16,0,125,1,16,125,10,64,125,48,0,132,80,0,132,112,0,132,144,0,132,176,0,132,
208,0,132,240,0,132,16,1,132,48,1,132,80,1,132,112,1,132,48,16,132,80,16,132,112,16,132,144,16,132,176,16,132,208,16,132,240,16,132,16,17,132,45,17,132,74,17,132,
102,17,132,48,32,132,80,32,132,112,32,132,144,32,132,176,32,132,206,32,132,236,32,132,9,33,132,38,33,132,68,33,132,97,33,132,48,64,132,80,64,132,112,64,132,144,64,132,
176,64,132,208,64,132,240,64,132,16,65,132,48,65,132,80,65,132,111,65,132,16,72,132,48,72,132,80,72,132,112,72,132,138,72,132,161,72,132,48,80,132,80,80,132,111,80,132,
141,80,132,171,80,132,201,80,132,231,80,132,5,81,132,35,81,132,65,81,132,42,96,132,72,96,132,103,96,132,134,96,132,164,96,132,195,96,132,226,96,132,0,97,132,48,128,132,
80,128,132,112,128,132,144,128,132,176,128,132,208,128,132,240,128,132,16,129,132,48,129,132,80,129,132,111,129,132,16,130,132,48,130,132,80,130,132,112,130,132,138,130,132,161,130,132,
16,132,132,48,132,132,80,132,132,112,132,132,138,132,132,161,132,132,16,134,132,48,134,132,80,134,132,112,134,132,138,134,132,161,134,132,48,144,132,80,144,132,111,144,132,141,144,132,
171,144,132,201,144,132,231,144,132,5,145,132,35,145,132,65,145,132,42,160,132,72,160,132,103,160,132,134,160,132,164,160,132,195,160,132,226,160,132,0,161,132,48,192,132,80,192,132,
112,192,132,144,192,132,176,192,132,208,192,132,240,192,132,15,193,132,44,193,132,74,193,132,103,193,132,16,194,132,48,194,132,78,194,132,105,194,132,132,194,132,16,196,132,48,196,132,
78,196,132,105,196,132,132,196,132,16,198,132,48,198,132,78,198,132,105,198,132,132,198,132,42,208,132,72,208,132,103,208,132,134,208,132,164,208,132,195,208,132,226,208,132,0,209,132,
36,224,132,67,224,132,98,224,132,129,224,132,160,224,132,48,0,133,80,0,133,112,0,133,144,0,133,176,0,133,208,0,133,240,0,133,15,1,133,44,1,133,74,1,133,103,1,133,
16,2,133,48,2,133,78,2,133,105,2,133,132,2,133,16,4,133,48,4,133,78,4,133,105,4,133,132,4,133,16,6,133,48,6,133,78,6,133,105,6,133,132,6,133,16,8,133,
48,8,133,78,8,133,105,8,133,132,8,133,42,16,133,72,16,133,103,16,133,134,16,133,164,16,133,195,16,133,226,16,133,0,17,133,36,32,133,67,32,133,98,32,133,129,32,133,
160,32,133,48,64,133,80,64,133,112,64,133,144,64,133,175,64,133,205,64,133,236,64,133,9,65,133,39,65,133,70,65,133,99,65,133,16,66,133,45,66,133,73,66,133,100,66,133,
129,66,133,16,68,133,45,68,133,73,68,133,100,68,133,129,68,133,16,70,133,45,70,133,73,70,133,100,70,133,129,70,133,16,72,133,45,72,133,73,72,133,100,72,133,129,72,133,
37,80,133,68,80,133,99,80,133,130,80,133,161,80,133,192,80,133,16,0,134,48,0,134,80,0,134,112,0,134,144,0,134,176,0,134,208,0,134,240,0,134,14,1,134,16,16,134,
48,16,134,80,16,134,112,16,134,144,16,134,172,16,134,198,16,134,225,16,134,16,32,134,48,32,134,80,32,134,109,32,134,138,32,134,165,32,134,193,32,134,16,64,134,48,64,134,
80,64,134,112,64,134,144,64,134,176,64,134,207,64,134,234,64,134,3,65,134,16,72,134,48,72,134,65,72,134,16,80,134,46,80,134,75,80,134,104,80,134,133,80,134,162,80,134,
10,96,134,39,96,134,68,96,134,98,96,134,129,96,134,16,128,134,48,128,134,80,128,134,112,128,134,144,128,134,176,128,134,207,128,134,234,128,134,3,129,134,16,130,134,48,130,134,
65,130,134,16,132,134,48,132,134,65,132,134,16,134,134,48,134,134,65,134,134,16,144,134,46,144,134,75,144,134,104,144,134,133,144,134,162,144,134,10,160,134,39,160,134,68,160,134,
98,160,134,129,160,134,16,192,134,48,192,134,80,192,134,112,192,134,144,192,134,171,192,134,199,192,134,228,192,134,16,194,134,40,194,134,16,196,134,40,196,134,16,198,134,40,198,134,
10,208,134,39,208,134,68,208,134,98,208,134,129,208,134,4,224,134,34,224,134,64,224,134,16,0,135,48,0,135,80,0,135,112,0,135,144,0,135,171,0,135,199,0,135,228,0,135,
16,2,135,40,2,135,16,4,135,40,4,135,16,6,135,40,6,135,16,8,135,40,8,135,10,16,135,39,16,135,68,16,135,98,16,135,129,16,135,4,32,135,34,32,135,64,32,135,
16,64,135,48,64,135,79,64,135,108,64,135,138,64,135,166,64,135,195,64,135,225,64,135,15,66,135,36,66,135,15,68,135,36,68,135,15,70,135,36,70,135,15,72,135,36,72,135,
6,80,135,35,80,135,65,80,135,96,80,135,16,0,136,48,0,136,80,0,136,112,0,136,144,0,136,174,0,136,16,16,136,48,16,136,80,16,136,106,16,136,131,16,136,16,32,136,
47,32,136,73,32,136,100,32,136,16,64,136,48,64,136,80,64,136,112,64,136,140,64,136,163,64,136,16,72,136,16,80,136,41,80,136,69,80,136,97,80,136,8,96,136,35,96,136,
64,96,136,16,128,136,48,128,136,80,128,136,112,128,136,140,128,136,163,128,136,16,130,136,16,132,136,16,134,136,16,144,136,41,144,136,69,144,136,97,144,136,8,160,136,35,160,136,
64,160,136,16,192,136,48,192,136,79,192,136,106,192,136,133,192,136,14,194,136,14,196,136,14,198,136,8,208,136,35,208,136,64,208,136,3,224,136,32,224,136,16,0,137,48,0,137,
79,0,137,106,0,137,133,0,137,14,2,137,14,4,137,14,6,137,14,8,137,8,16,137,35,16,137,64,16,137,3,32,137,32,32,137,16,64,137,46,64,137,73,64,137,101,64,137,
130,64,137,9,66,137,9,68,137,9,70,137,9,72,137,4,80,137,32,80,137,16,0,138,48,0,138,80,0,138,112,0,138,16,16,138,48,16,138,70,16,138,16,32,138,41,32,138,
65,32,138,16,64,138,48,64,138,79,64,138,100,64,138,14,80,138,37,80,138,6,96,138,32,96,138,16,128,138,48,128,138,79,128,138,100,128,138,14,144,138,37,144,138,6,160,138,
32,160,138,16,192,138,47,192,138,71,192,138,96,192,138,6,208,138,32,208,138,1,224,138,16,0,139,47,0,139,71,0,139,96,0,139,6,16,139,32,16,139,1,32,139,16,64,139,
41,64,139,67,64,139,3,80,139,16,0,140,48,0,140,78,0,140,16,16,140,40,16,140,16,32,140,35,32,140,16,64,140,48,64,140,67,64,140,11,80,140,32,80,140,4,96,140,
16,128,140,48,128,140,67,128,140,11,144,140,32,144,140,4,160,140,16,192,140,41,192,140,4,208,140,0,224,140,16,0,141,41,0,141,4,16,141,0,32,141,15,64,141,36,64,141,
1,80,141,16,0,142,48,0,142,16,16,142,13,32,142,16,64,142,39,64,142,8,80,142,2,96,142,16,128,142,39,128,142,8,144,142,2,160,142,16,192,142,34,192,142,2,208,142,
16,0,143,34,0,143,2,16,143,12,64,143,32,64,143,0,80,143,16,0,144,16,16,144,9,32,144,16,64,144,5,80,144,0,96,144,16,128,144,5,144,144,0,160,144,15,192,144,
0,208,144,15,0,145,0,16,145,9,64,145,48,0,154,80,0,154,112,0,154,144,0,154,176,0,154,208,0,154,240,0,154,16,1,154,48,1,154,80,1,154,112,1,154,48,16,154,
80,16,154,112,16,154,144,16,154,176,16,154,208,16,154,240,16,154,12,17,154,39,17,154,68,17,154,48,32,154,80,32,154,112,32,154,144,32,154,174,32,154,203,32,154,233,32,154,
5,33,154,34,33,154,64,33,154,48,64,154,80,64,154,112,64,154,144,64,154,176,64,154,208,64,154,240,64,154,16,65,154,48,65,154,77,65,154,103,65,154,16,72,154,48,72,154,
80,72,154,106,72,154,131,72,154,48,80,154,79,80,154,109,80,154,139,80,154,169,80,154,198,80,154,228,80,154,2,81,154,32,81,154,41,96,154,71,96,154,102,96,154,133,96,154,
163,96,154,193,96,154,224,96,154,48,128,154,80,128,154,112,128,154,144,128,154,176,128,154,208,128,154,240,128,154,16,129,154,48,129,154,77,129,154,103,129,154,16,130,154,48,130,154,
80,130,154,106,130,154,131,130,154,16,132,154,48,132,154,80,132,154,106,132,154,131,132,154,16,134,154,48,134,154,80,134,154,106,134,154,131,134,154,48,144,154,79,144,154,109,144,154,
139,144,154,169,144,154,198,144,154,228,144,154,2,145,154,32,145,154,41,160,154,71,160,154,102,160,154,133,160,154,163,160,154,193,160,154,224,160,154,48,192,154,80,192,154,112,192,154,
144,192,154,176,192,154,208,192,154,239,192,154,11,193,154,40,193,154,70,193,154,98,193,154,16,194,154,48,194,154,74,194,154,100,194,154,16,196,154,48,196,154,74,196,154,100,196,154,
16,198,154,48,198,154,74,198,154,100,198,154,41,208,154,71,208,154,102,208,154,133,208,154,163,208,154,193,208,154,224,208,154,35,224,154,66,224,154,97,224,154,128,224,154,48,0,155,
80,0,155,112,0,155,144,0,155,176,0,155,208,0,155,239,0,155,11,1,155,40,1,155,70,1,155,98,1,155,16,2,155,48,2,155,74,2,155,100,2,155,16,4,155,48,4,155,
74,4,155,100,4,155,16,6,155,48,6,155,74,6,155,100,6,155,16,8,155,48,8,155,74,8,155,100,8,155,41,16,155,71,16,155,102,16,155,133,16,155,163,16,155,193,16,155,
224,16,155,35,32,155,66,32,155,97,32,155,128,32,155,48,64,155,80,64,155,112,64,155,144,64,155,173,64,155,203,64,155,233,64,155,6,65,155,36,65,155,66,65,155,96,65,155,
16,66,155,43,66,155,70,66,155,97,66,155,16,68,155,43,68,155,70,68,155,97,68,155,16,70,155,43,70,155,70,70,155,97,70,155,16,72,155,43,72,155,70,72,155,97,72,155,
37,80,155,67,80,155,98,80,155,129,80,155,160,80,155,16,0,156,48,0,156,80,0,156,112,0,156,144,0,156,176,0,156,208,0,156,16,16,156,48,16,156,80,16,156,112,16,156,
141,16,156,165,16,156,16,32,156,48,32,156,78,32,156,106,32,156,134,32,156,161,32,156,16,64,156,48,64,156,80,64,156,112,64,156,144,64,156,174,64,156,199,64,156,16,72,156,
40,72,156,16,80,156,44,80,156,73,80,156,101,80,156,130,80,156,10,96,156,37,96,156,67,96,156,97,96,156,16,128,156,48,128,156,80,128,156,112,128,156,144,128,156,174,128,156,
199,128,156,16,130,156,40,130,156,16,132,156,40,132,156,16,134,156,40,134,156,16,144,156,44,144,156,73,144,156,101,144,156,130,144,156,10,160,156,37,160,156,67,160,156,97,160,156,
16,192,156,48,192,156,80,192,156,112,192,156,140,192,156,167,192,156,194,192,156,16,194,156,35,194,156,16,196,156,35,196,156,16,198,156,35,198,156,10,208,156,37,208,156,67,208,156,
97,208,156,4,224,156,33,224,156,16,0,157,48,0,157,80,0,157,112,0,157,140,0,157,167,0,157,194,0,157,16,2,157,35,2,157,16,4,157,35,4,157,16,6,157,35,6,157,
16,8,157,35,8,157,10,16,157,37,16,157,67,16,157,97,16,157,4,32,157,33,32,157,16,64,157,48,64,157,77,64,157,106,64,157,135,64,157,163,64,157,192,64,157,12,66,157,
32,66,157,12,68,157,32,68,157,12,70,157,32,70,157,12,72,157,32,72,157,5,80,157,34,80,157,64,80,157,16,0,158,48,0,158,80,0,158,112,0,158,144,0,158,16,16,158,
48,16,158,76,16,158,99,16,158,16,32,158,44,32,158,69,32,158,16,64,158,48,64,158,80,64,158,108,64,158,132,64,158,15,80,158,39,80,158,66,80,158,7,96,158,34,96,158,
16,128,158,48,128,158,80,128,158,108,128,158,132,128,158,15,144,158,39,144,158,66,144,158,7,160,158,34,160,158,16,192,158,48,192,158,75,192,158,101,192,158,128,192,158,7,208,158,
34,208,158,2,224,158,16,0,159,48,0,159,75,0,159,101,0,159,128,0,159,7,16,159,34,16,159,2,32,159,16,64,159,44,64,159,70,64,159,98,64,159,3,80,159,16,0,160,
48,0,160,80,0,160,16,16,160,44,16,160,16,32,160,37,32,160,16,64,160,48,64,160,71,64,160,12,80,160,34,80,160,5,96,160,16,128,160,48,128,160,71,128,160,12,144,160,
34,144,160,5,160,160,16,192,160,43,192,160,66,192,160,5,208,160,1,224,160,16,0,161,43,0,161,66,0,161,5,16,161,1,32,161,16,64,161,38,64,161,64,64,161,2,80,161,
16,0,162,48,0,162,16,16,162,33,16,162,14,32,162,16,64,162,42,64,162,9,80,162,3,96,162,16,128,162,42,128,162,9,144,162,3,160,162,16,192,162,36,192,162,3,208,162,
16,0,163,36,0,163,3,16,163,13,64,163,33,64,163,0,80,163,16,0,164,16,16,164,10,32,164,16,64,164,5,80,164,1,96,164,16,128,164,5,144,164,1,160,164,16,192,164,
1,208,164,16,0,165,1,16,165,10,64,165,48,0,176,80,0,176,112,0,176,144,0,176,176,0,176,208,0,176,240,0,176,16,1,176,48,1,176,80,1,176,48,16,176,80,16,176,
112,16,176,144,16,176,176,16,176,208,16,176,236,16,176,6,17,176,33,17,176,48,32,176,80,32,176,112,32,176,143,32,176,171,32,176,200,32,176,229,32,176,1,33,176,48,64,176,
80,64,176,112,64,176,144,64,176,176,64,176,208,64,176,240,64,176,15,65,176,42,65,176,70,65,176,16,72,176,48,72,176,77,72,176,99,72,176,48,80,176,78,80,176,107,80,176,
137,80,176,166,80,176,196,80,176,226,80,176,40,96,176,70,96,176,101,96,176,131,96,176,161,96,176,192,96,176,48,128,176,80,128,176,112,128,176,144,128,176,176,128,176,208,128,176,
240,128,176,15,129,176,42,129,176,70,129,176,16,130,176,48,130,176,77,130,176,99,130,176,16,132,176,48,132,176,77,132,176,99,132,176,16,134,176,48,134,176,77,134,176,99,134,176,
48,144,176,78,144,176,107,144,176,137,144,176,166,144,176,196,144,176,226,144,176,40,160,176,70,160,176,101,160,176,131,160,176,161,160,176,192,160,176,48,192,176,80,192,176,112,192,176,
144,192,176,176,192,176,206,192,176,235,192,176,7,193,176,36,193,176,65,193,176,16,194,176,46,194,176,70,194,176,16,196,176,46,196,176,70,196,176,16,198,176,46,198,176,70,198,176,
40,208,176,70,208,176,101,208,176,131,208,176,161,208,176,192,208,176,35,224,176,65,224,176,96,224,176,128,224,176,48,0,177,80,0,177,112,0,177,144,0,177,176,0,177,206,0,177,
235,0,177,7,1,177,36,1,177,65,1,177,16,2,177,46,2,177,70,2,177,16,4,177,46,4,177,70,4,177,16,6,177,46,6,177,70,6,177,16,8,177,46,8,177,70,8,177,
40,16,177,70,16,177,101,16,177,131,16,177,161,16,177,192,16,177,35,32,177,65,32,177,96,32,177,128,32,177,48,64,177,80,64,177,112,64,177,142,64,177,171,64,177,200,64,177,
230,64,177,3,65,177,33,65,177,16,66,177,41,66,177,67,66,177,16,68,177,41,68,177,67,68,177,16,70,177,41,70,177,67,70,177,16,72,177,41,72,177,67,72,177,36,80,177,
67,80,177,97,80,177,128,80,177,16,0,178,48,0,178,80,0,178,112,0,178,144,0,178,176,0,178,16,16,178,48,16,178,80,16,178,109,16,178,135,16,178,16,32,178,48,32,178,
75,32,178,102,32,178,130,32,178,16,64,178,48,64,178,80,64,178,112,64,178,144,64,178,167,64,178,16,72,178,33,72,178,16,80,178,43,80,178,70,80,178,99,80,178,128,80,178,
9,96,178,36,96,178,65,96,178,16,128,178,48,128,178,80,128,178,112,128,178,144,128,178,167,128,178,16,130,178,33,130,178,16,132,178,33,132,178,16,134,178,33,134,178,16,144,178,
43,144,178,70,144,178,99,144,178,128,144,178,9,160,178,36,160,178,65,160,178,16,192,178,48,192,178,80,192,178,108,192,178,136,192,178,162,192,178,16,194,178,16,196,178,16,198,178,
9,208,178,36,208,178,65,208,178,3,224,178,32,224,178,16,0,179,48,0,179,80,0,179,108,0,179,136,0,179,162,0,179,16,2,179,16,4,179,16,6,179,16,8,179,9,16,179,
36,16,179,65,16,179,3,32,179,32,32,179,16,64,179,47,64,179,75,64,179,103,64,179,132,64,179,160,64,179,10,66,179,10,68,179,10,70,179,10,72,179,4,80,179,33,80,179,
16,0,180,48,0,180,80,0,180,112,0,180,16,16,180,48,16,180,70,16,180,16,32,180,41,32,180,65,32,180,16,64,180,48,64,180,79,64,180,100,64,180,14,80,180,37,80,180,
6,96,180,32,96,180,16,128,180,48,128,180,79,128,180,100,128,180,14,144,180,37,144,180,6,160,180,32,160,180,16,192,180,47,192,180,71,192,180,96,192,180,6,208,180,32,208,180,
1,224,180,16,0,181,47,0,181,71,0,181,96,0,181,6,16,181,32,16,181,1,32,181,16,64,181,41,64,181,67,64,181,3,80,181,16,0,182,48,0,182,16,16,182,38,16,182,
16,32,182,33,32,182,16,64,182,47,64,182,10,80,182,4,96,182,16,128,182,47,128,182,10,144,182,4,160,182,16,192,182,39,192,182,4,208,182,0,224,182,16,0,183,39,0,183,
4,16,183,0,32,183,15,64,183,35,64,183,1,80,183,16,0,184,46,0,184,16,16,184,11,32,184,16,64,184,35,64,184,6,80,184,1,96,184,16,128,184,35,128,184,6,144,184,
1,160,184,16,192,184,1,208,184,16,0,185,1,16,185,11,64,185,48,0,198,80,0,198,112,0,198,144,0,198,176,0,198,208,0,198,240,0,198,16,1,198,46,1,198,48,16,198,
80,16,198,112,16,198,144,16,198,176,16,198,202,16,198,230,16,198,0,17,198,48,32,198,80,32,198,111,32,198,140,32,198,168,32,198,196,32,198,225,32,198,48,64,198,80,64,198,
112,64,198,144,64,198,176,64,198,208,64,198,239,64,198,9,65,198,35,65,198,16,72,198,48,72,198,71,72,198,47,80,198,76,80,198,105,80,198,135,80,198,164,80,198,193,80,198,
39,96,198,69,96,198,99,96,198,130,96,198,160,96,198,48,128,198,80,128,198,112,128,198,144,128,198,176,128,198,208,128,198,239,128,198,9,129,198,35,129,198,16,130,198,48,130,198,
71,130,198,16,132,198,48,132,198,71,132,198,16,134,198,48,134,198,71,134,198,47,144,198,76,144,198,105,144,198,135,144,198,164,144,198,193,144,198,39,160,198,69,160,198,99,160,198,
130,160,198,160,160,198,48,192,198,80,192,198,112,192,198,144,192,198,174,192,198,202,192,198,231,192,198,3,193,198,16,194,198,43,194,198,66,194,198,16,196,198,43,196,198,66,196,198,
16,198,198,43,198,198,66,198,198,39,208,198,69,208,198,99,208,198,130,208,198,160,208,198,34,224,198,65,224,198,96,224,198,48,0,199,80,0,199,112,0,199,144,0,199,174,0,199,
202,0,199,231,0,199,3,1,199,16,2,199,43,2,199,66,2,199,16,4,199,43,4,199,66,4,199,16,6,199,43,6,199,66,6,199,16,8,199,43,8,199,66,8,199,39,16,199,
69,16,199,99,16,199,130,16,199,160,16,199,34,32,199,65,32,199,96,32,199,48,64,199,80,64,199,110,64,199,140,64,199,169,64,199,198,64,199,227,64,199,0,65,199,16,66,199,
38,66,199,64,66,199,16,68,199,38,68,199,64,68,199,16,70,199,38,70,199,64,70,199,16,72,199,38,72,199,64,72,199,35,80,199,66,80,199,96,80,199,16,0,200,48,0,200,
80,0,200,112,0,200,144,0,200,16,16,200,48,16,200,80,16,200,104,16,200,129,16,200,16,32,200,47,32,200,72,32,200,99,32,200,16,64,200,48,64,200,80,64,200,112,64,200,
138,64,200,16,80,200,41,80,200,68,80,200,96,80,200,8,96,200,35,96,200,64,96,200,16,128,200,48,128,200,80,128,200,112,128,200,138,128,200,16,144,200,41,144,200,68,144,200,
96,144,200,8,160,200,35,160,200,64,160,200,16,192,200,48,192,200,78,192,200,105,192,200,132,192,200,8,208,200,35,208,200,64,208,200,3,224,200,16,0,201,48,0,201,78,0,201,
105,0,201,132,0,201,8,16,201,35,16,201,64,16,201,3,32,201,16,64,201,45,64,201,73,64,201,100,64,201,129,64,201,4,80,201,32,80,201,16,0,202,48,0,202,80,0,202,
16,16,202,45,16,202,64,16,202,16,32,202,38,32,202,16,64,202,48,64,202,73,64,202,12,80,202,34,80,202,5,96,202,16,128,202,48,128,202,73,128,202,12,144,202,34,144,202,
5,160,202,16,192,202,44,192,202,67,192,202,5,208,202,1,224,202,16,0,203,44,0,203,67,0,203,5,16,203,1,32,203,16,64,203,39,64,203,64,64,203,2,80,203,16,0,204,
48,0,204,16,16,204,32,16,204,14,32,204,16,64,204,41,64,204,8,80,204,3,96,204,16,128,204,41,128,204,8,144,204,3,160,204,16,192,204,35,192,204,3,208,204,16,0,205,
35,0,205,3,16,205,13,64,205,32,64,205,0,80,205,16,0,220,48,0,220,80,0,220,112,0,220,144,0,220,176,0,220,208,0,220,240,0,220,14,1,220,16,16,220,48,16,220,
80,16,220,112,16,220,144,16,220,172,16,220,198,16,220,225,16,220,16,32,220,48,32,220,80,32,220,109,32,220,138,32,220,165,32,220,193,32,220,16,64,220,48,64,220,80,64,220,
112,64,220,144,64,220,176,64,220,207,64,220,234,64,220,3,65,220,16,72,220,48,72,220,65,72,220,16,80,220,46,80,220,75,80,220,104,80,220,133,80,220,162,80,220,10,96,220,
39,96,220,68,96,220,98,96,220,129,96,220,16,128,220,48,128,220,80,128,220,112,128,220,144,128,220,176,128,220,207,128,220,234,128,220,3,129,220,16,130,220,48,130,220,65,130,220,
16,132,220,48,132,220,65,132,220,16,134,220,48,134,220,65,134,220,16,144,220,46,144,220,75,144,220,104,144,220,133,144,220,162,144,220,10,160,220,39,160,220,68,160,220,98,160,220,
129,160,220,16,192,220,48,192,220,80,192,220,112,192,220,144,192,220,171,192,220,199,192,220,228,192,220,16,194,220,40,194,220,16,196,220,40,196,220,16,198,220,40,198,220,10,208,220,
39,208,220,68,208,220,98,208,220,129,208,220,4,224,220,34,224,220,64,224,220,16,0,221,48,0,221,80,0,221,112,0,221,144,0,221,171,0,221,199,0,221,228,0,221,16,2,221,
40,2,221,16,4,221,40,4,221,16,6,221,40,6,221,16,8,221,40,8,221,10,16,221,39,16,221,68,16,221,98,16,221,129,16,221,4,32,221,34,32,221,64,32,221,16,64,221,
48,64,221,79,64,221,108,64,221,138,64,221,166,64,221,195,64,221,225,64,221,15,66,221,36,66,221,15,68,221,36,68,221,15,70,221,36,70,221,15,72,221,36,72,221,6,80,221,
35,80,221,65,80,221,96,80,221,16,0,222,48,0,222,80,0,222,112,0,222,144,0,222,16,16,222,48,16,222,76,16,222,99,16,222,16,32,222,44,32,222,69,32,222,16,64,222,
48,64,222,80,64,222,108,64,222,132,64,222,15,80,222,39,80,222,66,80,222,7,96,222,34,96,222,16,128,222,48,128,222,80,128,222,108,128,222,132,128,222,15,144,222,39,144,222,
66,144,222,7,160,222,34,160,222,16,192,222,48,192,222,75,192,222,101,192,222,128,192,222,7,208,222,34,208,222,2,224,222,16,0,223,48,0,223,75,0,223,101,0,223,128,0,223,
7,16,223,34,16,223,2,32,223,16,64,223,44,64,223,70,64,223,98,64,223,3,80,223,16,0,224,48,0,224,78,0,224,16,16,224,40,16,224,16,32,224,35,32,224,16,64,224,
48,64,224,67,64,224,11,80,224,32,80,224,4,96,224,16,128,224,48,128,224,67,128,224,11,144,224,32,144,224,4,160,224,16,192,224,41,192,224,4,208,224,0,224,224,16,0,225,
41,0,225,4,16,225,0,32,225,15,64,225,36,64,225,1,80,225,16,0,226,46,0,226,16,16,226,11,32,226,16,64,226,35,64,226,6,80,226,1,96,226,16,128,226,35,128,226,
6,144,226,1,160,226,16,192,226,1,208,226,16,0,227,1,16,227,11,64,227
};

---

Appendix 3: Reuse XY Delta Table

Thie table is also used by UASTC HDR 6x6.

uint32_t REUSE_XY_DELTA_BITS = 5;
uint32_t NUM_REUSE_XY_DELTAS = 1 << REUSE_XY_DELTA_BITS;

const reuse_xy_delta g_reuse_xy_deltas[NUM_REUSE_XY_DELTAS] =
{
	{ -1, 0 }, { -2, 0 }, { -3, 0 }, { -4, 0 },
	{ 3, -1 }, { 2, -1 }, { 1, -1 }, { 0, -1 }, { -1, -1 }, { -2, -1 }, { -3, -1 }, { -4, -1 },
	{ 3, -2 }, { 2, -2 }, { 1, -2 }, { 0, -2 }, { -1, -2 }, { -2, -2 }, { -3, -2 }, { -4, -2 },
	{ 3, -3 }, { 2, -3 }, { 1, -3 }, { 0, -3 }, { -1, -3 }, { -2, -3 }, { -3, -3 }, { -4, -3 },
	{ 3, -4 }, { 2, -4 }, { 1, -4 }, { 0, -4 }
};