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16x16 "Pseudoku" generator
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generate16.c
/*
* This is free and unencumbered software released into the public domain.
*/
#include <time.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <limits.h>
#ifndef N
# define N 4
#endif
#define DEFAULT_BAILOUT 100000L
/* Validation table */
#if N == 4
static const unsigned char checks[256][39] = {
{0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x40, 0x50, 0x60,
0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0},
{0x00, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x41, 0x51, 0x61,
0x71, 0x81, 0x91, 0xa1, 0xb1, 0xc1, 0xd1, 0xe1, 0xf1},
{0x00, 0x01, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x42, 0x52, 0x62,
0x72, 0x82, 0x92, 0xa2, 0xb2, 0xc2, 0xd2, 0xe2, 0xf2},
{0x00, 0x01, 0x02, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x43, 0x53, 0x63,
0x73, 0x83, 0x93, 0xa3, 0xb3, 0xc3, 0xd3, 0xe3, 0xf3},
{0x00, 0x01, 0x02, 0x03, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x14, 0x15, 0x16, 0x17, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x44, 0x54, 0x64,
0x74, 0x84, 0x94, 0xa4, 0xb4, 0xc4, 0xd4, 0xe4, 0xf4},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x14, 0x15, 0x16, 0x17, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x45, 0x55, 0x65,
0x75, 0x85, 0x95, 0xa5, 0xb5, 0xc5, 0xd5, 0xe5, 0xf5},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x14, 0x15, 0x16, 0x17, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x46, 0x56, 0x66,
0x76, 0x86, 0x96, 0xa6, 0xb6, 0xc6, 0xd6, 0xe6, 0xf6},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x08, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x14, 0x15, 0x16, 0x17, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x47, 0x57, 0x67,
0x77, 0x87, 0x97, 0xa7, 0xb7, 0xc7, 0xd7, 0xe7, 0xf7},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x09, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x48, 0x58, 0x68,
0x78, 0x88, 0x98, 0xa8, 0xb8, 0xc8, 0xd8, 0xe8, 0xf8},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x0a,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x49, 0x59, 0x69,
0x79, 0x89, 0x99, 0xa9, 0xb9, 0xc9, 0xd9, 0xe9, 0xf9},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x4a, 0x5a, 0x6a,
0x7a, 0x8a, 0x9a, 0xaa, 0xba, 0xca, 0xda, 0xea, 0xfa},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0a, 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x4b, 0x5b, 0x6b,
0x7b, 0x8b, 0x9b, 0xab, 0xbb, 0xcb, 0xdb, 0xeb, 0xfb},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0a, 0x0b, 0x0d, 0x0e, 0x0f, 0x1c, 0x1d, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4c, 0x5c, 0x6c,
0x7c, 0x8c, 0x9c, 0xac, 0xbc, 0xcc, 0xdc, 0xec, 0xfc},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0a, 0x0b, 0x0c, 0x0e, 0x0f, 0x1c, 0x1d, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4d, 0x5d, 0x6d,
0x7d, 0x8d, 0x9d, 0xad, 0xbd, 0xcd, 0xdd, 0xed, 0xfd},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0a, 0x0b, 0x0c, 0x0d, 0x0f, 0x1c, 0x1d, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4e, 0x5e, 0x6e,
0x7e, 0x8e, 0x9e, 0xae, 0xbe, 0xce, 0xde, 0xee, 0xfe},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x1c, 0x1d, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4f, 0x5f, 0x6f,
0x7f, 0x8f, 0x9f, 0xaf, 0xbf, 0xcf, 0xdf, 0xef, 0xff},
{0x00, 0x01, 0x02, 0x03, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x40, 0x50, 0x60,
0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x12, 0x13, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x41, 0x51, 0x61,
0x71, 0x81, 0x91, 0xa1, 0xb1, 0xc1, 0xd1, 0xe1, 0xf1},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x13, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x42, 0x52, 0x62,
0x72, 0x82, 0x92, 0xa2, 0xb2, 0xc2, 0xd2, 0xe2, 0xf2},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
0x21, 0x22, 0x23, 0x30, 0x31, 0x32, 0x33, 0x43, 0x53, 0x63,
0x73, 0x83, 0x93, 0xa3, 0xb3, 0xc3, 0xd3, 0xe3, 0xf3},
{0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x44, 0x54, 0x64,
0x74, 0x84, 0x94, 0xa4, 0xb4, 0xc4, 0xd4, 0xe4, 0xf4},
{0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 0x14, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x45, 0x55, 0x65,
0x75, 0x85, 0x95, 0xa5, 0xb5, 0xc5, 0xd5, 0xe5, 0xf5},
{0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x46, 0x56, 0x66,
0x76, 0x86, 0x96, 0xa6, 0xb6, 0xc6, 0xd6, 0xe6, 0xf6},
{0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x24,
0x25, 0x26, 0x27, 0x34, 0x35, 0x36, 0x37, 0x47, 0x57, 0x67,
0x77, 0x87, 0x97, 0xa7, 0xb7, 0xc7, 0xd7, 0xe7, 0xf7},
{0x08, 0x09, 0x0a, 0x0b, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x48, 0x58, 0x68,
0x78, 0x88, 0x98, 0xa8, 0xb8, 0xc8, 0xd8, 0xe8, 0xf8},
{0x08, 0x09, 0x0a, 0x0b, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x49, 0x59, 0x69,
0x79, 0x89, 0x99, 0xa9, 0xb9, 0xc9, 0xd9, 0xe9, 0xf9},
{0x08, 0x09, 0x0a, 0x0b, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x4a, 0x5a, 0x6a,
0x7a, 0x8a, 0x9a, 0xaa, 0xba, 0xca, 0xda, 0xea, 0xfa},
{0x08, 0x09, 0x0a, 0x0b, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1a, 0x1c, 0x1d, 0x1e, 0x1f, 0x28,
0x29, 0x2a, 0x2b, 0x38, 0x39, 0x3a, 0x3b, 0x4b, 0x5b, 0x6b,
0x7b, 0x8b, 0x9b, 0xab, 0xbb, 0xcb, 0xdb, 0xeb, 0xfb},
{0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1d, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4c, 0x5c, 0x6c,
0x7c, 0x8c, 0x9c, 0xac, 0xbc, 0xcc, 0xdc, 0xec, 0xfc},
{0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1e, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4d, 0x5d, 0x6d,
0x7d, 0x8d, 0x9d, 0xad, 0xbd, 0xcd, 0xdd, 0xed, 0xfd},
{0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1f, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4e, 0x5e, 0x6e,
0x7e, 0x8e, 0x9e, 0xae, 0xbe, 0xce, 0xde, 0xee, 0xfe},
{0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x2c,
0x2d, 0x2e, 0x2f, 0x3c, 0x3d, 0x3e, 0x3f, 0x4f, 0x5f, 0x6f,
0x7f, 0x8f, 0x9f, 0xaf, 0xbf, 0xcf, 0xdf, 0xef, 0xff},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x13, 0x21, 0x22,
0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x40, 0x50, 0x60,
0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x13, 0x20, 0x22,
0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x41, 0x51, 0x61,
0x71, 0x81, 0x91, 0xa1, 0xb1, 0xc1, 0xd1, 0xe1, 0xf1},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x13, 0x20, 0x21,
0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x42, 0x52, 0x62,
0x72, 0x82, 0x92, 0xa2, 0xb2, 0xc2, 0xd2, 0xe2, 0xf2},
{0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x13, 0x20, 0x21,
0x22, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x43, 0x53, 0x63,
0x73, 0x83, 0x93, 0xa3, 0xb3, 0xc3, 0xd3, 0xe3, 0xf3},
{0x04, 0x05, 0x06, 0x07, 0x14, 0x15, 0x16, 0x17, 0x20, 0x21,
0x22, 0x23, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x34, 0x35, 0x36, 0x37, 0x44, 0x54, 0x64,
0x74, 0x84, 0x94, 0xa4, 0xb4, 0xc4, 0xd4, 0xe4, 0xf4},
{0x04, 0x05, 0x06, 0x07, 0x14, 0x15, 0x16, 0x17, 0x20, 0x21,
0x22, 0x23, 0x24, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x34, 0x35, 0x36, 0x37, 0x45, 0x55, 0x65,
0x75, 0x85, 0x95, 0xa5, 0xb5, 0xc5, 0xd5, 0xe5, 0xf5},
{0x04, 0x05, 0x06, 0x07, 0x14, 0x15, 0x16, 0x17, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x34, 0x35, 0x36, 0x37, 0x46, 0x56, 0x66,
0x76, 0x86, 0x96, 0xa6, 0xb6, 0xc6, 0xd6, 0xe6, 0xf6},
{0x04, 0x05, 0x06, 0x07, 0x14, 0x15, 0x16, 0x17, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x28, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x34, 0x35, 0x36, 0x37, 0x47, 0x57, 0x67,
0x77, 0x87, 0x97, 0xa7, 0xb7, 0xc7, 0xd7, 0xe7, 0xf7},
{0x08, 0x09, 0x0a, 0x0b, 0x18, 0x19, 0x1a, 0x1b, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x29, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x38, 0x39, 0x3a, 0x3b, 0x48, 0x58, 0x68,
0x78, 0x88, 0x98, 0xa8, 0xb8, 0xc8, 0xd8, 0xe8, 0xf8},
{0x08, 0x09, 0x0a, 0x0b, 0x18, 0x19, 0x1a, 0x1b, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x2a, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x38, 0x39, 0x3a, 0x3b, 0x49, 0x59, 0x69,
0x79, 0x89, 0x99, 0xa9, 0xb9, 0xc9, 0xd9, 0xe9, 0xf9},
{0x08, 0x09, 0x0a, 0x0b, 0x18, 0x19, 0x1a, 0x1b, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2b, 0x2c,
0x2d, 0x2e, 0x2f, 0x38, 0x39, 0x3a, 0x3b, 0x4a, 0x5a, 0x6a,
0x7a, 0x8a, 0x9a, 0xaa, 0xba, 0xca, 0xda, 0xea, 0xfa},
{0x08, 0x09, 0x0a, 0x0b, 0x18, 0x19, 0x1a, 0x1b, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2c,
0x2d, 0x2e, 0x2f, 0x38, 0x39, 0x3a, 0x3b, 0x4b, 0x5b, 0x6b,
0x7b, 0x8b, 0x9b, 0xab, 0xbb, 0xcb, 0xdb, 0xeb, 0xfb},
{0x0c, 0x0d, 0x0e, 0x0f, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21,
0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b,
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0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe6, 0xe7, 0xe8, 0xe9, 0xea,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf4, 0xf5, 0xf6, 0xf7},
{0x06, 0x16, 0x26, 0x36, 0x46, 0x56, 0x66, 0x76, 0x86, 0x96,
0xa6, 0xb6, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe7, 0xe8, 0xe9, 0xea,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf4, 0xf5, 0xf6, 0xf7},
{0x07, 0x17, 0x27, 0x37, 0x47, 0x57, 0x67, 0x77, 0x87, 0x97,
0xa7, 0xb7, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe8, 0xe9, 0xea,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf4, 0xf5, 0xf6, 0xf7},
{0x08, 0x18, 0x28, 0x38, 0x48, 0x58, 0x68, 0x78, 0x88, 0x98,
0xa8, 0xb8, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe9, 0xea,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf8, 0xf9, 0xfa, 0xfb},
{0x09, 0x19, 0x29, 0x39, 0x49, 0x59, 0x69, 0x79, 0x89, 0x99,
0xa9, 0xb9, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xea,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf8, 0xf9, 0xfa, 0xfb},
{0x0a, 0x1a, 0x2a, 0x3a, 0x4a, 0x5a, 0x6a, 0x7a, 0x8a, 0x9a,
0xaa, 0xba, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xeb, 0xec, 0xed, 0xee, 0xef, 0xf8, 0xf9, 0xfa, 0xfb},
{0x0b, 0x1b, 0x2b, 0x3b, 0x4b, 0x5b, 0x6b, 0x7b, 0x8b, 0x9b,
0xab, 0xbb, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xea, 0xec, 0xed, 0xee, 0xef, 0xf8, 0xf9, 0xfa, 0xfb},
{0x0c, 0x1c, 0x2c, 0x3c, 0x4c, 0x5c, 0x6c, 0x7c, 0x8c, 0x9c,
0xac, 0xbc, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xea, 0xeb, 0xed, 0xee, 0xef, 0xfc, 0xfd, 0xfe, 0xff},
{0x0d, 0x1d, 0x2d, 0x3d, 0x4d, 0x5d, 0x6d, 0x7d, 0x8d, 0x9d,
0xad, 0xbd, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xea, 0xeb, 0xec, 0xee, 0xef, 0xfc, 0xfd, 0xfe, 0xff},
{0x0e, 0x1e, 0x2e, 0x3e, 0x4e, 0x5e, 0x6e, 0x7e, 0x8e, 0x9e,
0xae, 0xbe, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xea, 0xeb, 0xec, 0xed, 0xef, 0xfc, 0xfd, 0xfe, 0xff},
{0x0f, 0x1f, 0x2f, 0x3f, 0x4f, 0x5f, 0x6f, 0x7f, 0x8f, 0x9f,
0xaf, 0xbf, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9,
0xea, 0xeb, 0xec, 0xed, 0xee, 0xfc, 0xfd, 0xfe, 0xff},
{0x00, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90,
0xa0, 0xb0, 0xc0, 0xc1, 0xc2, 0xc3, 0xd0, 0xd1, 0xd2, 0xd3,
0xe0, 0xe1, 0xe2, 0xe3, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x01, 0x11, 0x21, 0x31, 0x41, 0x51, 0x61, 0x71, 0x81, 0x91,
0xa1, 0xb1, 0xc0, 0xc1, 0xc2, 0xc3, 0xd0, 0xd1, 0xd2, 0xd3,
0xe0, 0xe1, 0xe2, 0xe3, 0xf0, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x02, 0x12, 0x22, 0x32, 0x42, 0x52, 0x62, 0x72, 0x82, 0x92,
0xa2, 0xb2, 0xc0, 0xc1, 0xc2, 0xc3, 0xd0, 0xd1, 0xd2, 0xd3,
0xe0, 0xe1, 0xe2, 0xe3, 0xf0, 0xf1, 0xf3, 0xf4, 0xf5, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x03, 0x13, 0x23, 0x33, 0x43, 0x53, 0x63, 0x73, 0x83, 0x93,
0xa3, 0xb3, 0xc0, 0xc1, 0xc2, 0xc3, 0xd0, 0xd1, 0xd2, 0xd3,
0xe0, 0xe1, 0xe2, 0xe3, 0xf0, 0xf1, 0xf2, 0xf4, 0xf5, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x04, 0x14, 0x24, 0x34, 0x44, 0x54, 0x64, 0x74, 0x84, 0x94,
0xa4, 0xb4, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe4, 0xe5, 0xe6, 0xe7, 0xf0, 0xf1, 0xf2, 0xf3, 0xf5, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x05, 0x15, 0x25, 0x35, 0x45, 0x55, 0x65, 0x75, 0x85, 0x95,
0xa5, 0xb5, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe4, 0xe5, 0xe6, 0xe7, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf6,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x06, 0x16, 0x26, 0x36, 0x46, 0x56, 0x66, 0x76, 0x86, 0x96,
0xa6, 0xb6, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe4, 0xe5, 0xe6, 0xe7, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x07, 0x17, 0x27, 0x37, 0x47, 0x57, 0x67, 0x77, 0x87, 0x97,
0xa7, 0xb7, 0xc4, 0xc5, 0xc6, 0xc7, 0xd4, 0xd5, 0xd6, 0xd7,
0xe4, 0xe5, 0xe6, 0xe7, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x08, 0x18, 0x28, 0x38, 0x48, 0x58, 0x68, 0x78, 0x88, 0x98,
0xa8, 0xb8, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe8, 0xe9, 0xea, 0xeb, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x09, 0x19, 0x29, 0x39, 0x49, 0x59, 0x69, 0x79, 0x89, 0x99,
0xa9, 0xb9, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe8, 0xe9, 0xea, 0xeb, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x0a, 0x1a, 0x2a, 0x3a, 0x4a, 0x5a, 0x6a, 0x7a, 0x8a, 0x9a,
0xaa, 0xba, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe8, 0xe9, 0xea, 0xeb, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfb, 0xfc, 0xfd, 0xfe, 0xff},
{0x0b, 0x1b, 0x2b, 0x3b, 0x4b, 0x5b, 0x6b, 0x7b, 0x8b, 0x9b,
0xab, 0xbb, 0xc8, 0xc9, 0xca, 0xcb, 0xd8, 0xd9, 0xda, 0xdb,
0xe8, 0xe9, 0xea, 0xeb, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfc, 0xfd, 0xfe, 0xff},
{0x0c, 0x1c, 0x2c, 0x3c, 0x4c, 0x5c, 0x6c, 0x7c, 0x8c, 0x9c,
0xac, 0xbc, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfd, 0xfe, 0xff},
{0x0d, 0x1d, 0x2d, 0x3d, 0x4d, 0x5d, 0x6d, 0x7d, 0x8d, 0x9d,
0xad, 0xbd, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfe, 0xff},
{0x0e, 0x1e, 0x2e, 0x3e, 0x4e, 0x5e, 0x6e, 0x7e, 0x8e, 0x9e,
0xae, 0xbe, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xff},
{0x0f, 0x1f, 0x2f, 0x3f, 0x4f, 0x5f, 0x6f, 0x7f, 0x8f, 0x9f,
0xaf, 0xbf, 0xcc, 0xcd, 0xce, 0xcf, 0xdc, 0xdd, 0xde, 0xdf,
0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5,
0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe},
};
#elif N == 3
static const unsigned char checks[81][20] = {
{0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x12, 0x13, 0x14, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48},
{0x00, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x12, 0x13, 0x14, 0x1c, 0x25, 0x2e, 0x37, 0x40, 0x49},
{0x00, 0x01, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a,
0x0b, 0x12, 0x13, 0x14, 0x1d, 0x26, 0x2f, 0x38, 0x41, 0x4a},
{0x00, 0x01, 0x02, 0x04, 0x05, 0x06, 0x07, 0x08, 0x0c, 0x0d,
0x0e, 0x15, 0x16, 0x17, 0x1e, 0x27, 0x30, 0x39, 0x42, 0x4b},
{0x00, 0x01, 0x02, 0x03, 0x05, 0x06, 0x07, 0x08, 0x0c, 0x0d,
0x0e, 0x15, 0x16, 0x17, 0x1f, 0x28, 0x31, 0x3a, 0x43, 0x4c},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x06, 0x07, 0x08, 0x0c, 0x0d,
0x0e, 0x15, 0x16, 0x17, 0x20, 0x29, 0x32, 0x3b, 0x44, 0x4d},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x07, 0x08, 0x0f, 0x10,
0x11, 0x18, 0x19, 0x1a, 0x21, 0x2a, 0x33, 0x3c, 0x45, 0x4e},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x08, 0x0f, 0x10,
0x11, 0x18, 0x19, 0x1a, 0x22, 0x2b, 0x34, 0x3d, 0x46, 0x4f},
{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x0f, 0x10,
0x11, 0x18, 0x19, 0x1a, 0x23, 0x2c, 0x35, 0x3e, 0x47, 0x50},
{0x00, 0x01, 0x02, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10,
0x11, 0x12, 0x13, 0x14, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48},
{0x00, 0x01, 0x02, 0x09, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10,
0x11, 0x12, 0x13, 0x14, 0x1c, 0x25, 0x2e, 0x37, 0x40, 0x49},
{0x00, 0x01, 0x02, 0x09, 0x0a, 0x0c, 0x0d, 0x0e, 0x0f, 0x10,
0x11, 0x12, 0x13, 0x14, 0x1d, 0x26, 0x2f, 0x38, 0x41, 0x4a},
{0x03, 0x04, 0x05, 0x09, 0x0a, 0x0b, 0x0d, 0x0e, 0x0f, 0x10,
0x11, 0x15, 0x16, 0x17, 0x1e, 0x27, 0x30, 0x39, 0x42, 0x4b},
{0x03, 0x04, 0x05, 0x09, 0x0a, 0x0b, 0x0c, 0x0e, 0x0f, 0x10,
0x11, 0x15, 0x16, 0x17, 0x1f, 0x28, 0x31, 0x3a, 0x43, 0x4c},
{0x03, 0x04, 0x05, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0f, 0x10,
0x11, 0x15, 0x16, 0x17, 0x20, 0x29, 0x32, 0x3b, 0x44, 0x4d},
{0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x10,
0x11, 0x18, 0x19, 0x1a, 0x21, 0x2a, 0x33, 0x3c, 0x45, 0x4e},
{0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x11, 0x18, 0x19, 0x1a, 0x22, 0x2b, 0x34, 0x3d, 0x46, 0x4f},
{0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x10, 0x18, 0x19, 0x1a, 0x23, 0x2c, 0x35, 0x3e, 0x47, 0x50},
{0x00, 0x01, 0x02, 0x09, 0x0a, 0x0b, 0x13, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48},
{0x00, 0x01, 0x02, 0x09, 0x0a, 0x0b, 0x12, 0x14, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1c, 0x25, 0x2e, 0x37, 0x40, 0x49},
{0x00, 0x01, 0x02, 0x09, 0x0a, 0x0b, 0x12, 0x13, 0x15, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1d, 0x26, 0x2f, 0x38, 0x41, 0x4a},
{0x03, 0x04, 0x05, 0x0c, 0x0d, 0x0e, 0x12, 0x13, 0x14, 0x16,
0x17, 0x18, 0x19, 0x1a, 0x1e, 0x27, 0x30, 0x39, 0x42, 0x4b},
{0x03, 0x04, 0x05, 0x0c, 0x0d, 0x0e, 0x12, 0x13, 0x14, 0x15,
0x17, 0x18, 0x19, 0x1a, 0x1f, 0x28, 0x31, 0x3a, 0x43, 0x4c},
{0x03, 0x04, 0x05, 0x0c, 0x0d, 0x0e, 0x12, 0x13, 0x14, 0x15,
0x16, 0x18, 0x19, 0x1a, 0x20, 0x29, 0x32, 0x3b, 0x44, 0x4d},
{0x06, 0x07, 0x08, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x19, 0x1a, 0x21, 0x2a, 0x33, 0x3c, 0x45, 0x4e},
{0x06, 0x07, 0x08, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x1a, 0x22, 0x2b, 0x34, 0x3d, 0x46, 0x4f},
{0x06, 0x07, 0x08, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
0x16, 0x17, 0x18, 0x19, 0x23, 0x2c, 0x35, 0x3e, 0x47, 0x50},
{0x00, 0x09, 0x12, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21, 0x22,
0x23, 0x24, 0x25, 0x26, 0x2d, 0x2e, 0x2f, 0x36, 0x3f, 0x48},
{0x01, 0x0a, 0x13, 0x1b, 0x1d, 0x1e, 0x1f, 0x20, 0x21, 0x22,
0x23, 0x24, 0x25, 0x26, 0x2d, 0x2e, 0x2f, 0x37, 0x40, 0x49},
{0x02, 0x0b, 0x14, 0x1b, 0x1c, 0x1e, 0x1f, 0x20, 0x21, 0x22,
0x23, 0x24, 0x25, 0x26, 0x2d, 0x2e, 0x2f, 0x38, 0x41, 0x4a},
{0x03, 0x0c, 0x15, 0x1b, 0x1c, 0x1d, 0x1f, 0x20, 0x21, 0x22,
0x23, 0x27, 0x28, 0x29, 0x30, 0x31, 0x32, 0x39, 0x42, 0x4b},
{0x04, 0x0d, 0x16, 0x1b, 0x1c, 0x1d, 0x1e, 0x20, 0x21, 0x22,
0x23, 0x27, 0x28, 0x29, 0x30, 0x31, 0x32, 0x3a, 0x43, 0x4c},
{0x05, 0x0e, 0x17, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x21, 0x22,
0x23, 0x27, 0x28, 0x29, 0x30, 0x31, 0x32, 0x3b, 0x44, 0x4d},
{0x06, 0x0f, 0x18, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x22,
0x23, 0x2a, 0x2b, 0x2c, 0x33, 0x34, 0x35, 0x3c, 0x45, 0x4e},
{0x07, 0x10, 0x19, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21,
0x23, 0x2a, 0x2b, 0x2c, 0x33, 0x34, 0x35, 0x3d, 0x46, 0x4f},
{0x08, 0x11, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21,
0x22, 0x2a, 0x2b, 0x2c, 0x33, 0x34, 0x35, 0x3e, 0x47, 0x50},
{0x00, 0x09, 0x12, 0x1b, 0x1c, 0x1d, 0x25, 0x26, 0x27, 0x28,
0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x36, 0x3f, 0x48},
{0x01, 0x0a, 0x13, 0x1b, 0x1c, 0x1d, 0x24, 0x26, 0x27, 0x28,
0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x37, 0x40, 0x49},
{0x02, 0x0b, 0x14, 0x1b, 0x1c, 0x1d, 0x24, 0x25, 0x27, 0x28,
0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x38, 0x41, 0x4a},
{0x03, 0x0c, 0x15, 0x1e, 0x1f, 0x20, 0x24, 0x25, 0x26, 0x28,
0x29, 0x2a, 0x2b, 0x2c, 0x30, 0x31, 0x32, 0x39, 0x42, 0x4b},
{0x04, 0x0d, 0x16, 0x1e, 0x1f, 0x20, 0x24, 0x25, 0x26, 0x27,
0x29, 0x2a, 0x2b, 0x2c, 0x30, 0x31, 0x32, 0x3a, 0x43, 0x4c},
{0x05, 0x0e, 0x17, 0x1e, 0x1f, 0x20, 0x24, 0x25, 0x26, 0x27,
0x28, 0x2a, 0x2b, 0x2c, 0x30, 0x31, 0x32, 0x3b, 0x44, 0x4d},
{0x06, 0x0f, 0x18, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2b, 0x2c, 0x33, 0x34, 0x35, 0x3c, 0x45, 0x4e},
{0x07, 0x10, 0x19, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2a, 0x2c, 0x33, 0x34, 0x35, 0x3d, 0x46, 0x4f},
{0x08, 0x11, 0x1a, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2a, 0x2b, 0x33, 0x34, 0x35, 0x3e, 0x47, 0x50},
{0x00, 0x09, 0x12, 0x1b, 0x1c, 0x1d, 0x24, 0x25, 0x26, 0x2e,
0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x3f, 0x48},
{0x01, 0x0a, 0x13, 0x1b, 0x1c, 0x1d, 0x24, 0x25, 0x26, 0x2d,
0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x37, 0x40, 0x49},
{0x02, 0x0b, 0x14, 0x1b, 0x1c, 0x1d, 0x24, 0x25, 0x26, 0x2d,
0x2e, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x38, 0x41, 0x4a},
{0x03, 0x0c, 0x15, 0x1e, 0x1f, 0x20, 0x27, 0x28, 0x29, 0x2d,
0x2e, 0x2f, 0x31, 0x32, 0x33, 0x34, 0x35, 0x39, 0x42, 0x4b},
{0x04, 0x0d, 0x16, 0x1e, 0x1f, 0x20, 0x27, 0x28, 0x29, 0x2d,
0x2e, 0x2f, 0x30, 0x32, 0x33, 0x34, 0x35, 0x3a, 0x43, 0x4c},
{0x05, 0x0e, 0x17, 0x1e, 0x1f, 0x20, 0x27, 0x28, 0x29, 0x2d,
0x2e, 0x2f, 0x30, 0x31, 0x33, 0x34, 0x35, 0x3b, 0x44, 0x4d},
{0x06, 0x0f, 0x18, 0x21, 0x22, 0x23, 0x2a, 0x2b, 0x2c, 0x2d,
0x2e, 0x2f, 0x30, 0x31, 0x32, 0x34, 0x35, 0x3c, 0x45, 0x4e},
{0x07, 0x10, 0x19, 0x21, 0x22, 0x23, 0x2a, 0x2b, 0x2c, 0x2d,
0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x35, 0x3d, 0x46, 0x4f},
{0x08, 0x11, 0x1a, 0x21, 0x22, 0x23, 0x2a, 0x2b, 0x2c, 0x2d,
0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x3e, 0x47, 0x50},
{0x00, 0x09, 0x12, 0x1b, 0x24, 0x2d, 0x37, 0x38, 0x39, 0x3a,
0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x48, 0x49, 0x4a},
{0x01, 0x0a, 0x13, 0x1c, 0x25, 0x2e, 0x36, 0x38, 0x39, 0x3a,
0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x48, 0x49, 0x4a},
{0x02, 0x0b, 0x14, 0x1d, 0x26, 0x2f, 0x36, 0x37, 0x39, 0x3a,
0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x48, 0x49, 0x4a},
{0x03, 0x0c, 0x15, 0x1e, 0x27, 0x30, 0x36, 0x37, 0x38, 0x3a,
0x3b, 0x3c, 0x3d, 0x3e, 0x42, 0x43, 0x44, 0x4b, 0x4c, 0x4d},
{0x04, 0x0d, 0x16, 0x1f, 0x28, 0x31, 0x36, 0x37, 0x38, 0x39,
0x3b, 0x3c, 0x3d, 0x3e, 0x42, 0x43, 0x44, 0x4b, 0x4c, 0x4d},
{0x05, 0x0e, 0x17, 0x20, 0x29, 0x32, 0x36, 0x37, 0x38, 0x39,
0x3a, 0x3c, 0x3d, 0x3e, 0x42, 0x43, 0x44, 0x4b, 0x4c, 0x4d},
{0x06, 0x0f, 0x18, 0x21, 0x2a, 0x33, 0x36, 0x37, 0x38, 0x39,
0x3a, 0x3b, 0x3d, 0x3e, 0x45, 0x46, 0x47, 0x4e, 0x4f, 0x50},
{0x07, 0x10, 0x19, 0x22, 0x2b, 0x34, 0x36, 0x37, 0x38, 0x39,
0x3a, 0x3b, 0x3c, 0x3e, 0x45, 0x46, 0x47, 0x4e, 0x4f, 0x50},
{0x08, 0x11, 0x1a, 0x23, 0x2c, 0x35, 0x36, 0x37, 0x38, 0x39,
0x3a, 0x3b, 0x3c, 0x3d, 0x45, 0x46, 0x47, 0x4e, 0x4f, 0x50},
{0x00, 0x09, 0x12, 0x1b, 0x24, 0x2d, 0x36, 0x37, 0x38, 0x40,
0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a},
{0x01, 0x0a, 0x13, 0x1c, 0x25, 0x2e, 0x36, 0x37, 0x38, 0x3f,
0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a},
{0x02, 0x0b, 0x14, 0x1d, 0x26, 0x2f, 0x36, 0x37, 0x38, 0x3f,
0x40, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a},
{0x03, 0x0c, 0x15, 0x1e, 0x27, 0x30, 0x39, 0x3a, 0x3b, 0x3f,
0x40, 0x41, 0x43, 0x44, 0x45, 0x46, 0x47, 0x4b, 0x4c, 0x4d},
{0x04, 0x0d, 0x16, 0x1f, 0x28, 0x31, 0x39, 0x3a, 0x3b, 0x3f,
0x40, 0x41, 0x42, 0x44, 0x45, 0x46, 0x47, 0x4b, 0x4c, 0x4d},
{0x05, 0x0e, 0x17, 0x20, 0x29, 0x32, 0x39, 0x3a, 0x3b, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x45, 0x46, 0x47, 0x4b, 0x4c, 0x4d},
{0x06, 0x0f, 0x18, 0x21, 0x2a, 0x33, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x46, 0x47, 0x4e, 0x4f, 0x50},
{0x07, 0x10, 0x19, 0x22, 0x2b, 0x34, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x47, 0x4e, 0x4f, 0x50},
{0x08, 0x11, 0x1a, 0x23, 0x2c, 0x35, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x4e, 0x4f, 0x50},
{0x00, 0x09, 0x12, 0x1b, 0x24, 0x2d, 0x36, 0x37, 0x38, 0x3f,
0x40, 0x41, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x50},
{0x01, 0x0a, 0x13, 0x1c, 0x25, 0x2e, 0x36, 0x37, 0x38, 0x3f,
0x40, 0x41, 0x48, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x50},
{0x02, 0x0b, 0x14, 0x1d, 0x26, 0x2f, 0x36, 0x37, 0x38, 0x3f,
0x40, 0x41, 0x48, 0x49, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x50},
{0x03, 0x0c, 0x15, 0x1e, 0x27, 0x30, 0x39, 0x3a, 0x3b, 0x42,
0x43, 0x44, 0x48, 0x49, 0x4a, 0x4c, 0x4d, 0x4e, 0x4f, 0x50},
{0x04, 0x0d, 0x16, 0x1f, 0x28, 0x31, 0x39, 0x3a, 0x3b, 0x42,
0x43, 0x44, 0x48, 0x49, 0x4a, 0x4b, 0x4d, 0x4e, 0x4f, 0x50},
{0x05, 0x0e, 0x17, 0x20, 0x29, 0x32, 0x39, 0x3a, 0x3b, 0x42,
0x43, 0x44, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4e, 0x4f, 0x50},
{0x06, 0x0f, 0x18, 0x21, 0x2a, 0x33, 0x3c, 0x3d, 0x3e, 0x45,
0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4f, 0x50},
{0x07, 0x10, 0x19, 0x22, 0x2b, 0x34, 0x3c, 0x3d, 0x3e, 0x45,
0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x50},
{0x08, 0x11, 0x1a, 0x23, 0x2c, 0x35, 0x3c, 0x3d, 0x3e, 0x45,
0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f},
};
#endif
/* PRNG */
static uint64_t
xorshift(uint64_t *state)
{
uint64_t x = *state;
x ^= x >> 12;
x ^= x << 25;
x ^= x >> 27;
*state = x;
return x * UINT64_C(2685821657736338717);
}
/**
* Fill GRID with a valid random arrangement. Use BAILOUT to tune
* worse-case situations. Keep count until the grid has been filled
* COUNT times.
*/
static enum {FILL_BAILOUT = -1, FILL_FAILURE, FILL_SUCCESS}
fill(char *grid, uint64_t *rng, long bailout, int count)
{
char locked[N * N * N * N];
char index[N * N * N * N];
char candidates[N * N * N * N][N * N];
/* Initialize data structures. */
for (int p = 0; p < N * N * N * N; p++)
locked[p] = !!grid[p];
for (int p = 0; p < N * N * N * N; p++) {
if (locked[p])
continue;
grid[p] = 0;
index[p] = 0;
/* Shuffle candidate order (Fisher-Yates) */
for (int i = 0; i < N * N; i++)
candidates[p][i] = i + 'A';
if (rng) {
for (int i = N * N - 1; i > 0; i--) {
int j = xorshift(rng) % (i + 1);
int tmp = candidates[p][j];
candidates[p][j] = candidates[p][i];
candidates[p][i] = tmp;
}
}
}
for (int p = 0; bailout; bailout--) {
if (locked[p]) {
p++; // skip
} else if (index[p] == N * N) {
/* Fail to fit anything. */
grid[p] = 0;
do
p--; // rollback
while (p >= 0 && locked[p]);
if (p < 0)
return FILL_FAILURE; // can't rollback any further
} else {
int i = index[p]++;
int c = candidates[p][i];
int valid = 1;
/* Check candidate against validation tables. */
for (int j = 0; j < N * N + (N * N - N) * 2 - 1; j++) {
if (grid[checks[p][j]] == c) {
valid = 0;
break;
}
}
if (valid) {
/* Fill in this slot and advance. */
grid[p] = c;
do
p++;
while (p < N * N * N * N && locked[p]);
if (p < N * N * N * N)
index[p] = 0; // start fresh on next slot
}
}
if (p == N * N * N * N) {
if (--count) {
/* Find another solution by pretending to fail. */
do
p--; // rollback
while (locked[p]);
} else {
/* Done finding solutions. */
return FILL_SUCCESS;
}
}
}
return FILL_BAILOUT;
}
static void
print(char *grid)
{
for (int i = 0; i < N * N * N * N; i++) {
putchar(grid[i] ? grid[i] : '_');
if (i % N == N - 1)
putchar(' ');
if (i % (N * N) == N * N - 1)
putchar('\n');
else
putchar(' ');
if (i != N * N * N * N - 1 &&
i % (N * N * N) == N * N * N - 1)
putchar('\n');
}
}
int
main(void)
{
uint64_t rng = time(0);
/* First fill an empty grid. */
char grid[N * N * N * N] = {0};
while (fill(grid, &rng, DEFAULT_BAILOUT, 1) == FILL_BAILOUT)
memset(grid, 0, sizeof(grid));
/* Tracks empty slots ("holes"). */
int nholes = 0;
unsigned char holes[N * N * N * N];
/* Candidates for empty slots. */
int ncandidates = N * N * N * N;
unsigned char candidates[N * N * N * N];
for (int i = 0; i < N * N * N * N; i++)
candidates[i] = i;
/* Try all candidates in a random order. */
while (ncandidates) {
int i = xorshift(&rng) % ncandidates;
holes[nholes++] = candidates[i];
candidates[i] = candidates[--ncandidates];
/* Fill out holes in test grid. */
char test[N * N * N * N];
memcpy(test, grid, sizeof(test));
for (int i = 0; i < nholes; i++)
test[holes[i]] = 0;
/* Check for multiple solutions. "Failure" means it could only
* find one solution: keep this "hole."
*/
if (fill(test, 0, DEFAULT_BAILOUT, 2) != FILL_FAILURE)
nholes--;
}
/* Print out the final puzzle. */
for (int i = 0; i < nholes; i++)
grid[holes[i]] = 0;
print(grid);
return 0;
}
Raw
Makefile
CC = c99
CFLAGS = -Wall -Wextra -O3 -g3
generate16: generate16.c
clean:
rm -f generate16
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