2 * common functions for Indeo Video Interactive codecs (Indeo4 and Indeo5)
4 * Copyright (c) 2009 Maxim Poliakovski
6 * This file is part of FFmpeg.
8 * FFmpeg is free software; you can redistribute it and/or
9 * modify it under the terms of the GNU Lesser General Public
10 * License as published by the Free Software Foundation; either
11 * version 2.1 of the License, or (at your option) any later version.
13 * FFmpeg is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 * Lesser General Public License for more details.
18 * You should have received a copy of the GNU Lesser General Public
19 * License along with FFmpeg; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
25 * This file contains functions and data shared by both Indeo4 and
29 #define BITSTREAM_READER_LE
32 #include "ivi_common.h"
33 #include "libavutil/common.h"
36 extern const IVIHuffDesc ff_ivi_mb_huff_desc[8]; ///< static macroblock huffman tables
37 extern const IVIHuffDesc ff_ivi_blk_huff_desc[8]; ///< static block huffman tables
39 VLC ff_ivi_mb_vlc_tabs [8];
40 VLC ff_ivi_blk_vlc_tabs[8];
43 * Reverse "nbits" bits of the value "val" and return the result
44 * in the least significant bits.
46 static uint16_t inv_bits(uint16_t val, int nbits)
51 res = av_reverse[val] >> (8-nbits);
53 res = ((av_reverse[val & 0xFF] << 8) + (av_reverse[val >> 8])) >> (16-nbits);
58 int ff_ivi_create_huff_from_desc(const IVIHuffDesc *cb, VLC *vlc, int flag)
60 int pos, i, j, codes_per_row, prefix, not_last_row;
61 uint16_t codewords[256]; /* FIXME: move this temporal storage out? */
64 pos = 0; /* current position = 0 */
66 for (i = 0; i < cb->num_rows; i++) {
67 codes_per_row = 1 << cb->xbits[i];
68 not_last_row = (i != cb->num_rows - 1);
69 prefix = ((1 << i) - 1) << (cb->xbits[i] + not_last_row);
71 for (j = 0; j < codes_per_row; j++) {
72 if (pos >= 256) /* Some Indeo5 codebooks can have more than 256 */
73 break; /* elements, but only 256 codes are allowed! */
75 bits[pos] = i + cb->xbits[i] + not_last_row;
76 if (bits[pos] > IVI_VLC_BITS)
77 return -1; /* invalid descriptor */
79 codewords[pos] = inv_bits((prefix | j), bits[pos]);
87 /* number of codewords = pos */
88 return init_vlc(vlc, IVI_VLC_BITS, pos, bits, 1, 1, codewords, 2, 2,
89 (flag ? INIT_VLC_USE_NEW_STATIC : 0) | INIT_VLC_LE);
92 void ff_ivi_init_static_vlc(void)
95 static VLC_TYPE table_data[8192 * 16][2];
96 static int initialized_vlcs = 0;
100 for (i = 0; i < 8; i++) {
101 ff_ivi_mb_vlc_tabs[i].table = table_data + i * 2 * 8192;
102 ff_ivi_mb_vlc_tabs[i].table_allocated = 8192;
103 ff_ivi_create_huff_from_desc(&ff_ivi_mb_huff_desc[i], &ff_ivi_mb_vlc_tabs[i], 1);
104 ff_ivi_blk_vlc_tabs[i].table = table_data + (i * 2 + 1) * 8192;
105 ff_ivi_blk_vlc_tabs[i].table_allocated = 8192;
106 ff_ivi_create_huff_from_desc(&ff_ivi_blk_huff_desc[i], &ff_ivi_blk_vlc_tabs[i], 1);
108 initialized_vlcs = 1;
111 int ff_ivi_dec_huff_desc(GetBitContext *gb, int desc_coded, int which_tab,
112 IVIHuffTab *huff_tab, AVCodecContext *avctx)
115 IVIHuffDesc new_huff;
118 /* select default table */
119 huff_tab->tab = (which_tab) ? &ff_ivi_blk_vlc_tabs[7]
120 : &ff_ivi_mb_vlc_tabs [7];
122 huff_tab->tab_sel = get_bits(gb, 3);
123 if (huff_tab->tab_sel == 7) {
124 /* custom huffman table (explicitly encoded) */
125 new_huff.num_rows = get_bits(gb, 4);
127 for (i = 0; i < new_huff.num_rows; i++)
128 new_huff.xbits[i] = get_bits(gb, 4);
130 /* Have we got the same custom table? Rebuild if not. */
131 if (ff_ivi_huff_desc_cmp(&new_huff, &huff_tab->cust_desc)) {
132 ff_ivi_huff_desc_copy(&huff_tab->cust_desc, &new_huff);
134 if (huff_tab->cust_tab.table)
135 ff_free_vlc(&huff_tab->cust_tab);
136 result = ff_ivi_create_huff_from_desc(&huff_tab->cust_desc,
137 &huff_tab->cust_tab, 0);
139 av_log(avctx, AV_LOG_ERROR,
140 "Error while initializing custom vlc table!\n");
144 huff_tab->tab = &huff_tab->cust_tab;
146 /* select one of predefined tables */
147 huff_tab->tab = (which_tab) ? &ff_ivi_blk_vlc_tabs[huff_tab->tab_sel]
148 : &ff_ivi_mb_vlc_tabs [huff_tab->tab_sel];
155 int ff_ivi_huff_desc_cmp(const IVIHuffDesc *desc1, const IVIHuffDesc *desc2)
157 return desc1->num_rows != desc2->num_rows
158 || memcmp(desc1->xbits, desc2->xbits, desc1->num_rows);
161 void ff_ivi_huff_desc_copy(IVIHuffDesc *dst, const IVIHuffDesc *src)
163 dst->num_rows = src->num_rows;
164 memcpy(dst->xbits, src->xbits, src->num_rows);
167 int av_cold ff_ivi_init_planes(IVIPlaneDesc *planes, const IVIPicConfig *cfg)
170 uint32_t b_width, b_height, align_fac, width_aligned, height_aligned, buf_size;
173 ff_ivi_free_buffers(planes);
175 /* fill in the descriptor of the luminance plane */
176 planes[0].width = cfg->pic_width;
177 planes[0].height = cfg->pic_height;
178 planes[0].num_bands = cfg->luma_bands;
180 /* fill in the descriptors of the chrominance planes */
181 planes[1].width = planes[2].width = (cfg->pic_width + 3) >> 2;
182 planes[1].height = planes[2].height = (cfg->pic_height + 3) >> 2;
183 planes[1].num_bands = planes[2].num_bands = cfg->chroma_bands;
185 for (p = 0; p < 3; p++) {
186 planes[p].bands = av_mallocz(planes[p].num_bands * sizeof(IVIBandDesc));
187 if (!planes[p].bands)
188 return AVERROR(ENOMEM);
190 /* select band dimensions: if there is only one band then it
191 * has the full size, if there are several bands each of them
192 * has only half size */
193 b_width = planes[p].num_bands == 1 ? planes[p].width : (planes[p].width + 1) >> 1;
194 b_height = planes[p].num_bands == 1 ? planes[p].height : (planes[p].height + 1) >> 1;
196 /* luma band buffers will be aligned on 16x16 (max macroblock size) */
197 /* chroma band buffers will be aligned on 8x8 (max macroblock size) */
198 align_fac = p ? 8 : 16;
199 width_aligned = FFALIGN(b_width , align_fac);
200 height_aligned = FFALIGN(b_height, align_fac);
201 buf_size = width_aligned * height_aligned * sizeof(int16_t);
203 for (b = 0; b < planes[p].num_bands; b++) {
204 band = &planes[p].bands[b]; /* select appropriate plane/band */
207 band->width = b_width;
208 band->height = b_height;
209 band->pitch = width_aligned;
210 band->bufs[0] = av_malloc(buf_size);
211 band->bufs[1] = av_malloc(buf_size);
212 band->bufsize = buf_size/2;
213 if (!band->bufs[0] || !band->bufs[1])
214 return AVERROR(ENOMEM);
216 /* allocate the 3rd band buffer for scalability mode */
217 if (cfg->luma_bands > 1) {
218 band->bufs[2] = av_malloc(buf_size);
220 return AVERROR(ENOMEM);
223 planes[p].bands[0].blk_vlc.cust_desc.num_rows = 0; /* reset custom vlc */
230 void av_cold ff_ivi_free_buffers(IVIPlaneDesc *planes)
234 for (p = 0; p < 3; p++) {
235 for (b = 0; b < planes[p].num_bands; b++) {
236 av_freep(&planes[p].bands[b].bufs[0]);
237 av_freep(&planes[p].bands[b].bufs[1]);
238 av_freep(&planes[p].bands[b].bufs[2]);
240 if (planes[p].bands[b].blk_vlc.cust_tab.table)
241 ff_free_vlc(&planes[p].bands[b].blk_vlc.cust_tab);
242 for (t = 0; t < planes[p].bands[b].num_tiles; t++)
243 av_freep(&planes[p].bands[b].tiles[t].mbs);
244 av_freep(&planes[p].bands[b].tiles);
246 av_freep(&planes[p].bands);
250 int av_cold ff_ivi_init_tiles(IVIPlaneDesc *planes, int tile_width, int tile_height)
252 int p, b, x, y, x_tiles, y_tiles, t_width, t_height;
254 IVITile *tile, *ref_tile;
256 for (p = 0; p < 3; p++) {
257 t_width = !p ? tile_width : (tile_width + 3) >> 2;
258 t_height = !p ? tile_height : (tile_height + 3) >> 2;
260 if (!p && planes[0].num_bands == 4) {
264 if(t_width<=0 || t_height<=0)
265 return AVERROR(EINVAL);
267 for (b = 0; b < planes[p].num_bands; b++) {
268 band = &planes[p].bands[b];
269 x_tiles = IVI_NUM_TILES(band->width, t_width);
270 y_tiles = IVI_NUM_TILES(band->height, t_height);
271 band->num_tiles = x_tiles * y_tiles;
273 av_freep(&band->tiles);
274 band->tiles = av_mallocz(band->num_tiles * sizeof(IVITile));
276 return AVERROR(ENOMEM);
280 /* use the first luma band as reference for motion vectors
282 ref_tile = planes[0].bands[0].tiles;
284 for (y = 0; y < band->height; y += t_height) {
285 for (x = 0; x < band->width; x += t_width) {
288 tile->width = FFMIN(band->width - x, t_width);
289 tile->height = FFMIN(band->height - y, t_height);
290 tile->is_empty = tile->data_size = 0;
291 /* calculate number of macroblocks */
292 tile->num_MBs = IVI_MBs_PER_TILE(tile->width, tile->height,
295 av_freep(&tile->mbs);
296 tile->mbs = av_malloc(tile->num_MBs * sizeof(IVIMbInfo));
298 return AVERROR(ENOMEM);
302 tile->ref_mbs = ref_tile->mbs;
316 int ff_ivi_dec_tile_data_size(GetBitContext *gb)
322 len = get_bits(gb, 8);
324 len = get_bits_long(gb, 24);
327 /* align the bitstream reader on the byte boundary */
333 int ff_ivi_decode_blocks(GetBitContext *gb, IVIBandDesc *band, IVITile *tile)
335 int mbn, blk, num_blocks, num_coeffs, blk_size, scan_pos, run, val,
336 pos, is_intra, mc_type, mv_x, mv_y, col_mask;
337 uint8_t col_flags[8];
338 int32_t prev_dc, trvec[64];
339 uint32_t cbp, sym, lo, hi, quant, buf_offs, q;
341 RVMapDesc *rvmap = band->rv_map;
342 void (*mc_with_delta_func)(int16_t *buf, const int16_t *ref_buf, uint32_t pitch, int mc_type);
343 void (*mc_no_delta_func) (int16_t *buf, const int16_t *ref_buf, uint32_t pitch, int mc_type);
344 const uint16_t *base_tab;
345 const uint8_t *scale_tab;
347 prev_dc = 0; /* init intra prediction for the DC coefficient */
349 blk_size = band->blk_size;
350 col_mask = blk_size - 1; /* column mask for tracking non-zero coeffs */
351 num_blocks = (band->mb_size != blk_size) ? 4 : 1; /* number of blocks per mb */
352 num_coeffs = blk_size * blk_size;
354 mc_with_delta_func = ff_ivi_mc_8x8_delta;
355 mc_no_delta_func = ff_ivi_mc_8x8_no_delta;
357 mc_with_delta_func = ff_ivi_mc_4x4_delta;
358 mc_no_delta_func = ff_ivi_mc_4x4_no_delta;
361 for (mbn = 0, mb = tile->mbs; mbn < tile->num_MBs; mb++, mbn++) {
362 is_intra = !mb->type;
364 buf_offs = mb->buf_offs;
366 quant = av_clip(band->glob_quant + mb->q_delta, 0, 23);
368 base_tab = is_intra ? band->intra_base : band->inter_base;
369 scale_tab = is_intra ? band->intra_scale : band->inter_scale;
371 quant = scale_tab[quant];
376 if (!band->is_halfpel) {
377 mc_type = 0; /* we have only fullpel vectors */
379 mc_type = ((mv_y & 1) << 1) | (mv_x & 1);
381 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
385 for (blk = 0; blk < num_blocks; blk++) {
386 /* adjust block position in the buffer according to its number */
388 buf_offs += blk_size;
389 } else if (blk == 2) {
390 buf_offs -= blk_size;
391 buf_offs += blk_size * band->pitch;
394 if (cbp & 1) { /* block coded ? */
396 memset(trvec, 0, num_coeffs*sizeof(trvec[0])); /* zero transform vector */
397 memset(col_flags, 0, sizeof(col_flags)); /* zero column flags */
399 while (scan_pos <= num_coeffs) {
400 sym = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
401 if (sym == rvmap->eob_sym)
402 break; /* End of block */
404 if (sym == rvmap->esc_sym) { /* Escape - run/val explicitly coded using 3 vlc codes */
405 run = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1) + 1;
406 lo = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
407 hi = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
408 val = IVI_TOSIGNED((hi << 6) | lo); /* merge them and convert into signed val */
411 av_log(NULL, AV_LOG_ERROR, "Invalid sym encountered: %d.\n", sym);
414 run = rvmap->runtab[sym];
415 val = rvmap->valtab[sym];
418 /* de-zigzag and dequantize */
420 if (scan_pos >= num_coeffs)
422 pos = band->scan[scan_pos];
425 av_dlog(NULL, "Val = 0 encountered!\n");
427 q = (base_tab[pos] * quant) >> 9;
429 val = val * q + FFSIGN(val) * (((q ^ 1) - 1) >> 1);
431 col_flags[pos & col_mask] |= !!val; /* track columns containing non-zero coeffs */
434 if (scan_pos >= num_coeffs && sym != rvmap->eob_sym)
435 return -1; /* corrupt block data */
437 /* undoing DC coeff prediction for intra-blocks */
438 if (is_intra && band->is_2d_trans) {
441 col_flags[0] |= !!prev_dc;
444 /* apply inverse transform */
445 band->inv_transform(trvec, band->buf + buf_offs,
446 band->pitch, col_flags);
448 /* apply motion compensation */
450 mc_with_delta_func(band->buf + buf_offs,
451 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
452 band->pitch, mc_type);
454 /* block not coded */
455 /* for intra blocks apply the dc slant transform */
456 /* for inter - perform the motion compensation without delta */
457 if (is_intra && band->dc_transform) {
458 band->dc_transform(&prev_dc, band->buf + buf_offs,
459 band->pitch, blk_size);
461 mc_no_delta_func(band->buf + buf_offs,
462 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
463 band->pitch, mc_type);
475 void ff_ivi_process_empty_tile(AVCodecContext *avctx, IVIBandDesc *band,
476 IVITile *tile, int32_t mv_scale)
478 int x, y, need_mc, mbn, blk, num_blocks, mv_x, mv_y, mc_type;
479 int offs, mb_offset, row_offset;
480 IVIMbInfo *mb, *ref_mb;
483 void (*mc_no_delta_func)(int16_t *buf, const int16_t *ref_buf, uint32_t pitch,
486 offs = tile->ypos * band->pitch + tile->xpos;
488 ref_mb = tile->ref_mbs;
489 row_offset = band->mb_size * band->pitch;
490 need_mc = 0; /* reset the mc tracking flag */
492 for (y = tile->ypos; y < (tile->ypos + tile->height); y += band->mb_size) {
495 for (x = tile->xpos; x < (tile->xpos + tile->width); x += band->mb_size) {
498 mb->buf_offs = mb_offset;
500 mb->type = 1; /* set the macroblocks type = INTER */
501 mb->cbp = 0; /* all blocks are empty */
503 if (!band->qdelta_present && !band->plane && !band->band_num) {
504 mb->q_delta = band->glob_quant;
509 if (band->inherit_qdelta && ref_mb)
510 mb->q_delta = ref_mb->q_delta;
512 if (band->inherit_mv && ref_mb) {
513 /* motion vector inheritance */
515 mb->mv_x = ivi_scale_mv(ref_mb->mv_x, mv_scale);
516 mb->mv_y = ivi_scale_mv(ref_mb->mv_y, mv_scale);
518 mb->mv_x = ref_mb->mv_x;
519 mb->mv_y = ref_mb->mv_y;
521 need_mc |= mb->mv_x || mb->mv_y; /* tracking non-zero motion vectors */
527 mb_offset += band->mb_size;
532 if (band->inherit_mv && need_mc) { /* apply motion compensation if there is at least one non-zero motion vector */
533 num_blocks = (band->mb_size != band->blk_size) ? 4 : 1; /* number of blocks per mb */
534 mc_no_delta_func = (band->blk_size == 8) ? ff_ivi_mc_8x8_no_delta
535 : ff_ivi_mc_4x4_no_delta;
537 for (mbn = 0, mb = tile->mbs; mbn < tile->num_MBs; mb++, mbn++) {
540 if (!band->is_halfpel) {
541 mc_type = 0; /* we have only fullpel vectors */
543 mc_type = ((mv_y & 1) << 1) | (mv_x & 1);
545 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
548 for (blk = 0; blk < num_blocks; blk++) {
549 /* adjust block position in the buffer according with its number */
550 offs = mb->buf_offs + band->blk_size * ((blk & 1) + !!(blk & 2) * band->pitch);
551 mc_no_delta_func(band->buf + offs,
552 band->ref_buf + offs + mv_y * band->pitch + mv_x,
553 band->pitch, mc_type);
557 /* copy data from the reference tile into the current one */
558 src = band->ref_buf + tile->ypos * band->pitch + tile->xpos;
559 dst = band->buf + tile->ypos * band->pitch + tile->xpos;
560 for (y = 0; y < tile->height; y++) {
561 memcpy(dst, src, tile->width*sizeof(band->buf[0]));
570 uint16_t ivi_calc_band_checksum (IVIBandDesc *band)
573 int16_t *src, checksum;
578 for (y = 0; y < band->height; src += band->pitch, y++)
579 for (x = 0; x < band->width; x++)
585 int ivi_check_band (IVIBandDesc *band, const uint8_t *ref, int pitch)
594 for (y = 0; y < band->height; src += band->pitch, y++) {
595 for (x = 0; x < band->width; x++) {
596 t1 = av_clip(src[x] + 128, 0, 255);
599 av_log(NULL, AV_LOG_ERROR, "Data mismatch: row %d, column %d\n",
600 y / band->blk_size, x / band->blk_size);
611 void ff_ivi_output_plane(IVIPlaneDesc *plane, uint8_t *dst, int dst_pitch)
614 const int16_t *src = plane->bands[0].buf;
615 uint32_t pitch = plane->bands[0].pitch;
620 for (y = 0; y < plane->height; y++) {
621 for (x = 0; x < plane->width; x++)
622 dst[x] = av_clip_uint8(src[x] + 128);
630 * These are 2x8 predefined Huffman codebooks for coding macroblock/block
631 * signals. They are specified using "huffman descriptors" in order to
632 * avoid huge static tables. The decoding tables will be generated at
633 * startup from these descriptors.
635 const IVIHuffDesc ff_ivi_mb_huff_desc[8] = {
636 {8, {0, 4, 5, 4, 4, 4, 6, 6}},
637 {12, {0, 2, 2, 3, 3, 3, 3, 5, 3, 2, 2, 2}},
638 {12, {0, 2, 3, 4, 3, 3, 3, 3, 4, 3, 2, 2}},
639 {12, {0, 3, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2}},
640 {13, {0, 4, 4, 3, 3, 3, 3, 2, 3, 3, 2, 1, 1}},
641 {9, {0, 4, 4, 4, 4, 3, 3, 3, 2}},
642 {10, {0, 4, 4, 4, 4, 3, 3, 2, 2, 2}},
643 {12, {0, 4, 4, 4, 3, 3, 2, 3, 2, 2, 2, 2}}
646 const IVIHuffDesc ff_ivi_blk_huff_desc[8] = {
647 {10, {1, 2, 3, 4, 4, 7, 5, 5, 4, 1}},
648 {11, {2, 3, 4, 4, 4, 7, 5, 4, 3, 3, 2}},
649 {12, {2, 4, 5, 5, 5, 5, 6, 4, 4, 3, 1, 1}},
650 {13, {3, 3, 4, 4, 5, 6, 6, 4, 4, 3, 2, 1, 1}},
651 {11, {3, 4, 4, 5, 5, 5, 6, 5, 4, 2, 2}},
652 {13, {3, 4, 5, 5, 5, 5, 6, 4, 3, 3, 2, 1, 1}},
653 {13, {3, 4, 5, 5, 5, 6, 5, 4, 3, 3, 2, 1, 1}},
654 {9, {3, 4, 4, 5, 5, 5, 6, 5, 5}}
659 * Scan patterns shared between indeo4 and indeo5
661 const uint8_t ff_ivi_vertical_scan_8x8[64] = {
662 0, 8, 16, 24, 32, 40, 48, 56,
663 1, 9, 17, 25, 33, 41, 49, 57,
664 2, 10, 18, 26, 34, 42, 50, 58,
665 3, 11, 19, 27, 35, 43, 51, 59,
666 4, 12, 20, 28, 36, 44, 52, 60,
667 5, 13, 21, 29, 37, 45, 53, 61,
668 6, 14, 22, 30, 38, 46, 54, 62,
669 7, 15, 23, 31, 39, 47, 55, 63
672 const uint8_t ff_ivi_horizontal_scan_8x8[64] = {
673 0, 1, 2, 3, 4, 5, 6, 7,
674 8, 9, 10, 11, 12, 13, 14, 15,
675 16, 17, 18, 19, 20, 21, 22, 23,
676 24, 25, 26, 27, 28, 29, 30, 31,
677 32, 33, 34, 35, 36, 37, 38, 39,
678 40, 41, 42, 43, 44, 45, 46, 47,
679 48, 49, 50, 51, 52, 53, 54, 55,
680 56, 57, 58, 59, 60, 61, 62, 63
683 const uint8_t ff_ivi_direct_scan_4x4[16] = {
684 0, 1, 4, 8, 5, 2, 3, 6, 9, 12, 13, 10, 7, 11, 14, 15
689 * Run-value (RLE) tables.
691 const RVMapDesc ff_ivi_rvmap_tabs[9] = {
696 {1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 3, 3,
697 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 1, 1, 2, 2, 5, 5,
698 1, 1, 3, 3, 1, 1, 6, 6, 1, 2, 1, 2, 7, 7, 1, 1,
699 8, 8, 1, 1, 4, 2, 1, 4, 2, 1, 3, 3, 1, 1, 1, 9,
700 9, 1, 2, 1, 2, 1, 5, 5, 1, 1, 10, 10, 1, 1, 3, 3,
701 2, 2, 1, 1, 11, 11, 6, 4, 4, 1, 6, 1, 2, 1, 2, 12,
702 8, 1, 12, 7, 8, 7, 1, 16, 1, 16, 1, 3, 3, 13, 1, 13,
703 2, 2, 1, 15, 1, 5, 14, 15, 1, 5, 14, 1, 17, 8, 17, 8,
704 1, 4, 4, 2, 2, 1, 25, 25, 24, 24, 1, 3, 1, 3, 1, 8,
705 6, 7, 6, 1, 18, 8, 18, 1, 7, 23, 2, 2, 23, 1, 1, 21,
706 22, 9, 9, 22, 19, 1, 21, 5, 19, 5, 1, 33, 20, 33, 20, 8,
707 4, 4, 1, 32, 2, 2, 8, 3, 32, 26, 3, 1, 7, 7, 26, 6,
708 1, 6, 1, 1, 16, 1, 10, 1, 10, 2, 16, 29, 28, 2, 29, 28,
709 1, 27, 5, 8, 5, 27, 1, 8, 3, 7, 3, 31, 41, 31, 1, 41,
710 6, 1, 6, 7, 4, 4, 1, 1, 2, 1, 2, 11, 34, 30, 11, 1,
711 30, 15, 15, 34, 36, 40, 36, 40, 35, 35, 37, 37, 39, 39, 38, 38},
714 { 1, -1, 0, 2, -2, 0, 3, -3, 1, -1, 4, -4, 5, -5, 1, -1,
715 6, -6, 2, -2, 7, -7, 1, -1, 8, -8, 9, -9, 3, -3, 1, -1,
716 10, -10, 2, -2, 11, -11, 1, -1, 12, 4, -12, -4, 1, -1, 13, -13,
717 1, -1, 14, -14, 2, 5, 15, -2, -5, -15, -3, 3, 16, -16, 17, 1,
718 -1, -17, 6, 18, -6, -18, 2, -2, 19, -19, 1, -1, 20, -20, 4, -4,
719 7, -7, 21, -21, 1, -1, 2, 3, -3, 22, -2, -22, 8, 23, -8, 1,
720 2, -23, -1, 2, -2, -2, 24, 1, -24, -1, 25, 5, -5, 1, -25, -1,
721 9, -9, 26, 1, -26, 3, 1, -1, 27, -3, -1, -27, 1, 3, -1, -3,
722 28, -4, 4, 10, -10, -28, 1, -1, 1, -1, 29, 6, -29, -6, 30, -4,
723 3, 3, -3, -30, 1, 4, -1, 31, -3, 1, 11, -11, -1, -31, 32, -1,
724 -1, 2, -2, 1, 1, -32, 1, 4, -1, -4, 33, -1, 1, 1, -1, 5,
725 5, -5, -33, -1, -12, 12, -5, -7, 1, 1, 7, 34, 4, -4, -1, 4,
726 -34, -4, 35, 36, -2, -35, -2, -36, 2, 13, 2, -1, 1, -13, 1, -1,
727 37, 1, -5, 6, 5, -1, 38, -6, -8, 5, 8, -1, 1, 1, -37, -1,
728 5, 39, -5, -5, 6, -6, -38, -39, -14, 40, 14, 2, 1, 1, -2, -40,
729 -1, -2, 2, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1}
735 {0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 8, 6, 8, 7,
736 7, 9, 9, 10, 10, 11, 11, 1, 12, 1, 12, 13, 13, 16, 14, 16,
737 14, 15, 15, 17, 17, 18, 0, 18, 19, 20, 21, 19, 22, 21, 20, 22,
738 25, 24, 2, 25, 24, 23, 23, 2, 26, 28, 26, 28, 29, 27, 29, 27,
739 33, 33, 1, 32, 1, 3, 32, 30, 36, 3, 36, 30, 31, 31, 35, 34,
740 37, 41, 34, 35, 37, 4, 41, 4, 49, 8, 8, 49, 40, 38, 5, 38,
741 40, 39, 5, 39, 42, 43, 42, 7, 57, 6, 43, 44, 6, 50, 7, 44,
742 57, 48, 50, 48, 45, 45, 46, 47, 51, 46, 47, 58, 1, 51, 58, 1,
743 52, 59, 53, 9, 52, 55, 55, 59, 53, 56, 54, 56, 54, 9, 64, 64,
744 60, 63, 60, 63, 61, 62, 61, 62, 2, 10, 2, 10, 11, 1, 11, 13,
745 12, 1, 12, 13, 16, 16, 8, 8, 14, 3, 3, 15, 14, 15, 4, 4,
746 1, 17, 17, 5, 1, 7, 7, 5, 6, 1, 2, 2, 6, 22, 1, 25,
747 21, 22, 8, 24, 1, 21, 25, 24, 8, 18, 18, 23, 9, 20, 23, 33,
748 29, 33, 20, 1, 19, 1, 29, 36, 9, 36, 19, 41, 28, 57, 32, 3,
749 28, 3, 1, 27, 49, 49, 1, 32, 26, 26, 2, 4, 4, 7, 57, 41,
750 2, 7, 10, 5, 37, 16, 10, 27, 8, 8, 13, 16, 37, 13, 1, 5},
753 {0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1,
754 -1, 1, -1, 1, -1, 1, -1, 2, 1, -2, -1, 1, -1, 1, 1, -1,
755 -1, 1, -1, 1, -1, 1, 0, -1, 1, 1, 1, -1, 1, -1, -1, -1,
756 1, 1, 2, -1, -1, 1, -1, -2, 1, 1, -1, -1, 1, 1, -1, -1,
757 1, -1, 3, 1, -3, 2, -1, 1, 1, -2, -1, -1, -1, 1, 1, 1,
758 1, 1, -1, -1, -1, 2, -1, -2, 1, 2, -2, -1, 1, 1, 2, -1,
759 -1, 1, -2, -1, 1, 1, -1, 2, 1, 2, -1, 1, -2, -1, -2, -1,
760 -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 4, -1, -1, -4,
761 1, 1, 1, 2, -1, -1, 1, -1, -1, 1, -1, -1, 1, -2, 1, -1,
762 1, 1, -1, -1, 1, 1, -1, -1, 3, 2, -3, -2, 2, 5, -2, 2,
763 2, -5, -2, -2, -2, 2, -3, 3, 2, 3, -3, 2, -2, -2, 3, -3,
764 6, 2, -2, 3, -6, 3, -3, -3, 3, 7, -4, 4, -3, 2, -7, 2,
765 2, -2, -4, 2, 8, -2, -2, -2, 4, 2, -2, 2, 3, 2, -2, -2,
766 2, 2, -2, -8, -2, 9, -2, 2, -3, -2, 2, -2, 2, 2, 2, 4,
767 -2, -4, 10, 2, 2, -2, -9, -2, 2, -2, 5, 4, -4, 4, -2, 2,
768 -5, -4, -3, 4, 2, -3, 3, -2, -5, 5, 3, 3, -2, -3, -10, -4}
774 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 0, 1, 1, 5, 5,
775 2, 2, 6, 6, 7, 7, 1, 8, 1, 8, 3, 3, 9, 9, 1, 2,
776 2, 1, 4, 10, 4, 10, 11, 11, 1, 5, 12, 12, 1, 5, 13, 13,
777 3, 3, 6, 6, 2, 2, 14, 14, 16, 16, 15, 7, 15, 8, 8, 7,
778 1, 1, 17, 17, 4, 4, 1, 1, 18, 18, 2, 2, 5, 5, 25, 3,
779 9, 3, 25, 9, 19, 24, 19, 24, 1, 21, 20, 1, 21, 22, 20, 22,
780 23, 23, 8, 6, 33, 6, 8, 33, 7, 7, 26, 26, 1, 32, 1, 32,
781 28, 4, 28, 10, 29, 27, 27, 10, 41, 4, 29, 2, 2, 41, 36, 31,
782 49, 31, 34, 30, 34, 36, 30, 35, 1, 49, 11, 5, 35, 11, 1, 3,
783 3, 5, 37, 37, 8, 40, 8, 40, 12, 12, 42, 42, 1, 38, 16, 57,
784 1, 6, 16, 39, 38, 6, 7, 7, 13, 13, 39, 43, 2, 43, 57, 2,
785 50, 9, 44, 9, 50, 4, 15, 48, 44, 4, 1, 15, 48, 14, 14, 1,
786 45, 45, 8, 3, 5, 8, 51, 47, 3, 46, 46, 47, 5, 51, 1, 17,
787 17, 58, 1, 58, 2, 52, 52, 2, 53, 7, 59, 6, 6, 56, 53, 55,
788 7, 55, 1, 54, 59, 56, 54, 10, 1, 10, 4, 60, 1, 60, 8, 4,
789 8, 64, 64, 61, 1, 63, 3, 63, 62, 61, 5, 11, 5, 3, 11, 62},
792 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 0, 3, -3, 1, -1,
793 2, -2, 1, -1, 1, -1, 4, 1, -4, -1, 2, -2, 1, -1, 5, 3,
794 -3, -5, 2, 1, -2, -1, 1, -1, 6, 2, 1, -1, -6, -2, 1, -1,
795 3, -3, 2, -2, 4, -4, 1, -1, 1, -1, 1, 2, -1, 2, -2, -2,
796 7, -7, 1, -1, 3, -3, 8, -8, 1, -1, 5, -5, 3, -3, 1, 4,
797 2, -4, -1, -2, 1, 1, -1, -1, 9, 1, 1, -9, -1, 1, -1, -1,
798 1, -1, 3, -3, 1, 3, -3, -1, 3, -3, 1, -1, 10, 1, -10, -1,
799 1, 4, -1, 2, 1, -1, 1, -2, 1, -4, -1, 6, -6, -1, 1, 1,
800 1, -1, 1, 1, -1, -1, -1, 1, 11, -1, -2, 4, -1, 2, -11, 5,
801 -5, -4, -1, 1, 4, 1, -4, -1, -2, 2, 1, -1, 12, 1, -2, 1,
802 -12, 4, 2, 1, -1, -4, 4, -4, 2, -2, -1, 1, 7, -1, -1, -7,
803 -1, -3, 1, 3, 1, 5, 2, 1, -1, -5, 13, -2, -1, 2, -2, -13,
804 1, -1, 5, 6, 5, -5, 1, 1, -6, 1, -1, -1, -5, -1, 14, 2,
805 -2, 1, -14, -1, 8, 1, -1, -8, 1, 5, 1, 5, -5, 1, -1, 1,
806 -5, -1, 15, 1, -1, -1, -1, 3, -15, -3, 6, 1, 16, -1, 6, -6,
807 -6, 1, -1, 1, -16, 1, 7, -1, 1, -1, -6, -3, 6, -7, 3, -1}
813 {0, 1, 1, 2, 2, 3, 3, 4, 4, 1, 1, 5, 5, 6, 6, 7,
814 7, 8, 8, 9, 9, 2, 2, 10, 10, 1, 1, 11, 11, 12, 12, 3,
815 3, 13, 13, 0, 14, 14, 16, 15, 16, 15, 4, 4, 17, 1, 17, 1,
816 5, 5, 18, 18, 2, 2, 6, 6, 8, 19, 7, 8, 7, 19, 20, 20,
817 21, 21, 22, 24, 22, 24, 23, 23, 1, 1, 25, 25, 3, 3, 26, 26,
818 9, 9, 27, 27, 28, 28, 33, 29, 4, 33, 29, 1, 4, 1, 32, 32,
819 2, 2, 31, 10, 30, 10, 30, 31, 34, 34, 5, 5, 36, 36, 35, 41,
820 35, 11, 41, 11, 37, 1, 8, 8, 37, 6, 1, 6, 40, 7, 7, 40,
821 12, 38, 12, 39, 39, 38, 49, 13, 49, 13, 3, 42, 3, 42, 16, 16,
822 43, 43, 14, 14, 1, 1, 44, 15, 44, 15, 2, 2, 57, 48, 50, 48,
823 57, 50, 4, 45, 45, 4, 46, 47, 47, 46, 1, 51, 1, 17, 17, 51,
824 8, 9, 9, 5, 58, 8, 58, 5, 52, 52, 55, 56, 53, 56, 55, 59,
825 59, 53, 54, 1, 6, 54, 7, 7, 6, 1, 2, 3, 2, 3, 64, 60,
826 60, 10, 10, 64, 61, 62, 61, 63, 1, 63, 62, 1, 18, 24, 18, 4,
827 25, 4, 8, 21, 21, 1, 24, 22, 25, 22, 8, 11, 19, 11, 23, 1,
828 20, 23, 19, 20, 5, 12, 5, 1, 16, 2, 12, 13, 2, 13, 1, 16},
831 { 0, 1, -1, 1, -1, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 1,
832 -1, 1, -1, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 1, -1, 2,
833 -2, 1, -1, 0, 1, -1, 1, 1, -1, -1, 2, -2, 1, 4, -1, -4,
834 2, -2, 1, -1, -3, 3, 2, -2, 2, 1, 2, -2, -2, -1, 1, -1,
835 1, -1, 1, 1, -1, -1, 1, -1, 5, -5, 1, -1, 3, -3, 1, -1,
836 2, -2, 1, -1, 1, -1, 1, 1, 3, -1, -1, 6, -3, -6, -1, 1,
837 4, -4, 1, 2, 1, -2, -1, -1, 1, -1, 3, -3, 1, -1, 1, 1,
838 -1, 2, -1, -2, 1, 7, -3, 3, -1, 3, -7, -3, 1, -3, 3, -1,
839 2, 1, -2, 1, -1, -1, 1, 2, -1, -2, -4, -1, 4, 1, 2, -2,
840 1, -1, -2, 2, 8, -8, -1, 2, 1, -2, -5, 5, 1, -1, -1, 1,
841 -1, 1, 4, -1, 1, -4, -1, -1, 1, 1, 9, 1, -9, 2, -2, -1,
842 -4, 3, -3, -4, -1, 4, 1, 4, 1, -1, 1, -1, 1, 1, -1, 1,
843 -1, -1, -1, 10, 4, 1, 4, -4, -4, -10, 6, 5, -6, -5, 1, -1,
844 1, 3, -3, -1, 1, -1, -1, -1, 11, 1, 1, -11, -2, -2, 2, 5,
845 -2, -5, -5, 2, -2, 12, 2, -2, 2, 2, 5, -3, -2, 3, -2, -12,
846 -2, 2, 2, 2, -5, 3, 5, 13, -3, 7, -3, -3, -7, 3, -13, 3}
852 {0, 1, 1, 1, 2, 2, 1, 3, 3, 1, 1, 1, 4, 4, 1, 5,
853 2, 1, 5, 2, 1, 1, 6, 6, 1, 1, 1, 1, 1, 7, 3, 1,
854 2, 3, 0, 1, 2, 7, 1, 1, 1, 8, 1, 1, 8, 1, 1, 1,
855 9, 1, 9, 1, 2, 1, 1, 2, 1, 1, 10, 4, 1, 10, 1, 4,
856 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1,
857 2, 5, 1, 11, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
858 2, 1, 6, 1, 6, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 12,
859 3, 1, 12, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1,
860 4, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1,
861 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 5,
862 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 2, 3, 1, 1, 1, 1,
863 5, 1, 1, 1, 1, 1, 1, 2, 13, 1, 1, 1, 1, 1, 1, 1,
864 1, 1, 1, 1, 1, 1, 1, 1, 13, 2, 1, 1, 4, 1, 1, 1,
865 3, 1, 6, 1, 1, 1, 14, 1, 1, 1, 1, 1, 14, 6, 1, 1,
866 1, 1, 15, 2, 4, 1, 2, 3, 15, 1, 1, 1, 8, 1, 1, 8,
867 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1},
870 { 0, 1, -1, 2, 1, -1, -2, 1, -1, 3, -3, 4, 1, -1, -4, 1,
871 2, 5, -1, -2, -5, 6, 1, -1, -6, 7, -7, 8, -8, 1, 2, 9,
872 3, -2, 0, -9, -3, -1, 10, -10, 11, 1, -11, 12, -1, -12, 13, -13,
873 1, 14, -1, -14, 4, 15, -15, -4, 16, -16, 1, 2, 17, -1, -17, -2,
874 18, -18, 19, -19, 20, 3, -20, 21, -21, -3, 5, 22, 2, -22, -23, 23,
875 -5, -2, 24, 1, -24, -1, 25, -25, 26, -26, -27, 27, 28, 29, -28, -29,
876 6, 30, 2, -31, -2, -30, 31, -6, -32, 32, 33, -33, 34, -35, -34, 1,
877 4, -36, -1, 35, 37, 36, 7, -37, 38, -4, -38, 39, 41, 40, -40, -39,
878 3, 42, -43, -41, -7, -42, 43, -3, 44, -44, 45, -45, 46, 47, 8, -47,
879 -48, -46, 50, -50, 48, 49, 51, -49, 52, -52, 5, -51, -8, -53, 53, 3,
880 -56, 56, 55, 54, -54, 2, 60, -2, -55, 58, 9, -5, 59, 57, -57, -63,
881 -3, -58, -60, -61, 61, -59, -62, -9, 1, 64, 62, 69, -64, 63, 65, -67,
882 -68, 66, -65, 68, -66, -69, 67, -70, -1, 10, 71, -71, 4, 73, 72, 70,
883 6, -76, -3, 74, -78, -74, 1, 78, 80, -72, -75, 76, -1, 3, -73, 79,
884 75, 77, 1, 11, -4, -79, -10, -6, -1, -77, -83, -80, 2, 81, -84, -2,
885 83, -81, 82, -82, 84, -87, -86, 85, -11, -85, 86, -89, 87, -88, 88, 89}
891 {1, 1, 0, 2, 1, 2, 1, 3, 3, 1, 1, 4, 4, 2, 2, 1,
892 1, 5, 5, 6, 1, 6, 1, 7, 7, 3, 3, 2, 8, 2, 8, 1,
893 1, 0, 9, 9, 1, 1, 10, 4, 10, 4, 11, 11, 2, 1, 2, 1,
894 12, 12, 3, 3, 1, 1, 13, 5, 5, 13, 14, 1, 1, 14, 2, 2,
895 6, 6, 15, 1, 1, 15, 16, 4, 7, 16, 4, 7, 1, 1, 3, 3,
896 8, 8, 2, 2, 1, 1, 17, 17, 1, 1, 18, 18, 5, 5, 2, 2,
897 1, 1, 9, 19, 9, 19, 20, 3, 3, 20, 1, 10, 21, 1, 10, 4,
898 4, 21, 22, 6, 6, 22, 1, 1, 23, 24, 2, 2, 23, 24, 11, 1,
899 1, 11, 7, 25, 7, 1, 1, 25, 8, 8, 3, 26, 3, 1, 12, 2,
900 2, 26, 1, 12, 5, 5, 27, 4, 1, 4, 1, 27, 28, 1, 28, 13,
901 1, 13, 2, 29, 2, 1, 32, 6, 1, 30, 14, 29, 14, 6, 3, 31,
902 3, 1, 30, 1, 32, 31, 33, 9, 33, 1, 1, 7, 9, 7, 2, 2,
903 1, 1, 4, 36, 34, 4, 5, 10, 10, 5, 34, 1, 1, 35, 8, 8,
904 36, 3, 35, 1, 15, 3, 2, 1, 16, 15, 16, 2, 37, 1, 37, 1,
905 1, 1, 6, 6, 38, 1, 38, 11, 1, 39, 39, 40, 11, 2, 41, 4,
906 40, 1, 2, 4, 1, 1, 1, 41, 3, 1, 3, 1, 5, 7, 5, 7},
909 { 1, -1, 0, 1, 2, -1, -2, 1, -1, 3, -3, 1, -1, 2, -2, 4,
910 -4, 1, -1, 1, 5, -1, -5, 1, -1, 2, -2, 3, 1, -3, -1, 6,
911 -6, 0, 1, -1, 7, -7, 1, 2, -1, -2, 1, -1, 4, 8, -4, -8,
912 1, -1, 3, -3, 9, -9, 1, 2, -2, -1, 1, 10, -10, -1, 5, -5,
913 2, -2, 1, 11, -11, -1, 1, 3, 2, -1, -3, -2, 12, -12, 4, -4,
914 2, -2, -6, 6, 13, -13, 1, -1, 14, -14, 1, -1, 3, -3, 7, -7,
915 15, -15, 2, 1, -2, -1, 1, 5, -5, -1, -16, 2, 1, 16, -2, 4,
916 -4, -1, 1, 3, -3, -1, 17, -17, 1, 1, -8, 8, -1, -1, 2, 18,
917 -18, -2, 3, 1, -3, 19, -19, -1, 3, -3, 6, 1, -6, 20, 2, 9,
918 -9, -1, -20, -2, 4, -4, 1, -5, 21, 5, -21, -1, 1, -22, -1, 2,
919 22, -2, 10, 1, -10, 23, 1, 4, -23, 1, 2, -1, -2, -4, -7, 1,
920 7, -24, -1, 24, -1, -1, 1, 3, -1, -25, 25, 4, -3, -4, 11, -11,
921 26, -26, 6, 1, 1, -6, -5, -3, 3, 5, -1, -27, 27, 1, 4, -4,
922 -1, -8, -1, 28, 2, 8, -12, -28, -2, -2, 2, 12, -1, 29, 1, -29,
923 30, -30, 5, -5, 1, -31, -1, 3, 31, -1, 1, 1, -3, -13, 1, -7,
924 -1, -32, 13, 7, 32, 33, -33, -1, -9, -34, 9, 34, -6, 5, 6, -5}
930 {1, 1, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 0, 2, 2,
931 4, 1, 4, 1, 1, 1, 5, 5, 1, 1, 6, 6, 2, 2, 1, 1,
932 3, 3, 7, 7, 1, 1, 8, 8, 1, 1, 2, 2, 1, 9, 1, 9,
933 4, 4, 10, 1, 1, 10, 1, 1, 11, 11, 3, 3, 1, 2, 1, 2,
934 1, 1, 12, 12, 5, 5, 1, 1, 13, 1, 1, 13, 2, 2, 1, 1,
935 6, 6, 1, 1, 4, 14, 4, 14, 3, 1, 3, 1, 1, 1, 15, 7,
936 15, 2, 2, 7, 1, 1, 1, 8, 1, 8, 16, 16, 1, 1, 1, 1,
937 2, 1, 1, 2, 1, 1, 3, 5, 5, 3, 4, 1, 1, 4, 1, 1,
938 17, 17, 9, 1, 1, 9, 2, 2, 1, 1, 10, 10, 1, 6, 1, 1,
939 6, 18, 1, 1, 18, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 1,
940 4, 1, 19, 1, 19, 7, 1, 1, 20, 1, 4, 20, 1, 7, 11, 2,
941 1, 11, 21, 2, 8, 5, 1, 8, 1, 5, 21, 1, 1, 1, 22, 1,
942 1, 22, 1, 1, 3, 3, 1, 23, 2, 12, 24, 1, 1, 2, 1, 1,
943 12, 23, 1, 1, 24, 1, 1, 1, 4, 1, 1, 1, 2, 1, 6, 6,
944 4, 2, 1, 1, 1, 1, 1, 1, 1, 14, 13, 3, 1, 25, 9, 25,
945 14, 1, 9, 3, 13, 1, 1, 1, 1, 1, 10, 1, 1, 2, 10, 2},
948 {-20, -1, 0, 2, -2, 1, -1, 3, -3, 1, -1, 4, -4, 0, 2, -2,
949 1, 5, -1, -5, 6, -6, 1, -1, 7, -7, 1, -1, 3, -3, 8, -8,
950 2, -2, 1, -1, 9, -9, 1, -1, 10, -10, 4, -4, 11, 1, -11, -1,
951 2, -2, 1, 12, -12, -1, 13, -13, 1, -1, 3, -3, 14, 5, -14, -5,
952 -15, 15, -1, 1, 2, -2, 16, -16, 1, 17, -17, -1, 6, -6, 18, -18,
953 2, -2, -19, 19, -3, 1, 3, -1, 4, 20, -4, 1, -21, 21, 1, 2,
954 -1, -7, 7, -2, 22, -22, 23, 2, -23, -2, 1, -1, -24, 24, -25, 25,
955 -8, -26, 26, 8, -27, 27, 5, 3, -3, -5, -4, 28, -28, 4, 29, -29,
956 1, -1, -2, -30, 30, 2, 9, -9, -31, 31, 2, -2, -32, 3, 32, -33,
957 -3, 1, 33, -34, -1, 34, -35, 35, -10, 10, -6, 36, 6, -36, 37, -37,
958 -5, 38, 1, -38, -1, 3, 39, -39, -1, 40, 5, 1, -40, -3, 2, -11,
959 -41, -2, 1, 11, -3, -4, 41, 3, 42, 4, -1, -43, -42, 43, 1, -44,
960 45, -1, 44, -45, -7, 7, -46, 1, -12, 2, 1, -47, 46, 12, 47, 48,
961 -2, -1, -48, 49, -1, -50, -49, 50, -6, -51, 51, 52, -13, 53, -4, 4,
962 6, 13, -53, -52, -54, 55, 54, -55, -56, -2, 2, -8, 56, 1, -3, -1,
963 2, 58, 3, 8, -2, 57, -58, -60, -59, -57, -3, 60, 59, -14, 3, 14}
969 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 5, 5, 1, 1, 6,
970 6, 2, 2, 7, 7, 8, 8, 1, 1, 3, 3, 9, 9, 10, 10, 1,
971 1, 2, 2, 4, 4, 11, 0, 11, 12, 12, 13, 13, 1, 1, 5, 5,
972 14, 14, 15, 16, 15, 16, 3, 3, 1, 6, 1, 6, 2, 2, 7, 7,
973 8, 8, 17, 17, 1, 1, 4, 4, 18, 18, 2, 2, 1, 19, 1, 20,
974 19, 20, 21, 21, 3, 3, 22, 22, 5, 5, 24, 1, 1, 23, 9, 23,
975 24, 9, 2, 2, 10, 1, 1, 10, 6, 6, 25, 4, 4, 25, 7, 7,
976 26, 8, 1, 8, 3, 1, 26, 3, 11, 11, 27, 27, 2, 28, 1, 2,
977 28, 1, 12, 12, 5, 5, 29, 13, 13, 29, 32, 1, 1, 33, 31, 30,
978 32, 4, 30, 33, 4, 31, 3, 14, 1, 1, 3, 34, 34, 2, 2, 14,
979 6, 6, 35, 36, 35, 36, 1, 15, 1, 16, 16, 15, 7, 9, 7, 9,
980 37, 8, 8, 37, 1, 1, 39, 2, 38, 39, 2, 40, 5, 38, 40, 5,
981 3, 3, 4, 4, 10, 10, 1, 1, 1, 1, 41, 2, 41, 2, 6, 6,
982 1, 1, 11, 42, 11, 43, 3, 42, 3, 17, 4, 43, 1, 17, 7, 1,
983 8, 44, 4, 7, 44, 5, 8, 2, 5, 1, 2, 48, 45, 1, 12, 45,
984 12, 48, 13, 13, 1, 9, 9, 46, 1, 46, 47, 47, 49, 18, 18, 49},
987 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 1, -1, 3, -3, 1,
988 -1, -2, 2, 1, -1, 1, -1, 4, -4, -2, 2, 1, -1, 1, -1, 5,
989 -5, -3, 3, 2, -2, 1, 0, -1, 1, -1, 1, -1, 6, -6, 2, -2,
990 1, -1, 1, 1, -1, -1, -3, 3, 7, 2, -7, -2, -4, 4, 2, -2,
991 2, -2, 1, -1, 8, -8, 3, -3, 1, -1, -5, 5, 9, 1, -9, 1,
992 -1, -1, 1, -1, -4, 4, 1, -1, 3, -3, 1, -10, 10, 1, 2, -1,
993 -1, -2, 6, -6, 2, 11, -11, -2, 3, -3, 1, -4, 4, -1, 3, -3,
994 1, 3, 12, -3, -5, -12, -1, 5, 2, -2, 1, -1, -7, 1, 13, 7,
995 -1, -13, 2, -2, 4, -4, 1, 2, -2, -1, 1, 14, -14, 1, 1, 1,
996 -1, -5, -1, -1, 5, -1, -6, 2, -15, 15, 6, 1, -1, -8, 8, -2,
997 -4, 4, 1, 1, -1, -1, 16, 2, -16, -2, 2, -2, 4, 3, -4, -3,
998 -1, -4, 4, 1, -17, 17, -1, -9, 1, 1, 9, 1, -5, -1, -1, 5,
999 -7, 7, 6, -6, 3, -3, 18, -18, 19, -19, 1, -10, -1, 10, -5, 5,
1000 20, -20, -3, 1, 3, 1, 8, -1, -8, 2, 7, -1, -21, -2, 5, 21,
1001 5, -1, -7, -5, 1, -6, -5, -11, 6, 22, 11, 1, 1, -22, -3, -1,
1002 3, -1, 3, -3, -23, 4, -4, 1, 23, -1, 1, -1, 1, -2, 2, -1}
1008 {1, 1, 1, 1, 0, 2, 2, 1, 1, 3, 3, 0, 1, 1, 2, 2,
1009 4, 4, 1, 1, 5, 5, 1, 1, 2, 2, 3, 3, 6, 6, 1, 1,
1010 7, 7, 8, 1, 8, 2, 2, 1, 4, 4, 1, 3, 1, 3, 9, 9,
1011 2, 2, 1, 5, 1, 5, 10, 10, 1, 1, 11, 11, 3, 6, 3, 4,
1012 4, 6, 2, 2, 1, 12, 1, 12, 7, 13, 7, 13, 1, 1, 8, 8,
1013 2, 2, 14, 14, 16, 15, 16, 5, 5, 1, 3, 15, 1, 3, 4, 4,
1014 1, 1, 17, 17, 2, 2, 6, 6, 1, 18, 1, 18, 22, 21, 22, 21,
1015 25, 24, 25, 19, 9, 20, 9, 23, 19, 24, 20, 3, 23, 7, 3, 1,
1016 1, 7, 28, 26, 29, 5, 28, 26, 5, 8, 29, 4, 8, 27, 2, 2,
1017 4, 27, 1, 1, 10, 36, 10, 33, 33, 36, 30, 1, 32, 32, 1, 30,
1018 6, 31, 31, 35, 3, 6, 11, 11, 3, 2, 35, 2, 34, 1, 34, 1,
1019 37, 37, 12, 7, 12, 5, 41, 5, 4, 7, 1, 8, 13, 4, 1, 41,
1020 13, 38, 8, 38, 9, 1, 40, 40, 9, 1, 39, 2, 2, 49, 39, 42,
1021 3, 3, 14, 16, 49, 14, 16, 42, 43, 43, 6, 6, 15, 1, 1, 15,
1022 44, 44, 1, 1, 50, 48, 4, 5, 4, 7, 5, 2, 10, 10, 48, 7,
1023 50, 45, 2, 1, 45, 8, 8, 1, 46, 46, 3, 47, 47, 3, 1, 1},
1026 { 1, -1, 2, -2, 0, 1, -1, 3, -3, 1, -1, 0, 4, -4, 2, -2,
1027 1, -1, 5, -5, 1, -1, 6, -6, 3, -3, 2, -2, 1, -1, 7, -7,
1028 1, -1, 1, 8, -1, 4, -4, -8, 2, -2, 9, 3, -9, -3, 1, -1,
1029 5, -5, 10, 2, -10, -2, 1, -1, 11, -11, 1, -1, -4, 2, 4, 3,
1030 -3, -2, 6, -6, 12, 1, -12, -1, 2, 1, -2, -1, 13, -13, 2, -2,
1031 7, -7, 1, -1, 1, 1, -1, 3, -3, 14, 5, -1, -14, -5, 4, -4,
1032 15, -15, 1, -1, 8, -8, -3, 3, 16, 1, -16, -1, 1, 1, -1, -1,
1033 1, 1, -1, 1, 2, 1, -2, 1, -1, -1, -1, 6, -1, 3, -6, 17,
1034 -17, -3, 1, 1, 1, 4, -1, -1, -4, 3, -1, 5, -3, -1, -9, 9,
1035 -5, 1, 18, -18, 2, 1, -2, 1, -1, -1, 1, 19, -1, 1, -19, -1,
1036 4, 1, -1, 1, 7, -4, -2, 2, -7, 10, -1, -10, 1, 20, -1, -20,
1037 1, -1, 2, 4, -2, 5, 1, -5, 6, -4, 21, 4, 2, -6, -21, -1,
1038 -2, 1, -4, -1, -3, 22, -1, 1, 3, -22, -1, 11, -11, 1, 1, 1,
1039 8, -8, 2, 2, -1, -2, -2, -1, 1, -1, -5, 5, 2, 23, -23, -2,
1040 1, -1, 24, -24, -1, -1, 7, 6, -7, 5, -6, 12, -3, 3, 1, -5,
1041 1, 1, -12, 25, -1, -5, 5, -25, -1, 1, 9, 1, -1, -9, 26, -26}