2 * common functions for Indeo Video Interactive codecs (Indeo4 and Indeo5)
4 * Copyright (c) 2009 Maxim Poliakovski
6 * This file is part of Libav.
8 * Libav 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 * Libav 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 Libav; 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 av_cold int 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 if (!band->bufs[0] || !band->bufs[1])
213 return AVERROR(ENOMEM);
215 /* allocate the 3rd band buffer for scalability mode */
216 if (cfg->luma_bands > 1) {
217 band->bufs[2] = av_malloc(buf_size);
219 return AVERROR(ENOMEM);
222 planes[p].bands[0].blk_vlc.cust_desc.num_rows = 0; /* reset custom vlc */
229 av_cold void ff_ivi_free_buffers(IVIPlaneDesc *planes)
233 for (p = 0; p < 3; p++) {
234 for (b = 0; b < planes[p].num_bands; b++) {
235 av_freep(&planes[p].bands[b].bufs[0]);
236 av_freep(&planes[p].bands[b].bufs[1]);
237 av_freep(&planes[p].bands[b].bufs[2]);
239 if (planes[p].bands[b].blk_vlc.cust_tab.table)
240 ff_free_vlc(&planes[p].bands[b].blk_vlc.cust_tab);
241 for (t = 0; t < planes[p].bands[b].num_tiles; t++)
242 av_freep(&planes[p].bands[b].tiles[t].mbs);
243 av_freep(&planes[p].bands[b].tiles);
245 av_freep(&planes[p].bands);
249 av_cold int ff_ivi_init_tiles(IVIPlaneDesc *planes, int tile_width, int tile_height)
251 int p, b, x, y, x_tiles, y_tiles, t_width, t_height;
253 IVITile *tile, *ref_tile;
255 for (p = 0; p < 3; p++) {
256 t_width = !p ? tile_width : (tile_width + 3) >> 2;
257 t_height = !p ? tile_height : (tile_height + 3) >> 2;
259 if (!p && planes[0].num_bands == 4) {
264 for (b = 0; b < planes[p].num_bands; b++) {
265 band = &planes[p].bands[b];
266 x_tiles = IVI_NUM_TILES(band->width, t_width);
267 y_tiles = IVI_NUM_TILES(band->height, t_height);
268 band->num_tiles = x_tiles * y_tiles;
270 av_freep(&band->tiles);
271 band->tiles = av_mallocz(band->num_tiles * sizeof(IVITile));
273 return AVERROR(ENOMEM);
277 /* use the first luma band as reference for motion vectors
279 ref_tile = planes[0].bands[0].tiles;
281 for (y = 0; y < band->height; y += t_height) {
282 for (x = 0; x < band->width; x += t_width) {
285 tile->width = FFMIN(band->width - x, t_width);
286 tile->height = FFMIN(band->height - y, t_height);
287 tile->is_empty = tile->data_size = 0;
288 /* calculate number of macroblocks */
289 tile->num_MBs = IVI_MBs_PER_TILE(tile->width, tile->height,
292 av_freep(&tile->mbs);
293 tile->mbs = av_malloc(tile->num_MBs * sizeof(IVIMbInfo));
295 return AVERROR(ENOMEM);
299 tile->ref_mbs = ref_tile->mbs;
313 int ff_ivi_dec_tile_data_size(GetBitContext *gb)
319 len = get_bits(gb, 8);
321 len = get_bits_long(gb, 24);
324 /* align the bitstream reader on the byte boundary */
330 int ff_ivi_decode_blocks(GetBitContext *gb, IVIBandDesc *band, IVITile *tile)
332 int mbn, blk, num_blocks, num_coeffs, blk_size, scan_pos, run, val,
333 pos, is_intra, mc_type = 0, mv_x, mv_y, col_mask;
334 uint8_t col_flags[8];
335 int32_t prev_dc, trvec[64];
336 uint32_t cbp, sym, lo, hi, quant, buf_offs, q;
338 RVMapDesc *rvmap = band->rv_map;
339 void (*mc_with_delta_func)(int16_t *buf, const int16_t *ref_buf, uint32_t pitch, int mc_type);
340 void (*mc_no_delta_func) (int16_t *buf, const int16_t *ref_buf, uint32_t pitch, int mc_type);
341 const uint16_t *base_tab;
342 const uint8_t *scale_tab;
344 prev_dc = 0; /* init intra prediction for the DC coefficient */
346 blk_size = band->blk_size;
347 col_mask = blk_size - 1; /* column mask for tracking non-zero coeffs */
348 num_blocks = (band->mb_size != blk_size) ? 4 : 1; /* number of blocks per mb */
349 num_coeffs = blk_size * blk_size;
351 mc_with_delta_func = ff_ivi_mc_8x8_delta;
352 mc_no_delta_func = ff_ivi_mc_8x8_no_delta;
354 mc_with_delta_func = ff_ivi_mc_4x4_delta;
355 mc_no_delta_func = ff_ivi_mc_4x4_no_delta;
358 for (mbn = 0, mb = tile->mbs; mbn < tile->num_MBs; mb++, mbn++) {
359 is_intra = !mb->type;
361 buf_offs = mb->buf_offs;
363 quant = av_clip(band->glob_quant + mb->q_delta, 0, 23);
365 base_tab = is_intra ? band->intra_base : band->inter_base;
366 scale_tab = is_intra ? band->intra_scale : band->inter_scale;
368 quant = scale_tab[quant];
373 if (band->is_halfpel) {
374 mc_type = ((mv_y & 1) << 1) | (mv_x & 1);
376 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
380 for (blk = 0; blk < num_blocks; blk++) {
381 /* adjust block position in the buffer according to its number */
383 buf_offs += blk_size;
384 } else if (blk == 2) {
385 buf_offs -= blk_size;
386 buf_offs += blk_size * band->pitch;
389 if (cbp & 1) { /* block coded ? */
391 memset(trvec, 0, num_coeffs*sizeof(trvec[0])); /* zero transform vector */
392 memset(col_flags, 0, sizeof(col_flags)); /* zero column flags */
394 while (scan_pos <= num_coeffs) {
395 sym = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
396 if (sym == rvmap->eob_sym)
397 break; /* End of block */
399 if (sym == rvmap->esc_sym) { /* Escape - run/val explicitly coded using 3 vlc codes */
400 run = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1) + 1;
401 lo = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
402 hi = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
403 val = IVI_TOSIGNED((hi << 6) | lo); /* merge them and convert into signed val */
406 av_log(NULL, AV_LOG_ERROR, "Invalid sym encountered: %d.\n", sym);
409 run = rvmap->runtab[sym];
410 val = rvmap->valtab[sym];
413 /* de-zigzag and dequantize */
415 if (scan_pos >= num_coeffs)
417 pos = band->scan[scan_pos];
420 av_dlog(NULL, "Val = 0 encountered!\n");
422 q = (base_tab[pos] * quant) >> 9;
424 val = val * q + FFSIGN(val) * (((q ^ 1) - 1) >> 1);
426 col_flags[pos & col_mask] |= !!val; /* track columns containing non-zero coeffs */
429 if (scan_pos >= num_coeffs && sym != rvmap->eob_sym)
430 return -1; /* corrupt block data */
432 /* undoing DC coeff prediction for intra-blocks */
433 if (is_intra && band->is_2d_trans) {
436 col_flags[0] |= !!prev_dc;
439 /* apply inverse transform */
440 band->inv_transform(trvec, band->buf + buf_offs,
441 band->pitch, col_flags);
443 /* apply motion compensation */
445 mc_with_delta_func(band->buf + buf_offs,
446 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
447 band->pitch, mc_type);
449 /* block not coded */
450 /* for intra blocks apply the dc slant transform */
451 /* for inter - perform the motion compensation without delta */
452 if (is_intra && band->dc_transform) {
453 band->dc_transform(&prev_dc, band->buf + buf_offs,
454 band->pitch, blk_size);
456 mc_no_delta_func(band->buf + buf_offs,
457 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
458 band->pitch, mc_type);
470 void ff_ivi_process_empty_tile(AVCodecContext *avctx, IVIBandDesc *band,
471 IVITile *tile, int32_t mv_scale)
473 int x, y, need_mc, mbn, blk, num_blocks, mv_x, mv_y, mc_type;
474 int offs, mb_offset, row_offset;
475 IVIMbInfo *mb, *ref_mb;
478 void (*mc_no_delta_func)(int16_t *buf, const int16_t *ref_buf, uint32_t pitch,
481 offs = tile->ypos * band->pitch + tile->xpos;
483 ref_mb = tile->ref_mbs;
484 row_offset = band->mb_size * band->pitch;
485 need_mc = 0; /* reset the mc tracking flag */
487 for (y = tile->ypos; y < (tile->ypos + tile->height); y += band->mb_size) {
490 for (x = tile->xpos; x < (tile->xpos + tile->width); x += band->mb_size) {
493 mb->buf_offs = mb_offset;
495 mb->type = 1; /* set the macroblocks type = INTER */
496 mb->cbp = 0; /* all blocks are empty */
498 if (!band->qdelta_present && !band->plane && !band->band_num) {
499 mb->q_delta = band->glob_quant;
504 if (band->inherit_qdelta && ref_mb)
505 mb->q_delta = ref_mb->q_delta;
507 if (band->inherit_mv) {
508 /* motion vector inheritance */
510 mb->mv_x = ivi_scale_mv(ref_mb->mv_x, mv_scale);
511 mb->mv_y = ivi_scale_mv(ref_mb->mv_y, mv_scale);
513 mb->mv_x = ref_mb->mv_x;
514 mb->mv_y = ref_mb->mv_y;
516 need_mc |= mb->mv_x || mb->mv_y; /* tracking non-zero motion vectors */
522 mb_offset += band->mb_size;
527 if (band->inherit_mv && need_mc) { /* apply motion compensation if there is at least one non-zero motion vector */
528 num_blocks = (band->mb_size != band->blk_size) ? 4 : 1; /* number of blocks per mb */
529 mc_no_delta_func = (band->blk_size == 8) ? ff_ivi_mc_8x8_no_delta
530 : ff_ivi_mc_4x4_no_delta;
532 for (mbn = 0, mb = tile->mbs; mbn < tile->num_MBs; mb++, mbn++) {
535 if (!band->is_halfpel) {
536 mc_type = 0; /* we have only fullpel vectors */
538 mc_type = ((mv_y & 1) << 1) | (mv_x & 1);
540 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
543 for (blk = 0; blk < num_blocks; blk++) {
544 /* adjust block position in the buffer according with its number */
545 offs = mb->buf_offs + band->blk_size * ((blk & 1) + !!(blk & 2) * band->pitch);
546 mc_no_delta_func(band->buf + offs,
547 band->ref_buf + offs + mv_y * band->pitch + mv_x,
548 band->pitch, mc_type);
552 /* copy data from the reference tile into the current one */
553 src = band->ref_buf + tile->ypos * band->pitch + tile->xpos;
554 dst = band->buf + tile->ypos * band->pitch + tile->xpos;
555 for (y = 0; y < tile->height; y++) {
556 memcpy(dst, src, tile->width*sizeof(band->buf[0]));
565 uint16_t ivi_calc_band_checksum (IVIBandDesc *band)
568 int16_t *src, checksum;
573 for (y = 0; y < band->height; src += band->pitch, y++)
574 for (x = 0; x < band->width; x++)
580 int ivi_check_band (IVIBandDesc *band, const uint8_t *ref, int pitch)
589 for (y = 0; y < band->height; src += band->pitch, y++) {
590 for (x = 0; x < band->width; x++) {
591 t1 = av_clip(src[x] + 128, 0, 255);
594 av_log(NULL, AV_LOG_ERROR, "Data mismatch: row %d, column %d\n",
595 y / band->blk_size, x / band->blk_size);
606 void ff_ivi_output_plane(IVIPlaneDesc *plane, uint8_t *dst, int dst_pitch)
609 const int16_t *src = plane->bands[0].buf;
610 uint32_t pitch = plane->bands[0].pitch;
615 for (y = 0; y < plane->height; y++) {
616 for (x = 0; x < plane->width; x++)
617 dst[x] = av_clip_uint8(src[x] + 128);
625 * These are 2x8 predefined Huffman codebooks for coding macroblock/block
626 * signals. They are specified using "huffman descriptors" in order to
627 * avoid huge static tables. The decoding tables will be generated at
628 * startup from these descriptors.
630 const IVIHuffDesc ff_ivi_mb_huff_desc[8] = {
631 {8, {0, 4, 5, 4, 4, 4, 6, 6}},
632 {12, {0, 2, 2, 3, 3, 3, 3, 5, 3, 2, 2, 2}},
633 {12, {0, 2, 3, 4, 3, 3, 3, 3, 4, 3, 2, 2}},
634 {12, {0, 3, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2}},
635 {13, {0, 4, 4, 3, 3, 3, 3, 2, 3, 3, 2, 1, 1}},
636 {9, {0, 4, 4, 4, 4, 3, 3, 3, 2}},
637 {10, {0, 4, 4, 4, 4, 3, 3, 2, 2, 2}},
638 {12, {0, 4, 4, 4, 3, 3, 2, 3, 2, 2, 2, 2}}
641 const IVIHuffDesc ff_ivi_blk_huff_desc[8] = {
642 {10, {1, 2, 3, 4, 4, 7, 5, 5, 4, 1}},
643 {11, {2, 3, 4, 4, 4, 7, 5, 4, 3, 3, 2}},
644 {12, {2, 4, 5, 5, 5, 5, 6, 4, 4, 3, 1, 1}},
645 {13, {3, 3, 4, 4, 5, 6, 6, 4, 4, 3, 2, 1, 1}},
646 {11, {3, 4, 4, 5, 5, 5, 6, 5, 4, 2, 2}},
647 {13, {3, 4, 5, 5, 5, 5, 6, 4, 3, 3, 2, 1, 1}},
648 {13, {3, 4, 5, 5, 5, 6, 5, 4, 3, 3, 2, 1, 1}},
649 {9, {3, 4, 4, 5, 5, 5, 6, 5, 5}}
654 * Scan patterns shared between indeo4 and indeo5
656 const uint8_t ff_ivi_vertical_scan_8x8[64] = {
657 0, 8, 16, 24, 32, 40, 48, 56,
658 1, 9, 17, 25, 33, 41, 49, 57,
659 2, 10, 18, 26, 34, 42, 50, 58,
660 3, 11, 19, 27, 35, 43, 51, 59,
661 4, 12, 20, 28, 36, 44, 52, 60,
662 5, 13, 21, 29, 37, 45, 53, 61,
663 6, 14, 22, 30, 38, 46, 54, 62,
664 7, 15, 23, 31, 39, 47, 55, 63
667 const uint8_t ff_ivi_horizontal_scan_8x8[64] = {
668 0, 1, 2, 3, 4, 5, 6, 7,
669 8, 9, 10, 11, 12, 13, 14, 15,
670 16, 17, 18, 19, 20, 21, 22, 23,
671 24, 25, 26, 27, 28, 29, 30, 31,
672 32, 33, 34, 35, 36, 37, 38, 39,
673 40, 41, 42, 43, 44, 45, 46, 47,
674 48, 49, 50, 51, 52, 53, 54, 55,
675 56, 57, 58, 59, 60, 61, 62, 63
678 const uint8_t ff_ivi_direct_scan_4x4[16] = {
679 0, 1, 4, 8, 5, 2, 3, 6, 9, 12, 13, 10, 7, 11, 14, 15
684 * Run-value (RLE) tables.
686 const RVMapDesc ff_ivi_rvmap_tabs[9] = {
691 {1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 3, 3,
692 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 1, 1, 2, 2, 5, 5,
693 1, 1, 3, 3, 1, 1, 6, 6, 1, 2, 1, 2, 7, 7, 1, 1,
694 8, 8, 1, 1, 4, 2, 1, 4, 2, 1, 3, 3, 1, 1, 1, 9,
695 9, 1, 2, 1, 2, 1, 5, 5, 1, 1, 10, 10, 1, 1, 3, 3,
696 2, 2, 1, 1, 11, 11, 6, 4, 4, 1, 6, 1, 2, 1, 2, 12,
697 8, 1, 12, 7, 8, 7, 1, 16, 1, 16, 1, 3, 3, 13, 1, 13,
698 2, 2, 1, 15, 1, 5, 14, 15, 1, 5, 14, 1, 17, 8, 17, 8,
699 1, 4, 4, 2, 2, 1, 25, 25, 24, 24, 1, 3, 1, 3, 1, 8,
700 6, 7, 6, 1, 18, 8, 18, 1, 7, 23, 2, 2, 23, 1, 1, 21,
701 22, 9, 9, 22, 19, 1, 21, 5, 19, 5, 1, 33, 20, 33, 20, 8,
702 4, 4, 1, 32, 2, 2, 8, 3, 32, 26, 3, 1, 7, 7, 26, 6,
703 1, 6, 1, 1, 16, 1, 10, 1, 10, 2, 16, 29, 28, 2, 29, 28,
704 1, 27, 5, 8, 5, 27, 1, 8, 3, 7, 3, 31, 41, 31, 1, 41,
705 6, 1, 6, 7, 4, 4, 1, 1, 2, 1, 2, 11, 34, 30, 11, 1,
706 30, 15, 15, 34, 36, 40, 36, 40, 35, 35, 37, 37, 39, 39, 38, 38},
709 { 1, -1, 0, 2, -2, 0, 3, -3, 1, -1, 4, -4, 5, -5, 1, -1,
710 6, -6, 2, -2, 7, -7, 1, -1, 8, -8, 9, -9, 3, -3, 1, -1,
711 10, -10, 2, -2, 11, -11, 1, -1, 12, 4, -12, -4, 1, -1, 13, -13,
712 1, -1, 14, -14, 2, 5, 15, -2, -5, -15, -3, 3, 16, -16, 17, 1,
713 -1, -17, 6, 18, -6, -18, 2, -2, 19, -19, 1, -1, 20, -20, 4, -4,
714 7, -7, 21, -21, 1, -1, 2, 3, -3, 22, -2, -22, 8, 23, -8, 1,
715 2, -23, -1, 2, -2, -2, 24, 1, -24, -1, 25, 5, -5, 1, -25, -1,
716 9, -9, 26, 1, -26, 3, 1, -1, 27, -3, -1, -27, 1, 3, -1, -3,
717 28, -4, 4, 10, -10, -28, 1, -1, 1, -1, 29, 6, -29, -6, 30, -4,
718 3, 3, -3, -30, 1, 4, -1, 31, -3, 1, 11, -11, -1, -31, 32, -1,
719 -1, 2, -2, 1, 1, -32, 1, 4, -1, -4, 33, -1, 1, 1, -1, 5,
720 5, -5, -33, -1, -12, 12, -5, -7, 1, 1, 7, 34, 4, -4, -1, 4,
721 -34, -4, 35, 36, -2, -35, -2, -36, 2, 13, 2, -1, 1, -13, 1, -1,
722 37, 1, -5, 6, 5, -1, 38, -6, -8, 5, 8, -1, 1, 1, -37, -1,
723 5, 39, -5, -5, 6, -6, -38, -39, -14, 40, 14, 2, 1, 1, -2, -40,
724 -1, -2, 2, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1}
730 {0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 8, 6, 8, 7,
731 7, 9, 9, 10, 10, 11, 11, 1, 12, 1, 12, 13, 13, 16, 14, 16,
732 14, 15, 15, 17, 17, 18, 0, 18, 19, 20, 21, 19, 22, 21, 20, 22,
733 25, 24, 2, 25, 24, 23, 23, 2, 26, 28, 26, 28, 29, 27, 29, 27,
734 33, 33, 1, 32, 1, 3, 32, 30, 36, 3, 36, 30, 31, 31, 35, 34,
735 37, 41, 34, 35, 37, 4, 41, 4, 49, 8, 8, 49, 40, 38, 5, 38,
736 40, 39, 5, 39, 42, 43, 42, 7, 57, 6, 43, 44, 6, 50, 7, 44,
737 57, 48, 50, 48, 45, 45, 46, 47, 51, 46, 47, 58, 1, 51, 58, 1,
738 52, 59, 53, 9, 52, 55, 55, 59, 53, 56, 54, 56, 54, 9, 64, 64,
739 60, 63, 60, 63, 61, 62, 61, 62, 2, 10, 2, 10, 11, 1, 11, 13,
740 12, 1, 12, 13, 16, 16, 8, 8, 14, 3, 3, 15, 14, 15, 4, 4,
741 1, 17, 17, 5, 1, 7, 7, 5, 6, 1, 2, 2, 6, 22, 1, 25,
742 21, 22, 8, 24, 1, 21, 25, 24, 8, 18, 18, 23, 9, 20, 23, 33,
743 29, 33, 20, 1, 19, 1, 29, 36, 9, 36, 19, 41, 28, 57, 32, 3,
744 28, 3, 1, 27, 49, 49, 1, 32, 26, 26, 2, 4, 4, 7, 57, 41,
745 2, 7, 10, 5, 37, 16, 10, 27, 8, 8, 13, 16, 37, 13, 1, 5},
748 {0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1,
749 -1, 1, -1, 1, -1, 1, -1, 2, 1, -2, -1, 1, -1, 1, 1, -1,
750 -1, 1, -1, 1, -1, 1, 0, -1, 1, 1, 1, -1, 1, -1, -1, -1,
751 1, 1, 2, -1, -1, 1, -1, -2, 1, 1, -1, -1, 1, 1, -1, -1,
752 1, -1, 3, 1, -3, 2, -1, 1, 1, -2, -1, -1, -1, 1, 1, 1,
753 1, 1, -1, -1, -1, 2, -1, -2, 1, 2, -2, -1, 1, 1, 2, -1,
754 -1, 1, -2, -1, 1, 1, -1, 2, 1, 2, -1, 1, -2, -1, -2, -1,
755 -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 4, -1, -1, -4,
756 1, 1, 1, 2, -1, -1, 1, -1, -1, 1, -1, -1, 1, -2, 1, -1,
757 1, 1, -1, -1, 1, 1, -1, -1, 3, 2, -3, -2, 2, 5, -2, 2,
758 2, -5, -2, -2, -2, 2, -3, 3, 2, 3, -3, 2, -2, -2, 3, -3,
759 6, 2, -2, 3, -6, 3, -3, -3, 3, 7, -4, 4, -3, 2, -7, 2,
760 2, -2, -4, 2, 8, -2, -2, -2, 4, 2, -2, 2, 3, 2, -2, -2,
761 2, 2, -2, -8, -2, 9, -2, 2, -3, -2, 2, -2, 2, 2, 2, 4,
762 -2, -4, 10, 2, 2, -2, -9, -2, 2, -2, 5, 4, -4, 4, -2, 2,
763 -5, -4, -3, 4, 2, -3, 3, -2, -5, 5, 3, 3, -2, -3, -10, -4}
769 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 0, 1, 1, 5, 5,
770 2, 2, 6, 6, 7, 7, 1, 8, 1, 8, 3, 3, 9, 9, 1, 2,
771 2, 1, 4, 10, 4, 10, 11, 11, 1, 5, 12, 12, 1, 5, 13, 13,
772 3, 3, 6, 6, 2, 2, 14, 14, 16, 16, 15, 7, 15, 8, 8, 7,
773 1, 1, 17, 17, 4, 4, 1, 1, 18, 18, 2, 2, 5, 5, 25, 3,
774 9, 3, 25, 9, 19, 24, 19, 24, 1, 21, 20, 1, 21, 22, 20, 22,
775 23, 23, 8, 6, 33, 6, 8, 33, 7, 7, 26, 26, 1, 32, 1, 32,
776 28, 4, 28, 10, 29, 27, 27, 10, 41, 4, 29, 2, 2, 41, 36, 31,
777 49, 31, 34, 30, 34, 36, 30, 35, 1, 49, 11, 5, 35, 11, 1, 3,
778 3, 5, 37, 37, 8, 40, 8, 40, 12, 12, 42, 42, 1, 38, 16, 57,
779 1, 6, 16, 39, 38, 6, 7, 7, 13, 13, 39, 43, 2, 43, 57, 2,
780 50, 9, 44, 9, 50, 4, 15, 48, 44, 4, 1, 15, 48, 14, 14, 1,
781 45, 45, 8, 3, 5, 8, 51, 47, 3, 46, 46, 47, 5, 51, 1, 17,
782 17, 58, 1, 58, 2, 52, 52, 2, 53, 7, 59, 6, 6, 56, 53, 55,
783 7, 55, 1, 54, 59, 56, 54, 10, 1, 10, 4, 60, 1, 60, 8, 4,
784 8, 64, 64, 61, 1, 63, 3, 63, 62, 61, 5, 11, 5, 3, 11, 62},
787 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 0, 3, -3, 1, -1,
788 2, -2, 1, -1, 1, -1, 4, 1, -4, -1, 2, -2, 1, -1, 5, 3,
789 -3, -5, 2, 1, -2, -1, 1, -1, 6, 2, 1, -1, -6, -2, 1, -1,
790 3, -3, 2, -2, 4, -4, 1, -1, 1, -1, 1, 2, -1, 2, -2, -2,
791 7, -7, 1, -1, 3, -3, 8, -8, 1, -1, 5, -5, 3, -3, 1, 4,
792 2, -4, -1, -2, 1, 1, -1, -1, 9, 1, 1, -9, -1, 1, -1, -1,
793 1, -1, 3, -3, 1, 3, -3, -1, 3, -3, 1, -1, 10, 1, -10, -1,
794 1, 4, -1, 2, 1, -1, 1, -2, 1, -4, -1, 6, -6, -1, 1, 1,
795 1, -1, 1, 1, -1, -1, -1, 1, 11, -1, -2, 4, -1, 2, -11, 5,
796 -5, -4, -1, 1, 4, 1, -4, -1, -2, 2, 1, -1, 12, 1, -2, 1,
797 -12, 4, 2, 1, -1, -4, 4, -4, 2, -2, -1, 1, 7, -1, -1, -7,
798 -1, -3, 1, 3, 1, 5, 2, 1, -1, -5, 13, -2, -1, 2, -2, -13,
799 1, -1, 5, 6, 5, -5, 1, 1, -6, 1, -1, -1, -5, -1, 14, 2,
800 -2, 1, -14, -1, 8, 1, -1, -8, 1, 5, 1, 5, -5, 1, -1, 1,
801 -5, -1, 15, 1, -1, -1, -1, 3, -15, -3, 6, 1, 16, -1, 6, -6,
802 -6, 1, -1, 1, -16, 1, 7, -1, 1, -1, -6, -3, 6, -7, 3, -1}
808 {0, 1, 1, 2, 2, 3, 3, 4, 4, 1, 1, 5, 5, 6, 6, 7,
809 7, 8, 8, 9, 9, 2, 2, 10, 10, 1, 1, 11, 11, 12, 12, 3,
810 3, 13, 13, 0, 14, 14, 16, 15, 16, 15, 4, 4, 17, 1, 17, 1,
811 5, 5, 18, 18, 2, 2, 6, 6, 8, 19, 7, 8, 7, 19, 20, 20,
812 21, 21, 22, 24, 22, 24, 23, 23, 1, 1, 25, 25, 3, 3, 26, 26,
813 9, 9, 27, 27, 28, 28, 33, 29, 4, 33, 29, 1, 4, 1, 32, 32,
814 2, 2, 31, 10, 30, 10, 30, 31, 34, 34, 5, 5, 36, 36, 35, 41,
815 35, 11, 41, 11, 37, 1, 8, 8, 37, 6, 1, 6, 40, 7, 7, 40,
816 12, 38, 12, 39, 39, 38, 49, 13, 49, 13, 3, 42, 3, 42, 16, 16,
817 43, 43, 14, 14, 1, 1, 44, 15, 44, 15, 2, 2, 57, 48, 50, 48,
818 57, 50, 4, 45, 45, 4, 46, 47, 47, 46, 1, 51, 1, 17, 17, 51,
819 8, 9, 9, 5, 58, 8, 58, 5, 52, 52, 55, 56, 53, 56, 55, 59,
820 59, 53, 54, 1, 6, 54, 7, 7, 6, 1, 2, 3, 2, 3, 64, 60,
821 60, 10, 10, 64, 61, 62, 61, 63, 1, 63, 62, 1, 18, 24, 18, 4,
822 25, 4, 8, 21, 21, 1, 24, 22, 25, 22, 8, 11, 19, 11, 23, 1,
823 20, 23, 19, 20, 5, 12, 5, 1, 16, 2, 12, 13, 2, 13, 1, 16},
826 { 0, 1, -1, 1, -1, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 1,
827 -1, 1, -1, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 1, -1, 2,
828 -2, 1, -1, 0, 1, -1, 1, 1, -1, -1, 2, -2, 1, 4, -1, -4,
829 2, -2, 1, -1, -3, 3, 2, -2, 2, 1, 2, -2, -2, -1, 1, -1,
830 1, -1, 1, 1, -1, -1, 1, -1, 5, -5, 1, -1, 3, -3, 1, -1,
831 2, -2, 1, -1, 1, -1, 1, 1, 3, -1, -1, 6, -3, -6, -1, 1,
832 4, -4, 1, 2, 1, -2, -1, -1, 1, -1, 3, -3, 1, -1, 1, 1,
833 -1, 2, -1, -2, 1, 7, -3, 3, -1, 3, -7, -3, 1, -3, 3, -1,
834 2, 1, -2, 1, -1, -1, 1, 2, -1, -2, -4, -1, 4, 1, 2, -2,
835 1, -1, -2, 2, 8, -8, -1, 2, 1, -2, -5, 5, 1, -1, -1, 1,
836 -1, 1, 4, -1, 1, -4, -1, -1, 1, 1, 9, 1, -9, 2, -2, -1,
837 -4, 3, -3, -4, -1, 4, 1, 4, 1, -1, 1, -1, 1, 1, -1, 1,
838 -1, -1, -1, 10, 4, 1, 4, -4, -4, -10, 6, 5, -6, -5, 1, -1,
839 1, 3, -3, -1, 1, -1, -1, -1, 11, 1, 1, -11, -2, -2, 2, 5,
840 -2, -5, -5, 2, -2, 12, 2, -2, 2, 2, 5, -3, -2, 3, -2, -12,
841 -2, 2, 2, 2, -5, 3, 5, 13, -3, 7, -3, -3, -7, 3, -13, 3}
847 {0, 1, 1, 1, 2, 2, 1, 3, 3, 1, 1, 1, 4, 4, 1, 5,
848 2, 1, 5, 2, 1, 1, 6, 6, 1, 1, 1, 1, 1, 7, 3, 1,
849 2, 3, 0, 1, 2, 7, 1, 1, 1, 8, 1, 1, 8, 1, 1, 1,
850 9, 1, 9, 1, 2, 1, 1, 2, 1, 1, 10, 4, 1, 10, 1, 4,
851 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1,
852 2, 5, 1, 11, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
853 2, 1, 6, 1, 6, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 12,
854 3, 1, 12, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1,
855 4, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1,
856 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 5,
857 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 2, 3, 1, 1, 1, 1,
858 5, 1, 1, 1, 1, 1, 1, 2, 13, 1, 1, 1, 1, 1, 1, 1,
859 1, 1, 1, 1, 1, 1, 1, 1, 13, 2, 1, 1, 4, 1, 1, 1,
860 3, 1, 6, 1, 1, 1, 14, 1, 1, 1, 1, 1, 14, 6, 1, 1,
861 1, 1, 15, 2, 4, 1, 2, 3, 15, 1, 1, 1, 8, 1, 1, 8,
862 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1},
865 { 0, 1, -1, 2, 1, -1, -2, 1, -1, 3, -3, 4, 1, -1, -4, 1,
866 2, 5, -1, -2, -5, 6, 1, -1, -6, 7, -7, 8, -8, 1, 2, 9,
867 3, -2, 0, -9, -3, -1, 10, -10, 11, 1, -11, 12, -1, -12, 13, -13,
868 1, 14, -1, -14, 4, 15, -15, -4, 16, -16, 1, 2, 17, -1, -17, -2,
869 18, -18, 19, -19, 20, 3, -20, 21, -21, -3, 5, 22, 2, -22, -23, 23,
870 -5, -2, 24, 1, -24, -1, 25, -25, 26, -26, -27, 27, 28, 29, -28, -29,
871 6, 30, 2, -31, -2, -30, 31, -6, -32, 32, 33, -33, 34, -35, -34, 1,
872 4, -36, -1, 35, 37, 36, 7, -37, 38, -4, -38, 39, 41, 40, -40, -39,
873 3, 42, -43, -41, -7, -42, 43, -3, 44, -44, 45, -45, 46, 47, 8, -47,
874 -48, -46, 50, -50, 48, 49, 51, -49, 52, -52, 5, -51, -8, -53, 53, 3,
875 -56, 56, 55, 54, -54, 2, 60, -2, -55, 58, 9, -5, 59, 57, -57, -63,
876 -3, -58, -60, -61, 61, -59, -62, -9, 1, 64, 62, 69, -64, 63, 65, -67,
877 -68, 66, -65, 68, -66, -69, 67, -70, -1, 10, 71, -71, 4, 73, 72, 70,
878 6, -76, -3, 74, -78, -74, 1, 78, 80, -72, -75, 76, -1, 3, -73, 79,
879 75, 77, 1, 11, -4, -79, -10, -6, -1, -77, -83, -80, 2, 81, -84, -2,
880 83, -81, 82, -82, 84, -87, -86, 85, -11, -85, 86, -89, 87, -88, 88, 89}
886 {1, 1, 0, 2, 1, 2, 1, 3, 3, 1, 1, 4, 4, 2, 2, 1,
887 1, 5, 5, 6, 1, 6, 1, 7, 7, 3, 3, 2, 8, 2, 8, 1,
888 1, 0, 9, 9, 1, 1, 10, 4, 10, 4, 11, 11, 2, 1, 2, 1,
889 12, 12, 3, 3, 1, 1, 13, 5, 5, 13, 14, 1, 1, 14, 2, 2,
890 6, 6, 15, 1, 1, 15, 16, 4, 7, 16, 4, 7, 1, 1, 3, 3,
891 8, 8, 2, 2, 1, 1, 17, 17, 1, 1, 18, 18, 5, 5, 2, 2,
892 1, 1, 9, 19, 9, 19, 20, 3, 3, 20, 1, 10, 21, 1, 10, 4,
893 4, 21, 22, 6, 6, 22, 1, 1, 23, 24, 2, 2, 23, 24, 11, 1,
894 1, 11, 7, 25, 7, 1, 1, 25, 8, 8, 3, 26, 3, 1, 12, 2,
895 2, 26, 1, 12, 5, 5, 27, 4, 1, 4, 1, 27, 28, 1, 28, 13,
896 1, 13, 2, 29, 2, 1, 32, 6, 1, 30, 14, 29, 14, 6, 3, 31,
897 3, 1, 30, 1, 32, 31, 33, 9, 33, 1, 1, 7, 9, 7, 2, 2,
898 1, 1, 4, 36, 34, 4, 5, 10, 10, 5, 34, 1, 1, 35, 8, 8,
899 36, 3, 35, 1, 15, 3, 2, 1, 16, 15, 16, 2, 37, 1, 37, 1,
900 1, 1, 6, 6, 38, 1, 38, 11, 1, 39, 39, 40, 11, 2, 41, 4,
901 40, 1, 2, 4, 1, 1, 1, 41, 3, 1, 3, 1, 5, 7, 5, 7},
904 { 1, -1, 0, 1, 2, -1, -2, 1, -1, 3, -3, 1, -1, 2, -2, 4,
905 -4, 1, -1, 1, 5, -1, -5, 1, -1, 2, -2, 3, 1, -3, -1, 6,
906 -6, 0, 1, -1, 7, -7, 1, 2, -1, -2, 1, -1, 4, 8, -4, -8,
907 1, -1, 3, -3, 9, -9, 1, 2, -2, -1, 1, 10, -10, -1, 5, -5,
908 2, -2, 1, 11, -11, -1, 1, 3, 2, -1, -3, -2, 12, -12, 4, -4,
909 2, -2, -6, 6, 13, -13, 1, -1, 14, -14, 1, -1, 3, -3, 7, -7,
910 15, -15, 2, 1, -2, -1, 1, 5, -5, -1, -16, 2, 1, 16, -2, 4,
911 -4, -1, 1, 3, -3, -1, 17, -17, 1, 1, -8, 8, -1, -1, 2, 18,
912 -18, -2, 3, 1, -3, 19, -19, -1, 3, -3, 6, 1, -6, 20, 2, 9,
913 -9, -1, -20, -2, 4, -4, 1, -5, 21, 5, -21, -1, 1, -22, -1, 2,
914 22, -2, 10, 1, -10, 23, 1, 4, -23, 1, 2, -1, -2, -4, -7, 1,
915 7, -24, -1, 24, -1, -1, 1, 3, -1, -25, 25, 4, -3, -4, 11, -11,
916 26, -26, 6, 1, 1, -6, -5, -3, 3, 5, -1, -27, 27, 1, 4, -4,
917 -1, -8, -1, 28, 2, 8, -12, -28, -2, -2, 2, 12, -1, 29, 1, -29,
918 30, -30, 5, -5, 1, -31, -1, 3, 31, -1, 1, 1, -3, -13, 1, -7,
919 -1, -32, 13, 7, 32, 33, -33, -1, -9, -34, 9, 34, -6, 5, 6, -5}
925 {1, 1, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 0, 2, 2,
926 4, 1, 4, 1, 1, 1, 5, 5, 1, 1, 6, 6, 2, 2, 1, 1,
927 3, 3, 7, 7, 1, 1, 8, 8, 1, 1, 2, 2, 1, 9, 1, 9,
928 4, 4, 10, 1, 1, 10, 1, 1, 11, 11, 3, 3, 1, 2, 1, 2,
929 1, 1, 12, 12, 5, 5, 1, 1, 13, 1, 1, 13, 2, 2, 1, 1,
930 6, 6, 1, 1, 4, 14, 4, 14, 3, 1, 3, 1, 1, 1, 15, 7,
931 15, 2, 2, 7, 1, 1, 1, 8, 1, 8, 16, 16, 1, 1, 1, 1,
932 2, 1, 1, 2, 1, 1, 3, 5, 5, 3, 4, 1, 1, 4, 1, 1,
933 17, 17, 9, 1, 1, 9, 2, 2, 1, 1, 10, 10, 1, 6, 1, 1,
934 6, 18, 1, 1, 18, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 1,
935 4, 1, 19, 1, 19, 7, 1, 1, 20, 1, 4, 20, 1, 7, 11, 2,
936 1, 11, 21, 2, 8, 5, 1, 8, 1, 5, 21, 1, 1, 1, 22, 1,
937 1, 22, 1, 1, 3, 3, 1, 23, 2, 12, 24, 1, 1, 2, 1, 1,
938 12, 23, 1, 1, 24, 1, 1, 1, 4, 1, 1, 1, 2, 1, 6, 6,
939 4, 2, 1, 1, 1, 1, 1, 1, 1, 14, 13, 3, 1, 25, 9, 25,
940 14, 1, 9, 3, 13, 1, 1, 1, 1, 1, 10, 1, 1, 2, 10, 2},
943 {-20, -1, 0, 2, -2, 1, -1, 3, -3, 1, -1, 4, -4, 0, 2, -2,
944 1, 5, -1, -5, 6, -6, 1, -1, 7, -7, 1, -1, 3, -3, 8, -8,
945 2, -2, 1, -1, 9, -9, 1, -1, 10, -10, 4, -4, 11, 1, -11, -1,
946 2, -2, 1, 12, -12, -1, 13, -13, 1, -1, 3, -3, 14, 5, -14, -5,
947 -15, 15, -1, 1, 2, -2, 16, -16, 1, 17, -17, -1, 6, -6, 18, -18,
948 2, -2, -19, 19, -3, 1, 3, -1, 4, 20, -4, 1, -21, 21, 1, 2,
949 -1, -7, 7, -2, 22, -22, 23, 2, -23, -2, 1, -1, -24, 24, -25, 25,
950 -8, -26, 26, 8, -27, 27, 5, 3, -3, -5, -4, 28, -28, 4, 29, -29,
951 1, -1, -2, -30, 30, 2, 9, -9, -31, 31, 2, -2, -32, 3, 32, -33,
952 -3, 1, 33, -34, -1, 34, -35, 35, -10, 10, -6, 36, 6, -36, 37, -37,
953 -5, 38, 1, -38, -1, 3, 39, -39, -1, 40, 5, 1, -40, -3, 2, -11,
954 -41, -2, 1, 11, -3, -4, 41, 3, 42, 4, -1, -43, -42, 43, 1, -44,
955 45, -1, 44, -45, -7, 7, -46, 1, -12, 2, 1, -47, 46, 12, 47, 48,
956 -2, -1, -48, 49, -1, -50, -49, 50, -6, -51, 51, 52, -13, 53, -4, 4,
957 6, 13, -53, -52, -54, 55, 54, -55, -56, -2, 2, -8, 56, 1, -3, -1,
958 2, 58, 3, 8, -2, 57, -58, -60, -59, -57, -3, 60, 59, -14, 3, 14}
964 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 5, 5, 1, 1, 6,
965 6, 2, 2, 7, 7, 8, 8, 1, 1, 3, 3, 9, 9, 10, 10, 1,
966 1, 2, 2, 4, 4, 11, 0, 11, 12, 12, 13, 13, 1, 1, 5, 5,
967 14, 14, 15, 16, 15, 16, 3, 3, 1, 6, 1, 6, 2, 2, 7, 7,
968 8, 8, 17, 17, 1, 1, 4, 4, 18, 18, 2, 2, 1, 19, 1, 20,
969 19, 20, 21, 21, 3, 3, 22, 22, 5, 5, 24, 1, 1, 23, 9, 23,
970 24, 9, 2, 2, 10, 1, 1, 10, 6, 6, 25, 4, 4, 25, 7, 7,
971 26, 8, 1, 8, 3, 1, 26, 3, 11, 11, 27, 27, 2, 28, 1, 2,
972 28, 1, 12, 12, 5, 5, 29, 13, 13, 29, 32, 1, 1, 33, 31, 30,
973 32, 4, 30, 33, 4, 31, 3, 14, 1, 1, 3, 34, 34, 2, 2, 14,
974 6, 6, 35, 36, 35, 36, 1, 15, 1, 16, 16, 15, 7, 9, 7, 9,
975 37, 8, 8, 37, 1, 1, 39, 2, 38, 39, 2, 40, 5, 38, 40, 5,
976 3, 3, 4, 4, 10, 10, 1, 1, 1, 1, 41, 2, 41, 2, 6, 6,
977 1, 1, 11, 42, 11, 43, 3, 42, 3, 17, 4, 43, 1, 17, 7, 1,
978 8, 44, 4, 7, 44, 5, 8, 2, 5, 1, 2, 48, 45, 1, 12, 45,
979 12, 48, 13, 13, 1, 9, 9, 46, 1, 46, 47, 47, 49, 18, 18, 49},
982 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 1, -1, 3, -3, 1,
983 -1, -2, 2, 1, -1, 1, -1, 4, -4, -2, 2, 1, -1, 1, -1, 5,
984 -5, -3, 3, 2, -2, 1, 0, -1, 1, -1, 1, -1, 6, -6, 2, -2,
985 1, -1, 1, 1, -1, -1, -3, 3, 7, 2, -7, -2, -4, 4, 2, -2,
986 2, -2, 1, -1, 8, -8, 3, -3, 1, -1, -5, 5, 9, 1, -9, 1,
987 -1, -1, 1, -1, -4, 4, 1, -1, 3, -3, 1, -10, 10, 1, 2, -1,
988 -1, -2, 6, -6, 2, 11, -11, -2, 3, -3, 1, -4, 4, -1, 3, -3,
989 1, 3, 12, -3, -5, -12, -1, 5, 2, -2, 1, -1, -7, 1, 13, 7,
990 -1, -13, 2, -2, 4, -4, 1, 2, -2, -1, 1, 14, -14, 1, 1, 1,
991 -1, -5, -1, -1, 5, -1, -6, 2, -15, 15, 6, 1, -1, -8, 8, -2,
992 -4, 4, 1, 1, -1, -1, 16, 2, -16, -2, 2, -2, 4, 3, -4, -3,
993 -1, -4, 4, 1, -17, 17, -1, -9, 1, 1, 9, 1, -5, -1, -1, 5,
994 -7, 7, 6, -6, 3, -3, 18, -18, 19, -19, 1, -10, -1, 10, -5, 5,
995 20, -20, -3, 1, 3, 1, 8, -1, -8, 2, 7, -1, -21, -2, 5, 21,
996 5, -1, -7, -5, 1, -6, -5, -11, 6, 22, 11, 1, 1, -22, -3, -1,
997 3, -1, 3, -3, -23, 4, -4, 1, 23, -1, 1, -1, 1, -2, 2, -1}
1003 {1, 1, 1, 1, 0, 2, 2, 1, 1, 3, 3, 0, 1, 1, 2, 2,
1004 4, 4, 1, 1, 5, 5, 1, 1, 2, 2, 3, 3, 6, 6, 1, 1,
1005 7, 7, 8, 1, 8, 2, 2, 1, 4, 4, 1, 3, 1, 3, 9, 9,
1006 2, 2, 1, 5, 1, 5, 10, 10, 1, 1, 11, 11, 3, 6, 3, 4,
1007 4, 6, 2, 2, 1, 12, 1, 12, 7, 13, 7, 13, 1, 1, 8, 8,
1008 2, 2, 14, 14, 16, 15, 16, 5, 5, 1, 3, 15, 1, 3, 4, 4,
1009 1, 1, 17, 17, 2, 2, 6, 6, 1, 18, 1, 18, 22, 21, 22, 21,
1010 25, 24, 25, 19, 9, 20, 9, 23, 19, 24, 20, 3, 23, 7, 3, 1,
1011 1, 7, 28, 26, 29, 5, 28, 26, 5, 8, 29, 4, 8, 27, 2, 2,
1012 4, 27, 1, 1, 10, 36, 10, 33, 33, 36, 30, 1, 32, 32, 1, 30,
1013 6, 31, 31, 35, 3, 6, 11, 11, 3, 2, 35, 2, 34, 1, 34, 1,
1014 37, 37, 12, 7, 12, 5, 41, 5, 4, 7, 1, 8, 13, 4, 1, 41,
1015 13, 38, 8, 38, 9, 1, 40, 40, 9, 1, 39, 2, 2, 49, 39, 42,
1016 3, 3, 14, 16, 49, 14, 16, 42, 43, 43, 6, 6, 15, 1, 1, 15,
1017 44, 44, 1, 1, 50, 48, 4, 5, 4, 7, 5, 2, 10, 10, 48, 7,
1018 50, 45, 2, 1, 45, 8, 8, 1, 46, 46, 3, 47, 47, 3, 1, 1},
1021 { 1, -1, 2, -2, 0, 1, -1, 3, -3, 1, -1, 0, 4, -4, 2, -2,
1022 1, -1, 5, -5, 1, -1, 6, -6, 3, -3, 2, -2, 1, -1, 7, -7,
1023 1, -1, 1, 8, -1, 4, -4, -8, 2, -2, 9, 3, -9, -3, 1, -1,
1024 5, -5, 10, 2, -10, -2, 1, -1, 11, -11, 1, -1, -4, 2, 4, 3,
1025 -3, -2, 6, -6, 12, 1, -12, -1, 2, 1, -2, -1, 13, -13, 2, -2,
1026 7, -7, 1, -1, 1, 1, -1, 3, -3, 14, 5, -1, -14, -5, 4, -4,
1027 15, -15, 1, -1, 8, -8, -3, 3, 16, 1, -16, -1, 1, 1, -1, -1,
1028 1, 1, -1, 1, 2, 1, -2, 1, -1, -1, -1, 6, -1, 3, -6, 17,
1029 -17, -3, 1, 1, 1, 4, -1, -1, -4, 3, -1, 5, -3, -1, -9, 9,
1030 -5, 1, 18, -18, 2, 1, -2, 1, -1, -1, 1, 19, -1, 1, -19, -1,
1031 4, 1, -1, 1, 7, -4, -2, 2, -7, 10, -1, -10, 1, 20, -1, -20,
1032 1, -1, 2, 4, -2, 5, 1, -5, 6, -4, 21, 4, 2, -6, -21, -1,
1033 -2, 1, -4, -1, -3, 22, -1, 1, 3, -22, -1, 11, -11, 1, 1, 1,
1034 8, -8, 2, 2, -1, -2, -2, -1, 1, -1, -5, 5, 2, 23, -23, -2,
1035 1, -1, 24, -24, -1, -1, 7, 6, -7, 5, -6, 12, -3, 3, 1, -5,
1036 1, 1, -12, 25, -1, -5, 5, -25, -1, 1, 9, 1, -1, -9, 26, -26}