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) || !huff_tab->cust_tab.table) {
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 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 av_cold void 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 av_cold int 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 = 0, 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 = ((mv_y & 1) << 1) | (mv_x & 1);
379 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
383 for (blk = 0; blk < num_blocks; blk++) {
384 /* adjust block position in the buffer according to its number */
386 buf_offs += blk_size;
387 } else if (blk == 2) {
388 buf_offs -= blk_size;
389 buf_offs += blk_size * band->pitch;
392 if (cbp & 1) { /* block coded ? */
394 memset(trvec, 0, num_coeffs*sizeof(trvec[0])); /* zero transform vector */
395 memset(col_flags, 0, sizeof(col_flags)); /* zero column flags */
397 while (scan_pos <= num_coeffs) {
398 sym = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
399 if (sym == rvmap->eob_sym)
400 break; /* End of block */
402 if (sym == rvmap->esc_sym) { /* Escape - run/val explicitly coded using 3 vlc codes */
403 run = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1) + 1;
404 lo = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
405 hi = get_vlc2(gb, band->blk_vlc.tab->table, IVI_VLC_BITS, 1);
406 val = IVI_TOSIGNED((hi << 6) | lo); /* merge them and convert into signed val */
409 av_log(NULL, AV_LOG_ERROR, "Invalid sym encountered: %d.\n", sym);
412 run = rvmap->runtab[sym];
413 val = rvmap->valtab[sym];
416 /* de-zigzag and dequantize */
418 if (scan_pos >= (unsigned)num_coeffs)
420 pos = band->scan[scan_pos];
423 av_dlog(NULL, "Val = 0 encountered!\n");
425 q = (base_tab[pos] * quant) >> 9;
427 val = val * q + FFSIGN(val) * (((q ^ 1) - 1) >> 1);
429 col_flags[pos & col_mask] |= !!val; /* track columns containing non-zero coeffs */
432 if (scan_pos >= num_coeffs && sym != rvmap->eob_sym)
433 return -1; /* corrupt block data */
435 /* undoing DC coeff prediction for intra-blocks */
436 if (is_intra && band->is_2d_trans) {
439 col_flags[0] |= !!prev_dc;
441 if(band->transform_size > band->blk_size){
442 av_log(0, AV_LOG_ERROR, "Too large transform\n");
443 return AVERROR_INVALIDDATA;
445 /* apply inverse transform */
446 band->inv_transform(trvec, band->buf + buf_offs,
447 band->pitch, col_flags);
449 /* apply motion compensation */
451 mc_with_delta_func(band->buf + buf_offs,
452 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
453 band->pitch, mc_type);
455 /* block not coded */
456 /* for intra blocks apply the dc slant transform */
457 /* for inter - perform the motion compensation without delta */
458 if (is_intra && band->dc_transform) {
459 band->dc_transform(&prev_dc, band->buf + buf_offs,
460 band->pitch, blk_size);
462 mc_no_delta_func(band->buf + buf_offs,
463 band->ref_buf + buf_offs + mv_y * band->pitch + mv_x,
464 band->pitch, mc_type);
476 void ff_ivi_process_empty_tile(AVCodecContext *avctx, IVIBandDesc *band,
477 IVITile *tile, int32_t mv_scale)
479 int x, y, need_mc, mbn, blk, num_blocks, mv_x, mv_y, mc_type;
480 int offs, mb_offset, row_offset;
481 IVIMbInfo *mb, *ref_mb;
484 void (*mc_no_delta_func)(int16_t *buf, const int16_t *ref_buf, uint32_t pitch,
487 if( tile->num_MBs != IVI_MBs_PER_TILE(tile->width, tile->height, band->mb_size) ){
488 av_log(avctx, AV_LOG_ERROR, "allocated tile size %d mismatches parameters %d in ff_ivi_process_empty_tile()\n",
489 tile->num_MBs, IVI_MBs_PER_TILE(tile->width, tile->height, band->mb_size));
493 offs = tile->ypos * band->pitch + tile->xpos;
495 ref_mb = tile->ref_mbs;
496 row_offset = band->mb_size * band->pitch;
497 need_mc = 0; /* reset the mc tracking flag */
499 for (y = tile->ypos; y < (tile->ypos + tile->height); y += band->mb_size) {
502 for (x = tile->xpos; x < (tile->xpos + tile->width); x += band->mb_size) {
505 mb->buf_offs = mb_offset;
507 mb->type = 1; /* set the macroblocks type = INTER */
508 mb->cbp = 0; /* all blocks are empty */
510 if (!band->qdelta_present && !band->plane && !band->band_num) {
511 mb->q_delta = band->glob_quant;
516 if (band->inherit_qdelta && ref_mb)
517 mb->q_delta = ref_mb->q_delta;
519 if (band->inherit_mv && ref_mb) {
520 /* motion vector inheritance */
522 mb->mv_x = ivi_scale_mv(ref_mb->mv_x, mv_scale);
523 mb->mv_y = ivi_scale_mv(ref_mb->mv_y, mv_scale);
525 mb->mv_x = ref_mb->mv_x;
526 mb->mv_y = ref_mb->mv_y;
528 need_mc |= mb->mv_x || mb->mv_y; /* tracking non-zero motion vectors */
534 mb_offset += band->mb_size;
539 if (band->inherit_mv && need_mc) { /* apply motion compensation if there is at least one non-zero motion vector */
540 num_blocks = (band->mb_size != band->blk_size) ? 4 : 1; /* number of blocks per mb */
541 mc_no_delta_func = (band->blk_size == 8) ? ff_ivi_mc_8x8_no_delta
542 : ff_ivi_mc_4x4_no_delta;
544 for (mbn = 0, mb = tile->mbs; mbn < tile->num_MBs; mb++, mbn++) {
547 if (!band->is_halfpel) {
548 mc_type = 0; /* we have only fullpel vectors */
550 mc_type = ((mv_y & 1) << 1) | (mv_x & 1);
552 mv_y >>= 1; /* convert halfpel vectors into fullpel ones */
555 for (blk = 0; blk < num_blocks; blk++) {
556 /* adjust block position in the buffer according with its number */
557 offs = mb->buf_offs + band->blk_size * ((blk & 1) + !!(blk & 2) * band->pitch);
558 mc_no_delta_func(band->buf + offs,
559 band->ref_buf + offs + mv_y * band->pitch + mv_x,
560 band->pitch, mc_type);
564 /* copy data from the reference tile into the current one */
565 src = band->ref_buf + tile->ypos * band->pitch + tile->xpos;
566 dst = band->buf + tile->ypos * band->pitch + tile->xpos;
567 for (y = 0; y < tile->height; y++) {
568 memcpy(dst, src, tile->width*sizeof(band->buf[0]));
577 uint16_t ivi_calc_band_checksum (IVIBandDesc *band)
580 int16_t *src, checksum;
585 for (y = 0; y < band->height; src += band->pitch, y++)
586 for (x = 0; x < band->width; x++)
592 int ivi_check_band (IVIBandDesc *band, const uint8_t *ref, int pitch)
601 for (y = 0; y < band->height; src += band->pitch, y++) {
602 for (x = 0; x < band->width; x++) {
603 t1 = av_clip(src[x] + 128, 0, 255);
606 av_log(NULL, AV_LOG_ERROR, "Data mismatch: row %d, column %d\n",
607 y / band->blk_size, x / band->blk_size);
618 void ff_ivi_output_plane(IVIPlaneDesc *plane, uint8_t *dst, int dst_pitch)
621 const int16_t *src = plane->bands[0].buf;
622 uint32_t pitch = plane->bands[0].pitch;
627 for (y = 0; y < plane->height; y++) {
628 for (x = 0; x < plane->width; x++)
629 dst[x] = av_clip_uint8(src[x] + 128);
637 * These are 2x8 predefined Huffman codebooks for coding macroblock/block
638 * signals. They are specified using "huffman descriptors" in order to
639 * avoid huge static tables. The decoding tables will be generated at
640 * startup from these descriptors.
642 const IVIHuffDesc ff_ivi_mb_huff_desc[8] = {
643 {8, {0, 4, 5, 4, 4, 4, 6, 6}},
644 {12, {0, 2, 2, 3, 3, 3, 3, 5, 3, 2, 2, 2}},
645 {12, {0, 2, 3, 4, 3, 3, 3, 3, 4, 3, 2, 2}},
646 {12, {0, 3, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2}},
647 {13, {0, 4, 4, 3, 3, 3, 3, 2, 3, 3, 2, 1, 1}},
648 {9, {0, 4, 4, 4, 4, 3, 3, 3, 2}},
649 {10, {0, 4, 4, 4, 4, 3, 3, 2, 2, 2}},
650 {12, {0, 4, 4, 4, 3, 3, 2, 3, 2, 2, 2, 2}}
653 const IVIHuffDesc ff_ivi_blk_huff_desc[8] = {
654 {10, {1, 2, 3, 4, 4, 7, 5, 5, 4, 1}},
655 {11, {2, 3, 4, 4, 4, 7, 5, 4, 3, 3, 2}},
656 {12, {2, 4, 5, 5, 5, 5, 6, 4, 4, 3, 1, 1}},
657 {13, {3, 3, 4, 4, 5, 6, 6, 4, 4, 3, 2, 1, 1}},
658 {11, {3, 4, 4, 5, 5, 5, 6, 5, 4, 2, 2}},
659 {13, {3, 4, 5, 5, 5, 5, 6, 4, 3, 3, 2, 1, 1}},
660 {13, {3, 4, 5, 5, 5, 6, 5, 4, 3, 3, 2, 1, 1}},
661 {9, {3, 4, 4, 5, 5, 5, 6, 5, 5}}
666 * Scan patterns shared between indeo4 and indeo5
668 const uint8_t ff_ivi_vertical_scan_8x8[64] = {
669 0, 8, 16, 24, 32, 40, 48, 56,
670 1, 9, 17, 25, 33, 41, 49, 57,
671 2, 10, 18, 26, 34, 42, 50, 58,
672 3, 11, 19, 27, 35, 43, 51, 59,
673 4, 12, 20, 28, 36, 44, 52, 60,
674 5, 13, 21, 29, 37, 45, 53, 61,
675 6, 14, 22, 30, 38, 46, 54, 62,
676 7, 15, 23, 31, 39, 47, 55, 63
679 const uint8_t ff_ivi_horizontal_scan_8x8[64] = {
680 0, 1, 2, 3, 4, 5, 6, 7,
681 8, 9, 10, 11, 12, 13, 14, 15,
682 16, 17, 18, 19, 20, 21, 22, 23,
683 24, 25, 26, 27, 28, 29, 30, 31,
684 32, 33, 34, 35, 36, 37, 38, 39,
685 40, 41, 42, 43, 44, 45, 46, 47,
686 48, 49, 50, 51, 52, 53, 54, 55,
687 56, 57, 58, 59, 60, 61, 62, 63
690 const uint8_t ff_ivi_direct_scan_4x4[16] = {
691 0, 1, 4, 8, 5, 2, 3, 6, 9, 12, 13, 10, 7, 11, 14, 15
696 * Run-value (RLE) tables.
698 const RVMapDesc ff_ivi_rvmap_tabs[9] = {
703 {1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 3, 3,
704 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 1, 1, 2, 2, 5, 5,
705 1, 1, 3, 3, 1, 1, 6, 6, 1, 2, 1, 2, 7, 7, 1, 1,
706 8, 8, 1, 1, 4, 2, 1, 4, 2, 1, 3, 3, 1, 1, 1, 9,
707 9, 1, 2, 1, 2, 1, 5, 5, 1, 1, 10, 10, 1, 1, 3, 3,
708 2, 2, 1, 1, 11, 11, 6, 4, 4, 1, 6, 1, 2, 1, 2, 12,
709 8, 1, 12, 7, 8, 7, 1, 16, 1, 16, 1, 3, 3, 13, 1, 13,
710 2, 2, 1, 15, 1, 5, 14, 15, 1, 5, 14, 1, 17, 8, 17, 8,
711 1, 4, 4, 2, 2, 1, 25, 25, 24, 24, 1, 3, 1, 3, 1, 8,
712 6, 7, 6, 1, 18, 8, 18, 1, 7, 23, 2, 2, 23, 1, 1, 21,
713 22, 9, 9, 22, 19, 1, 21, 5, 19, 5, 1, 33, 20, 33, 20, 8,
714 4, 4, 1, 32, 2, 2, 8, 3, 32, 26, 3, 1, 7, 7, 26, 6,
715 1, 6, 1, 1, 16, 1, 10, 1, 10, 2, 16, 29, 28, 2, 29, 28,
716 1, 27, 5, 8, 5, 27, 1, 8, 3, 7, 3, 31, 41, 31, 1, 41,
717 6, 1, 6, 7, 4, 4, 1, 1, 2, 1, 2, 11, 34, 30, 11, 1,
718 30, 15, 15, 34, 36, 40, 36, 40, 35, 35, 37, 37, 39, 39, 38, 38},
721 { 1, -1, 0, 2, -2, 0, 3, -3, 1, -1, 4, -4, 5, -5, 1, -1,
722 6, -6, 2, -2, 7, -7, 1, -1, 8, -8, 9, -9, 3, -3, 1, -1,
723 10, -10, 2, -2, 11, -11, 1, -1, 12, 4, -12, -4, 1, -1, 13, -13,
724 1, -1, 14, -14, 2, 5, 15, -2, -5, -15, -3, 3, 16, -16, 17, 1,
725 -1, -17, 6, 18, -6, -18, 2, -2, 19, -19, 1, -1, 20, -20, 4, -4,
726 7, -7, 21, -21, 1, -1, 2, 3, -3, 22, -2, -22, 8, 23, -8, 1,
727 2, -23, -1, 2, -2, -2, 24, 1, -24, -1, 25, 5, -5, 1, -25, -1,
728 9, -9, 26, 1, -26, 3, 1, -1, 27, -3, -1, -27, 1, 3, -1, -3,
729 28, -4, 4, 10, -10, -28, 1, -1, 1, -1, 29, 6, -29, -6, 30, -4,
730 3, 3, -3, -30, 1, 4, -1, 31, -3, 1, 11, -11, -1, -31, 32, -1,
731 -1, 2, -2, 1, 1, -32, 1, 4, -1, -4, 33, -1, 1, 1, -1, 5,
732 5, -5, -33, -1, -12, 12, -5, -7, 1, 1, 7, 34, 4, -4, -1, 4,
733 -34, -4, 35, 36, -2, -35, -2, -36, 2, 13, 2, -1, 1, -13, 1, -1,
734 37, 1, -5, 6, 5, -1, 38, -6, -8, 5, 8, -1, 1, 1, -37, -1,
735 5, 39, -5, -5, 6, -6, -38, -39, -14, 40, 14, 2, 1, 1, -2, -40,
736 -1, -2, 2, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1}
742 {0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 8, 6, 8, 7,
743 7, 9, 9, 10, 10, 11, 11, 1, 12, 1, 12, 13, 13, 16, 14, 16,
744 14, 15, 15, 17, 17, 18, 0, 18, 19, 20, 21, 19, 22, 21, 20, 22,
745 25, 24, 2, 25, 24, 23, 23, 2, 26, 28, 26, 28, 29, 27, 29, 27,
746 33, 33, 1, 32, 1, 3, 32, 30, 36, 3, 36, 30, 31, 31, 35, 34,
747 37, 41, 34, 35, 37, 4, 41, 4, 49, 8, 8, 49, 40, 38, 5, 38,
748 40, 39, 5, 39, 42, 43, 42, 7, 57, 6, 43, 44, 6, 50, 7, 44,
749 57, 48, 50, 48, 45, 45, 46, 47, 51, 46, 47, 58, 1, 51, 58, 1,
750 52, 59, 53, 9, 52, 55, 55, 59, 53, 56, 54, 56, 54, 9, 64, 64,
751 60, 63, 60, 63, 61, 62, 61, 62, 2, 10, 2, 10, 11, 1, 11, 13,
752 12, 1, 12, 13, 16, 16, 8, 8, 14, 3, 3, 15, 14, 15, 4, 4,
753 1, 17, 17, 5, 1, 7, 7, 5, 6, 1, 2, 2, 6, 22, 1, 25,
754 21, 22, 8, 24, 1, 21, 25, 24, 8, 18, 18, 23, 9, 20, 23, 33,
755 29, 33, 20, 1, 19, 1, 29, 36, 9, 36, 19, 41, 28, 57, 32, 3,
756 28, 3, 1, 27, 49, 49, 1, 32, 26, 26, 2, 4, 4, 7, 57, 41,
757 2, 7, 10, 5, 37, 16, 10, 27, 8, 8, 13, 16, 37, 13, 1, 5},
760 {0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1,
761 -1, 1, -1, 1, -1, 1, -1, 2, 1, -2, -1, 1, -1, 1, 1, -1,
762 -1, 1, -1, 1, -1, 1, 0, -1, 1, 1, 1, -1, 1, -1, -1, -1,
763 1, 1, 2, -1, -1, 1, -1, -2, 1, 1, -1, -1, 1, 1, -1, -1,
764 1, -1, 3, 1, -3, 2, -1, 1, 1, -2, -1, -1, -1, 1, 1, 1,
765 1, 1, -1, -1, -1, 2, -1, -2, 1, 2, -2, -1, 1, 1, 2, -1,
766 -1, 1, -2, -1, 1, 1, -1, 2, 1, 2, -1, 1, -2, -1, -2, -1,
767 -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 4, -1, -1, -4,
768 1, 1, 1, 2, -1, -1, 1, -1, -1, 1, -1, -1, 1, -2, 1, -1,
769 1, 1, -1, -1, 1, 1, -1, -1, 3, 2, -3, -2, 2, 5, -2, 2,
770 2, -5, -2, -2, -2, 2, -3, 3, 2, 3, -3, 2, -2, -2, 3, -3,
771 6, 2, -2, 3, -6, 3, -3, -3, 3, 7, -4, 4, -3, 2, -7, 2,
772 2, -2, -4, 2, 8, -2, -2, -2, 4, 2, -2, 2, 3, 2, -2, -2,
773 2, 2, -2, -8, -2, 9, -2, 2, -3, -2, 2, -2, 2, 2, 2, 4,
774 -2, -4, 10, 2, 2, -2, -9, -2, 2, -2, 5, 4, -4, 4, -2, 2,
775 -5, -4, -3, 4, 2, -3, 3, -2, -5, 5, 3, 3, -2, -3, -10, -4}
781 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 0, 1, 1, 5, 5,
782 2, 2, 6, 6, 7, 7, 1, 8, 1, 8, 3, 3, 9, 9, 1, 2,
783 2, 1, 4, 10, 4, 10, 11, 11, 1, 5, 12, 12, 1, 5, 13, 13,
784 3, 3, 6, 6, 2, 2, 14, 14, 16, 16, 15, 7, 15, 8, 8, 7,
785 1, 1, 17, 17, 4, 4, 1, 1, 18, 18, 2, 2, 5, 5, 25, 3,
786 9, 3, 25, 9, 19, 24, 19, 24, 1, 21, 20, 1, 21, 22, 20, 22,
787 23, 23, 8, 6, 33, 6, 8, 33, 7, 7, 26, 26, 1, 32, 1, 32,
788 28, 4, 28, 10, 29, 27, 27, 10, 41, 4, 29, 2, 2, 41, 36, 31,
789 49, 31, 34, 30, 34, 36, 30, 35, 1, 49, 11, 5, 35, 11, 1, 3,
790 3, 5, 37, 37, 8, 40, 8, 40, 12, 12, 42, 42, 1, 38, 16, 57,
791 1, 6, 16, 39, 38, 6, 7, 7, 13, 13, 39, 43, 2, 43, 57, 2,
792 50, 9, 44, 9, 50, 4, 15, 48, 44, 4, 1, 15, 48, 14, 14, 1,
793 45, 45, 8, 3, 5, 8, 51, 47, 3, 46, 46, 47, 5, 51, 1, 17,
794 17, 58, 1, 58, 2, 52, 52, 2, 53, 7, 59, 6, 6, 56, 53, 55,
795 7, 55, 1, 54, 59, 56, 54, 10, 1, 10, 4, 60, 1, 60, 8, 4,
796 8, 64, 64, 61, 1, 63, 3, 63, 62, 61, 5, 11, 5, 3, 11, 62},
799 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 0, 3, -3, 1, -1,
800 2, -2, 1, -1, 1, -1, 4, 1, -4, -1, 2, -2, 1, -1, 5, 3,
801 -3, -5, 2, 1, -2, -1, 1, -1, 6, 2, 1, -1, -6, -2, 1, -1,
802 3, -3, 2, -2, 4, -4, 1, -1, 1, -1, 1, 2, -1, 2, -2, -2,
803 7, -7, 1, -1, 3, -3, 8, -8, 1, -1, 5, -5, 3, -3, 1, 4,
804 2, -4, -1, -2, 1, 1, -1, -1, 9, 1, 1, -9, -1, 1, -1, -1,
805 1, -1, 3, -3, 1, 3, -3, -1, 3, -3, 1, -1, 10, 1, -10, -1,
806 1, 4, -1, 2, 1, -1, 1, -2, 1, -4, -1, 6, -6, -1, 1, 1,
807 1, -1, 1, 1, -1, -1, -1, 1, 11, -1, -2, 4, -1, 2, -11, 5,
808 -5, -4, -1, 1, 4, 1, -4, -1, -2, 2, 1, -1, 12, 1, -2, 1,
809 -12, 4, 2, 1, -1, -4, 4, -4, 2, -2, -1, 1, 7, -1, -1, -7,
810 -1, -3, 1, 3, 1, 5, 2, 1, -1, -5, 13, -2, -1, 2, -2, -13,
811 1, -1, 5, 6, 5, -5, 1, 1, -6, 1, -1, -1, -5, -1, 14, 2,
812 -2, 1, -14, -1, 8, 1, -1, -8, 1, 5, 1, 5, -5, 1, -1, 1,
813 -5, -1, 15, 1, -1, -1, -1, 3, -15, -3, 6, 1, 16, -1, 6, -6,
814 -6, 1, -1, 1, -16, 1, 7, -1, 1, -1, -6, -3, 6, -7, 3, -1}
820 {0, 1, 1, 2, 2, 3, 3, 4, 4, 1, 1, 5, 5, 6, 6, 7,
821 7, 8, 8, 9, 9, 2, 2, 10, 10, 1, 1, 11, 11, 12, 12, 3,
822 3, 13, 13, 0, 14, 14, 16, 15, 16, 15, 4, 4, 17, 1, 17, 1,
823 5, 5, 18, 18, 2, 2, 6, 6, 8, 19, 7, 8, 7, 19, 20, 20,
824 21, 21, 22, 24, 22, 24, 23, 23, 1, 1, 25, 25, 3, 3, 26, 26,
825 9, 9, 27, 27, 28, 28, 33, 29, 4, 33, 29, 1, 4, 1, 32, 32,
826 2, 2, 31, 10, 30, 10, 30, 31, 34, 34, 5, 5, 36, 36, 35, 41,
827 35, 11, 41, 11, 37, 1, 8, 8, 37, 6, 1, 6, 40, 7, 7, 40,
828 12, 38, 12, 39, 39, 38, 49, 13, 49, 13, 3, 42, 3, 42, 16, 16,
829 43, 43, 14, 14, 1, 1, 44, 15, 44, 15, 2, 2, 57, 48, 50, 48,
830 57, 50, 4, 45, 45, 4, 46, 47, 47, 46, 1, 51, 1, 17, 17, 51,
831 8, 9, 9, 5, 58, 8, 58, 5, 52, 52, 55, 56, 53, 56, 55, 59,
832 59, 53, 54, 1, 6, 54, 7, 7, 6, 1, 2, 3, 2, 3, 64, 60,
833 60, 10, 10, 64, 61, 62, 61, 63, 1, 63, 62, 1, 18, 24, 18, 4,
834 25, 4, 8, 21, 21, 1, 24, 22, 25, 22, 8, 11, 19, 11, 23, 1,
835 20, 23, 19, 20, 5, 12, 5, 1, 16, 2, 12, 13, 2, 13, 1, 16},
838 { 0, 1, -1, 1, -1, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 1,
839 -1, 1, -1, 1, -1, 2, -2, 1, -1, 3, -3, 1, -1, 1, -1, 2,
840 -2, 1, -1, 0, 1, -1, 1, 1, -1, -1, 2, -2, 1, 4, -1, -4,
841 2, -2, 1, -1, -3, 3, 2, -2, 2, 1, 2, -2, -2, -1, 1, -1,
842 1, -1, 1, 1, -1, -1, 1, -1, 5, -5, 1, -1, 3, -3, 1, -1,
843 2, -2, 1, -1, 1, -1, 1, 1, 3, -1, -1, 6, -3, -6, -1, 1,
844 4, -4, 1, 2, 1, -2, -1, -1, 1, -1, 3, -3, 1, -1, 1, 1,
845 -1, 2, -1, -2, 1, 7, -3, 3, -1, 3, -7, -3, 1, -3, 3, -1,
846 2, 1, -2, 1, -1, -1, 1, 2, -1, -2, -4, -1, 4, 1, 2, -2,
847 1, -1, -2, 2, 8, -8, -1, 2, 1, -2, -5, 5, 1, -1, -1, 1,
848 -1, 1, 4, -1, 1, -4, -1, -1, 1, 1, 9, 1, -9, 2, -2, -1,
849 -4, 3, -3, -4, -1, 4, 1, 4, 1, -1, 1, -1, 1, 1, -1, 1,
850 -1, -1, -1, 10, 4, 1, 4, -4, -4, -10, 6, 5, -6, -5, 1, -1,
851 1, 3, -3, -1, 1, -1, -1, -1, 11, 1, 1, -11, -2, -2, 2, 5,
852 -2, -5, -5, 2, -2, 12, 2, -2, 2, 2, 5, -3, -2, 3, -2, -12,
853 -2, 2, 2, 2, -5, 3, 5, 13, -3, 7, -3, -3, -7, 3, -13, 3}
859 {0, 1, 1, 1, 2, 2, 1, 3, 3, 1, 1, 1, 4, 4, 1, 5,
860 2, 1, 5, 2, 1, 1, 6, 6, 1, 1, 1, 1, 1, 7, 3, 1,
861 2, 3, 0, 1, 2, 7, 1, 1, 1, 8, 1, 1, 8, 1, 1, 1,
862 9, 1, 9, 1, 2, 1, 1, 2, 1, 1, 10, 4, 1, 10, 1, 4,
863 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1,
864 2, 5, 1, 11, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
865 2, 1, 6, 1, 6, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 12,
866 3, 1, 12, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1,
867 4, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1,
868 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 5,
869 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 2, 3, 1, 1, 1, 1,
870 5, 1, 1, 1, 1, 1, 1, 2, 13, 1, 1, 1, 1, 1, 1, 1,
871 1, 1, 1, 1, 1, 1, 1, 1, 13, 2, 1, 1, 4, 1, 1, 1,
872 3, 1, 6, 1, 1, 1, 14, 1, 1, 1, 1, 1, 14, 6, 1, 1,
873 1, 1, 15, 2, 4, 1, 2, 3, 15, 1, 1, 1, 8, 1, 1, 8,
874 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1},
877 { 0, 1, -1, 2, 1, -1, -2, 1, -1, 3, -3, 4, 1, -1, -4, 1,
878 2, 5, -1, -2, -5, 6, 1, -1, -6, 7, -7, 8, -8, 1, 2, 9,
879 3, -2, 0, -9, -3, -1, 10, -10, 11, 1, -11, 12, -1, -12, 13, -13,
880 1, 14, -1, -14, 4, 15, -15, -4, 16, -16, 1, 2, 17, -1, -17, -2,
881 18, -18, 19, -19, 20, 3, -20, 21, -21, -3, 5, 22, 2, -22, -23, 23,
882 -5, -2, 24, 1, -24, -1, 25, -25, 26, -26, -27, 27, 28, 29, -28, -29,
883 6, 30, 2, -31, -2, -30, 31, -6, -32, 32, 33, -33, 34, -35, -34, 1,
884 4, -36, -1, 35, 37, 36, 7, -37, 38, -4, -38, 39, 41, 40, -40, -39,
885 3, 42, -43, -41, -7, -42, 43, -3, 44, -44, 45, -45, 46, 47, 8, -47,
886 -48, -46, 50, -50, 48, 49, 51, -49, 52, -52, 5, -51, -8, -53, 53, 3,
887 -56, 56, 55, 54, -54, 2, 60, -2, -55, 58, 9, -5, 59, 57, -57, -63,
888 -3, -58, -60, -61, 61, -59, -62, -9, 1, 64, 62, 69, -64, 63, 65, -67,
889 -68, 66, -65, 68, -66, -69, 67, -70, -1, 10, 71, -71, 4, 73, 72, 70,
890 6, -76, -3, 74, -78, -74, 1, 78, 80, -72, -75, 76, -1, 3, -73, 79,
891 75, 77, 1, 11, -4, -79, -10, -6, -1, -77, -83, -80, 2, 81, -84, -2,
892 83, -81, 82, -82, 84, -87, -86, 85, -11, -85, 86, -89, 87, -88, 88, 89}
898 {1, 1, 0, 2, 1, 2, 1, 3, 3, 1, 1, 4, 4, 2, 2, 1,
899 1, 5, 5, 6, 1, 6, 1, 7, 7, 3, 3, 2, 8, 2, 8, 1,
900 1, 0, 9, 9, 1, 1, 10, 4, 10, 4, 11, 11, 2, 1, 2, 1,
901 12, 12, 3, 3, 1, 1, 13, 5, 5, 13, 14, 1, 1, 14, 2, 2,
902 6, 6, 15, 1, 1, 15, 16, 4, 7, 16, 4, 7, 1, 1, 3, 3,
903 8, 8, 2, 2, 1, 1, 17, 17, 1, 1, 18, 18, 5, 5, 2, 2,
904 1, 1, 9, 19, 9, 19, 20, 3, 3, 20, 1, 10, 21, 1, 10, 4,
905 4, 21, 22, 6, 6, 22, 1, 1, 23, 24, 2, 2, 23, 24, 11, 1,
906 1, 11, 7, 25, 7, 1, 1, 25, 8, 8, 3, 26, 3, 1, 12, 2,
907 2, 26, 1, 12, 5, 5, 27, 4, 1, 4, 1, 27, 28, 1, 28, 13,
908 1, 13, 2, 29, 2, 1, 32, 6, 1, 30, 14, 29, 14, 6, 3, 31,
909 3, 1, 30, 1, 32, 31, 33, 9, 33, 1, 1, 7, 9, 7, 2, 2,
910 1, 1, 4, 36, 34, 4, 5, 10, 10, 5, 34, 1, 1, 35, 8, 8,
911 36, 3, 35, 1, 15, 3, 2, 1, 16, 15, 16, 2, 37, 1, 37, 1,
912 1, 1, 6, 6, 38, 1, 38, 11, 1, 39, 39, 40, 11, 2, 41, 4,
913 40, 1, 2, 4, 1, 1, 1, 41, 3, 1, 3, 1, 5, 7, 5, 7},
916 { 1, -1, 0, 1, 2, -1, -2, 1, -1, 3, -3, 1, -1, 2, -2, 4,
917 -4, 1, -1, 1, 5, -1, -5, 1, -1, 2, -2, 3, 1, -3, -1, 6,
918 -6, 0, 1, -1, 7, -7, 1, 2, -1, -2, 1, -1, 4, 8, -4, -8,
919 1, -1, 3, -3, 9, -9, 1, 2, -2, -1, 1, 10, -10, -1, 5, -5,
920 2, -2, 1, 11, -11, -1, 1, 3, 2, -1, -3, -2, 12, -12, 4, -4,
921 2, -2, -6, 6, 13, -13, 1, -1, 14, -14, 1, -1, 3, -3, 7, -7,
922 15, -15, 2, 1, -2, -1, 1, 5, -5, -1, -16, 2, 1, 16, -2, 4,
923 -4, -1, 1, 3, -3, -1, 17, -17, 1, 1, -8, 8, -1, -1, 2, 18,
924 -18, -2, 3, 1, -3, 19, -19, -1, 3, -3, 6, 1, -6, 20, 2, 9,
925 -9, -1, -20, -2, 4, -4, 1, -5, 21, 5, -21, -1, 1, -22, -1, 2,
926 22, -2, 10, 1, -10, 23, 1, 4, -23, 1, 2, -1, -2, -4, -7, 1,
927 7, -24, -1, 24, -1, -1, 1, 3, -1, -25, 25, 4, -3, -4, 11, -11,
928 26, -26, 6, 1, 1, -6, -5, -3, 3, 5, -1, -27, 27, 1, 4, -4,
929 -1, -8, -1, 28, 2, 8, -12, -28, -2, -2, 2, 12, -1, 29, 1, -29,
930 30, -30, 5, -5, 1, -31, -1, 3, 31, -1, 1, 1, -3, -13, 1, -7,
931 -1, -32, 13, 7, 32, 33, -33, -1, -9, -34, 9, 34, -6, 5, 6, -5}
937 {1, 1, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 0, 2, 2,
938 4, 1, 4, 1, 1, 1, 5, 5, 1, 1, 6, 6, 2, 2, 1, 1,
939 3, 3, 7, 7, 1, 1, 8, 8, 1, 1, 2, 2, 1, 9, 1, 9,
940 4, 4, 10, 1, 1, 10, 1, 1, 11, 11, 3, 3, 1, 2, 1, 2,
941 1, 1, 12, 12, 5, 5, 1, 1, 13, 1, 1, 13, 2, 2, 1, 1,
942 6, 6, 1, 1, 4, 14, 4, 14, 3, 1, 3, 1, 1, 1, 15, 7,
943 15, 2, 2, 7, 1, 1, 1, 8, 1, 8, 16, 16, 1, 1, 1, 1,
944 2, 1, 1, 2, 1, 1, 3, 5, 5, 3, 4, 1, 1, 4, 1, 1,
945 17, 17, 9, 1, 1, 9, 2, 2, 1, 1, 10, 10, 1, 6, 1, 1,
946 6, 18, 1, 1, 18, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 1,
947 4, 1, 19, 1, 19, 7, 1, 1, 20, 1, 4, 20, 1, 7, 11, 2,
948 1, 11, 21, 2, 8, 5, 1, 8, 1, 5, 21, 1, 1, 1, 22, 1,
949 1, 22, 1, 1, 3, 3, 1, 23, 2, 12, 24, 1, 1, 2, 1, 1,
950 12, 23, 1, 1, 24, 1, 1, 1, 4, 1, 1, 1, 2, 1, 6, 6,
951 4, 2, 1, 1, 1, 1, 1, 1, 1, 14, 13, 3, 1, 25, 9, 25,
952 14, 1, 9, 3, 13, 1, 1, 1, 1, 1, 10, 1, 1, 2, 10, 2},
955 {-20, -1, 0, 2, -2, 1, -1, 3, -3, 1, -1, 4, -4, 0, 2, -2,
956 1, 5, -1, -5, 6, -6, 1, -1, 7, -7, 1, -1, 3, -3, 8, -8,
957 2, -2, 1, -1, 9, -9, 1, -1, 10, -10, 4, -4, 11, 1, -11, -1,
958 2, -2, 1, 12, -12, -1, 13, -13, 1, -1, 3, -3, 14, 5, -14, -5,
959 -15, 15, -1, 1, 2, -2, 16, -16, 1, 17, -17, -1, 6, -6, 18, -18,
960 2, -2, -19, 19, -3, 1, 3, -1, 4, 20, -4, 1, -21, 21, 1, 2,
961 -1, -7, 7, -2, 22, -22, 23, 2, -23, -2, 1, -1, -24, 24, -25, 25,
962 -8, -26, 26, 8, -27, 27, 5, 3, -3, -5, -4, 28, -28, 4, 29, -29,
963 1, -1, -2, -30, 30, 2, 9, -9, -31, 31, 2, -2, -32, 3, 32, -33,
964 -3, 1, 33, -34, -1, 34, -35, 35, -10, 10, -6, 36, 6, -36, 37, -37,
965 -5, 38, 1, -38, -1, 3, 39, -39, -1, 40, 5, 1, -40, -3, 2, -11,
966 -41, -2, 1, 11, -3, -4, 41, 3, 42, 4, -1, -43, -42, 43, 1, -44,
967 45, -1, 44, -45, -7, 7, -46, 1, -12, 2, 1, -47, 46, 12, 47, 48,
968 -2, -1, -48, 49, -1, -50, -49, 50, -6, -51, 51, 52, -13, 53, -4, 4,
969 6, 13, -53, -52, -54, 55, 54, -55, -56, -2, 2, -8, 56, 1, -3, -1,
970 2, 58, 3, 8, -2, 57, -58, -60, -59, -57, -3, 60, 59, -14, 3, 14}
976 {1, 1, 0, 2, 2, 1, 1, 3, 3, 4, 4, 5, 5, 1, 1, 6,
977 6, 2, 2, 7, 7, 8, 8, 1, 1, 3, 3, 9, 9, 10, 10, 1,
978 1, 2, 2, 4, 4, 11, 0, 11, 12, 12, 13, 13, 1, 1, 5, 5,
979 14, 14, 15, 16, 15, 16, 3, 3, 1, 6, 1, 6, 2, 2, 7, 7,
980 8, 8, 17, 17, 1, 1, 4, 4, 18, 18, 2, 2, 1, 19, 1, 20,
981 19, 20, 21, 21, 3, 3, 22, 22, 5, 5, 24, 1, 1, 23, 9, 23,
982 24, 9, 2, 2, 10, 1, 1, 10, 6, 6, 25, 4, 4, 25, 7, 7,
983 26, 8, 1, 8, 3, 1, 26, 3, 11, 11, 27, 27, 2, 28, 1, 2,
984 28, 1, 12, 12, 5, 5, 29, 13, 13, 29, 32, 1, 1, 33, 31, 30,
985 32, 4, 30, 33, 4, 31, 3, 14, 1, 1, 3, 34, 34, 2, 2, 14,
986 6, 6, 35, 36, 35, 36, 1, 15, 1, 16, 16, 15, 7, 9, 7, 9,
987 37, 8, 8, 37, 1, 1, 39, 2, 38, 39, 2, 40, 5, 38, 40, 5,
988 3, 3, 4, 4, 10, 10, 1, 1, 1, 1, 41, 2, 41, 2, 6, 6,
989 1, 1, 11, 42, 11, 43, 3, 42, 3, 17, 4, 43, 1, 17, 7, 1,
990 8, 44, 4, 7, 44, 5, 8, 2, 5, 1, 2, 48, 45, 1, 12, 45,
991 12, 48, 13, 13, 1, 9, 9, 46, 1, 46, 47, 47, 49, 18, 18, 49},
994 { 1, -1, 0, 1, -1, 2, -2, 1, -1, 1, -1, 1, -1, 3, -3, 1,
995 -1, -2, 2, 1, -1, 1, -1, 4, -4, -2, 2, 1, -1, 1, -1, 5,
996 -5, -3, 3, 2, -2, 1, 0, -1, 1, -1, 1, -1, 6, -6, 2, -2,
997 1, -1, 1, 1, -1, -1, -3, 3, 7, 2, -7, -2, -4, 4, 2, -2,
998 2, -2, 1, -1, 8, -8, 3, -3, 1, -1, -5, 5, 9, 1, -9, 1,
999 -1, -1, 1, -1, -4, 4, 1, -1, 3, -3, 1, -10, 10, 1, 2, -1,
1000 -1, -2, 6, -6, 2, 11, -11, -2, 3, -3, 1, -4, 4, -1, 3, -3,
1001 1, 3, 12, -3, -5, -12, -1, 5, 2, -2, 1, -1, -7, 1, 13, 7,
1002 -1, -13, 2, -2, 4, -4, 1, 2, -2, -1, 1, 14, -14, 1, 1, 1,
1003 -1, -5, -1, -1, 5, -1, -6, 2, -15, 15, 6, 1, -1, -8, 8, -2,
1004 -4, 4, 1, 1, -1, -1, 16, 2, -16, -2, 2, -2, 4, 3, -4, -3,
1005 -1, -4, 4, 1, -17, 17, -1, -9, 1, 1, 9, 1, -5, -1, -1, 5,
1006 -7, 7, 6, -6, 3, -3, 18, -18, 19, -19, 1, -10, -1, 10, -5, 5,
1007 20, -20, -3, 1, 3, 1, 8, -1, -8, 2, 7, -1, -21, -2, 5, 21,
1008 5, -1, -7, -5, 1, -6, -5, -11, 6, 22, 11, 1, 1, -22, -3, -1,
1009 3, -1, 3, -3, -23, 4, -4, 1, 23, -1, 1, -1, 1, -2, 2, -1}
1015 {1, 1, 1, 1, 0, 2, 2, 1, 1, 3, 3, 0, 1, 1, 2, 2,
1016 4, 4, 1, 1, 5, 5, 1, 1, 2, 2, 3, 3, 6, 6, 1, 1,
1017 7, 7, 8, 1, 8, 2, 2, 1, 4, 4, 1, 3, 1, 3, 9, 9,
1018 2, 2, 1, 5, 1, 5, 10, 10, 1, 1, 11, 11, 3, 6, 3, 4,
1019 4, 6, 2, 2, 1, 12, 1, 12, 7, 13, 7, 13, 1, 1, 8, 8,
1020 2, 2, 14, 14, 16, 15, 16, 5, 5, 1, 3, 15, 1, 3, 4, 4,
1021 1, 1, 17, 17, 2, 2, 6, 6, 1, 18, 1, 18, 22, 21, 22, 21,
1022 25, 24, 25, 19, 9, 20, 9, 23, 19, 24, 20, 3, 23, 7, 3, 1,
1023 1, 7, 28, 26, 29, 5, 28, 26, 5, 8, 29, 4, 8, 27, 2, 2,
1024 4, 27, 1, 1, 10, 36, 10, 33, 33, 36, 30, 1, 32, 32, 1, 30,
1025 6, 31, 31, 35, 3, 6, 11, 11, 3, 2, 35, 2, 34, 1, 34, 1,
1026 37, 37, 12, 7, 12, 5, 41, 5, 4, 7, 1, 8, 13, 4, 1, 41,
1027 13, 38, 8, 38, 9, 1, 40, 40, 9, 1, 39, 2, 2, 49, 39, 42,
1028 3, 3, 14, 16, 49, 14, 16, 42, 43, 43, 6, 6, 15, 1, 1, 15,
1029 44, 44, 1, 1, 50, 48, 4, 5, 4, 7, 5, 2, 10, 10, 48, 7,
1030 50, 45, 2, 1, 45, 8, 8, 1, 46, 46, 3, 47, 47, 3, 1, 1},
1033 { 1, -1, 2, -2, 0, 1, -1, 3, -3, 1, -1, 0, 4, -4, 2, -2,
1034 1, -1, 5, -5, 1, -1, 6, -6, 3, -3, 2, -2, 1, -1, 7, -7,
1035 1, -1, 1, 8, -1, 4, -4, -8, 2, -2, 9, 3, -9, -3, 1, -1,
1036 5, -5, 10, 2, -10, -2, 1, -1, 11, -11, 1, -1, -4, 2, 4, 3,
1037 -3, -2, 6, -6, 12, 1, -12, -1, 2, 1, -2, -1, 13, -13, 2, -2,
1038 7, -7, 1, -1, 1, 1, -1, 3, -3, 14, 5, -1, -14, -5, 4, -4,
1039 15, -15, 1, -1, 8, -8, -3, 3, 16, 1, -16, -1, 1, 1, -1, -1,
1040 1, 1, -1, 1, 2, 1, -2, 1, -1, -1, -1, 6, -1, 3, -6, 17,
1041 -17, -3, 1, 1, 1, 4, -1, -1, -4, 3, -1, 5, -3, -1, -9, 9,
1042 -5, 1, 18, -18, 2, 1, -2, 1, -1, -1, 1, 19, -1, 1, -19, -1,
1043 4, 1, -1, 1, 7, -4, -2, 2, -7, 10, -1, -10, 1, 20, -1, -20,
1044 1, -1, 2, 4, -2, 5, 1, -5, 6, -4, 21, 4, 2, -6, -21, -1,
1045 -2, 1, -4, -1, -3, 22, -1, 1, 3, -22, -1, 11, -11, 1, 1, 1,
1046 8, -8, 2, 2, -1, -2, -2, -1, 1, -1, -5, 5, 2, 23, -23, -2,
1047 1, -1, 24, -24, -1, -1, 7, 6, -7, 5, -6, 12, -3, 3, 1, -5,
1048 1, 1, -12, 25, -1, -5, 5, -25, -1, 1, 9, 1, -1, -9, 26, -26}