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ffmpeg/libavcodec/aom_film_grain.c
Niklas Haas f50382cba6 avcodec/aom_film_grain: implement AFGS1 parsing 
Based on the AOMedia Film Grain Synthesis 1 (AFGS1) spec:
  https://aomediacodec.github.io/afgs1-spec/

The parsing has been changed substantially relative to the AV1 film
grain OBU. In particular:

1. There is the possibility of maintaining multiple independent film
   grain parameter sets, and decoders/players are recommended to pick
   the one most appropriate for the intended display resolution. This
   could also be used to e.g. switch between different grain profiles
   without having to re-signal the appropriate coefficients.

2. Supporting this, it's possible to *predict* the grain coefficients
   from previously signalled parameter sets, transmitting only the
   residual.

3. When not predicting, the parameter sets are now stored as a series of
   increments, rather than being directly transmitted.

4. There are several new AFGS1-exclusive fields.

I placed this parser in its own file, rather than h2645_sei.c, since
nothing in the generic AFGS1 film grain payload is specific to T.35, and
to compartmentalize the code base.
2024-03-23 18:55:21 +01:00

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/*
* AOM film grain synthesis
* Copyright (c) 2023 Niklas Haas <ffmpeg@haasn.xyz>
*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
/**
* @file
* AOM film grain synthesis.
* @author Niklas Haas <ffmpeg@haasn.xyz>
*/
#include "libavutil/avassert.h"
#include "libavutil/imgutils.h"
#include "aom_film_grain.h"
#include "get_bits.h"
// Common/shared helpers (not dependent on BIT_DEPTH)
static inline int get_random_number(const int bits, unsigned *const state) {
const int r = *state;
unsigned bit = ((r >> 0) ^ (r >> 1) ^ (r >> 3) ^ (r >> 12)) & 1;
*state = (r >> 1) | (bit << 15);
return (*state >> (16 - bits)) & ((1 << bits) - 1);
}
static inline int round2(const int x, const uint64_t shift) {
return (x + ((1 << shift) >> 1)) >> shift;
}
enum {
GRAIN_WIDTH = 82,
GRAIN_HEIGHT = 73,
SUB_GRAIN_WIDTH = 44,
SUB_GRAIN_HEIGHT = 38,
FG_BLOCK_SIZE = 32,
};
static const int16_t gaussian_sequence[2048];
#define BIT_DEPTH 16
#include "aom_film_grain_template.c"
#undef BIT_DEPTH
#define BIT_DEPTH 8
#include "aom_film_grain_template.c"
#undef BIT_DEPTH
int ff_aom_apply_film_grain(AVFrame *out, const AVFrame *in,
const AVFilmGrainParams *params)
{
const AVFilmGrainAOMParams *const data = &params->codec.aom;
const AVPixFmtDescriptor *desc = av_pix_fmt_desc_get(out->format);
const int subx = desc->log2_chroma_w, suby = desc->log2_chroma_h;
const int pxstep = desc->comp[0].step;
av_assert0(out->format == in->format);
av_assert0(params->type == AV_FILM_GRAIN_PARAMS_AV1);
// Copy over the non-modified planes
if (!params->codec.aom.num_y_points) {
av_image_copy_plane(out->data[0], out->linesize[0],
in->data[0], in->linesize[0],
out->width * pxstep, out->height);
}
for (int uv = 0; uv < 2; uv++) {
if (!data->num_uv_points[uv]) {
av_image_copy_plane(out->data[1+uv], out->linesize[1+uv],
in->data[1+uv], in->linesize[1+uv],
AV_CEIL_RSHIFT(out->width, subx) * pxstep,
AV_CEIL_RSHIFT(out->height, suby));
}
}
switch (in->format) {
case AV_PIX_FMT_GRAY8:
case AV_PIX_FMT_YUV420P:
case AV_PIX_FMT_YUV422P:
case AV_PIX_FMT_YUV444P:
case AV_PIX_FMT_YUVJ420P:
case AV_PIX_FMT_YUVJ422P:
case AV_PIX_FMT_YUVJ444P:
return apply_film_grain_8(out, in, params);
case AV_PIX_FMT_GRAY9:
case AV_PIX_FMT_YUV420P9:
case AV_PIX_FMT_YUV422P9:
case AV_PIX_FMT_YUV444P9:
return apply_film_grain_16(out, in, params, 9);
case AV_PIX_FMT_GRAY10:
case AV_PIX_FMT_YUV420P10:
case AV_PIX_FMT_YUV422P10:
case AV_PIX_FMT_YUV444P10:
return apply_film_grain_16(out, in, params, 10);
case AV_PIX_FMT_GRAY12:
case AV_PIX_FMT_YUV420P12:
case AV_PIX_FMT_YUV422P12:
case AV_PIX_FMT_YUV444P12:
return apply_film_grain_16(out, in, params, 12);
}
/* The AV1 spec only defines film grain synthesis for these formats */
return AVERROR_INVALIDDATA;
}
int ff_aom_parse_film_grain_sets(AVFilmGrainAFGS1Params *s,
const uint8_t *payload, int payload_size)
{
GetBitContext gbc, *gb = &gbc;
AVFilmGrainAOMParams *aom;
AVFilmGrainParams *fgp, *ref = NULL;
int ret, num_sets, n, i, uv, num_y_coeffs, update_grain, luma_only;
ret = init_get_bits8(gb, payload, payload_size);
if (ret < 0)
return ret;
s->enable = get_bits1(gb);
if (!s->enable)
return 0;
skip_bits(gb, 4); // reserved
num_sets = get_bits(gb, 3) + 1;
for (n = 0; n < num_sets; n++) {
int payload_4byte, payload_size, set_idx, apply_units_log2, vsc_flag;
int predict_scaling, predict_y_scaling, predict_uv_scaling[2];
int payload_bits, start_position;
start_position = get_bits_count(gb);
payload_4byte = get_bits1(gb);
payload_size = get_bits(gb, payload_4byte ? 2 : 8);
set_idx = get_bits(gb, 3);
fgp = &s->sets[set_idx];
aom = &fgp->codec.aom;
fgp->type = get_bits1(gb) ? AV_FILM_GRAIN_PARAMS_AV1 : AV_FILM_GRAIN_PARAMS_NONE;
if (!fgp->type)
continue;
fgp->seed = get_bits(gb, 16);
update_grain = get_bits1(gb);
if (!update_grain)
continue;
apply_units_log2 = get_bits(gb, 4);
fgp->width = get_bits(gb, 12) << apply_units_log2;
fgp->height = get_bits(gb, 12) << apply_units_log2;
luma_only = get_bits1(gb);
if (luma_only) {
fgp->subsampling_x = fgp->subsampling_y = 0;
} else {
fgp->subsampling_x = get_bits1(gb);
fgp->subsampling_y = get_bits1(gb);
}
fgp->bit_depth_luma = fgp->bit_depth_chroma = 0;
fgp->color_primaries = AVCOL_PRI_UNSPECIFIED;
fgp->color_trc = AVCOL_TRC_UNSPECIFIED;
fgp->color_space = AVCOL_SPC_UNSPECIFIED;
fgp->color_range = AVCOL_RANGE_UNSPECIFIED;
vsc_flag = get_bits1(gb); // video_signal_characteristics_flag
if (vsc_flag) {
int cicp_flag;
fgp->bit_depth_luma = get_bits(gb, 3) + 8;
if (!luma_only)
fgp->bit_depth_chroma = fgp->bit_depth_luma;
cicp_flag = get_bits1(gb);
if (cicp_flag) {
fgp->color_primaries = get_bits(gb, 8);
fgp->color_trc = get_bits(gb, 8);
fgp->color_space = get_bits(gb, 8);
fgp->color_range = get_bits1(gb) ? AVCOL_RANGE_JPEG : AVCOL_RANGE_MPEG;
if (fgp->color_primaries > AVCOL_PRI_NB ||
fgp->color_primaries == AVCOL_PRI_RESERVED ||
fgp->color_primaries == AVCOL_PRI_RESERVED0 ||
fgp->color_trc > AVCOL_TRC_NB ||
fgp->color_trc == AVCOL_TRC_RESERVED ||
fgp->color_trc == AVCOL_TRC_RESERVED0 ||
fgp->color_space > AVCOL_SPC_NB ||
fgp->color_space == AVCOL_SPC_RESERVED)
goto error;
}
}
predict_scaling = get_bits1(gb);
if (predict_scaling && (!ref || ref == fgp))
goto error; // prediction must be from valid, different set
predict_y_scaling = predict_scaling ? get_bits1(gb) : 0;
if (predict_y_scaling) {
int y_scale, y_offset, bits_res;
y_scale = get_bits(gb, 9) - 256;
y_offset = get_bits(gb, 9) - 256;
bits_res = get_bits(gb, 3);
if (bits_res) {
int res[14], pred, granularity;
aom->num_y_points = ref->codec.aom.num_y_points;
for (i = 0; i < aom->num_y_points; i++)
res[i] = get_bits(gb, bits_res);
granularity = get_bits(gb, 3);
for (i = 0; i < aom->num_y_points; i++) {
pred = ref->codec.aom.y_points[i][1];
pred = ((pred * y_scale + 8) >> 4) + y_offset;
pred += (res[i] - (1 << (bits_res - 1))) * granularity;
aom->y_points[i][0] = ref->codec.aom.y_points[i][0];
aom->y_points[i][1] = av_clip_uint8(pred);
}
}
} else {
aom->num_y_points = get_bits(gb, 4);
if (aom->num_y_points > 14) {
goto error;
} else if (aom->num_y_points) {
int bits_inc, bits_scaling;
int y_value = 0;
bits_inc = get_bits(gb, 3) + 1;
bits_scaling = get_bits(gb, 2) + 5;
for (i = 0; i < aom->num_y_points; i++) {
y_value += get_bits(gb, bits_inc);
if (y_value > UINT8_MAX)
goto error;
aom->y_points[i][0] = y_value;
aom->y_points[i][1] = get_bits(gb, bits_scaling);
}
}
}
if (luma_only) {
aom->chroma_scaling_from_luma = 0;
aom->num_uv_points[0] = aom->num_uv_points[1] = 0;
} else {
aom->chroma_scaling_from_luma = get_bits1(gb);
if (aom->chroma_scaling_from_luma) {
aom->num_uv_points[0] = aom->num_uv_points[1] = 0;
} else {
for (uv = 0; uv < 2; uv++) {
predict_uv_scaling[uv] = predict_scaling ? get_bits1(gb) : 0;
if (predict_uv_scaling[uv]) {
int uv_scale, uv_offset, bits_res;
uv_scale = get_bits(gb, 9) - 256;
uv_offset = get_bits(gb, 9) - 256;
bits_res = get_bits(gb, 3);
aom->uv_mult[uv] = ref->codec.aom.uv_mult[uv];
aom->uv_mult_luma[uv] = ref->codec.aom.uv_mult_luma[uv];
aom->uv_offset[uv] = ref->codec.aom.uv_offset[uv];
if (bits_res) {
int res[10], pred, granularity;
aom->num_uv_points[uv] = ref->codec.aom.num_uv_points[uv];
for (i = 0; i < aom->num_uv_points[uv]; i++)
res[i] = get_bits(gb, bits_res);
granularity = get_bits(gb, 3);
for (i = 0; i < aom->num_uv_points[uv]; i++) {
pred = ref->codec.aom.uv_points[uv][i][1];
pred = ((pred * uv_scale + 8) >> 4) + uv_offset;
pred += (res[i] - (1 << (bits_res - 1))) * granularity;
aom->uv_points[uv][i][0] = ref->codec.aom.uv_points[uv][i][0];
aom->uv_points[uv][i][1] = av_clip_uint8(pred);
}
}
} else {
int bits_inc, bits_scaling, uv_offset;
int uv_value = 0;
aom->num_uv_points[uv] = get_bits(gb, 4);
if (aom->num_uv_points[uv] > 10)
goto error;
bits_inc = get_bits(gb, 3) + 1;
bits_scaling = get_bits(gb, 2) + 5;
uv_offset = get_bits(gb, 8);
for (i = 0; i < aom->num_uv_points[uv]; i++) {
uv_value += get_bits(gb, bits_inc);
if (uv_value > UINT8_MAX)
goto error;
aom->uv_points[uv][i][0] = uv_value;
aom->uv_points[uv][i][1] = get_bits(gb, bits_scaling) + uv_offset;
}
}
}
}
}
aom->scaling_shift = get_bits(gb, 2) + 8;
aom->ar_coeff_lag = get_bits(gb, 2);
num_y_coeffs = 2 * aom->ar_coeff_lag * (aom->ar_coeff_lag + 1);
if (aom->num_y_points) {
int ar_bits = get_bits(gb, 2) + 5;
for (i = 0; i < num_y_coeffs; i++)
aom->ar_coeffs_y[i] = get_bits(gb, ar_bits) - (1 << (ar_bits - 1));
}
for (uv = 0; uv < 2; uv++) {
if (aom->chroma_scaling_from_luma || aom->num_uv_points[uv]) {
int ar_bits = get_bits(gb, 2) + 5;
for (i = 0; i < num_y_coeffs + !!aom->num_y_points; i++)
aom->ar_coeffs_uv[uv][i] = get_bits(gb, ar_bits) - (1 << (ar_bits - 1));
}
}
aom->ar_coeff_shift = get_bits(gb, 2) + 6;
aom->grain_scale_shift = get_bits(gb, 2);
for (uv = 0; uv < 2; uv++) {
if (aom->num_uv_points[uv] && !predict_uv_scaling[uv]) {
aom->uv_mult[uv] = get_bits(gb, 8) - 128;
aom->uv_mult_luma[uv] = get_bits(gb, 8) - 128;
aom->uv_offset[uv] = get_bits(gb, 9) - 256;
}
}
aom->overlap_flag = get_bits1(gb);
aom->limit_output_range = get_bits1(gb);
// use first set as reference only if it was fully transmitted
if (n == 0)
ref = fgp;
payload_bits = get_bits_count(gb) - start_position;
if (payload_bits > payload_size * 8)
goto error;
skip_bits(gb, payload_size * 8 - payload_bits);
}
return 0;
error:
memset(s, 0, sizeof(*s));
return AVERROR_INVALIDDATA;
}
int ff_aom_attach_film_grain_sets(const AVFilmGrainAFGS1Params *s, AVFrame *frame)
{
AVFilmGrainParams *fgp;
if (!s->enable)
return 0;
for (int i = 0; i < FF_ARRAY_ELEMS(s->sets); i++) {
if (s->sets[i].type != AV_FILM_GRAIN_PARAMS_AV1)
continue;
fgp = av_film_grain_params_create_side_data(frame);
if (!fgp)
return AVERROR(ENOMEM);
memcpy(fgp, &s->sets[i], sizeof(*fgp));
}
return 0;
}
// Taken from the AV1 spec. Range is [-2048, 2047], mean is 0 and stddev is 512
static const int16_t gaussian_sequence[2048] = {
56, 568, -180, 172, 124, -84, 172, -64, -900, 24, 820,
224, 1248, 996, 272, -8, -916, -388, -732, -104, -188, 800,
112, -652, -320, -376, 140, -252, 492, -168, 44, -788, 588,
-584, 500, -228, 12, 680, 272, -476, 972, -100, 652, 368,
432, -196, -720, -192, 1000, -332, 652, -136, -552, -604, -4,
192, -220, -136, 1000, -52, 372, -96, -624, 124, -24, 396,
540, -12, -104, 640, 464, 244, -208, -84, 368, -528, -740,
248, -968, -848, 608, 376, -60, -292, -40, -156, 252, -292,
248, 224, -280, 400, -244, 244, -60, 76, -80, 212, 532,
340, 128, -36, 824, -352, -60, -264, -96, -612, 416, -704,
220, -204, 640, -160, 1220, -408, 900, 336, 20, -336, -96,
-792, 304, 48, -28, -1232, -1172, -448, 104, -292, -520, 244,
60, -948, 0, -708, 268, 108, 356, -548, 488, -344, -136,
488, -196, -224, 656, -236, -1128, 60, 4, 140, 276, -676,
-376, 168, -108, 464, 8, 564, 64, 240, 308, -300, -400,
-456, -136, 56, 120, -408, -116, 436, 504, -232, 328, 844,
-164, -84, 784, -168, 232, -224, 348, -376, 128, 568, 96,
-1244, -288, 276, 848, 832, -360, 656, 464, -384, -332, -356,
728, -388, 160, -192, 468, 296, 224, 140, -776, -100, 280,
4, 196, 44, -36, -648, 932, 16, 1428, 28, 528, 808,
772, 20, 268, 88, -332, -284, 124, -384, -448, 208, -228,
-1044, -328, 660, 380, -148, -300, 588, 240, 540, 28, 136,
-88, -436, 256, 296, -1000, 1400, 0, -48, 1056, -136, 264,
-528, -1108, 632, -484, -592, -344, 796, 124, -668, -768, 388,
1296, -232, -188, -200, -288, -4, 308, 100, -168, 256, -500,
204, -508, 648, -136, 372, -272, -120, -1004, -552, -548, -384,
548, -296, 428, -108, -8, -912, -324, -224, -88, -112, -220,
-100, 996, -796, 548, 360, -216, 180, 428, -200, -212, 148,
96, 148, 284, 216, -412, -320, 120, -300, -384, -604, -572,
-332, -8, -180, -176, 696, 116, -88, 628, 76, 44, -516,
240, -208, -40, 100, -592, 344, -308, -452, -228, 20, 916,
-1752, -136, -340, -804, 140, 40, 512, 340, 248, 184, -492,
896, -156, 932, -628, 328, -688, -448, -616, -752, -100, 560,
-1020, 180, -800, -64, 76, 576, 1068, 396, 660, 552, -108,
-28, 320, -628, 312, -92, -92, -472, 268, 16, 560, 516,
-672, -52, 492, -100, 260, 384, 284, 292, 304, -148, 88,
-152, 1012, 1064, -228, 164, -376, -684, 592, -392, 156, 196,
-524, -64, -884, 160, -176, 636, 648, 404, -396, -436, 864,
424, -728, 988, -604, 904, -592, 296, -224, 536, -176, -920,
436, -48, 1176, -884, 416, -776, -824, -884, 524, -548, -564,
-68, -164, -96, 692, 364, -692, -1012, -68, 260, -480, 876,
-1116, 452, -332, -352, 892, -1088, 1220, -676, 12, -292, 244,
496, 372, -32, 280, 200, 112, -440, -96, 24, -644, -184,
56, -432, 224, -980, 272, -260, 144, -436, 420, 356, 364,
-528, 76, 172, -744, -368, 404, -752, -416, 684, -688, 72,
540, 416, 92, 444, 480, -72, -1416, 164, -1172, -68, 24,
424, 264, 1040, 128, -912, -524, -356, 64, 876, -12, 4,
-88, 532, 272, -524, 320, 276, -508, 940, 24, -400, -120,
756, 60, 236, -412, 100, 376, -484, 400, -100, -740, -108,
-260, 328, -268, 224, -200, -416, 184, -604, -564, -20, 296,
60, 892, -888, 60, 164, 68, -760, 216, -296, 904, -336,
-28, 404, -356, -568, -208, -1480, -512, 296, 328, -360, -164,
-1560, -776, 1156, -428, 164, -504, -112, 120, -216, -148, -264,
308, 32, 64, -72, 72, 116, 176, -64, -272, 460, -536,
-784, -280, 348, 108, -752, -132, 524, -540, -776, 116, -296,
-1196, -288, -560, 1040, -472, 116, -848, -1116, 116, 636, 696,
284, -176, 1016, 204, -864, -648, -248, 356, 972, -584, -204,
264, 880, 528, -24, -184, 116, 448, -144, 828, 524, 212,
-212, 52, 12, 200, 268, -488, -404, -880, 824, -672, -40,
908, -248, 500, 716, -576, 492, -576, 16, 720, -108, 384,
124, 344, 280, 576, -500, 252, 104, -308, 196, -188, -8,
1268, 296, 1032, -1196, 436, 316, 372, -432, -200, -660, 704,
-224, 596, -132, 268, 32, -452, 884, 104, -1008, 424, -1348,
-280, 4, -1168, 368, 476, 696, 300, -8, 24, 180, -592,
-196, 388, 304, 500, 724, -160, 244, -84, 272, -256, -420,
320, 208, -144, -156, 156, 364, 452, 28, 540, 316, 220,
-644, -248, 464, 72, 360, 32, -388, 496, -680, -48, 208,
-116, -408, 60, -604, -392, 548, -840, 784, -460, 656, -544,
-388, -264, 908, -800, -628, -612, -568, 572, -220, 164, 288,
-16, -308, 308, -112, -636, -760, 280, -668, 432, 364, 240,
-196, 604, 340, 384, 196, 592, -44, -500, 432, -580, -132,
636, -76, 392, 4, -412, 540, 508, 328, -356, -36, 16,
-220, -64, -248, -60, 24, -192, 368, 1040, 92, -24, -1044,
-32, 40, 104, 148, 192, -136, -520, 56, -816, -224, 732,
392, 356, 212, -80, -424, -1008, -324, 588, -1496, 576, 460,
-816, -848, 56, -580, -92, -1372, -112, -496, 200, 364, 52,
-140, 48, -48, -60, 84, 72, 40, 132, -356, -268, -104,
-284, -404, 732, -520, 164, -304, -540, 120, 328, -76, -460,
756, 388, 588, 236, -436, -72, -176, -404, -316, -148, 716,
-604, 404, -72, -88, -888, -68, 944, 88, -220, -344, 960,
472, 460, -232, 704, 120, 832, -228, 692, -508, 132, -476,
844, -748, -364, -44, 1116, -1104, -1056, 76, 428, 552, -692,
60, 356, 96, -384, -188, -612, -576, 736, 508, 892, 352,
-1132, 504, -24, -352, 324, 332, -600, -312, 292, 508, -144,
-8, 484, 48, 284, -260, -240, 256, -100, -292, -204, -44,
472, -204, 908, -188, -1000, -256, 92, 1164, -392, 564, 356,
652, -28, -884, 256, 484, -192, 760, -176, 376, -524, -452,
-436, 860, -736, 212, 124, 504, -476, 468, 76, -472, 552,
-692, -944, -620, 740, -240, 400, 132, 20, 192, -196, 264,
-668, -1012, -60, 296, -316, -828, 76, -156, 284, -768, -448,
-832, 148, 248, 652, 616, 1236, 288, -328, -400, -124, 588,
220, 520, -696, 1032, 768, -740, -92, -272, 296, 448, -464,
412, -200, 392, 440, -200, 264, -152, -260, 320, 1032, 216,
320, -8, -64, 156, -1016, 1084, 1172, 536, 484, -432, 132,
372, -52, -256, 84, 116, -352, 48, 116, 304, -384, 412,
924, -300, 528, 628, 180, 648, 44, -980, -220, 1320, 48,
332, 748, 524, -268, -720, 540, -276, 564, -344, -208, -196,
436, 896, 88, -392, 132, 80, -964, -288, 568, 56, -48,
-456, 888, 8, 552, -156, -292, 948, 288, 128, -716, -292,
1192, -152, 876, 352, -600, -260, -812, -468, -28, -120, -32,
-44, 1284, 496, 192, 464, 312, -76, -516, -380, -456, -1012,
-48, 308, -156, 36, 492, -156, -808, 188, 1652, 68, -120,
-116, 316, 160, -140, 352, 808, -416, 592, 316, -480, 56,
528, -204, -568, 372, -232, 752, -344, 744, -4, 324, -416,
-600, 768, 268, -248, -88, -132, -420, -432, 80, -288, 404,
-316, -1216, -588, 520, -108, 92, -320, 368, -480, -216, -92,
1688, -300, 180, 1020, -176, 820, -68, -228, -260, 436, -904,
20, 40, -508, 440, -736, 312, 332, 204, 760, -372, 728,
96, -20, -632, -520, -560, 336, 1076, -64, -532, 776, 584,
192, 396, -728, -520, 276, -188, 80, -52, -612, -252, -48,
648, 212, -688, 228, -52, -260, 428, -412, -272, -404, 180,
816, -796, 48, 152, 484, -88, -216, 988, 696, 188, -528,
648, -116, -180, 316, 476, 12, -564, 96, 476, -252, -364,
-376, -392, 556, -256, -576, 260, -352, 120, -16, -136, -260,
-492, 72, 556, 660, 580, 616, 772, 436, 424, -32, -324,
-1268, 416, -324, -80, 920, 160, 228, 724, 32, -516, 64,
384, 68, -128, 136, 240, 248, -204, -68, 252, -932, -120,
-480, -628, -84, 192, 852, -404, -288, -132, 204, 100, 168,
-68, -196, -868, 460, 1080, 380, -80, 244, 0, 484, -888,
64, 184, 352, 600, 460, 164, 604, -196, 320, -64, 588,
-184, 228, 12, 372, 48, -848, -344, 224, 208, -200, 484,
128, -20, 272, -468, -840, 384, 256, -720, -520, -464, -580,
112, -120, 644, -356, -208, -608, -528, 704, 560, -424, 392,
828, 40, 84, 200, -152, 0, -144, 584, 280, -120, 80,
-556, -972, -196, -472, 724, 80, 168, -32, 88, 160, -688,
0, 160, 356, 372, -776, 740, -128, 676, -248, -480, 4,
-364, 96, 544, 232, -1032, 956, 236, 356, 20, -40, 300,
24, -676, -596, 132, 1120, -104, 532, -1096, 568, 648, 444,
508, 380, 188, -376, -604, 1488, 424, 24, 756, -220, -192,
716, 120, 920, 688, 168, 44, -460, 568, 284, 1144, 1160,
600, 424, 888, 656, -356, -320, 220, 316, -176, -724, -188,
-816, -628, -348, -228, -380, 1012, -452, -660, 736, 928, 404,
-696, -72, -268, -892, 128, 184, -344, -780, 360, 336, 400,
344, 428, 548, -112, 136, -228, -216, -820, -516, 340, 92,
-136, 116, -300, 376, -244, 100, -316, -520, -284, -12, 824,
164, -548, -180, -128, 116, -924, -828, 268, -368, -580, 620,
192, 160, 0, -1676, 1068, 424, -56, -360, 468, -156, 720,
288, -528, 556, -364, 548, -148, 504, 316, 152, -648, -620,
-684, -24, -376, -384, -108, -920, -1032, 768, 180, -264, -508,
-1268, -260, -60, 300, -240, 988, 724, -376, -576, -212, -736,
556, 192, 1092, -620, -880, 376, -56, -4, -216, -32, 836,
268, 396, 1332, 864, -600, 100, 56, -412, -92, 356, 180,
884, -468, -436, 292, -388, -804, -704, -840, 368, -348, 140,
-724, 1536, 940, 372, 112, -372, 436, -480, 1136, 296, -32,
-228, 132, -48, -220, 868, -1016, -60, -1044, -464, 328, 916,
244, 12, -736, -296, 360, 468, -376, -108, -92, 788, 368,
-56, 544, 400, -672, -420, 728, 16, 320, 44, -284, -380,
-796, 488, 132, 204, -596, -372, 88, -152, -908, -636, -572,
-624, -116, -692, -200, -56, 276, -88, 484, -324, 948, 864,
1000, -456, -184, -276, 292, -296, 156, 676, 320, 160, 908,
-84, -1236, -288, -116, 260, -372, -644, 732, -756, -96, 84,
344, -520, 348, -688, 240, -84, 216, -1044, -136, -676, -396,
-1500, 960, -40, 176, 168, 1516, 420, -504, -344, -364, -360,
1216, -940, -380, -212, 252, -660, -708, 484, -444, -152, 928,
-120, 1112, 476, -260, 560, -148, -344, 108, -196, 228, -288,
504, 560, -328, -88, 288, -1008, 460, -228, 468, -836, -196,
76, 388, 232, 412, -1168, -716, -644, 756, -172, -356, -504,
116, 432, 528, 48, 476, -168, -608, 448, 160, -532, -272,
28, -676, -12, 828, 980, 456, 520, 104, -104, 256, -344,
-4, -28, -368, -52, -524, -572, -556, -200, 768, 1124, -208,
-512, 176, 232, 248, -148, -888, 604, -600, -304, 804, -156,
-212, 488, -192, -804, -256, 368, -360, -916, -328, 228, -240,
-448, -472, 856, -556, -364, 572, -12, -156, -368, -340, 432,
252, -752, -152, 288, 268, -580, -848, -592, 108, -76, 244,
312, -716, 592, -80, 436, 360, 4, -248, 160, 516, 584,
732, 44, -468, -280, -292, -156, -588, 28, 308, 912, 24,
124, 156, 180, -252, 944, -924, -772, -520, -428, -624, 300,
-212, -1144, 32, -724, 800, -1128, -212, -1288, -848, 180, -416,
440, 192, -576, -792, -76, -1080, 80, -532, -352, -132, 380,
-820, 148, 1112, 128, 164, 456, 700, -924, 144, -668, -384,
648, -832, 508, 552, -52, -100, -656, 208, -568, 748, -88,
680, 232, 300, 192, -408, -1012, -152, -252, -268, 272, -876,
-664, -648, -332, -136, 16, 12, 1152, -28, 332, -536, 320,
-672, -460, -316, 532, -260, 228, -40, 1052, -816, 180, 88,
-496, -556, -672, -368, 428, 92, 356, 404, -408, 252, 196,
-176, -556, 792, 268, 32, 372, 40, 96, -332, 328, 120,
372, -900, -40, 472, -264, -592, 952, 128, 656, 112, 664,
-232, 420, 4, -344, -464, 556, 244, -416, -32, 252, 0,
-412, 188, -696, 508, -476, 324, -1096, 656, -312, 560, 264,
-136, 304, 160, -64, -580, 248, 336, -720, 560, -348, -288,
-276, -196, -500, 852, -544, -236, -1128, -992, -776, 116, 56,
52, 860, 884, 212, -12, 168, 1020, 512, -552, 924, -148,
716, 188, 164, -340, -520, -184, 880, -152, -680, -208, -1156,
-300, -528, -472, 364, 100, -744, -1056, -32, 540, 280, 144,
-676, -32, -232, -280, -224, 96, 568, -76, 172, 148, 148,
104, 32, -296, -32, 788, -80, 32, -16, 280, 288, 944,
428, -484
};
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