/* -----------------------------------------------------------------------------
The copyright in this software is being made available under the Clear BSD
License, included below. No patent rights, trademark rights and/or 
other Intellectual Property Rights other than the copyrights concerning 
the Software are granted under this license.

The Clear BSD License

Copyright (c) 2019-2024, Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. & The VVenC Authors.
All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
are permitted (subject to the limitations in the disclaimer below) provided that
the following conditions are met:

     * Redistributions of source code must retain the above copyright notice,
     this list of conditions and the following disclaimer.

     * Redistributions in binary form must reproduce the above copyright
     notice, this list of conditions and the following disclaimer in the
     documentation and/or other materials provided with the distribution.

     * Neither the name of the copyright holder nor the names of its
     contributors may be used to endorse or promote products derived from this
     software without specific prior written permission.

NO EXPRESS OR IMPLIED LICENSES TO ANY PARTY'S PATENT RIGHTS ARE GRANTED BY
THIS LICENSE. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.


------------------------------------------------------------------------------------------- */


/** \file     RomNSST.cpp
    \brief    Transformations
*/

#include "Rom.h"

//! \ingroup CommonLib
//! \{

namespace vvenc {

// DCT-2
#define DEFINE_DCT2_P2_MATRIX(a) \
{ \
  {a,  a}, \
  {a, -a}  \
}

#define DEFINE_DCT2_P4_MATRIX(a,b,c) \
{ \
  { a,  a,  a,  a}, \
  { b,  c, -c, -b}, \
  { a, -a, -a,  a}, \
  { c, -b,  b, -c}  \
}

#define DEFINE_DCT2_P8_MATRIX(a,b,c,d,e,f,g) \
{ \
  { a,  a,  a,  a,  a,  a,  a,  a}, \
  { d,  e,  f,  g, -g, -f, -e, -d}, \
  { b,  c, -c, -b, -b, -c,  c,  b}, \
  { e, -g, -d, -f,  f,  d,  g, -e}, \
  { a, -a, -a,  a,  a, -a, -a,  a}, \
  { f, -d,  g,  e, -e, -g,  d, -f}, \
  { c, -b,  b, -c, -c,  b, -b,  c}, \
  { g, -f,  e, -d,  d, -e,  f, -g}  \
}

#define DEFINE_DCT2_P16_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o) \
{ \
  { a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a}, \
  { h,  i,  j,  k,  l,  m,  n,  o, -o, -n, -m, -l, -k, -j, -i, -h}, \
  { d,  e,  f,  g, -g, -f, -e, -d, -d, -e, -f, -g,  g,  f,  e,  d}, \
  { i,  l,  o, -m, -j, -h, -k, -n,  n,  k,  h,  j,  m, -o, -l, -i}, \
  { b,  c, -c, -b, -b, -c,  c,  b,  b,  c, -c, -b, -b, -c,  c,  b}, \
  { j,  o, -k, -i, -n,  l,  h,  m, -m, -h, -l,  n,  i,  k, -o, -j}, \
  { e, -g, -d, -f,  f,  d,  g, -e, -e,  g,  d,  f, -f, -d, -g,  e}, \
  { k, -m, -i,  o,  h,  n, -j, -l,  l,  j, -n, -h, -o,  i,  m, -k}, \
  { a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a}, \
  { l, -j, -n,  h, -o, -i,  m,  k, -k, -m,  i,  o, -h,  n,  j, -l}, \
  { f, -d,  g,  e, -e, -g,  d, -f, -f,  d, -g, -e,  e,  g, -d,  f}, \
  { m, -h,  l,  n, -i,  k,  o, -j,  j, -o, -k,  i, -n, -l,  h, -m}, \
  { c, -b,  b, -c, -c,  b, -b,  c,  c, -b,  b, -c, -c,  b, -b,  c}, \
  { n, -k,  h, -j,  m,  o, -l,  i, -i,  l, -o, -m,  j, -h,  k, -n}, \
  { g, -f,  e, -d,  d, -e,  f, -g, -g,  f, -e,  d, -d,  e, -f,  g}, \
  { o, -n,  m, -l,  k, -j,  i, -h,  h, -i,  j, -k,  l, -m,  n, -o}  \
}

#define DEFINE_DCT2_P32_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E) \
{ \
  { a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a,  a}, \
  { p,  q,  r,  s,  t,  u,  v,  w,  x,  y,  z,  A,  B,  C,  D,  E, -E, -D, -C, -B, -A, -z, -y, -x, -w, -v, -u, -t, -s, -r, -q, -p}, \
  { h,  i,  j,  k,  l,  m,  n,  o, -o, -n, -m, -l, -k, -j, -i, -h, -h, -i, -j, -k, -l, -m, -n, -o,  o,  n,  m,  l,  k,  j,  i,  h}, \
  { q,  t,  w,  z,  C, -E, -B, -y, -v, -s, -p, -r, -u, -x, -A, -D,  D,  A,  x,  u,  r,  p,  s,  v,  y,  B,  E, -C, -z, -w, -t, -q}, \
  { d,  e,  f,  g, -g, -f, -e, -d, -d, -e, -f, -g,  g,  f,  e,  d,  d,  e,  f,  g, -g, -f, -e, -d, -d, -e, -f, -g,  g,  f,  e,  d}, \
  { r,  w,  B, -D, -y, -t, -p, -u, -z, -E,  A,  v,  q,  s,  x,  C, -C, -x, -s, -q, -v, -A,  E,  z,  u,  p,  t,  y,  D, -B, -w, -r}, \
  { i,  l,  o, -m, -j, -h, -k, -n,  n,  k,  h,  j,  m, -o, -l, -i, -i, -l, -o,  m,  j,  h,  k,  n, -n, -k, -h, -j, -m,  o,  l,  i}, \
  { s,  z, -D, -w, -p, -v, -C,  A,  t,  r,  y, -E, -x, -q, -u, -B,  B,  u,  q,  x,  E, -y, -r, -t, -A,  C,  v,  p,  w,  D, -z, -s}, \
  { b,  c, -c, -b, -b, -c,  c,  b,  b,  c, -c, -b, -b, -c,  c,  b,  b,  c, -c, -b, -b, -c,  c,  b,  b,  c, -c, -b, -b, -c,  c,  b}, \
  { t,  C, -y, -p, -x,  D,  u,  s,  B, -z, -q, -w,  E,  v,  r,  A, -A, -r, -v, -E,  w,  q,  z, -B, -s, -u, -D,  x,  p,  y, -C, -t}, \
  { j,  o, -k, -i, -n,  l,  h,  m, -m, -h, -l,  n,  i,  k, -o, -j, -j, -o,  k,  i,  n, -l, -h, -m,  m,  h,  l, -n, -i, -k,  o,  j}, \
  { u, -E, -t, -v,  D,  s,  w, -C, -r, -x,  B,  q,  y, -A, -p, -z,  z,  p,  A, -y, -q, -B,  x,  r,  C, -w, -s, -D,  v,  t,  E, -u}, \
  { e, -g, -d, -f,  f,  d,  g, -e, -e,  g,  d,  f, -f, -d, -g,  e,  e, -g, -d, -f,  f,  d,  g, -e, -e,  g,  d,  f, -f, -d, -g,  e}, \
  { v, -B, -p, -C,  u,  w, -A, -q, -D,  t,  x, -z, -r, -E,  s,  y, -y, -s,  E,  r,  z, -x, -t,  D,  q,  A, -w, -u,  C,  p,  B, -v}, \
  { k, -m, -i,  o,  h,  n, -j, -l,  l,  j, -n, -h, -o,  i,  m, -k, -k,  m,  i, -o, -h, -n,  j,  l, -l, -j,  n,  h,  o, -i, -m,  k}, \
  { w, -y, -u,  A,  s, -C, -q,  E,  p,  D, -r, -B,  t,  z, -v, -x,  x,  v, -z, -t,  B,  r, -D, -p, -E,  q,  C, -s, -A,  u,  y, -w}, \
  { a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a,  a, -a, -a,  a}, \
  { x, -v, -z,  t,  B, -r, -D,  p, -E, -q,  C,  s, -A, -u,  y,  w, -w, -y,  u,  A, -s, -C,  q,  E, -p,  D,  r, -B, -t,  z,  v, -x}, \
  { l, -j, -n,  h, -o, -i,  m,  k, -k, -m,  i,  o, -h,  n,  j, -l, -l,  j,  n, -h,  o,  i, -m, -k,  k,  m, -i, -o,  h, -n, -j,  l}, \
  { y, -s, -E,  r, -z, -x,  t,  D, -q,  A,  w, -u, -C,  p, -B, -v,  v,  B, -p,  C,  u, -w, -A,  q, -D, -t,  x,  z, -r,  E,  s, -y}, \
  { f, -d,  g,  e, -e, -g,  d, -f, -f,  d, -g, -e,  e,  g, -d,  f,  f, -d,  g,  e, -e, -g,  d, -f, -f,  d, -g, -e,  e,  g, -d,  f}, \
  { z, -p,  A,  y, -q,  B,  x, -r,  C,  w, -s,  D,  v, -t,  E,  u, -u, -E,  t, -v, -D,  s, -w, -C,  r, -x, -B,  q, -y, -A,  p, -z}, \
  { m, -h,  l,  n, -i,  k,  o, -j,  j, -o, -k,  i, -n, -l,  h, -m, -m,  h, -l, -n,  i, -k, -o,  j, -j,  o,  k, -i,  n,  l, -h,  m}, \
  { A, -r,  v, -E, -w,  q, -z, -B,  s, -u,  D,  x, -p,  y,  C, -t,  t, -C, -y,  p, -x, -D,  u, -s,  B,  z, -q,  w,  E, -v,  r, -A}, \
  { c, -b,  b, -c, -c,  b, -b,  c,  c, -b,  b, -c, -c,  b, -b,  c,  c, -b,  b, -c, -c,  b, -b,  c,  c, -b,  b, -c, -c,  b, -b,  c}, \
  { B, -u,  q, -x,  E,  y, -r,  t, -A, -C,  v, -p,  w, -D, -z,  s, -s,  z,  D, -w,  p, -v,  C,  A, -t,  r, -y, -E,  x, -q,  u, -B}, \
  { n, -k,  h, -j,  m,  o, -l,  i, -i,  l, -o, -m,  j, -h,  k, -n, -n,  k, -h,  j, -m, -o,  l, -i,  i, -l,  o,  m, -j,  h, -k,  n}, \
  { C, -x,  s, -q,  v, -A, -E,  z, -u,  p, -t,  y, -D, -B,  w, -r,  r, -w,  B,  D, -y,  t, -p,  u, -z,  E,  A, -v,  q, -s,  x, -C}, \
  { g, -f,  e, -d,  d, -e,  f, -g, -g,  f, -e,  d, -d,  e, -f,  g,  g, -f,  e, -d,  d, -e,  f, -g, -g,  f, -e,  d, -d,  e, -f,  g}, \
  { D, -A,  x, -u,  r, -p,  s, -v,  y, -B,  E,  C, -z,  w, -t,  q, -q,  t, -w,  z, -C, -E,  B, -y,  v, -s,  p, -r,  u, -x,  A, -D}, \
  { o, -n,  m, -l,  k, -j,  i, -h,  h, -i,  j, -k,  l, -m,  n, -o, -o,  n, -m,  l, -k,  j, -i,  h, -h,  i, -j,  k, -l,  m, -n,  o}, \
  { E, -D,  C, -B,  A, -z,  y, -x,  w, -v,  u, -t,  s, -r,  q, -p,  p, -q,  r, -s,  t, -u,  v, -w,  x, -y,  z, -A,  B, -C,  D, -E}  \
}


#define DEFINE_DCT2_P64_MATRIX(aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck) \
{ \
  { aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa,  aa }, \
  { bf,  bg,  bh,  bi,  bj,  bk,  bl,  bm,  bn,  bo,  bp,  bq,  br,  bs,  bt,  bu,  bv,  bw,  bx,  by,  bz,  ca,  cb,  cc,  cd,  ce,  cf,  cg,  ch,  ci,  cj,  ck, -ck, -cj, -ci, -ch, -cg, -cf, -ce, -cd, -cc, -cb, -ca, -bz, -by, -bx, -bw, -bv, -bu, -bt, -bs, -br, -bq, -bp, -bo, -bn, -bm, -bl, -bk, -bj, -bi, -bh, -bg, -bf }, \
  { ap,  aq,  ar,  as,  at,  au,  av,  aw,  ax,  ay,  az,  ba,  bb,  bc,  bd,  be, -be, -bd, -bc, -bb, -ba, -az, -ay, -ax, -aw, -av, -au, -at, -as, -ar, -aq, -ap, -ap, -aq, -ar, -as, -at, -au, -av, -aw, -ax, -ay, -az, -ba, -bb, -bc, -bd, -be,  be,  bd,  bc,  bb,  ba,  az,  ay,  ax,  aw,  av,  au,  at,  as,  ar,  aq,  ap }, \
  { bg,  bj,  bm,  bp,  bs,  bv,  by,  cb,  ce,  ch,  ck, -ci, -cf, -cc, -bz, -bw, -bt, -bq, -bn, -bk, -bh, -bf, -bi, -bl, -bo, -br, -bu, -bx, -ca, -cd, -cg, -cj,  cj,  cg,  cd,  ca,  bx,  bu,  br,  bo,  bl,  bi,  bf,  bh,  bk,  bn,  bq,  bt,  bw,  bz,  cc,  cf,  ci, -ck, -ch, -ce, -cb, -by, -bv, -bs, -bp, -bm, -bj, -bg }, \
  { ah,  ai,  aj,  ak,  al,  am,  an,  ao, -ao, -an, -am, -al, -ak, -aj, -ai, -ah, -ah, -ai, -aj, -ak, -al, -am, -an, -ao,  ao,  an,  am,  al,  ak,  aj,  ai,  ah,  ah,  ai,  aj,  ak,  al,  am,  an,  ao, -ao, -an, -am, -al, -ak, -aj, -ai, -ah, -ah, -ai, -aj, -ak, -al, -am, -an, -ao,  ao,  an,  am,  al,  ak,  aj,  ai,  ah }, \
  { bh,  bm,  br,  bw,  cb,  cg, -ck, -cf, -ca, -bv, -bq, -bl, -bg, -bi, -bn, -bs, -bx, -cc, -ch,  cj,  ce,  bz,  bu,  bp,  bk,  bf,  bj,  bo,  bt,  by,  cd,  ci, -ci, -cd, -by, -bt, -bo, -bj, -bf, -bk, -bp, -bu, -bz, -ce, -cj,  ch,  cc,  bx,  bs,  bn,  bi,  bg,  bl,  bq,  bv,  ca,  cf,  ck, -cg, -cb, -bw, -br, -bm, -bh }, \
  { aq,  at,  aw,  az,  bc, -be, -bb, -ay, -av, -as, -ap, -ar, -au, -ax, -ba, -bd,  bd,  ba,  ax,  au,  ar,  ap,  as,  av,  ay,  bb,  be, -bc, -az, -aw, -at, -aq, -aq, -at, -aw, -az, -bc,  be,  bb,  ay,  av,  as,  ap,  ar,  au,  ax,  ba,  bd, -bd, -ba, -ax, -au, -ar, -ap, -as, -av, -ay, -bb, -be,  bc,  az,  aw,  at,  aq }, \
  { bi,  bp,  bw,  cd,  ck, -ce, -bx, -bq, -bj, -bh, -bo, -bv, -cc, -cj,  cf,  by,  br,  bk,  bg,  bn,  bu,  cb,  ci, -cg, -bz, -bs, -bl, -bf, -bm, -bt, -ca, -ch,  ch,  ca,  bt,  bm,  bf,  bl,  bs,  bz,  cg, -ci, -cb, -bu, -bn, -bg, -bk, -br, -by, -cf,  cj,  cc,  bv,  bo,  bh,  bj,  bq,  bx,  ce, -ck, -cd, -bw, -bp, -bi }, \
  { ad,  ae,  af,  ag, -ag, -af, -ae, -ad, -ad, -ae, -af, -ag,  ag,  af,  ae,  ad,  ad,  ae,  af,  ag, -ag, -af, -ae, -ad, -ad, -ae, -af, -ag,  ag,  af,  ae,  ad,  ad,  ae,  af,  ag, -ag, -af, -ae, -ad, -ad, -ae, -af, -ag,  ag,  af,  ae,  ad,  ad,  ae,  af,  ag, -ag, -af, -ae, -ad, -ad, -ae, -af, -ag,  ag,  af,  ae,  ad }, \
  { bj,  bs,  cb,  ck, -cc, -bt, -bk, -bi, -br, -ca, -cj,  cd,  bu,  bl,  bh,  bq,  bz,  ci, -ce, -bv, -bm, -bg, -bp, -by, -ch,  cf,  bw,  bn,  bf,  bo,  bx,  cg, -cg, -bx, -bo, -bf, -bn, -bw, -cf,  ch,  by,  bp,  bg,  bm,  bv,  ce, -ci, -bz, -bq, -bh, -bl, -bu, -cd,  cj,  ca,  br,  bi,  bk,  bt,  cc, -ck, -cb, -bs, -bj }, \
  { ar,  aw,  bb, -bd, -ay, -at, -ap, -au, -az, -be,  ba,  av,  aq,  as,  ax,  bc, -bc, -ax, -as, -aq, -av, -ba,  be,  az,  au,  ap,  at,  ay,  bd, -bb, -aw, -ar, -ar, -aw, -bb,  bd,  ay,  at,  ap,  au,  az,  be, -ba, -av, -aq, -as, -ax, -bc,  bc,  ax,  as,  aq,  av,  ba, -be, -az, -au, -ap, -at, -ay, -bd,  bb,  aw,  ar }, \
  { bk,  bv,  cg, -ce, -bt, -bi, -bm, -bx, -ci,  cc,  br,  bg,  bo,  bz,  ck, -ca, -bp, -bf, -bq, -cb,  cj,  by,  bn,  bh,  bs,  cd, -ch, -bw, -bl, -bj, -bu, -cf,  cf,  bu,  bj,  bl,  bw,  ch, -cd, -bs, -bh, -bn, -by, -cj,  cb,  bq,  bf,  bp,  ca, -ck, -bz, -bo, -bg, -br, -cc,  ci,  bx,  bm,  bi,  bt,  ce, -cg, -bv, -bk }, \
  { ai,  al,  ao, -am, -aj, -ah, -ak, -an,  an,  ak,  ah,  aj,  am, -ao, -al, -ai, -ai, -al, -ao,  am,  aj,  ah,  ak,  an, -an, -ak, -ah, -aj, -am,  ao,  al,  ai,  ai,  al,  ao, -am, -aj, -ah, -ak, -an,  an,  ak,  ah,  aj,  am, -ao, -al, -ai, -ai, -al, -ao,  am,  aj,  ah,  ak,  an, -an, -ak, -ah, -aj, -am,  ao,  al,  ai }, \
  { bl,  by, -ck, -bx, -bk, -bm, -bz,  cj,  bw,  bj,  bn,  ca, -ci, -bv, -bi, -bo, -cb,  ch,  bu,  bh,  bp,  cc, -cg, -bt, -bg, -bq, -cd,  cf,  bs,  bf,  br,  ce, -ce, -br, -bf, -bs, -cf,  cd,  bq,  bg,  bt,  cg, -cc, -bp, -bh, -bu, -ch,  cb,  bo,  bi,  bv,  ci, -ca, -bn, -bj, -bw, -cj,  bz,  bm,  bk,  bx,  ck, -by, -bl }, \
  { as,  az, -bd, -aw, -ap, -av, -bc,  ba,  at,  ar,  ay, -be, -ax, -aq, -au, -bb,  bb,  au,  aq,  ax,  be, -ay, -ar, -at, -ba,  bc,  av,  ap,  aw,  bd, -az, -as, -as, -az,  bd,  aw,  ap,  av,  bc, -ba, -at, -ar, -ay,  be,  ax,  aq,  au,  bb, -bb, -au, -aq, -ax, -be,  ay,  ar,  at,  ba, -bc, -av, -ap, -aw, -bd,  az,  as }, \
  { bm,  cb, -cf, -bq, -bi, -bx,  cj,  bu,  bf,  bt,  ci, -by, -bj, -bp, -ce,  cc,  bn,  bl,  ca, -cg, -br, -bh, -bw,  ck,  bv,  bg,  bs,  ch, -bz, -bk, -bo, -cd,  cd,  bo,  bk,  bz, -ch, -bs, -bg, -bv, -ck,  bw,  bh,  br,  cg, -ca, -bl, -bn, -cc,  ce,  bp,  bj,  by, -ci, -bt, -bf, -bu, -cj,  bx,  bi,  bq,  cf, -cb, -bm }, \
  { ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab,  ab,  ac, -ac, -ab, -ab, -ac,  ac,  ab }, \
  { bn,  ce, -ca, -bj, -br, -ci,  bw,  bf,  bv, -cj, -bs, -bi, -bz,  cf,  bo,  bm,  cd, -cb, -bk, -bq, -ch,  bx,  bg,  bu, -ck, -bt, -bh, -by,  cg,  bp,  bl,  cc, -cc, -bl, -bp, -cg,  by,  bh,  bt,  ck, -bu, -bg, -bx,  ch,  bq,  bk,  cb, -cd, -bm, -bo, -cf,  bz,  bi,  bs,  cj, -bv, -bf, -bw,  ci,  br,  bj,  ca, -ce, -bn }, \
  { at,  bc, -ay, -ap, -ax,  bd,  au,  as,  bb, -az, -aq, -aw,  be,  av,  ar,  ba, -ba, -ar, -av, -be,  aw,  aq,  az, -bb, -as, -au, -bd,  ax,  ap,  ay, -bc, -at, -at, -bc,  ay,  ap,  ax, -bd, -au, -as, -bb,  az,  aq,  aw, -be, -av, -ar, -ba,  ba,  ar,  av,  be, -aw, -aq, -az,  bb,  as,  au,  bd, -ax, -ap, -ay,  bc,  at }, \
  { bo,  ch, -bv, -bh, -ca,  cc,  bj,  bt, -cj, -bq, -bm, -cf,  bx,  bf,  by, -ce, -bl, -br, -ck,  bs,  bk,  cd, -bz, -bg, -bw,  cg,  bn,  bp,  ci, -bu, -bi, -cb,  cb,  bi,  bu, -ci, -bp, -bn, -cg,  bw,  bg,  bz, -cd, -bk, -bs,  ck,  br,  bl,  ce, -by, -bf, -bx,  cf,  bm,  bq,  cj, -bt, -bj, -cc,  ca,  bh,  bv, -ch, -bo }, \
  { aj,  ao, -ak, -ai, -an,  al,  ah,  am, -am, -ah, -al,  an,  ai,  ak, -ao, -aj, -aj, -ao,  ak,  ai,  an, -al, -ah, -am,  am,  ah,  al, -an, -ai, -ak,  ao,  aj,  aj,  ao, -ak, -ai, -an,  al,  ah,  am, -am, -ah, -al,  an,  ai,  ak, -ao, -aj, -aj, -ao,  ak,  ai,  an, -al, -ah, -am,  am,  ah,  al, -an, -ai, -ak,  ao,  aj }, \
  { bp,  ck, -bq, -bo, -cj,  br,  bn,  ci, -bs, -bm, -ch,  bt,  bl,  cg, -bu, -bk, -cf,  bv,  bj,  ce, -bw, -bi, -cd,  bx,  bh,  cc, -by, -bg, -cb,  bz,  bf,  ca, -ca, -bf, -bz,  cb,  bg,  by, -cc, -bh, -bx,  cd,  bi,  bw, -ce, -bj, -bv,  cf,  bk,  bu, -cg, -bl, -bt,  ch,  bm,  bs, -ci, -bn, -br,  cj,  bo,  bq, -ck, -bp }, \
  { au, -be, -at, -av,  bd,  as,  aw, -bc, -ar, -ax,  bb,  aq,  ay, -ba, -ap, -az,  az,  ap,  ba, -ay, -aq, -bb,  ax,  ar,  bc, -aw, -as, -bd,  av,  at,  be, -au, -au,  be,  at,  av, -bd, -as, -aw,  bc,  ar,  ax, -bb, -aq, -ay,  ba,  ap,  az, -az, -ap, -ba,  ay,  aq,  bb, -ax, -ar, -bc,  aw,  as,  bd, -av, -at, -be,  au }, \
  { bq, -ci, -bl, -bv,  cd,  bg,  ca, -by, -bi, -cf,  bt,  bn,  ck, -bo, -bs,  cg,  bj,  bx, -cb, -bf, -cc,  bw,  bk,  ch, -br, -bp,  cj,  bm,  bu, -ce, -bh, -bz,  bz,  bh,  ce, -bu, -bm, -cj,  bp,  br, -ch, -bk, -bw,  cc,  bf,  cb, -bx, -bj, -cg,  bs,  bo, -ck, -bn, -bt,  cf,  bi,  by, -ca, -bg, -cd,  bv,  bl,  ci, -bq }, \
  { ae, -ag, -ad, -af,  af,  ad,  ag, -ae, -ae,  ag,  ad,  af, -af, -ad, -ag,  ae,  ae, -ag, -ad, -af,  af,  ad,  ag, -ae, -ae,  ag,  ad,  af, -af, -ad, -ag,  ae,  ae, -ag, -ad, -af,  af,  ad,  ag, -ae, -ae,  ag,  ad,  af, -af, -ad, -ag,  ae,  ae, -ag, -ad, -af,  af,  ad,  ag, -ae, -ae,  ag,  ad,  af, -af, -ad, -ag,  ae }, \
  { br, -cf, -bg, -cc,  bu,  bo, -ci, -bj, -bz,  bx,  bl,  ck, -bm, -bw,  ca,  bi,  ch, -bp, -bt,  cd,  bf,  ce, -bs, -bq,  cg,  bh,  cb, -bv, -bn,  cj,  bk,  by, -by, -bk, -cj,  bn,  bv, -cb, -bh, -cg,  bq,  bs, -ce, -bf, -cd,  bt,  bp, -ch, -bi, -ca,  bw,  bm, -ck, -bl, -bx,  bz,  bj,  ci, -bo, -bu,  cc,  bg,  cf, -br }, \
  { av, -bb, -ap, -bc,  au,  aw, -ba, -aq, -bd,  at,  ax, -az, -ar, -be,  as,  ay, -ay, -as,  be,  ar,  az, -ax, -at,  bd,  aq,  ba, -aw, -au,  bc,  ap,  bb, -av, -av,  bb,  ap,  bc, -au, -aw,  ba,  aq,  bd, -at, -ax,  az,  ar,  be, -as, -ay,  ay,  as, -be, -ar, -az,  ax,  at, -bd, -aq, -ba,  aw,  au, -bc, -ap, -bb,  av }, \
  { bs, -cc, -bi, -cj,  bl,  bz, -bv, -bp,  cf,  bf,  cg, -bo, -bw,  by,  bm, -ci, -bh, -cd,  br,  bt, -cb, -bj, -ck,  bk,  ca, -bu, -bq,  ce,  bg,  ch, -bn, -bx,  bx,  bn, -ch, -bg, -ce,  bq,  bu, -ca, -bk,  ck,  bj,  cb, -bt, -br,  cd,  bh,  ci, -bm, -by,  bw,  bo, -cg, -bf, -cf,  bp,  bv, -bz, -bl,  cj,  bi,  cc, -bs }, \
  { ak, -am, -ai,  ao,  ah,  an, -aj, -al,  al,  aj, -an, -ah, -ao,  ai,  am, -ak, -ak,  am,  ai, -ao, -ah, -an,  aj,  al, -al, -aj,  an,  ah,  ao, -ai, -am,  ak,  ak, -am, -ai,  ao,  ah,  an, -aj, -al,  al,  aj, -an, -ah, -ao,  ai,  am, -ak, -ak,  am,  ai, -ao, -ah, -an,  aj,  al, -al, -aj,  an,  ah,  ao, -ai, -am,  ak }, \
  { bt, -bz, -bn,  cf,  bh,  ck, -bi, -ce,  bo,  by, -bu, -bs,  ca,  bm, -cg, -bg, -cj,  bj,  cd, -bp, -bx,  bv,  br, -cb, -bl,  ch,  bf,  ci, -bk, -cc,  bq,  bw, -bw, -bq,  cc,  bk, -ci, -bf, -ch,  bl,  cb, -br, -bv,  bx,  bp, -cd, -bj,  cj,  bg,  cg, -bm, -ca,  bs,  bu, -by, -bo,  ce,  bi, -ck, -bh, -cf,  bn,  bz, -bt }, \
  { aw, -ay, -au,  ba,  as, -bc, -aq,  be,  ap,  bd, -ar, -bb,  at,  az, -av, -ax,  ax,  av, -az, -at,  bb,  ar, -bd, -ap, -be,  aq,  bc, -as, -ba,  au,  ay, -aw, -aw,  ay,  au, -ba, -as,  bc,  aq, -be, -ap, -bd,  ar,  bb, -at, -az,  av,  ax, -ax, -av,  az,  at, -bb, -ar,  bd,  ap,  be, -aq, -bc,  as,  ba, -au, -ay,  aw }, \
  { bu, -bw, -bs,  by,  bq, -ca, -bo,  cc,  bm, -ce, -bk,  cg,  bi, -ci, -bg,  ck,  bf,  cj, -bh, -ch,  bj,  cf, -bl, -cd,  bn,  cb, -bp, -bz,  br,  bx, -bt, -bv,  bv,  bt, -bx, -br,  bz,  bp, -cb, -bn,  cd,  bl, -cf, -bj,  ch,  bh, -cj, -bf, -ck,  bg,  ci, -bi, -cg,  bk,  ce, -bm, -cc,  bo,  ca, -bq, -by,  bs,  bw, -bu }, \
  { aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa,  aa, -aa, -aa,  aa }, \
  { bv, -bt, -bx,  br,  bz, -bp, -cb,  bn,  cd, -bl, -cf,  bj,  ch, -bh, -cj,  bf, -ck, -bg,  ci,  bi, -cg, -bk,  ce,  bm, -cc, -bo,  ca,  bq, -by, -bs,  bw,  bu, -bu, -bw,  bs,  by, -bq, -ca,  bo,  cc, -bm, -ce,  bk,  cg, -bi, -ci,  bg,  ck, -bf,  cj,  bh, -ch, -bj,  cf,  bl, -cd, -bn,  cb,  bp, -bz, -br,  bx,  bt, -bv }, \
  { ax, -av, -az,  at,  bb, -ar, -bd,  ap, -be, -aq,  bc,  as, -ba, -au,  ay,  aw, -aw, -ay,  au,  ba, -as, -bc,  aq,  be, -ap,  bd,  ar, -bb, -at,  az,  av, -ax, -ax,  av,  az, -at, -bb,  ar,  bd, -ap,  be,  aq, -bc, -as,  ba,  au, -ay, -aw,  aw,  ay, -au, -ba,  as,  bc, -aq, -be,  ap, -bd, -ar,  bb,  at, -az, -av,  ax }, \
  { bw, -bq, -cc,  bk,  ci, -bf,  ch,  bl, -cb, -br,  bv,  bx, -bp, -cd,  bj,  cj, -bg,  cg,  bm, -ca, -bs,  bu,  by, -bo, -ce,  bi,  ck, -bh,  cf,  bn, -bz, -bt,  bt,  bz, -bn, -cf,  bh, -ck, -bi,  ce,  bo, -by, -bu,  bs,  ca, -bm, -cg,  bg, -cj, -bj,  cd,  bp, -bx, -bv,  br,  cb, -bl, -ch,  bf, -ci, -bk,  cc,  bq, -bw }, \
  { al, -aj, -an,  ah, -ao, -ai,  am,  ak, -ak, -am,  ai,  ao, -ah,  an,  aj, -al, -al,  aj,  an, -ah,  ao,  ai, -am, -ak,  ak,  am, -ai, -ao,  ah, -an, -aj,  al,  al, -aj, -an,  ah, -ao, -ai,  am,  ak, -ak, -am,  ai,  ao, -ah,  an,  aj, -al, -al,  aj,  an, -ah,  ao,  ai, -am, -ak,  ak,  am, -ai, -ao,  ah, -an, -aj,  al }, \
  { bx, -bn, -ch,  bg, -ce, -bq,  bu,  ca, -bk, -ck,  bj, -cb, -bt,  br,  cd, -bh,  ci,  bm, -by, -bw,  bo,  cg, -bf,  cf,  bp, -bv, -bz,  bl,  cj, -bi,  cc,  bs, -bs, -cc,  bi, -cj, -bl,  bz,  bv, -bp, -cf,  bf, -cg, -bo,  bw,  by, -bm, -ci,  bh, -cd, -br,  bt,  cb, -bj,  ck,  bk, -ca, -bu,  bq,  ce, -bg,  ch,  bn, -bx }, \
  { ay, -as, -be,  ar, -az, -ax,  at,  bd, -aq,  ba,  aw, -au, -bc,  ap, -bb, -av,  av,  bb, -ap,  bc,  au, -aw, -ba,  aq, -bd, -at,  ax,  az, -ar,  be,  as, -ay, -ay,  as,  be, -ar,  az,  ax, -at, -bd,  aq, -ba, -aw,  au,  bc, -ap,  bb,  av, -av, -bb,  ap, -bc, -au,  aw,  ba, -aq,  bd,  at, -ax, -az,  ar, -be, -as,  ay }, \
  { by, -bk,  cj,  bn, -bv, -cb,  bh, -cg, -bq,  bs,  ce, -bf,  cd,  bt, -bp, -ch,  bi, -ca, -bw,  bm,  ck, -bl,  bx,  bz, -bj,  ci,  bo, -bu, -cc,  bg, -cf, -br,  br,  cf, -bg,  cc,  bu, -bo, -ci,  bj, -bz, -bx,  bl, -ck, -bm,  bw,  ca, -bi,  ch,  bp, -bt, -cd,  bf, -ce, -bs,  bq,  cg, -bh,  cb,  bv, -bn, -cj,  bk, -by }, \
  { af, -ad,  ag,  ae, -ae, -ag,  ad, -af, -af,  ad, -ag, -ae,  ae,  ag, -ad,  af,  af, -ad,  ag,  ae, -ae, -ag,  ad, -af, -af,  ad, -ag, -ae,  ae,  ag, -ad,  af,  af, -ad,  ag,  ae, -ae, -ag,  ad, -af, -af,  ad, -ag, -ae,  ae,  ag, -ad,  af,  af, -ad,  ag,  ae, -ae, -ag,  ad, -af, -af,  ad, -ag, -ae,  ae,  ag, -ad,  af }, \
  { bz, -bh,  ce,  bu, -bm,  cj,  bp, -br, -ch,  bk, -bw, -cc,  bf, -cb, -bx,  bj, -cg, -bs,  bo,  ck, -bn,  bt,  cf, -bi,  by,  ca, -bg,  cd,  bv, -bl,  ci,  bq, -bq, -ci,  bl, -bv, -cd,  bg, -ca, -by,  bi, -cf, -bt,  bn, -ck, -bo,  bs,  cg, -bj,  bx,  cb, -bf,  cc,  bw, -bk,  ch,  br, -bp, -cj,  bm, -bu, -ce,  bh, -bz }, \
  { az, -ap,  ba,  ay, -aq,  bb,  ax, -ar,  bc,  aw, -as,  bd,  av, -at,  be,  au, -au, -be,  at, -av, -bd,  as, -aw, -bc,  ar, -ax, -bb,  aq, -ay, -ba,  ap, -az, -az,  ap, -ba, -ay,  aq, -bb, -ax,  ar, -bc, -aw,  as, -bd, -av,  at, -be, -au,  au,  be, -at,  av,  bd, -as,  aw,  bc, -ar,  ax,  bb, -aq,  ay,  ba, -ap,  az }, \
  { ca, -bf,  bz,  cb, -bg,  by,  cc, -bh,  bx,  cd, -bi,  bw,  ce, -bj,  bv,  cf, -bk,  bu,  cg, -bl,  bt,  ch, -bm,  bs,  ci, -bn,  br,  cj, -bo,  bq,  ck, -bp,  bp, -ck, -bq,  bo, -cj, -br,  bn, -ci, -bs,  bm, -ch, -bt,  bl, -cg, -bu,  bk, -cf, -bv,  bj, -ce, -bw,  bi, -cd, -bx,  bh, -cc, -by,  bg, -cb, -bz,  bf, -ca }, \
  { am, -ah,  al,  an, -ai,  ak,  ao, -aj,  aj, -ao, -ak,  ai, -an, -al,  ah, -am, -am,  ah, -al, -an,  ai, -ak, -ao,  aj, -aj,  ao,  ak, -ai,  an,  al, -ah,  am,  am, -ah,  al,  an, -ai,  ak,  ao, -aj,  aj, -ao, -ak,  ai, -an, -al,  ah, -am, -am,  ah, -al, -an,  ai, -ak, -ao,  aj, -aj,  ao,  ak, -ai,  an,  al, -ah,  am }, \
  { cb, -bi,  bu,  ci, -bp,  bn, -cg, -bw,  bg, -bz, -cd,  bk, -bs, -ck,  br, -bl,  ce,  by, -bf,  bx,  cf, -bm,  bq, -cj, -bt,  bj, -cc, -ca,  bh, -bv, -ch,  bo, -bo,  ch,  bv, -bh,  ca,  cc, -bj,  bt,  cj, -bq,  bm, -cf, -bx,  bf, -by, -ce,  bl, -br,  ck,  bs, -bk,  cd,  bz, -bg,  bw,  cg, -bn,  bp, -ci, -bu,  bi, -cb }, \
  { ba, -ar,  av, -be, -aw,  aq, -az, -bb,  as, -au,  bd,  ax, -ap,  ay,  bc, -at,  at, -bc, -ay,  ap, -ax, -bd,  au, -as,  bb,  az, -aq,  aw,  be, -av,  ar, -ba, -ba,  ar, -av,  be,  aw, -aq,  az,  bb, -as,  au, -bd, -ax,  ap, -ay, -bc,  at, -at,  bc,  ay, -ap,  ax,  bd, -au,  as, -bb, -az,  aq, -aw, -be,  av, -ar,  ba }, \
  { cc, -bl,  bp, -cg, -by,  bh, -bt,  ck,  bu, -bg,  bx,  ch, -bq,  bk, -cb, -cd,  bm, -bo,  cf,  bz, -bi,  bs, -cj, -bv,  bf, -bw, -ci,  br, -bj,  ca,  ce, -bn,  bn, -ce, -ca,  bj, -br,  ci,  bw, -bf,  bv,  cj, -bs,  bi, -bz, -cf,  bo, -bm,  cd,  cb, -bk,  bq, -ch, -bx,  bg, -bu, -ck,  bt, -bh,  by,  cg, -bp,  bl, -cc }, \
  { ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac,  ac, -ab,  ab, -ac, -ac,  ab, -ab,  ac }, \
  { cd, -bo,  bk, -bz, -ch,  bs, -bg,  bv, -ck, -bw,  bh, -br,  cg,  ca, -bl,  bn, -cc, -ce,  bp, -bj,  by,  ci, -bt,  bf, -bu,  cj,  bx, -bi,  bq, -cf, -cb,  bm, -bm,  cb,  cf, -bq,  bi, -bx, -cj,  bu, -bf,  bt, -ci, -by,  bj, -bp,  ce,  cc, -bn,  bl, -ca, -cg,  br, -bh,  bw,  ck, -bv,  bg, -bs,  ch,  bz, -bk,  bo, -cd }, \
  { bb, -au,  aq, -ax,  be,  ay, -ar,  at, -ba, -bc,  av, -ap,  aw, -bd, -az,  as, -as,  az,  bd, -aw,  ap, -av,  bc,  ba, -at,  ar, -ay, -be,  ax, -aq,  au, -bb, -bb,  au, -aq,  ax, -be, -ay,  ar, -at,  ba,  bc, -av,  ap, -aw,  bd,  az, -as,  as, -az, -bd,  aw, -ap,  av, -bc, -ba,  at, -ar,  ay,  be, -ax,  aq, -au,  bb }, \
  { ce, -br,  bf, -bs,  cf,  cd, -bq,  bg, -bt,  cg,  cc, -bp,  bh, -bu,  ch,  cb, -bo,  bi, -bv,  ci,  ca, -bn,  bj, -bw,  cj,  bz, -bm,  bk, -bx,  ck,  by, -bl,  bl, -by, -ck,  bx, -bk,  bm, -bz, -cj,  bw, -bj,  bn, -ca, -ci,  bv, -bi,  bo, -cb, -ch,  bu, -bh,  bp, -cc, -cg,  bt, -bg,  bq, -cd, -cf,  bs, -bf,  br, -ce }, \
  { an, -ak,  ah, -aj,  am,  ao, -al,  ai, -ai,  al, -ao, -am,  aj, -ah,  ak, -an, -an,  ak, -ah,  aj, -am, -ao,  al, -ai,  ai, -al,  ao,  am, -aj,  ah, -ak,  an,  an, -ak,  ah, -aj,  am,  ao, -al,  ai, -ai,  al, -ao, -am,  aj, -ah,  ak, -an, -an,  ak, -ah,  aj, -am, -ao,  al, -ai,  ai, -al,  ao,  am, -aj,  ah, -ak,  an }, \
  { cf, -bu,  bj, -bl,  bw, -ch, -cd,  bs, -bh,  bn, -by,  cj,  cb, -bq,  bf, -bp,  ca,  ck, -bz,  bo, -bg,  br, -cc, -ci,  bx, -bm,  bi, -bt,  ce,  cg, -bv,  bk, -bk,  bv, -cg, -ce,  bt, -bi,  bm, -bx,  ci,  cc, -br,  bg, -bo,  bz, -ck, -ca,  bp, -bf,  bq, -cb, -cj,  by, -bn,  bh, -bs,  cd,  ch, -bw,  bl, -bj,  bu, -cf }, \
  { bc, -ax,  as, -aq,  av, -ba, -be,  az, -au,  ap, -at,  ay, -bd, -bb,  aw, -ar,  ar, -aw,  bb,  bd, -ay,  at, -ap,  au, -az,  be,  ba, -av,  aq, -as,  ax, -bc, -bc,  ax, -as,  aq, -av,  ba,  be, -az,  au, -ap,  at, -ay,  bd,  bb, -aw,  ar, -ar,  aw, -bb, -bd,  ay, -at,  ap, -au,  az, -be, -ba,  av, -aq,  as, -ax,  bc }, \
  { cg, -bx,  bo, -bf,  bn, -bw,  cf,  ch, -by,  bp, -bg,  bm, -bv,  ce,  ci, -bz,  bq, -bh,  bl, -bu,  cd,  cj, -ca,  br, -bi,  bk, -bt,  cc,  ck, -cb,  bs, -bj,  bj, -bs,  cb, -ck, -cc,  bt, -bk,  bi, -br,  ca, -cj, -cd,  bu, -bl,  bh, -bq,  bz, -ci, -ce,  bv, -bm,  bg, -bp,  by, -ch, -cf,  bw, -bn,  bf, -bo,  bx, -cg }, \
  { ag, -af,  ae, -ad,  ad, -ae,  af, -ag, -ag,  af, -ae,  ad, -ad,  ae, -af,  ag,  ag, -af,  ae, -ad,  ad, -ae,  af, -ag, -ag,  af, -ae,  ad, -ad,  ae, -af,  ag,  ag, -af,  ae, -ad,  ad, -ae,  af, -ag, -ag,  af, -ae,  ad, -ad,  ae, -af,  ag,  ag, -af,  ae, -ad,  ad, -ae,  af, -ag, -ag,  af, -ae,  ad, -ad,  ae, -af,  ag }, \
  { ch, -ca,  bt, -bm,  bf, -bl,  bs, -bz,  cg,  ci, -cb,  bu, -bn,  bg, -bk,  br, -by,  cf,  cj, -cc,  bv, -bo,  bh, -bj,  bq, -bx,  ce,  ck, -cd,  bw, -bp,  bi, -bi,  bp, -bw,  cd, -ck, -ce,  bx, -bq,  bj, -bh,  bo, -bv,  cc, -cj, -cf,  by, -br,  bk, -bg,  bn, -bu,  cb, -ci, -cg,  bz, -bs,  bl, -bf,  bm, -bt,  ca, -ch }, \
  { bd, -ba,  ax, -au,  ar, -ap,  as, -av,  ay, -bb,  be,  bc, -az,  aw, -at,  aq, -aq,  at, -aw,  az, -bc, -be,  bb, -ay,  av, -as,  ap, -ar,  au, -ax,  ba, -bd, -bd,  ba, -ax,  au, -ar,  ap, -as,  av, -ay,  bb, -be, -bc,  az, -aw,  at, -aq,  aq, -at,  aw, -az,  bc,  be, -bb,  ay, -av,  as, -ap,  ar, -au,  ax, -ba,  bd }, \
  { ci, -cd,  by, -bt,  bo, -bj,  bf, -bk,  bp, -bu,  bz, -ce,  cj,  ch, -cc,  bx, -bs,  bn, -bi,  bg, -bl,  bq, -bv,  ca, -cf,  ck,  cg, -cb,  bw, -br,  bm, -bh,  bh, -bm,  br, -bw,  cb, -cg, -ck,  cf, -ca,  bv, -bq,  bl, -bg,  bi, -bn,  bs, -bx,  cc, -ch, -cj,  ce, -bz,  bu, -bp,  bk, -bf,  bj, -bo,  bt, -by,  cd, -ci }, \
  { ao, -an,  am, -al,  ak, -aj,  ai, -ah,  ah, -ai,  aj, -ak,  al, -am,  an, -ao, -ao,  an, -am,  al, -ak,  aj, -ai,  ah, -ah,  ai, -aj,  ak, -al,  am, -an,  ao,  ao, -an,  am, -al,  ak, -aj,  ai, -ah,  ah, -ai,  aj, -ak,  al, -am,  an, -ao, -ao,  an, -am,  al, -ak,  aj, -ai,  ah, -ah,  ai, -aj,  ak, -al,  am, -an,  ao }, \
  { cj, -cg,  cd, -ca,  bx, -bu,  br, -bo,  bl, -bi,  bf, -bh,  bk, -bn,  bq, -bt,  bw, -bz,  cc, -cf,  ci,  ck, -ch,  ce, -cb,  by, -bv,  bs, -bp,  bm, -bj,  bg, -bg,  bj, -bm,  bp, -bs,  bv, -by,  cb, -ce,  ch, -ck, -ci,  cf, -cc,  bz, -bw,  bt, -bq,  bn, -bk,  bh, -bf,  bi, -bl,  bo, -br,  bu, -bx,  ca, -cd,  cg, -cj }, \
  { be, -bd,  bc, -bb,  ba, -az,  ay, -ax,  aw, -av,  au, -at,  as, -ar,  aq, -ap,  ap, -aq,  ar, -as,  at, -au,  av, -aw,  ax, -ay,  az, -ba,  bb, -bc,  bd, -be, -be,  bd, -bc,  bb, -ba,  az, -ay,  ax, -aw,  av, -au,  at, -as,  ar, -aq,  ap, -ap,  aq, -ar,  as, -at,  au, -av,  aw, -ax,  ay, -az,  ba, -bb,  bc, -bd,  be }, \
  { ck, -cj,  ci, -ch,  cg, -cf,  ce, -cd,  cc, -cb,  ca, -bz,  by, -bx,  bw, -bv,  bu, -bt,  bs, -br,  bq, -bp,  bo, -bn,  bm, -bl,  bk, -bj,  bi, -bh,  bg, -bf,  bf, -bg,  bh, -bi,  bj, -bk,  bl, -bm,  bn, -bo,  bp, -bq,  br, -bs,  bt, -bu,  bv, -bw,  bx, -by,  bz, -ca,  cb, -cc,  cd, -ce,  cf, -cg,  ch, -ci,  cj, -ck }, \
 }

// DCT-8
#define DEFINE_DCT8_P4_MATRIX(a,b,c,d) \
{ \
  {  a,  b,  c,  d,}, \
  {  b,  0, -b, -b,}, \
  {  c, -b, -d,  a,}, \
  {  d, -b,  a, -c,}, \
}

#define DEFINE_DCT8_P8_MATRIX(a,b,c,d,e,f,g,h) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,}, \
  {  b,  e,  h, -g, -d, -a, -c, -f,}, \
  {  c,  h, -e, -a, -f,  g,  b,  d,}, \
  {  d, -g, -a, -h,  c,  e, -f, -b,}, \
  {  e, -d, -f,  c,  g, -b, -h,  a,}, \
  {  f, -a,  g,  e, -b,  h,  d, -c,}, \
  {  g, -c,  b, -f, -h,  d, -a,  e,}, \
  {  h, -f,  d, -b,  a, -c,  e, -g,}, \
}

#define DEFINE_DCT8_P16_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,}, \
  {  b,  e,  h,  k,  n,  0, -n, -k, -h, -e, -b, -b, -e, -h, -k, -n,}, \
  {  c,  h,  m, -p, -k, -f, -a, -e, -j, -o,  n,  i,  d,  b,  g,  l,}, \
  {  d,  k, -p, -i, -b, -f, -m,  n,  g,  a,  h,  o, -l, -e, -c, -j,}, \
  {  e,  n, -k, -b, -h,  0,  h,  b,  k, -n, -e, -e, -n,  k,  b,  h,}, \
  {  f,  0, -f, -f,  0,  f,  f,  0, -f, -f,  0,  f,  f,  0, -f, -f,}, \
  {  g, -n, -a, -m,  h,  f, -o, -b, -l,  i,  e, -p, -c, -k,  j,  d,}, \
  {  h, -k, -e,  n,  b,  0, -b, -n,  e,  k, -h, -h,  k,  e, -n, -b,}, \
  {  i, -h, -j,  g,  k, -f, -l,  e,  m, -d, -n,  c,  o, -b, -p,  a,}, \
  {  j, -e, -o,  a, -n, -f,  i,  k, -d, -p,  b, -m, -g,  h,  l, -c,}, \
  {  k, -b,  n,  h, -e,  0,  e, -h, -n,  b, -k, -k,  b, -n, -h,  e,}, \
  {  l, -b,  i,  o, -e,  f, -p, -h,  c, -m, -k,  a, -j, -n,  d, -g,}, \
  {  m, -e,  d, -l, -n,  f, -c,  k,  o, -g,  b, -j, -p,  h, -a,  i,}, \
  {  n, -h,  b, -e,  k,  0, -k,  e, -b,  h, -n, -n,  h, -b,  e, -k,}, \
  {  o, -k,  g, -c,  b, -f,  j, -n, -p,  l, -h,  d, -a,  e, -i,  m,}, \
  {  p, -n,  l, -j,  h, -f,  d, -b,  a, -c,  e, -g,  i, -k,  m, -o,}, \
}

#define DEFINE_DCT8_P32_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,  q,  r,  s,  t,  u,  v,  w,  x,  y,  z,  A,  B,  C,  D,  E,  F,}, \
  {  b,  e,  h,  k,  n,  q,  t,  w,  z,  C,  F, -E, -B, -y, -v, -s, -p, -m, -j, -g, -d, -a, -c, -f, -i, -l, -o, -r, -u, -x, -A, -D,}, \
  {  c,  h,  m,  r,  w,  B,  0, -B, -w, -r, -m, -h, -c, -c, -h, -m, -r, -w, -B,  0,  B,  w,  r,  m,  h,  c,  c,  h,  m,  r,  w,  B,}, \
  {  d,  k,  r,  y,  F, -A, -t, -m, -f, -b, -i, -p, -w, -D,  C,  v,  o,  h,  a,  g,  n,  u,  B, -E, -x, -q, -j, -c, -e, -l, -s, -z,}, \
  {  e,  n,  w,  F, -y, -p, -g, -c, -l, -u, -D,  A,  r,  i,  a,  j,  s,  B, -C, -t, -k, -b, -h, -q, -z,  E,  v,  m,  d,  f,  o,  x,}, \
  {  f,  q,  B, -A, -p, -e, -g, -r, -C,  z,  o,  d,  h,  s,  D, -y, -n, -c, -i, -t, -E,  x,  m,  b,  j,  u,  F, -w, -l, -a, -k, -v,}, \
  {  g,  t,  0, -t, -g, -g, -t,  0,  t,  g,  g,  t,  0, -t, -g, -g, -t,  0,  t,  g,  g,  t,  0, -t, -g, -g, -t,  0,  t,  g,  g,  t,}, \
  {  h,  w, -B, -m, -c, -r,  0,  r,  c,  m,  B, -w, -h, -h, -w,  B,  m,  c,  r,  0, -r, -c, -m, -B,  w,  h,  h,  w, -B, -m, -c, -r,}, \
  {  i,  z, -w, -f, -l, -C,  t,  c,  o,  F, -q, -a, -r,  E,  n,  d,  u, -B, -k, -g, -x,  y,  h,  j,  A, -v, -e, -m, -D,  s,  b,  p,}, \
  {  j,  C, -r, -b, -u,  z,  g,  m,  F, -o, -e, -x,  w,  d,  p, -E, -l, -h, -A,  t,  a,  s, -B, -i, -k, -D,  q,  c,  v, -y, -f, -n,}, \
  {  k,  F, -m, -i, -D,  o,  g,  B, -q, -e, -z,  s,  c,  x, -u, -a, -v,  w,  b,  t, -y, -d, -r,  A,  f,  p, -C, -h, -n,  E,  j,  l,}, \
  {  l, -E, -h, -p,  A,  d,  t, -w, -a, -x,  s,  e,  B, -o, -i, -F,  k,  m, -D, -g, -q,  z,  c,  u, -v, -b, -y,  r,  f,  C, -n, -j,}, \
  {  m, -B, -c, -w,  r,  h,  0, -h, -r,  w,  c,  B, -m, -m,  B,  c,  w, -r, -h,  0,  h,  r, -w, -c, -B,  m,  m, -B, -c, -w,  r,  h,}, \
  {  n, -y, -c, -D,  i,  s, -t, -h,  E,  d,  x, -o, -m,  z,  b,  C, -j, -r,  u,  g, -F, -e, -w,  p,  l, -A, -a, -B,  k,  q, -v, -f,}, \
  {  o, -v, -h,  C,  a,  D, -g, -w,  n,  p, -u, -i,  B,  b,  E, -f, -x,  m,  q, -t, -j,  A,  c,  F, -e, -y,  l,  r, -s, -k,  z,  d,}, \
  {  p, -s, -m,  v,  j, -y, -g,  B,  d, -E, -a, -F,  c,  C, -f, -z,  i,  w, -l, -t,  o,  q, -r, -n,  u,  k, -x, -h,  A,  e, -D, -b,}, \
  {  q, -p, -r,  o,  s, -n, -t,  m,  u, -l, -v,  k,  w, -j, -x,  i,  y, -h, -z,  g,  A, -f, -B,  e,  C, -d, -D,  c,  E, -b, -F,  a,}, \
  {  r, -m, -w,  h,  B, -c,  0,  c, -B, -h,  w,  m, -r, -r,  m,  w, -h, -B,  c,  0, -c,  B,  h, -w, -m,  r,  r, -m, -w,  h,  B, -c,}, \
  {  s, -j, -B,  a, -C, -i,  t,  r, -k, -A,  b, -D, -h,  u,  q, -l, -z,  c, -E, -g,  v,  p, -m, -y,  d, -F, -f,  w,  o, -n, -x,  e,}, \
  {  t, -g,  0,  g, -t, -t,  g,  0, -g,  t,  t, -g,  0,  g, -t, -t,  g,  0, -g,  t,  t, -g,  0,  g, -t, -t,  g,  0, -g,  t,  t, -g,}, \
  {  u, -d,  B,  n, -k, -E,  g, -r, -x,  a, -y, -q,  h, -F, -j,  o,  A, -c,  v,  t, -e,  C,  m, -l, -D,  f, -s, -w,  b, -z, -p,  i,}, \
  {  v, -a,  w,  u, -b,  x,  t, -c,  y,  s, -d,  z,  r, -e,  A,  q, -f,  B,  p, -g,  C,  o, -h,  D,  n, -i,  E,  m, -j,  F,  l, -k,}, \
  {  w, -c,  r,  B, -h,  m,  0, -m,  h, -B, -r,  c, -w, -w,  c, -r, -B,  h, -m,  0,  m, -h,  B,  r, -c,  w,  w, -c,  r,  B, -h,  m,}, \
  {  x, -f,  m, -E, -q,  b, -t, -B,  j, -i,  A,  u, -c,  p,  F, -n,  e, -w, -y,  g, -l,  D,  r, -a,  s,  C, -k,  h, -z, -v,  d, -o,}, \
  {  y, -i,  h, -x, -z,  j, -g,  w,  A, -k,  f, -v, -B,  l, -e,  u,  C, -m,  d, -t, -D,  n, -c,  s,  E, -o,  b, -r, -F,  p, -a,  q,}, \
  {  z, -l,  c, -q,  E,  u, -g,  h, -v, -D,  p, -b,  m, -A, -y,  k, -d,  r, -F, -t,  f, -i,  w,  C, -o,  a, -n,  B,  x, -j,  e, -s,}, \
  {  A, -o,  c, -j,  v,  F, -t,  h, -e,  q, -C, -y,  m, -a,  l, -x, -D,  r, -f,  g, -s,  E,  w, -k,  b, -n,  z,  B, -p,  d, -i,  u,}, \
  {  B, -r,  h, -c,  m, -w,  0,  w, -m,  c, -h,  r, -B, -B,  r, -h,  c, -m,  w,  0, -w,  m, -c,  h, -r,  B,  B, -r,  h, -c,  m, -w,}, \
  {  C, -u,  m, -e,  d, -l,  t, -B, -D,  v, -n,  f, -c,  k, -s,  A,  E, -w,  o, -g,  b, -j,  r, -z, -F,  x, -p,  h, -a,  i, -q,  y,}, \
  {  D, -x,  r, -l,  f, -a,  g, -m,  s, -y,  E,  C, -w,  q, -k,  e, -b,  h, -n,  t, -z,  F,  B, -v,  p, -j,  d, -c,  i, -o,  u, -A,}, \
  {  E, -A,  w, -s,  o, -k,  g, -c,  b, -f,  j, -n,  r, -v,  z, -D, -F,  B, -x,  t, -p,  l, -h,  d, -a,  e, -i,  m, -q,  u, -y,  C,}, \
  {  F, -D,  B, -z,  x, -v,  t, -r,  p, -n,  l, -j,  h, -f,  d, -b,  a, -c,  e, -g,  i, -k,  m, -o,  q, -s,  u, -w,  y, -A,  C, -E,}, \
}


// DST-7
#define DEFINE_DST7_P4_MATRIX(a,b,c,d) \
{ \
  {  a,  b,  c,  d }, \
  {  c,  c,  0, -c }, \
  {  d, -a, -c,  b }, \
  {  b, -d,  c, -a }, \
}

#define DEFINE_DST7_P8_MATRIX(a,b,c,d,e,f,g,h) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,}, \
  {  c,  f,  h,  e,  b, -a, -d, -g,}, \
  {  e,  g,  b, -c, -h, -d,  a,  f,}, \
  {  g,  c, -d, -f,  a,  h,  b, -e,}, \
  {  h, -a, -g,  b,  f, -c, -e,  d,}, \
  {  f, -e, -a,  g, -d, -b,  h, -c,}, \
  {  d, -h,  e, -a, -c,  g, -f,  b,}, \
  {  b, -d,  f, -h,  g, -e,  c, -a,}, \
}

#define DEFINE_DST7_P16_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,}, \
  {  c,  f,  i,  l,  o,  o,  l,  i,  f,  c,  0, -c, -f, -i, -l, -o,}, \
  {  e,  j,  o,  m,  h,  c, -b, -g, -l, -p, -k, -f, -a,  d,  i,  n,}, \
  {  g,  n,  l,  e, -b, -i, -p, -j, -c,  d,  k,  o,  h,  a, -f, -m,}, \
  {  i,  o,  f, -c, -l, -l, -c,  f,  o,  i,  0, -i, -o, -f,  c,  l,}, \
  {  k,  k,  0, -k, -k,  0,  k,  k,  0, -k, -k,  0,  k,  k,  0, -k,}, \
  {  m,  g, -f, -n, -a,  l,  h, -e, -o, -b,  k,  i, -d, -p, -c,  j,}, \
  {  o,  c, -l, -f,  i,  i, -f, -l,  c,  o,  0, -o, -c,  l,  f, -i,}, \
  {  p, -a, -o,  b,  n, -c, -m,  d,  l, -e, -k,  f,  j, -g, -i,  h,}, \
  {  n, -e, -i,  j,  d, -o,  a,  m, -f, -h,  k,  c, -p,  b,  l, -g,}, \
  {  l, -i, -c,  o, -f, -f,  o, -c, -i,  l,  0, -l,  i,  c, -o,  f,}, \
  {  j, -m,  c,  g, -p,  f,  d, -n,  i,  a, -k,  l, -b, -h,  o, -e,}, \
  {  h, -p,  i, -a, -g,  o, -j,  b,  f, -n,  k, -c, -e,  m, -l,  d,}, \
  {  f, -l,  o, -i,  c,  c, -i,  o, -l,  f,  0, -f,  l, -o,  i, -c,}, \
  {  d, -h,  l, -p,  m, -i,  e, -a, -c,  g, -k,  o, -n,  j, -f,  b,}, \
  {  b, -d,  f, -h,  j, -l,  n, -p,  o, -m,  k, -i,  g, -e,  c, -a,}, \
}

#define DEFINE_DST7_P32_MATRIX(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F) \
{ \
  {  a,  b,  c,  d,  e,  f,  g,  h,  i,  j,  k,  l,  m,  n,  o,  p,  q,  r,  s,  t,  u,  v,  w,  x,  y,  z,  A,  B,  C,  D,  E,  F,}, \
  {  c,  f,  i,  l,  o,  r,  u,  x,  A,  D,  F,  C,  z,  w,  t,  q,  n,  k,  h,  e,  b, -a, -d, -g, -j, -m, -p, -s, -v, -y, -B, -E,}, \
  {  e,  j,  o,  t,  y,  D,  D,  y,  t,  o,  j,  e,  0, -e, -j, -o, -t, -y, -D, -D, -y, -t, -o, -j, -e,  0,  e,  j,  o,  t,  y,  D,}, \
  {  g,  n,  u,  B,  D,  w,  p,  i,  b, -e, -l, -s, -z, -F, -y, -r, -k, -d,  c,  j,  q,  x,  E,  A,  t,  m,  f, -a, -h, -o, -v, -C,}, \
  {  i,  r,  A,  C,  t,  k,  b, -g, -p, -y, -E, -v, -m, -d,  e,  n,  w,  F,  x,  o,  f, -c, -l, -u, -D, -z, -q, -h,  a,  j,  s,  B,}, \
  {  k,  v,  F,  u,  j, -a, -l, -w, -E, -t, -i,  b,  m,  x,  D,  s,  h, -c, -n, -y, -C, -r, -g,  d,  o,  z,  B,  q,  f, -e, -p, -A,}, \
  {  m,  z,  z,  m,  0, -m, -z, -z, -m,  0,  m,  z,  z,  m,  0, -m, -z, -z, -m,  0,  m,  z,  z,  m,  0, -m, -z, -z, -m,  0,  m,  z,}, \
  {  o,  D,  t,  e, -j, -y, -y, -j,  e,  t,  D,  o,  0, -o, -D, -t, -e,  j,  y,  y,  j, -e, -t, -D, -o,  0,  o,  D,  t,  e, -j, -y,}, \
  {  q,  E,  n, -c, -t, -B, -k,  f,  w,  y,  h, -i, -z, -v, -e,  l,  C,  s,  b, -o, -F, -p,  a,  r,  D,  m, -d, -u, -A, -j,  g,  x,}, \
  {  s,  A,  h, -k, -D, -p,  c,  v,  x,  e, -n, -F, -m,  f,  y,  u,  b, -q, -C, -j,  i,  B,  r, -a, -t, -z, -g,  l,  E,  o, -d, -w,}, \
  {  u,  w,  b, -s, -y, -d,  q,  A,  f, -o, -C, -h,  m,  E,  j, -k, -F, -l,  i,  D,  n, -g, -B, -p,  e,  z,  r, -c, -x, -t,  a,  v,}, \
  {  w,  s, -d, -A, -o,  h,  E,  k, -l, -D, -g,  p,  z,  c, -t, -v,  a,  x,  r, -e, -B, -n,  i,  F,  j, -m, -C, -f,  q,  y,  b, -u,}, \
  {  y,  o, -j, -D, -e,  t,  t, -e, -D, -j,  o,  y,  0, -y, -o,  j,  D,  e, -t, -t,  e,  D,  j, -o, -y,  0,  y,  o, -j, -D, -e,  t,}, \
  {  A,  k, -p, -v,  e,  F,  f, -u, -q,  j,  B,  a, -z, -l,  o,  w, -d, -E, -g,  t,  r, -i, -C, -b,  y,  m, -n, -x,  c,  D,  h, -s,}, \
  {  C,  g, -v, -n,  o,  u, -h, -B,  a,  D,  f, -w, -m,  p,  t, -i, -A,  b,  E,  e, -x, -l,  q,  s, -j, -z,  c,  F,  d, -y, -k,  r,}, \
  {  E,  c, -B, -f,  y,  i, -v, -l,  s,  o, -p, -r,  m,  u, -j, -x,  g,  A, -d, -D,  a,  F,  b, -C, -e,  z,  h, -w, -k,  t,  n, -q,}, \
  {  F, -a, -E,  b,  D, -c, -C,  d,  B, -e, -A,  f,  z, -g, -y,  h,  x, -i, -w,  j,  v, -k, -u,  l,  t, -m, -s,  n,  r, -o, -q,  p,}, \
  {  D, -e, -y,  j,  t, -o, -o,  t,  j, -y, -e,  D,  0, -D,  e,  y, -j, -t,  o,  o, -t, -j,  y,  e, -D,  0,  D, -e, -y,  j,  t, -o,}, \
  {  B, -i, -s,  r,  j, -A, -a,  C, -h, -t,  q,  k, -z, -b,  D, -g, -u,  p,  l, -y, -c,  E, -f, -v,  o,  m, -x, -d,  F, -e, -w,  n,}, \
  {  z, -m, -m,  z,  0, -z,  m,  m, -z,  0,  z, -m, -m,  z,  0, -z,  m,  m, -z,  0,  z, -m, -m,  z,  0, -z,  m,  m, -z,  0,  z, -m,}, \
  {  x, -q, -g,  E, -j, -n,  A, -c, -u,  t,  d, -B,  m,  k, -D,  f,  r, -w, -a,  y, -p, -h,  F, -i, -o,  z, -b, -v,  s,  e, -C,  l,}, \
  {  v, -u, -a,  w, -t, -b,  x, -s, -c,  y, -r, -d,  z, -q, -e,  A, -p, -f,  B, -o, -g,  C, -n, -h,  D, -m, -i,  E, -l, -j,  F, -k,}, \
  {  t, -y,  e,  o, -D,  j,  j, -D,  o,  e, -y,  t,  0, -t,  y, -e, -o,  D, -j, -j,  D, -o, -e,  y, -t,  0,  t, -y,  e,  o, -D,  j,}, \
  {  r, -C,  k,  g, -y,  v, -d, -n,  F, -o, -c,  u, -z,  h,  j, -B,  s, -a, -q,  D, -l, -f,  x, -w,  e,  m, -E,  p,  b, -t,  A, -i,}, \
  {  p, -F,  q, -a, -o,  E, -r,  b,  n, -D,  s, -c, -m,  C, -t,  d,  l, -B,  u, -e, -k,  A, -v,  f,  j, -z,  w, -g, -i,  y, -x,  h,}, \
  {  n, -B,  w, -i, -e,  s, -F,  r, -d, -j,  x, -A,  m,  a, -o,  C, -v,  h,  f, -t,  E, -q,  c,  k, -y,  z, -l, -b,  p, -D,  u, -g,}, \
  {  l, -x,  C, -q,  e,  g, -s,  E, -v,  j,  b, -n,  z, -A,  o, -c, -i,  u, -F,  t, -h, -d,  p, -B,  y, -m,  a,  k, -w,  D, -r,  f,}, \
  {  j, -t,  D, -y,  o, -e, -e,  o, -y,  D, -t,  j,  0, -j,  t, -D,  y, -o,  e,  e, -o,  y, -D,  t, -j,  0,  j, -t,  D, -y,  o, -e,}, \
  {  h, -p,  x, -F,  y, -q,  i, -a, -g,  o, -w,  E, -z,  r, -j,  b,  f, -n,  v, -D,  A, -s,  k, -c, -e,  m, -u,  C, -B,  t, -l,  d,}, \
  {  f, -l,  r, -x,  D, -C,  w, -q,  k, -e, -a,  g, -m,  s, -y,  E, -B,  v, -p,  j, -d, -b,  h, -n,  t, -z,  F, -A,  u, -o,  i, -c,}, \
  {  d, -h,  l, -p,  t, -x,  B, -F,  C, -y,  u, -q,  m, -i,  e, -a, -c,  g, -k,  o, -s,  w, -A,  E, -D,  z, -v,  r, -n,  j, -f,  b,}, \
  {  b, -d,  f, -h,  j, -l,  n, -p,  r, -t,  v, -x,  z, -B,  D, -F,  E, -C,  A, -y,  w, -u,  s, -q,  o, -m,  k, -i,  g, -e,  c, -a,}, \
}

//--------------------------------------------------------------------------------------------------
// DCT-2
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P2[TRANSFORM_NUMBER_OF_DIRECTIONS][2][2] ) =
{
  DEFINE_DCT2_P2_MATRIX(64),
  //DEFINE_DCT2_P2_MATRIX(64)
};

ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P4[TRANSFORM_NUMBER_OF_DIRECTIONS][4][4] ) =
{
  DEFINE_DCT2_P4_MATRIX(64,    83,    36),
  //DEFINE_DCT2_P4_MATRIX(64,    83,    36)
};

ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P8[TRANSFORM_NUMBER_OF_DIRECTIONS][8][8] ) =
{
  DEFINE_DCT2_P8_MATRIX(64,    83,    36,    89,    75,    50,    18),
  //DEFINE_DCT2_P8_MATRIX(64,    83,    36,    89,    75,    50,    18)
};

ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P16[TRANSFORM_NUMBER_OF_DIRECTIONS][16][16] ) =
{
  DEFINE_DCT2_P16_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9),
  //DEFINE_DCT2_P16_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9)
};

ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P32[TRANSFORM_NUMBER_OF_DIRECTIONS][32][32] ) =
{
  DEFINE_DCT2_P32_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9,    90,    90,    88,    85,    82,    78,    73,    67,    61,    54,    46,    38,    31,    22,    13,     4),
  //DEFINE_DCT2_P32_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9,    90,    90,    88,    85,    82,    78,    73,    67,    61,    54,    46,    38,    31,    22,    13,     4)
};

ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT2P64[TRANSFORM_NUMBER_OF_DIRECTIONS][64][64] ) =
{
  DEFINE_DCT2_P64_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9,    90,    90,    88,    85,    82,    78,    73,    67,    61,    54,    46,    38,    31,    22,    13,     4,    91,    90,    90,    90,    88,    87,    86,    84,    83,    81,    79,    77,    73,    71,    69,    65,    62,    59,    56,    52,    48,    44,    41,    37,    33,    28,    24,    20,    15,    11,     7,     2),
  //DEFINE_DCT2_P64_MATRIX(64,    83,    36,    89,    75,    50,    18,    90,    87,    80,    70,    57,    43,    25,     9,    90,    90,    88,    85,    82,    78,    73,    67,    61,    54,    46,    38,    31,    22,    13,     4,    91,    90,    90,    90,    88,    87,    86,    84,    83,    81,    79,    77,    73,    71,    69,    65,    62,    59,    56,    52,    48,    44,    41,    37,    33,    28,    24,    20,    15,    11,     7,     2)
};

// DCT-8
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT8P4[TRANSFORM_NUMBER_OF_DIRECTIONS][4][4] ) =
{
  DEFINE_DCT8_P4_MATRIX(84,     74,     55,     29),
  //DEFINE_DCT8_P4_MATRIX(84,     74,     55,     29)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT8P8[TRANSFORM_NUMBER_OF_DIRECTIONS][8][8] ) =
{
  DEFINE_DCT8_P8_MATRIX(86,     85,     78,     71,     60,     46,     32,     17),
  //DEFINE_DCT8_P8_MATRIX(86,     85,     78,     71,     60,     46,     32,     17)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT8P16[TRANSFORM_NUMBER_OF_DIRECTIONS][16][16] ) =
{
  DEFINE_DCT8_P16_MATRIX(88,     88,     87,     85,     81,     77,     73,     68,     62,     55,     48,     40,     33,     25,     17,      8),
  //DEFINE_DCT8_P16_MATRIX(88,     88,     87,     85,     81,     77,     73,     68,     62,     55,     48,     40,     33,     25,     17,      8)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDCT8P32[TRANSFORM_NUMBER_OF_DIRECTIONS][32][32] ) =
{
  DEFINE_DCT8_P32_MATRIX(90,     90,     89,     88,     87,     86,     85,     84,     82,     80,     78,     77,     74,     72,     68,     66,     63,     60,     56,     53,     50,     46,     42,     38,     34,     30,     26,     21,     17,     13,      9,      4),
  //DEFINE_DCT8_P32_MATRIX(90,     90,     89,     88,     87,     86,     85,     84,     82,     80,     78,     77,     74,     72,     68,     66,     63,     60,     56,     53,     50,     46,     42,     38,     34,     30,     26,     21,     17,     13,      9,      4)
};

// DST-7
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDST7P4[TRANSFORM_NUMBER_OF_DIRECTIONS][4][4] ) =
{
  DEFINE_DST7_P4_MATRIX(29,    55,    74,    84),
  //DEFINE_DST7_P4_MATRIX(29,    55,    74,    84)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDST7P8[TRANSFORM_NUMBER_OF_DIRECTIONS][8][8] ) =
{
  DEFINE_DST7_P8_MATRIX(17,    32,    46,    60,    71,    78,    85,    86),
  //DEFINE_DST7_P8_MATRIX(17,    32,    46,    60,    71,    78,    85,    86)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDST7P16[TRANSFORM_NUMBER_OF_DIRECTIONS][16][16] ) =
{
  DEFINE_DST7_P16_MATRIX(8,    17,    25,    33,    40,    48,    55,    62,    68,    73,    77,    81,    85,    87,    88,    88),
  //DEFINE_DST7_P16_MATRIX(8,    17,    25,    33,    40,    48,    55,    62,    68,    73,    77,    81,    85,    87,    88,    88)
};
ALIGN_DATA( MEMORY_ALIGN_DEF_SIZE, const TMatrixCoeff g_trCoreDST7P32[TRANSFORM_NUMBER_OF_DIRECTIONS][32][32] ) =
{
  DEFINE_DST7_P32_MATRIX(4,     9,    13,    17,    21,    26,    30,    34,    38,    42,    46,    50,    53,    56,    60,    63,    66,    68,    72,    74,    77,    78,    80,    82,    84,    85,    86,    87,    88,    89,    90,    90),
  //DEFINE_DST7_P32_MATRIX(4,     9,    13,    17,    21,    26,    30,    34,    38,    42,    46,    50,    53,    56,    60,    63,    66,    68,    72,    74,    77,    78,    80,    82,    84,    85,    86,    87,    88,    89,    90,    90)
};

//--------------------------------------------------------------------------------------------------

} // namespace vvenc

//! \}

