my @bits = (0 .. $dim - 1);
  for (0 .. $dim - 1) {
    $bits[$_] += 2 * $dim if $v & (1 << $_);
  }
  $bits[$height] += $dim;
  my @bitmap = map $_ % $dim, sort { $b <=> $a } @bits;

##</code><code>##

  # we now know what row should go where, so build and return the mapped result
  my @invmap = sort { $bitmap[$a] <=> $bitmap[$b] } 0 .. $dim - 1;
  my @vmap = (0);
  for (0 .. $dim - 1) { 
    my $mapped = 1 << $invmap[$_];
    push @vmap, map $_ + $mapped, @vmap;
  } 
  return ($bitmap[$height], [ @$args[ @vmap ] ]);