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

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