# 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 ] ]);