sub rearrange {
  my($dim, $height, $v, $args) = @_;
  my @bitmap = (0 .. $dim - 1);
  my($ones, $zeros) = (0, $dim - 1);

  # find holes in the ones looking from the bottom and plugs
  # in the zeros looking from the top, then swap them
  while ($ones < $zeros) { 
    ++$ones , next if ($v & (1 << $ones )) != 0;
    --$zeros, next if ($v & (1 << $zeros)) == 0;
    @bitmap[$ones, $zeros] = @bitmap[$zeros, $ones];
    ++$ones;
    --$zeros;
  } 
  ++$ones if $ones == $zeros && ($v & (1 << $ones)) != 0;
  # $ones is now a count of the number of 1-bits

  # may need an extra swap to get the 'x' at the right height
  if ($bitmap[$height] != $ones) { 
    my($lowest) = grep $bitmap[$_] == $ones, 0 .. $dim - 1;
    @bitmap[$height, $lowest] = @bitmap[$lowest, $height];
  }

  # 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 $_ + $mapped, @vmap;
  } 
  ($bitmap[$height], [ @$args[ @vmap ] ]);
}