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    return 1;
  };
  
  my $heap = Heap::Priority->new;
  $heap->lowest_first;
  $heap->add($_, $o{cost}->($_, $_+1)) for 0 .. $#q - 1;

  ###################################################################
  # I haven't found a good solution to maintain the heap and modify
  # the list, so as a workaround the heap identifies a mergable pair
  # with the key and when merging elements of a pair, the second
  # element is replaced by `undef` to maintain the size of the list,
  # so the heap keys, indices into the list, remain valid. This has
  # the consequence of producing gaps in the list, and the variables
  # below maintain how the gaps can be skipped.
  ###################################################################
  my %next = map { $_ => $_ + 1 } 0 .. $#q - 1;
  my %prev = map { $_ => $_ - 1 } 1 .. $#q - 1;

  for (my $count = @q;;) {
    my $ix = $heap->pop;