# This subroutine will adds a child as last child of parent:
  sub add_child
    { my( $parent, $child)= @_;
      my $prev_sibling= $parent->last_child;
      $child->{parent}= $parent;
      $parent->{last_child}= $child;
      $parent->{first_child}= $child unless( $parent->{first_child});
      if( $prev_sibling)
        { $child->{prev_sibling}= $prev_sibling ; 
          $prev_sibling->{next_sibling}= $child;
        }
    }