$i = 'A'; # the class label
  for $n (@temp) {
    next if defined $arrangements{$n}; # already classified it.

    @n = split /,/, $n;
    @classmates = ( $n, join(',', reverse @n) ); # n and its mirror
    @classmates = (@classmates, &M1(@n)); # Maz 1
    @classmates = (@classmates, &M2(@n)); # Maz 2
    @classmates = (@classmates, &M3(@n)); # Maz 3

    &ClassReunion( $i, \@classmates );
    $i++;
  }

##</code><code>##

sub M1 { map join(',', @_[$_..$#_], @_[0..$_-1]), 1..$#_ }


##</code><code>##

sub M2 {
  my %temp;
  @temp{(1..@_)} = @_;
  %temp = reverse %temp;
  return join(',', @temp{(1..@_)});
}