sub Prod {
    my( $i, $j )= @_;
    my $f= $i;
    $f *= $j   if  $i < $j;
    for my $p ( $i+1..$j-1 ) {
        $f *= $p*$p;
    }
    return $f;
}

sub Count {
    my( $parens, $len )= @_;
    return 1   if  1 == $len;
    return Prod($parens+1,$parens+$len)/Prod(1,$len)
}