sub unrank {
    my ($n, $rank) = @_;
    my @perm       = (0 .. $n);
    my @swap;

    for (reverse 2 .. $n) {
        $swap[$_] = $rank % $_;
        $rank = int($rank / $_);
    }

    for (2 .. $n) {
        @perm[ $swap[$_], $_ ] = @perm[ $_, $swap[$_] ] if $swap[$_];
    }
    
    return @perm[1 .. $n];
}