Problem:
Score : 500 points

Problem Statement

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle.
The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N-1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is o, the animal said that the two neighboring animals are of the same species, and if s_i is x, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered o if the two neighboring animals are both sheep or both wolves, and answered x otherwise.
Similarly, a wolf answered x if the two neighboring animals are both sheep or both wolves, and answered o otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print -1.

Constraints

3 ≤ N ≤ 10^{5}

s is a string of length N consisting of o and x.

Input

The input is given from Standard Input in the following format:

N
s

Output

If there does not exist an valid assignment that is consistent with s, print -1.
Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

t is a string of length N consisting of S and W.

If t_i is S, it indicates that the animal numbered i is a sheep. If t_i is W, it indicates that the animal numbered i is a wolf.

Sample Input 1

6
ooxoox

Sample Output 1

SSSWWS

For example, if the animals numbered 1, 2, 3, 4, 5 and 6 are respectively a sheep, sheep, sheep, wolf, wolf, and sheep, it is consistent with their responses. Besides, there is another valid assignment of species: a wolf, sheep, wolf, sheep, wolf and wolf.

Let us remind you: if the neiboring animals are of the same species, a sheep answers o and a wolf answers x. If the neiboring animals are of different species, a sheep answers x and a wolf answers o.

Sample Input 2

3
oox

Sample Output 2

-1

Print -1 if there is no valid assignment of species.

Sample Input 3

10
oxooxoxoox

Sample Output 3

SSWWSSSWWS

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn main(){
    let mut line1 = String::new();
    let mut line2 = String::new();
    let stdin = std::io::stdin();
    stdin.read_line(&mut line1).expect("Could not read line");;
    stdin.read_line(&mut line2).expect("Could not read line");
    let p : Vec<_> = line1.trim().split(' ').collect();
    let n : usize = p[0].parse().unwrap();
    let s = line2.trim().as_bytes();
    for c1 in vec!['S', 'W'] {
        for c2 in vec!['S', 'W'] {
            let mut ret = Vec::new();
            ret.push(c1);
            ret.push(c2);
            for i in 2 .. n {
                if ret[i - 1] == 'S' {
                    if s[i - 1] == b'o' {
                        let x = ret[i - 2];
                        ret.push(x);
                    }
                    else {
                        let x = if ret[i - 2] == 'S' {'W'} else {'S'};
                        ret.push(x);
                    }
                }
                else {
                    if s[i - 1] == b'o' {
                        let x = if ret[i - 2] == 'S' {'W'} else {'S'};
                        ret.push(x);
                    }
                    else {
                        let x = ret[i - 2];
                        ret.push(x);
                    }
                }
            }
            if ((ret[1] == ret[n - 1]) == ((ret[0] == 'S') ^ (s[0] != b'o'))) && 
                ((ret[0] == ret[n - 2]) == ((ret[n - 1] == 'S') ^ (s[n - 1] != b'o'))) {
                    for i in 0 ..n {
                print!("{}", ret[i]);
                    }
            println!("");
                    return;
                }
        }
    }
    println!("-1");
    return;
}