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 read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn check(v: &Vec<i32>, n: i32, a0: i32, a1: i32) -> Option<Vec<i32>> {
    let mut a: Vec<i32> = vec![];
    a.push(a0);
    a.push(a1);
    for i in 0..n {
        let tmp1 = a[i as usize];
        let tmp2 = a[(i + 1) as usize];
        let tmp = tmp1 * tmp2 * v[((i + 1) % n) as usize];
        a.push(tmp);
    }

    if a0 == a[n as usize] && a1 == a[(n + 1) as usize] {
        Some(a.clone())
    } else {
        None
    }
}

fn main() {
    let n: i32 = read();
    let s: String = read();
    let v: Vec<i32> = s.chars().map(|e| if e == 'o' { 1 } else { -1 }).collect();

    if let Some(a) = check(&v, n, 1, 1) {
        for i in 0..n {
            if a[i as usize] == 1 {
                print!("S");
            } else {
                print!("W");
            }
        }
    } else if let Some(a) = check(&v, n, 1, -1) {
        for i in 0..n {
            if a[i as usize] == 1 {
                print!("S");
            } else {
                print!("W");
            }
        }
    } else if let Some(a) = check(&v, n, -1, 1) {
        for i in 0..n {
            if a[i as usize] == 1 {
                print!("S");
            } else {
                print!("W");
            }
        }
    } else if let Some(a) = check(&v, n, -1, -1) {
        for i in 0..n {
            if a[i as usize] == 1 {
                print!("S");
            } else {
                print!("W");
            }
        }
    } else {
        print!("-1");
    }
    println!("");
}