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: Wrong Answer)

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(left: usize, central: usize, right: usize, is_sheeps: &Vec<bool>, s: &Vec<char>) -> bool {
    let n = is_sheeps.len();
    if is_sheeps[central] && s[central] == 'o' {
        if !is_sheeps[left] || !is_sheeps[right] {
            return false;
        }
    } else if !is_sheeps[central] && s[central] == 'x' {
        if is_sheeps[left] || is_sheeps[right] {
            return false;
        }
    } else if is_sheeps[left] == is_sheeps[right] {
        return false;
    }
    true
}

fn main() {
    let n: usize = read();
    let s: String = read();
    let s = s.chars().collect::<Vec<_>>();

    let trials = [(true, true), (false, false), (false, true), (true, false)];
    for trial in trials.iter() {
        let mut is_sheeps = vec![false; n];
        is_sheeps[0] = trial.0;
        is_sheeps[1] = trial.1;

        for i in 1..n - 1 {
            if is_sheeps[i] && s[i] == 'o' {
                is_sheeps[i + 1] = is_sheeps[i - 1];
            } else if !is_sheeps[i] && s[i] == 'x' {
                is_sheeps[i + 1] = is_sheeps[i - 1];
            } else {
                is_sheeps[i + 1] = !is_sheeps[i - 1];
            }
        }
        let mut succeeded = true;
        succeeded &= check(n - 2, n - 1, 0, &is_sheeps, &s);
        succeeded &= check(n - 1, 0, 1, &is_sheeps, &s);
        for i in 1..n - 1 {
            succeeded &= check(i - 1, i, i + 1, &is_sheeps, &s);
        }
        if succeeded {
            println!(
                "{}",
                is_sheeps
                    .iter()
                    .map(|&x| if x { "S" } else { "W" })
                    .collect::<Vec<_>>()
                    .join("")
            );
            return;
        }
    }
    println!("-1");
}