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 (1.42.0) (judge verdict: Wrong Answer)

use std::io::*;

fn putans(a: &Vec<usize>) {
    for &i in a.iter() {
        if i == 0 {
            print!("S");
        } else {
            print!("W");
        }
    }
}
fn check(s: &Vec<char>, a: &mut Vec<usize>, n: usize) -> bool {
    for i in 1..n - 1 {
        if s[i] == 'o' {
            if a[i] == 0 {
                a[i + 1] = a[i - 1];
            } else {
                a[i + 1] = a[i - 1] ^ 1;
            }
        } else {
            if a[i] == 0 {
                a[i + 1] = a[i - 1] ^ 1;
            } else {
                a[i + 1] = a[i - 1];
            }
        }
    }
    let last;
    let first;
    if s[n - 1] == 'o' {
        if a[n - 1] == 0 {
            last = a[n - 2];
        } else {
            last = a[n - 2] ^ 1;
        }
    } else {
        if a[n - 1] == 0 {
            last = a[n - 2] ^ 1;
        } else {
            last = a[n - 2];
        }
    }
    if s[0] == 'o' {
        first = a[1];
    } else {
        first = a[1] ^ 1;
    }
    first == a[n - 1] && last == a[0]
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let s: Vec<char> = itr.next().unwrap().chars().collect();

    // first S, second S
    let mut a = vec![0; n];
    if check(&s, &mut a, n) {
        putans(&a);
        return;
    }
    let mut a = vec![0; n];
    a[0] = 0;
    a[1] = 1;
    if check(&s, &mut a, n) {
        putans(&a);
        return;
    }
    let mut a = vec![0; n];
    a[0] = 1;
    a[1] = 0;
    if check(&s, &mut a, n) {
        putans(&a);
        return;
    }
    let mut a = vec![0; n];
    a[0] = 1;
    a[1] = 1;
    if check(&s, &mut a, n) {
        putans(&a);
        return;
    }
    println!("-1");
}