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)

#[test]
fn check_solve() {
    println!("input:\n6\nooxoox\noutput:\n{}\n", solve("6\nooxoox\n"));
    println!("input:\n3\noox\noutput:\n{}\n", solve("3\noox\n"));
    println!(
        "input:\n10\noxooxoxoox\noutput:\n{}\n",
        solve("10\noxooxoxoox\n")
    );
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);
    let n: usize = sc.read();
    let s: Vec<_> = sc.get().chars().collect();

    'lp: for &(t0, t1) in [('S', 'S'), ('S', 'W'), ('W', 'S'), ('W', 'W')].iter() {
        let mut t = Vec::new();
        t.push(t0);
        t.push(t1);
        for i in 2..n+1 {
            if (s[i-1] == 'o') ^ (t[i-1] == 'W') {
                let nxt = t[i-2];
                t.push(nxt);
            } else if t[i-2] == 'S' {
                t.push('W');
            } else {
                t.push('S');
            }
        }
        if t[0] != t[n] {
            continue;
        }
        if ((s[0] == 'o') ^ (t[0] == 'W')) != (t[n-1] == t[1]) {
            continue 'lp;
        }
        for i in 0..n-1 {
            if ((s[i+1] == 'o') ^ (t[i+1] == 'W')) != (t[i] == t[i+2]) {
                continue 'lp;
            }
        }
        t.pop();
        return t.into_iter().collect();
    }

    format!("-1\n")
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}