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)

use std::io::{BufRead, Write, stdin, stdout};

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    s.clear();
    input.read_line(&mut s).unwrap();
    let answers: Vec<bool> = s.trim().chars().map(|x| x == 'o').collect();
    let mut result: Vec<bool> = Vec::with_capacity(answers.len());
    for init in &[[true, true], [true, false], [false, true], [false, false]] {
        result.extend(init);
        for i in 2..answers.len() {
            let buf = !(result[i - 2] ^ !(answers[i - 1] ^ result[i - 1]));
            result.push(buf);
        }
        if (result[answers.len() - 2] == result[0]) ==
           !(answers[answers.len() - 1] ^ result[answers.len() - 1]) {
            break;
        } else {
            println!("{:?}", result);
            result.clear();
        }
    }
    writeln!(output,
             "{}",
             if result.is_empty() {
                 "-1".to_owned()
             } else {
                 result.iter().map(|&x| if x { 'S' } else { 'W' }).collect::<String>()
             })
        .unwrap();
}

fn main() {
    let stdin = stdin();
    solve(stdin.lock(), stdout());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("6
ooxoox\n",
             "SSSWWS\n");
    }
    #[test]
    fn case2() {
        test("3
oox\n",
             "-1\n");
    }
    #[test]
    fn case3() {
        test("10
oxooxoxoox\n",
             "SSWWSSSWWS\n");
    }
}