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)

use std::io;
use std::io::Read;

fn main() {
    let mut stdin = io::stdin();
    let mut lines = String::new();
    let _ = stdin.read_to_string(&mut lines);
    let vec = lines.lines().collect::<Vec<&str>>();
    let n :usize = vec[0].trim().parse().unwrap();
    let mut animalans :Vec<bool> = Vec::new();
    for c in vec[1].chars() {
        match c {
            'o' => {
                animalans.push(true);
            },
            'x' => {
                animalans.push(false);
            },
            _ => {}
        }
    }
    let animalans = animalans;
    let mut animalpattern :Vec<Vec<bool>> = vec![vec![true,true],vec![true,false],vec![false,true],vec![false,false]];
    for i in 1..(n-1) {
        for j in 0..4 {
            let nextanimal = if animalpattern[j][i] ^ animalans[i] {
                !animalpattern[j][i-1]
            } else {
                animalpattern[j][i-1]
            };
            animalpattern[j].push(nextanimal);
        }
    }
    let animalpattern = animalpattern;
    for j in 0..4 {
        if animalans[0] !=
            animalpattern[j][0] ^ (animalpattern[j][1] ^ animalpattern[j][n-1]) { continue; }
        if animalans[n-1] !=
            animalpattern[j][n-1] ^ (animalpattern[j][0] ^ animalpattern[j][n-2]) { continue; }
        for i in 0..n {
            if animalpattern[j][i] {
                print!("S");
            } else {
                print!("W");
            }
        }
        println!("");
        return;
    }
    println!("-1");
}