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::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn idx(i: i64, s: &Vec<char>) -> usize {
    if i < 0 {
        return s.len() - 1;
    }
    if i as usize >= s.len() {
        return 0;
    }

    return i as usize;
}

fn dfs(cn: usize, s: &Vec<char>, status: &mut Vec<i64>) -> bool {
    let mut next = 0;
    if s[cn] == 'o' {
        if status[cn] == 1 {
            next = status[cn - 1];
        } else {
            next = -status[cn - 1];
        }
    }
    if s[cn] == 'x' {
        if status[cn] == 1 {
            next = -status[cn - 1];
        } else {
            next = status[cn - 1];
        }
    }
    if cn == s.len() - 1 {
        return next == status[0];
    }
    status[cn + 1] = next;

    return dfs(cn + 1, s, status);
}

fn status_print(status: &Vec<i64>) {
    let animals = status.iter().map(|&x| match x {
        -1 => 'W',
        1 => 'S',
        _ => 'E',
    });

    for i in animals {
        print!("{}", i);
    }
}

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

    // SS
    let mut status: Vec<i64> = vec![0; n];
    status[0] = 1;
    status[1] = 1;
    if dfs(1, &s, &mut status) {
        status_print(&status);
        return;
    }
    // SW
    let mut status: Vec<i64> = vec![0; n];
    status[0] = 1;
    status[1] = -1;
    if dfs(1, &s, &mut status) {
        status_print(&status);
        return;
    }
    // // WW
    let mut status: Vec<i64> = vec![0; n];
    status[0] = -1;
    status[1] = -1;
    if dfs(1, &s, &mut status) {
        status_print(&status);
        return;
    }
    // // WS
    let mut status: Vec<i64> = vec![0; n];
    status[0] = -1;
    status[1] = 1;
    if dfs(1, &s, &mut status) {
        status_print(&status);
        return;
    }
    println!("{}", -1);
}