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 proconio::{fastout, input};
use std::io::*;
use std::str::FromStr;

use std::cmp::{max, min};
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};

fn main() {
    input! {
        n: usize,
        s: String,
    }
    let sc = s.chars().collect::<Vec<char>>();
    let mut ss = vec!['S'; n];
    let mut sw = vec!['S'; n];
    sw[1] = 'W';
    let mut ws = vec!['S'; n];
    ws[0] = 'W';
    let mut ww = vec!['S'; n];
    ww[0] = 'W';
    ww[1] = 'W';

    for i in 1..n - 1 {
        ss[i + 1] = forward(i, i - 1, &sc, &ss);
        sw[i + 1] = forward(i, i - 1, &sc, &sw);
        ws[i + 1] = forward(i, i - 1, &sc, &ws);
        ww[i + 1] = forward(i, i - 1, &sc, &ww);
    }
    let mut n = n - 1;

    if forward(n, n - 1, &sc, &ss) == ss[0] && forward(0, 1, &sc, &ss) == ss[n] {
        println!("{}", ss.iter().collect::<String>());
        return;
    }
    if forward(n, n - 1, &sc, &sw) == sw[0] && forward(0, 1, &sc, &sw) == sw[n] {
        println!("{}", ss.iter().collect::<String>());
        return;
    }
    if forward(n, n - 1, &sc, &ws) == ws[0] && forward(0, 1, &sc, &ws) == ws[n] {
        println!("{}", ws.iter().collect::<String>());
        return;
    }
    if forward(n, n - 1, &sc, &ww) == ww[0] && forward(0, 1, &sc, &ww) == ww[n] {
        println!("{}", ww.iter().collect::<String>());
        return;
    }
    println!("-1")
}

fn forward(cn: usize, pn: usize, s: &Vec<char>, v: &Vec<char>) -> char {
    match s[cn] {
        'o' => match v[cn] {
            'S' => match v[pn] {
                'S' => 'S',
                'W' => 'W',
                _ => ' ',
            },
            'W' => match v[pn] {
                'S' => 'W',
                'W' => 'S',
                _ => ' ',
            },
            _ => ' ',
        },
        'x' => match v[cn] {
            'S' => match v[pn] {
                'S' => 'W',
                'W' => 'S',
                _ => ' ',
            },
            'W' => match v[pn] {
                'S' => 'S',
                'W' => 'W',
                _ => ' ',
            },
            _ => ' ',
        },
        _ => ' ',
    }
}