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;
#[allow(unused_imports)]
use std::cmp;
use std::collections::LinkedList;

fn read_list() -> LinkedList<String> {
    let mut s = String::new();
    io::stdin().read_line(&mut s).expect("");
    s.split(' ').map(|x| x.to_string()).collect::<LinkedList<String>>()
}

fn pop_parse<T: std::str::FromStr>(list: &mut LinkedList<String>) -> T {
    list.pop_front().expect("").trim().parse::<T>().ok().unwrap()
}

fn align(s: &Vec<bool>, a: bool, b: bool) -> Option<Vec<bool>> {
    let mut ans = vec![a, b];
    for i in 1..s.len() {
        let next = ans[i-1] ^ ans[i] ^ s[i];
        ans.push(next);
    }
    if ans.pop().unwrap() == a && ans[s.len()-1] ^ a ^ s[0] == b {
        Some(ans)
    } else {
        None
    }
}

fn main() {
    let _: i32 = pop_parse(&mut read_list());
    let s: String = pop_parse(&mut read_list());
    let vs: Vec<bool> = s.into_bytes().into_iter()
        .map(|x| match x as char {
            'o' => true,
            'x' => false,
            _   => panic!(),
        }).collect();
    let mut ans: Option<Vec<bool>> = None;
    for (a,b) in vec![(true,true), (true,false), (false,true), (false,false)] {
        match align(&vs, a, b) {
            Some(v) => ans = Some(v),
            None => {},
        }
    }
    let ans = match ans {
        Some(v) => String::from_utf8(
            v.into_iter().map(|x| if x {'S' as u8} else {'W' as u8}).collect()).unwrap(),
        None => String::from("-1"),
    };
    println!("{}", ans);
}