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)

fn main() {
  let _: usize = read();
  let s: String = read();
  
  let ans =["SS","SW","WS","WW"].iter().filter_map(|pat| valid(&s, pat)).next();
  println!("{}", ans.unwrap_or("-1".to_string())); 
}

fn valid(s: &str, pat: &str) -> Option<String> {
  let s = s.chars().collect::<Vec<_>>();
  let mut pat = pat.chars().collect::<Vec<_>>();
  
  let l = s.len();
  for i in 1 .. l {
    let prev = pat[(i-1)%l];
    match (s[i%l], pat[i%l]) {
      ('o', 'S') => pat.push(prev),
      ('o', 'W') => pat.push(if prev=='S' {'W'} else {'S'}),
      ('x', 'S') => pat.push(if prev=='S' {'W'} else {'S'}),
      ('x', 'W') => pat.push(prev),
      _ => unreachable!()
    }
  }
  
  if pat[0] == pat[l] {
    pat.pop();
    Some(pat.iter().map(|&c| c).collect::<String>())
  } else {
    None
  }
}

fn read<T: std::str::FromStr>() -> T {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().parse::<T>().ok().unwrap()
}