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::input;

fn hoge(a0: usize, a1: usize, n: usize, v: &Vec<char>) {
	let mut a: [usize; 100000+1] = [0; 100000+1];
	a[0] = a0;
	a[1] = a1;
	for i in 2..n+1 {
		if a[i-2] == 0 {
			if a[i-1] == 0 {
				//SS
				if v[i-1] == 'o' {
					a[i] = 0;
				}
				else {
					a[i] = 1;
				}
			}
			else {
				//SW
				if v[i-1] == 'o' {
					a[i] = 1;
				}
				else {
					a[i] = 0;
				}
			}
		}
		else {
			if a[i-1] == 0 {
				//WS
				if v[i-1] == 'o' {
					a[i] = 1;
				}
				else {
					a[i] = 0;
				}
			}
			else {
				//WW
				if v[i-1] == 'o' {
					a[i] = 0;
				}
				else {
					a[i] = 1;
				}
			}
		}
	}
	if a[0] == a[n] {
		for i in 0..n {
			if a[i] == 0 {
				print!("S");
			}
			else {
				print!("W");
			}
		}
		println!("");
		std::process::exit(0);
	}
}

fn main() {
	input!(n: usize);
	input!(s: String);

	let v: Vec<char> = s.chars().collect();
	//SS
	hoge(0, 0, n, &v);
	//SW
	hoge(0, 1, n, &v);
	//WS
	hoge(1, 0, n, &v);
	//WW
	hoge(1, 1, n, &v);

	println!("-1");
}