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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String goal = br.readLine();
		generate("SS", goal);
		generate("WS", goal);
		generate("SW", goal);
		generate("WW", goal);
		System.out.println(-1);
	}
	
	public static void generate(String prefix, String goal) {
		char[] ret = new char[goal.length()];
		ret[0] = prefix.charAt(0);
		ret[1] = prefix.charAt(1);
		for(int i = 2; i < ret.length; i++) {
			if(ret[i-1] == 'S') {
				if(goal.charAt(i-1) == 'o') {
					ret[i] = ret[i-2];
				}
				else {
					ret[i] = (char)('S' + (int)'W' - ret[i-2]);
				}
			}
			else {
				if(goal.charAt(i-1) == 'x') {
					ret[i] = ret[i-2];
				}
				else {
					ret[i] = (char)('S' + (int)'W' - ret[i-2]);
				}
			}
		}
		if(isConsistent(ret, goal)) {
			System.out.println(new String(ret));
			System.exit(0);
		}
	}
	
	public static boolean isConsistent(char[] l, String s) {
		for(int i = 0; i < l.length; i++) {
			int lhs = (i+l.length-1)%l.length;
			int rhs = (i+1)%l.length;
			if(l[i] == 'S') {
				if(s.charAt(i) == 'o' && l[lhs] != l[rhs]) return false;
				if(s.charAt(i) == 'x' && l[lhs] == l[rhs]) return false;
			}
			else {
				if(s.charAt(i) == 'o' && l[lhs] == l[rhs]) return false;
				if(s.charAt(i) == 'x' && l[lhs] != l[rhs]) return false;
			}
		}
		return true;
	}
	
}