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: Time Limit Exceeded)

import java.util.*;
public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		String input = sc.next();
		String[] way = {"SS" , "SW" , "WS" , "WW" };
		char[]one = {'S' , 'S' , 'W' , 'W'};
		char[]two = {'S' , 'W' , 'S' , 'W'};
		char[]ans = new char[N];
		//String res ="";
		for(int i = 0 ; i<4; i++) {
			ans[0] = one[i];
			ans[1] = two[i];
		//	res = way[i];
		//	res = getAnswer(ans, input);
			ans = getAnswer(ans, input);
			boolean OK = judge(ans,input);
			if(OK) {
				String res = "";
				for(int j = 0 ; j<ans.length; j++) {
					res+=ans[j];
				}
				System.out.println(res);
				return;
			}
		}
		System.out.println(-1);
	}
	
	static char[] getAnswer(char[] ans, String input) {
		for(int i = 1; i<input.length()-1; i++) {
			if(input.charAt(i) == 'o') {
				if(ans[i] == 'S') {
					if(ans[i-1] == 'S') {
						ans[i+1]='S';
					}
					else {
						ans[i+1]='W';
					}
				}
				else {
					if(ans[i-1] == 'S') {
						ans[i+1]='W';
					}
					else {
						ans[i+1]='S';
					}
				}
			}
			else {
				if(ans[i] == 'S') {
					if(ans[i-1] == 'S') {
						ans[i+1]='W';
					}
					else {
						ans[i+1]='S';
					}
				}
				else {
					if(ans[i-1] =='S') {
						ans[i+1]='S';
					}
					else {
						ans[i+1]='W';
					}
				}
			}
		}
		return ans;
	}
	
	static boolean judge(char[] ans, String input) {
		if(input.charAt(input.length()-1) == 'o') {
			if(ans[ans.length-1] == 'S') {
				if(ans[ans.length-2] == 'S') {
					if(ans[0] == 'S') {
						return true;
					}
					else {
						return false;
					}
				}
				else {
					if(ans[0] == 'W') {
						return true;
					}
					else {
						return false;
					}
				}
			}
			else {
				if(ans[ans.length-2] == 'S') {
					if(ans[0] == 'S') {
						return false;
					}
					else {
						return true;
					}
				}
				else {
					if(ans[0] == 'W') {
						return false;
					}
					else {
						return true;
					}
				}
			}
		}
		else {
			if(ans[ans.length-1] == 'S') {
				if(ans[ans.length-2] == 'S') {
					if(ans[0] == 'S') {
						return false;
					}
					else {
						return true;
					}
				}
				else {
					if(ans[0] == 'W') {
						return false;
					}
					else {
						return true;
					}
				}
			}
			else {
				if(ans[ans.length-2] == 'S') {
					if(ans[0] == 'S') {
						return true;
					}
					else {
						return false;
					}
				}
				else {
					if(ans[0] == 'W') {
						return true;
					}
					else {
						return false;
					}
				}
			}
		}
	}
}