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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

int mumujun(string s, string temp, int k, int n){
	if (s[k] == 'o'){
		if (temp[k] == 'S' && temp[(k-1+n)%n] == temp[(k+1)%n]){
			return 1;
		}
		if (temp[k] == 'W' && temp[(k-1+n)%n] != temp[(k+1)%n]){
			return 1;
		}
	}
	if (s[k] == 'x'){
		if (temp[k] == 'W' && temp[(k-1+n)%n] == temp[(k+1)%n]){
			return 1;
		}
		if (temp[k] == 'S' && temp[(k-1+n)%n] != temp[(k+1)%n]){
			return 1;
		}
	}

}

int main(void){
	int n;
	string s;

	char zero[2] = {'S', 'W'}, one[2] = {'S', 'W'};


	cin >> n >> s;

	int ok = 0;

	string temp, res;

	for (int i = 0; i < 2; i++){
		for (int j = 0; j < 2; j++){
			temp = "";
			for (int k = 0; k < n; k++){
				if (k == 0){
					temp += zero[i];
				}
				else if (k == 1)
					temp += one[j];
				else {
					if (s[k-1] == 'o'){
						if (temp[k-1] == 'S')
							temp += temp[k-2];
						else {
							if (temp[k-2] == 'S')
								temp += "W";
							else
								temp += "S";
						}
					}
					else {
						if (temp[k-1] == 'W')
							temp += temp[k-2];
						else {
							if (temp[k-2] == 'S')
								temp += "W";
							else
								temp += "S";
						}
					}
				}

				if (k == n - 1 && ok == 0){
					if (mumujun(s, temp, k, n) && mumujun(s, temp, 0, n))
						ok = 1;

					if (ok == 1){
						res = temp;
					}
				}
			}
		}
	}

	if (ok)
		cout << res << endl;
	else
		cout << -1 << endl;


}