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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

_Bool rev(_Bool a){
	if(a == 0) return 1;
	else return 0;
}

char SW(_Bool a){
	if(a == 0) return 'S';
	else return 'W';
}

int main(){
	long N, i;
	int sc;
	sc = scanf("%ld", &N);
	char s[N + 1];
	sc = scanf("%s", s);
	
	s[N + 1] = s[N];
	s[N] = s[0];
	
	int j, k;
	
	_Bool wolf = 1, sheep = 0, animal[N + 1];
	
//	animal[0] = sheep;
//	animal[1] = sheep;   //0番目と1番目が羊
	for(j = 0; j < 2; j ++){
		for(k = 0; k < 2; k ++){
			animal[0] = j;
			animal[1] = k;
			
			
			for(i = 1; i < N + 1; i ++){
				if(s[i] == 'o'){
					if(animal[i] == sheep){
						animal[i + 1] = animal[i - 1];
					}else animal[i + 1] = rev(animal[i - 1]);
				}else{
					if(animal[i] == sheep){
						animal[i + 1] = rev(animal[i - 1]);
					}else animal[i + 1] = animal[i - 1];
				}
			}
			

			if(animal[N] == animal[0] && animal[N + 1] == animal[1]){
				for(i = 0; i < N; i ++){
					printf("%c", SW(animal[i]));
				}
				printf("\n");
				return 0;
			}
		}
	}
	printf("-1\n");
	return 0;
}