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>
#include <stdlib.h>
#define FOR(i,a,b) for(int i=a;i<b;i++)

int main(){
	int n;
	scanf("%d",&n);
	char *si = (char *)malloc(sizeof(char)*n);
	scanf("%s",si);

	int *s = (int *)malloc(sizeof(int)*n);
	FOR(i,0,n){									//o→1,x→-1
		if(si[i] == 'o') s[i] = 1;
		else s[i] = -1;
	}

	int *ans = (int *)malloc(sizeof(int)*n);
	FOR(i,0,2){
		FOR(j,0,2){

			if(i == 0)	ans[0] = 1;			//S→1,W→-1
			else		ans[0] = -1;
			if(j == 0)	ans[1] = 1;
			else		ans[1] = -1;

			FOR(k,1,n-1){
				if(ans[k] * s[k] == 1) ans[k+1] = ans[k-1];
				if(ans[k] * s[k] != 1) ans[k+1] = -ans[k-1];
			}

			int a=0,b=0;
			if(ans[0] * s[0] == 1 && ans[1] == ans[n-1]) a = 1;
			if(ans[0] * s[0] != 1 && ans[1] != ans[n-1]) a = 1;
			if(ans[n-1] * s[n-1] == 1 && ans[0] == ans[n-2]) b = 1;
			if(ans[n-1] * s[n-1] != 1 && ans[0] != ans[n-2]) b = 1;

			if(a*b != 0){
				FOR(l,0,n){
					if(ans[l] == 1) printf("S");
					else printf("W");
				}
				return 0;
			}
		}
	}
	printf("-1\n");
}