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>
#include<string.h>
char s[100005]={},ans[100005]={};
int check(int n)
{
	int l=n-1, r=1;
	for(int i=0;i<n;i++){
		if( (s[i]=='o'&&ans[i]=='S')||(s[i]=='x'&&ans[i]=='W') ){
			if(ans[l]!=ans[r]) return 0;
		}
		else{
			if(ans[l]==ans[r]) return 0;
		}
		l++; r++;
		if(l==n) l=0;
		if(r==n) r=0;
	}
	return 1;
}
void FS(int n)
{
	for(int k=1;k<=4;k++){ //四种假设情况
		memset(ans,0,sizeof(ans));
		if(k==1) {ans[0]='S'; ans[1]='S';} //羊羊
		if(k==2) {ans[0]='S'; ans[1]='W';} //羊狼
		if(k==3) {ans[0]='W'; ans[1]='S';} //狼羊
		if(k==4) {ans[0]='W'; ans[1]='W';} //狼狼
		for(int i=1;i<n-1;i++){
			if(s[i]=='o'){
				if(ans[i]=='S') ans[i+1]=ans[i-1]; //羊o则两边为同种动物
				else{ //狼o则两边为不同动物
					if(ans[i-1]=='S') ans[i+1]='W';
					else ans[i+1]='S';
				}
			}
			else{
				if(ans[i]=='S'){ //羊X则两边为不同动物
					if(ans[i-1]=='S') ans[i+1]='W';
					else ans[i+1]='S';
				}
				else ans[i+1]=ans[i-1]; //狼X则两边为同种动物
			}
		}
		if(check(n)==1){
			printf("%s\n",ans);
			return;
		}
	}
	printf("-1\n");
}
int main()
{
	int n;
	scanf("%d",&n);
	scanf("%s",s);
	FS(n);
	return 0;
}