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: Wrong Answer)

#include <stdio.h>

int main(){
	int n;
	scanf("%d",&n);
	
	char in[n+1];
	char out[n+1];
	int s_ok,w_ok;
	int i;
	
	scanf("%s",in);
	out[n] = '\0';
	
	s_ok = 1;
	out[0] = 'S';
	out[1] = 'S';
	for(i=1;i<n-1;i++){
		if((in[i]=='o'&&out[i]=='S')||(in[i]=='x'&&out[i]=='W')) out[i+1] = out[i-1];
		if((in[i]=='x'&&out[i]=='S')||(in[i]=='o'&&out[i]=='W')){
			if(out[i-1] == 'S') out[i+1] = 'W';
			else if(out[i-1] == 'W') out[i+1] = 'S';
		}
	}
	if((in[0]=='o'&&out[n-1]==out[1]) || (in[0]=='x'&&out[n-1]!=out[1])){
		printf("%s\n",out);
		return 0;
	}
	
	out[1] = 'W';
	for(i=1;i<n-1;i++){
		if((in[i]=='o'&&out[i]=='S')||(in[i]=='x'&&out[i]=='W')) out[i+1] = out[i-1];
		if((in[i]=='x'&&out[i]=='S')||(in[i]=='o'&&out[i]=='W')){
			if(out[i-1] == 'S') out[i+1] = 'W';
			else if(out[i-1] == 'W') out[i+1] = 'S';
		}
	}
	if((in[0]=='o'&&out[n-1]==out[1]) || (in[0]=='x'&&out[n-1]!=out[1])){
		printf("%s\n",out);
		return 0;
	}else{
		s_ok = 0;
	}
	
	
	
	w_ok = 1;
	out[0] = 'W';
	out[1] = 'S';
	for(i=1;i<n-1;i++){
		if((in[i]=='o'&&out[i]=='S')||(in[i]=='x'&&out[i]=='W')) out[i+1] = out[i-1];
		if((in[i]=='x'&&out[i]=='S')||(in[i]=='o'&&out[i]=='W')){
			if(out[i-1] == 'S') out[i+1] = 'W';
			else if(out[i-1] == 'W') out[i+1] = 'S';
		}
	}
	if((in[0]=='o'&&out[n-1]!=out[1]) || (in[0]=='x'&&out[n-1]==out[1])){
		printf("%s\n",out);
		return 0;
	}
	
	
	out[1] = 'W';
	for(i=1;i<n-1;i++){
		if((in[i]=='o'&&out[i]=='S')||(in[i]=='x'&&out[i]=='W')) out[i+1] = out[i-1];
		if((in[i]=='x'&&out[i]=='S')||(in[i]=='o'&&out[i]=='W')){
			if(out[i-1] == 'S') out[i+1] = 'W';
			else if(out[i-1] == 'W') out[i+1] = 'S';
		}
	}
	if((in[0]=='o'&&out[n-1]!=out[1]) || (in[0]=='x'&&out[n-1]==out[1])){
		printf("%s\n",out);
		return 0;
	}else{
		w_ok = 0;
	}
	
	if(s_ok==0 && w_ok==0) printf("%d\n",-1);
	
	return 0;
}