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>

#define S 100002

int N;
char list[S];
char s[S];

char getInv(char c){
	if( c == 'S' ){
		return 'W';
	}
	return 'S';
}

void output(){
	int i;
	for( i = 1; i <= N; i++ ){ printf("%c", list[i]); }
	printf("\n");
	return;
}

void say(){
	int r, i;
	const char Sans[2] = {'x', 'o'};
	const char Wans[2] = {'o', 'x'};
	list[0] = list[N];
	list[N+1] = list[1];
	for( i = 1; i <= N; i++ ){
		if( list[i-1] == list[i+1] ){
			r = 1;
		}else{
			r = 0;
		}
		if( list[i] == 'S' ){
			printf("%c", Sans[r]);
		}else{
			printf("%c", Wans[r]);
		}
	}
	printf("\n");
	return;
}

int get(int i){
	int re = 0;
	if( i > N ){
		if( list[1] == list[N+1] ){
			output();
			return 1;
		}
	}else if( i == 1 ){
		list[i+1] = 'S';
		re = get(i+1);
		if( re ){ return 1; }
		list[i+1] = 'W';
		re = get(i+1);
		if( re ){ return 1; }
	}else{
		if( list[i] == 'S' && s[i] == 'o' ){
			list[i+1] = list[i-1];
		}
		if( list[i] == 'S' && s[i] == 'x' ){
			list[i+1] = getInv(list[i-1]);
		}
		if( list[i] == 'W' && s[i] == 'o' ){
			list[i+1] = getInv(list[i-1]);
		}
		if( list[i] == 'W' && s[i] == 'x' ){
			list[i+1] = list[i-1];
		}
		re = get(i+1);
	}
	return re;
}

int main(){
	int i;
	scanf("%d\n", &N);
	for( i = 1; i <= N; i++ ){
		scanf("%c", &s[i]);
	}
	list[1] = 'S';
	if( get(1) ){ return 0; }
	list[1] = 'W';
	if( get(1) ){ return 0; }
	printf("-1\n");
	return 0;
}