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(void)
{
	//3つの狼の合計が偶数->〇
	//S->0 W->1
	//S->0x53
	//W->0x57
	//o->0x6f
	//x->0x78
	long long int N, i, h, x = 0, ok = 0;
	char c;
	static char say[100015];
	static long long int dou[100015];
	long long int  sta[2];
	scanf("%lld", &N);
	fflush(stdin);
	for (i = 0; i < N; i++) {
		scanf("%c", &say[i]);
	}
	for (h = 0; h < 4; h++) {
		if (h == 0) { sta[0] = 0; sta[1] = 0; }
		if (h == 1) { sta[0] = 0; sta[1] = 1; }
		if (h == 2) { sta[0] = 1; sta[1] = 0; }
		if (h == 3) { sta[0] = 1; sta[1] = 1; }
		dou[0] = sta[0];
		dou[1] = sta[1];
		for (i = 2; i < N + 2; i++) {
			if (say[i-1] == 0x6f) { x = 0; }else { x = 1; }
			if ((x+dou[i - 1] + dou[i - 2])%2==1) {dou[i] = 1;}else { dou[i] = 0;}
		}
		if (dou[N] == sta[0] && dou[N + 1] == sta[1]) {
			for (i = 1; i <= N; i++) {
				if (dou[i] == 0) { c = 0x53; }
				else { c = 0x57; }
				printf("%c", c);
				ok = 1;
			}
			break;
		}
	}
	if (ok == 0) { printf("-1"); }
	printf("\n");
	return 0;
}