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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>

#define S true
#define W false
#define undefined -1

#define O 'o'
#define X 'x'

#define before(i) (i == 0) ? N - 1 : i - 1
#define next(i) (i == N - 1) ? 0 : i + 1

bool checkValid(char *animals, char *comments, int N, int index) {
	return (comments[index] == O && (animals[next(index)] == animals[before(index)]) == animals[index])
	       || (comments[index] == X && (animals[next(index)] != animals[before(index)]) == animals[index]);
}
int main(void) {
	int N, i, j, nextJ;
	char *animals, *comments;
	char initial0[4] = {S, S, W, W}, initial1[4] = {S, W, S, W};
	scanf("%d", &N);
	animals = malloc(N * sizeof(char));
	comments = malloc(N * sizeof(char));
	scanf("%s", comments);
	for (i = 0; i < 4; i++) {
		for (j = 0; j < N; j++) {
			animals[j] = undefined;
		}
		animals[0] = initial0[i];
		animals[1] = initial1[i];
		for (j = 1; j < N - 1; j = nextJ) {
			nextJ = next(j);
			if (animals[j] == S) {
				if (comments[j] == O) {
					animals[nextJ] = animals[j - 1];
				}
				else {
					animals[nextJ] = !animals[j - 1];
				}
			}
			else {
				if (comments[j] == O) {
					animals[nextJ] = !animals[j - 1];
				}
				else {
					animals[nextJ] = animals[j - 1];
				}
			}
		}
		if (checkValid(animals, comments, N, 0) && checkValid(animals, comments, N, N - 1)) {
			for (j = 0; j < N; j++) {
				printf("%c", animals[j] == S ? 'S' : 'W');
			}
			printf("\n");
			return 0;
		}
	}
	printf("-1\n");
	return 0;
}