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>
#include <string.h>

void tamesu(int n, char *str, char *p, char now, char prev) {
	int i;

	memset(p, '\0', sizeof(p));
	p[0] = now;
	p[n - 1] = prev;
	for (i = 0; i < n - 1; i++) {
		now = p[(i + n - 1) % n];
		if ((p[i] == 'S') == (str[i] == 'x')) {
			if (now == 'S') {
				now = 'W';
			} else {
				now = 'S';
			}
		}
		if (p[i + 1] != '\0' && p[i + 1] != now) {
			p[0] = '\0';
			return;
		} else {
			p[i + 1] = now;
		}
	}
	p[n] = '\0';

	if (p[n - 1] == 'S') {
		if (str[n - 1] == 'o') {
			if (p[n - 2] != p[0]) {
				p[0] = '\0';
			}
		} else {
			if (p[n - 2] == p[0]) {
				p[0] = '\0';
			}
		}
	} else {
		if (str[n - 1] == 'o') {
			if (p[n - 2] == p[0]) {
				p[0] = '\0';
			}
		}
		else {
			if (p[n - 2] != p[0]) {
				p[0] = '\0';
			}
		}
	}
}

int main(void) {
	int n;
	char str[100001], p[100001];

	scanf("%d %s", &n, str);

	tamesu(n, str, p, 'S', 'S');
	if (p[0] == '\0') {
		tamesu(n, str, p, 'W', 'S');
	}
	if (p[0] == '\0') {
		tamesu(n, str, p, 'S', 'W');
	}
	if (p[0] == '\0') {
		tamesu(n, str, p, 'W', 'W');
	}
	printf("%s\n", p[0] == '\0' ? "-1" : p);

	return 0;
}