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>

char s[100005];
int animal[4][100005];

int main() {

	int N;

	scanf("%d",&N);

	scanf("%s",s);

	int i, j;

	if (s[0] == 'o') {
		animal[0][N - 1] = 0;
		animal[0][0] = 0;
		animal[0][1] = 0;

		animal[1][N - 1] = 1;
		animal[1][0] = 0;
		animal[1][1] = 1;

		animal[2][N - 1] = 0;
		animal[2][0] = 1;
		animal[2][1] = 1;

		animal[3][N - 1] = 1;
		animal[3][0] = 1;
		animal[3][1] = 0;
	}
	else {
		animal[0][N - 1] = 0;
		animal[0][0] = 0;
		animal[0][1] = 1;

		animal[1][N - 1] = 1;
		animal[1][0] = 0;
		animal[1][1] = 0;

		animal[2][N - 1] = 1;
		animal[2][0] = 1;
		animal[2][1] = 1;

		animal[3][N - 1] = 0;
		animal[3][0] = 1;
		animal[3][1] = 0;
	}

	for (j = 0; j < 4; j++) {


		for (i = 1; i < N - 1; i++) {
			if (animal[j][i] == 0) {
				if (animal[j][i - 1] == 0) {
					if (s[i] == 'o') { animal[j][i + 1] = 0; }
					else { animal[j][i + 1] = 1; }
				}
				else {
					if (s[i] == 'o') { animal[j][i + 1] = 1; }
					else { animal[j][i + 1] = 0; }
				}
			}
			else {
				if (animal[j][i - 1] == 0) {
					if (s[i] == 'o') { animal[j][i + 1] = 1; }
					else { animal[j][i + 1] = 0; }
				}
				else {
					if (s[i] == 'o') { animal[j][i + 1] = 0; }
					else { animal[j][i + 1] = 1; }
				}
			}
		}

		int a;

		if (animal[j][N - 1] == 0) {
			if (animal[j][N - 2] == 0) {
				if (s[N - 1] != 'o') {
					a = 1;
				}
				else {
					a = 0;
				}
			}
			else {
				if (s[N - 1] != 'o') {
					a = 0;
				}
				else {
					a = 1;
				}
			}
		}
		else {
			if (animal[j][N - 2] == 0) {
				if (s[N - 1] != 'o') {
					a = 0;
				}
				else {
					a = 1;
				}
			}
			else {
				if (s[N - 1] != 'o') {
					a = 1;
				}
				else {
					a = 0;
				}
			}
		}
		if (animal[j][0] == a) {
			for (i = 0; i < N; i++) {
				if (animal[j][i] == 0) {
					printf("S");
				}
				else {
					printf("W");
				}
			}
			printf("\n");
			return 0;
		}
	}

	printf("-1\n");

	return 0;
}