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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
 
using namespace std;

const int N = 100005;

bool a[N];
char ans[N];

int main() {
	int n;
	scanf("%d", &n);
	string str;
	cin >> str;
	for (int i = 0; i < n; i++) {
		ans[i] = '-';
		if (str[i] == 'o') a[i] = 1;
		else a[i] = 0;
	}
	int pos = 0;
	if (a[0]) {
		ans[0] = 'S';
		ans[1] = 'S';
		ans[n - 1] = 'S';
	} else {
		ans[0] = 'W';
		ans[1] = 'S';
		ans[n - 1] = 'S';
	}
	int cnt = 0;
	pos = 1;
	bool found = 0;
	while (!found && cnt < 20 * n) {
		int left = (pos == 0) ? n - 1 : pos - 1;
		int right = (pos == n - 1) ? 0 : pos + 1;
		if (ans[left] != '-' && ans[right] != '-' && pos == 0) {
			bool flag = a[pos];
			if (ans[pos] == 'W') flag ^= 1;
			if (flag) {
				if (ans[left] == ans[right]) found = 1;
			} else {
				if (ans[left] != ans[right]) found = 1;
			} 
		}
		if (found) break;
		bool ok = a[pos];
		if (ans[pos] == 'W') ok ^= 1;
		if (ok) {
			ans[right] = ans[left];
		} else {
			if (ans[left] == 'W') ans[right] = 'S';
			else ans[right] = 'W';	
		}	
		pos++;
		cnt++;
		pos %= n;
	}
	if (!found) {
		puts("-1");
		return 0;
	}
	for (int i = 0; i < n; i++) {
		putchar(ans[i]);
	}
	putchar('\n');
	return 0;
}