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 <stdint.h>
#include <iostream>
#include <string>
#include <memory>
using namespace std;

int main() {
	int N;
	string str;
	cin >> N >> str;
	unique_ptr<int[]>out = make_unique<int[]>(N);
	//-1 = 未設定,0 = 羊,1 = 狼
	auto check = [&](int v1,int vn)->bool{
		auto pstr = str.data();
		auto ptr = out.get();
		for (size_t i = 0; i < N; i++)
		{
			*ptr = -1;
			ptr++;
		}
		ptr = out.get();
		ptr[N - 1] = vn;
		ptr[0] = v1;
		for (size_t i = 0; i < N - 2; i++)
		{
			bool sim = ptr[i] == 0 && pstr[i] == 'o';
			if (sim) {
				ptr[(i + 1)] = ptr[(i + N - 1) % N];
			}
			else {
				ptr[(i + 1)] = (ptr[(i + N - 1) % N] == 0) ? 1 : 0;
			}
		}
		bool sim = ptr[N - 2] == 0 && pstr[N - 2] == 'o';
		if (sim) {
			sim = ptr[N - 3] == ptr[N - 1];
		}
		else {
			sim = ptr[N - 3] != ptr[N - 1];
		}
		if (!sim)return false;
		sim = ptr[N - 1] == 0 && pstr[N - 1] == 'o';
		if (sim) {
			return ptr[N - 2] == ptr[0];
		}
		else {
			return ptr[N - 2] != ptr[0];
		}	
	};
	auto dout = [&]()->void {
		auto ptr = out.get();
		for (size_t i = 0; i < N; i++)
		{
			cout << ((*ptr == 0) ? 'S' : 'W');
			ptr++;
		}
	};
	if (check(0, 0))dout();
	else if (check(0, 1))dout();
	else if (check(1, 0))dout();
	else if (check(1, 1))dout();
	else cout << -1;

	return 0;
}