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: Accepted)

#include <bits/stdc++.h>
typedef long long lint;

#define PI acos(-1)
#define INF64 1LL << 60
#define INF32 1 << 29
#define all(a) (a).begin(), (a).end()

using namespace std;

void execute()
{
	int N;
	string input;
	bool tmp;
	int ans_num = -1;
	cin >> N;
	cin >> input;
	input = input[N - 1] + input;
	vector<vector<bool>> ans(4, vector<bool>(N + 2));
	ans[0][0] = ans[0][1] = ans[1][0] = ans[2][1] = true;
	ans[1][1] = ans[2][0] = ans[3][0] = ans[3][1] = false;

	for (int i = 2; i < N + 2; i++)
	{
		for (int j = 0; j < 4; j++)
		{
			ans[j][i] = ans[j][i - 1] ^ ans[j][i - 2] ^ (input[i - 2] == 'o');
		}
	}

	for (int i = 0; i < 4; i++)
	{
		if (ans[i][0] == ans[i][N] && ans[i][1] == ans[i][N + 1])
			ans_num = i;
	}

	if (ans_num == -1)
	{
		cout << ans_num << endl;
		return;
	}
	for (int i = 2; i < N + 2; i++)
	{
		cout << (ans[ans_num][i] ? "S" : "W");
	}
	cout << endl;
	return;
}

int main()
{
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	execute();

	int stop;
	cin >> stop;

	return 0;
}