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>
#pragma warning(disable:4996)
using namespace std;
using ll = long long;
const int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 };
//#define int long long
int n;
string s;
bool check=false;
string judge(char a,char b) {
	string ans(n,'v');
	ans[0] = a;
	ans[0] = b;
	char ans_begin = '?';
	//char ans_end = '?';
	for (int i = 1; i < n; i++) {
		if (s[i] == 'o') {
			if (ans[i] == 'S') {
				if (1 <= i && i <= n - 2) {
					ans[i + 1] = ans[i - 1];
				}
				else if (i == n-1) {
					//ans[0] = ans[n - 2];
					ans_begin = ans[n - 2];
				}
				
			}
			else if(ans[i]=='W') {
				if (1 <= i && i <= n - 2) {
					if (ans[i - 1] == 'W') {
						ans[i + 1] = 'S';
					}
					else if (ans[i - 1] == 'S') {
						ans[i + 1] = 'W';
					}
				}
				else if (i == n - 1) {
					if (ans[n - 2] == 'S') {
						//ans[0] = 'W';
						ans_begin = 'W';
					}
					else if (ans[n - 2] == 'W') {
						//ans[0] = 'S';
						ans_begin = 'S';
					}
				}
			}
		}
		else if (s[i] == 'x') {
			if (ans[i] == 'S') {
				if (1 <= i && i <= n - 2) {
					if (ans[i - 1] == 'W') {
						ans[i + 1] = 'S';
					}
					else if (ans[i - 1] == 'S') {
						ans[i + 1] = 'W';
					}
				}
				else if (i == n - 1) {
					if (ans[n - 2] == 'S') {
						//ans[0] = 'W';
						ans_begin = 'W';
					}
					else if (ans[n - 2] == 'W') {
						//ans[0] = 'S';
						ans_begin = 'S';
					}
				}
			}
			else if (ans[i] == 'W') {
				if (1 <= i && i <= n - 2) {
					ans[i + 1] = ans[i - 1];
				}
				else if (i == n - 1) {
					//ans[0] = ans[n - 2];
					ans_begin = ans[n - 2];
				}
			}
		}
	}
	if (ans[0] == ans_begin) {
		check = true;
	}
	return ans;
}
signed main() {
	cin >> n;
	cin >> s;
	auto ans0 = judge('S', 'S');
	if (check) {
		cout << ans0 << endl; return 0;
	}
	auto ans1 = judge('S', 'W');
	if (check) {
		cout << ans1 << endl; return 0;
	}
	auto ans2 = judge('W', 'S');
	if (check) {
		cout << ans2 << endl; return 0;
	}
	auto ans3 = judge('W', 'W');
	if (check) {
		cout << ans3 << endl; return 0;
	}
	if (!check) {
		cout << -1 << endl;
	}
	return 0;
}