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>
#define l_ength size
const int inf = (1<<30);
const int mod = 1000000007;
using ll = long long;
using namespace std;

int main(){
	int n; cin >> n;
	string s; cin >> s;
	string scopy = s;
	string ans = "";
	ans += 'S';
	for( int i = 0; i < n-1; ++i ){
		if( s[i] == 'o' ){
			ans += 'S';
		} else {
			ans += 'W';
			s[i] = 'o';
			s[i+1] = ( s[i+1] == 'o' ) ? 'x' : 'o';
			if( i != n-2 ){
				s[i+2] = ( s[i+2] == 'o' ) ? 'x' : 'o';
			} else {
				s[0] = ( s[0] == 'o' ) ? 'x' : 'o';
			}
		}
	}
	bool flag = false;
	for( auto c : s ){
		if( c == 'x' ){
			flag = true;
			break;
		}
	}
	if( flag ){
		s = scopy;
		ans = "";
		ans += 'W';
		s[0] = ( s[0] == 'o' ) ? 'x' : 'o';
		s[1] = ( s[1] == 'o' ) ? 'x' : 'o';
		s[n-1] = ( s[n-1] == 'o' ) ? 'x' : 'o';
		for( int i = 0; i < n-1; ++i ){
			if( s[i] == 'o' ){
				ans += 'S';
			} else {
				ans += 'W';
				s[i] = 'o';
				s[i+1] = ( s[i+1] == 'o' ) ? 'x' : 'o';
				if( i != n-2 ){
					s[i+2] = ( s[i+2] == 'o' ) ? 'x' : 'o';
				} else {
					s[0] = ( s[0] == 'o' ) ? 'x' : 'o';
				}
			}
		}
		/*for( auto c : s ){
			if( c == 'x' ){
				cout << -1 << endl;
				return 0;
			}
		}*/
		cout << ans << endl;
	} else cout << ans << endl;
}