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 rep(i,n) for (int i = 0; i < n; ++i)
#define rep1(i,n) for (int i = 1; i <= n; ++i)
using namespace std;
typedef long long ll;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N; cin >> N;
  string s; cin >> s;

  rep(i, 2) {
    rep(j, 2) {
      int a[N]; // 1 = wolf, 0 = sheep
      a[1] = i;
      a[2] = j;

      for(int i = 3; i <= N; i++) {
				if(a[i - 1] == 0 && s[i - 1] == 'o' || a[i - 1] == 1 && s[i - 1] == 'x') {
				  a[i == N ? 0 : i] = a[i - 2];
        } else {
          a[i == N ? 0 : i] = a[i - 2] ^ 1;
        }
      }

      bool flag = false;
      if((a[1] == 1 && s[1] == 'x') || (a[1] == 0 && s[1] == 'o')) {
        if(a[0] == a[2]) {
          flag = true;
        }
      } else if((a[1] == 0 && s[1] == 'x') || (a[1] == 1 && s[1] == 'o')) {
        if(a[0] != a[2]) {
          flag = true;
        }
      }

      if(flag) {
        rep(i, N) {
          if(a[i]) {
            cout << 'W';
          } else {
            cout << 'S';
          }
        }
        cout << endl;
        return 0;
      }
    }
  }

  cout << -1 << endl;
}