#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
  int n;
  cin >> n;
  string s;
  cin >> s;
  s.push_back(s[0]);
  s.push_back(s[1]);
  bool f = false;
  vector<int> ans(n + 2); // 0 sheep, 1 wolf
  
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      ans[0] = i, ans[1] = j;
      for (int i = 2; i <= n+1; i++) {
        if (ans[i-1] == 0) {
          // previous sheep
          ans[i] = s[i-1] == 'o' ? ans[i-2] : !ans[i-2];
        } else {
          // previous wolf
          ans[i] = s[i-1] == 'x' ? ans[i-2] : !ans[i-2];
        }
      }
      if (ans[0] == ans[n] && ans[1] == ans[n+1]) {
        f = true;
        break;
      }
    }
    if (f) break;
  }
  
  if (f) {
    for (int i = 0; i < n; i++) cout << (ans[i] == 0 ? 'S' : 'W');
  } else {
    cout << -1;
  }
  cout << endl;
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

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.

Examples

Input

6
ooxoox


Output

SSSWWS


Input

3
oox


Output

-1


Input

10
oxooxoxoox


Output

SSWWSSSWWS

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
  int n;
  cin >> n;
  string s;
  cin >> s;
  s.push_back(s[0]);
  s.push_back(s[1]);
  bool f = false;
  vector<int> ans(n + 2); // 0 sheep, 1 wolf
  
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      ans[0] = i, ans[1] = j;
      for (int i = 2; i <= n+1; i++) {
        if (ans[i-1] == 0) {
          // previous sheep
          ans[i] = s[i-1] == 'o' ? ans[i-2] : !ans[i-2];
        } else {
          // previous wolf
          ans[i] = s[i-1] == 'x' ? ans[i-2] : !ans[i-2];
        }
      }
      if (ans[0] == ans[n] && ans[1] == ans[n+1]) {
        f = true;
        break;
      }
    }
    if (f) break;
  }
  
  if (f) {
    for (int i = 0; i < n; i++) cout << (ans[i] == 0 ? 'S' : 'W');
  } else {
    cout << -1;
  }
  cout << endl;
  return 0;
}

```