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>

using namespace std;

typedef long long int ll;

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

  int n;
  cin >> n;
  string s;
  cin >> s;
  string tmp = "SW";
  for(int p = 0; p < 2; p++){
    for(int q = 0; q < 2; q++){
      for(int r = 0; r < 2; r++){
        vector < char > res(n + 1);
        res[n] = tmp[p];
        res[1] = tmp[q];
        res[2] = tmp[r];
        if(res[1] == 'S'){
          if(s[0] == 'o'){
            if(res[n] != res[2]) continue;
          }else if(res[n] == res[2]) continue;
        }else{
          if(s[0] == 'o'){
            if(res[n] == res[2]) continue;
          }else if(res[n] != res[2]) continue;
        }

        for(int i = 1; i < n - 1; i++){
          if(res[i + 1] == 'S'){
            if(s[i] == 'o') res[i + 2] = res[i];
            else if(res[i] == 'S') res[i + 2] = 'W';
            else res[i + 2] = 'S';
          }else{
            if(s[i] == 'x') res[i + 2] = res[i];
            else if(res[i] == 'S') res[i + 2] = 'W';
            else res[i + 2] = 'S';
          }
        }

        if(res[n] == 'S'){
          if(s[n - 1] == 'o' && res[n - 1] != res[1]) continue;
          else if(s[n - 1] == 'x' && res[n - 1] == res[1]) continue;
        }else{
          if(s[n - 1] == 'o' && res[n - 1] == res[1]) continue;
          else if(s[n - 1] == 'x' && res[n - 1] != res[1]) continue;
        }

        for(int i = 1; i <= n; i++) cout << res[i];
        cout << endl;
        return 0;
      }
    }
  }

  cout << -1 << '\n';
}