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<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
using namespace std;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)
typedef long long ll;
typedef pair<int,int> pint;
typedef pair<ll,int> pli;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;
using namespace std;

int main(){
  int n;
  cin >> n;
  string s;
  cin >> s;
  s+=s[0];
  bool flag=false;
  vector<int> v(n+1);
  rep(i,2){
    rep(j,2){
      v.clear();
      v.resize(n+1);
      v[0]=i;
      v[1]=j;
      for(int k=2;k<n+1;k++){
        // 0:羊,1:狼
        if(s[k-1]=='o' && v[k-2]==0 && v[k-1]==0){
          v[k]=0;
        }
        if(s[k-1]=='o' && v[k-2]==0 && v[k-1]==1){
          v[k]=1;
        }
        if(s[k-1]=='o' && v[k-2]==1 && v[k-1]==0){
          v[k]=1;
        }
        if(s[k-1]=='o' && v[k-2]==1 && v[k-1]==1){
          v[k]=0;
        }
        if(s[k-1]=='x' && v[k-2]==0 && v[k-1]==0){
          v[k]=1;
        }
        if(s[k-1]=='x' && v[k-2]==0 && v[k-1]==1){
          v[k]=0;
        }
        if(s[k-1]=='x' && v[k-2]==1 && v[k-1]==0){
          v[k]=0;
        }
        if(s[k-1]=='x' && v[k-2]==1 && v[k-1]==1){
          v[k]=1;
        }
      }
      if(v[0]==v[n]){
        flag=true;
        break;
      }
    }
  }
  if(flag){
    rep(i,n){
      if(v[i]==0)cout << 'S';
      else cout << 'W';
    }
    cout << endl;
  }else cout << -1 << endl;
  return 0;
}