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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include<algorithm>
#define int long long
using namespace std;
typedef pair<int,int> P;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define INF 1000000000000

int MOD=1000000007;
int modpow(int a,int x){
  if(a<0)a+=MOD;
  int ans=1;
  while(x>0){
    if(x&1) ans=ans*a%MOD;
      a=a*a%MOD;
      x>>=1;
  }
  return ans;
}

int gyaku(int n){
    return modpow(n,MOD-2);
}

auto factor(int n){
  map<int,int>res;
  for(int i=2;i*i<=n;i++){
      for(; n%i==0;n/=i) res[i]++;
  }
  if(n>1)res[n]++;
  return res;
}
////////////////////////////////////////////////////////////
signed main() {
  int n;
  cin>>n;
  vector<char>mb(n);
  rep(i,n)cin>>mb[i];

  for(int kai=0;kai<=3;kai++){
  vector<int>a(n+1);
  a[0]=kai%2;
  a[1]=(kai/2)%2;
  a[n]=a[0];
  int t=0;
  rep(i,n-1){
    if(a[i+1]==1){
      if(mb[i+1]=='o')t=a[i];
      else  if(mb[i+1]=='x')t=1-a[i];
    }
    else{
      if(mb[i+1]=='o')t=1-a[i];
      else t=a[i];
    }
    if(i!=n-2){
      a[i+2]=t;
    }
    else{
      if(a[i+2]==t){
        rep(i,n){
          if(a[i]==0)cout<<'W';
          else cout<<'S';
        }
        exit(0);
      }
      else continue;
  }
}
}
  cout<<-1<<endl;
}