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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define Rep(i, N) for(int i = 0; i < N; i++)
#define Reps(i, x, N) for(int i = x; i < N; i++)

signed main()
{
  int N;
  string S;
  bool flag = false;
  
  cin >> N >> S;
  
  Rep(p, 4) {
    string T;
    Rep(i, 2) {
      if((p >> i) & 1) T += 'W';
      else T += 'S';
    }

    Reps(i, 2, N) {
      bool mask = false;
      if(T[i - 2] == 'W') mask ^= true;
      if(T[i - 1] == 'W') mask ^= true;
      if(S[i - 1] == 'x') mask ^= true;

      if(mask) T += 'W';
      else T += 'S';
    }

    int enf = T.size() - 1;

    if((p & 1) && S[0] == 'x' || !(p & 1) && S[0] == 'o') {
      if(T[1] != T[enf]) continue;
    } else {
      if(T[1] == T[enf]) continue;
    }
    if(S[enf] == 'o' && T[enf] == 'S' || S[enf] == 'x' && T[enf] == 'W') {
      if(T[enf - 1] != T[0]) continue;
    } else if(T[enf - 1] == T[0]) continue;

    cout << T << endl; flag = true;
    break;
  }

  if(!flag) cout << -1 << endl;
  return 0;
}