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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using System.Collections;
public class Remainder
{

  static long div = 1000000007;
  static char[] anima ;
  static string S;
  static int N;

    static public void Main()
    {
      N = int.Parse(Console.ReadLine());
      S = Console.ReadLine();//.Split(' ').Select(x => int.Parse(x)).ToArray();
      anima = new char[N];
      
      
      if(Search('S','S')){
        Console.WriteLine(String.Join("",anima));
      }else if (Search('S','W')){
        Console.WriteLine(String.Join("",anima));
      }else if (Search('W','S')){
        Console.WriteLine(String.Join("",anima));
      }else if (Search('W','W')){
        Console.WriteLine(String.Join("",anima));
      }else{
        Console.WriteLine((-1));
      }
      
      
      
    }
  
    //第一引数：1番目の動物の種類,第2引数：N-1番目の動物の種類
    static bool Search(char s,char l){
      var now  = 0;
      var left = N-1;
      anima[0] =    s;
      anima[left] = l;
      for(int i = 0; i < N-2 ;i++){
        if(left == N){
          left = 0;
        }
        if(S[now] == 'o'){
          if(anima[now] == 'S'){
            if(anima[left] == 'S'){
              now++;
              left++;
              anima[now] = 'S';
            }else if(anima[left] == 'W'){
              now++;
              left++;
              anima[now] = 'W';
            }
          }else if(anima[now] == 'W'){
            if(anima[left] == 'S'){
              now++;
              left++;
              anima[now] = 'W';
            }else if(anima[left] == 'W'){
              now++;
              left++;
              anima[now] = 'S';
            }
          }
        }else if(S[now] == 'x'){
          
          if(anima[now] == 'S'){
            if(anima[left] == 'S'){
              now++;
              left++;
              anima[now] = 'W';
            }else if(anima[left] == 'W'){
              now++;
              left++;
              anima[now] = 'S';
            }
          }else if(anima[now] == 'W'){
            if(anima[left] == 'S'){
              now++;
              left++;
              anima[now] = 'S';
            }else if(anima[left] == 'W'){
              now++;
              left++;
              anima[now] = 'W';
            }
          }
        }
      }
      
      if(S[N-1] == 'o'){
        if(anima[N-1] == 'S'){
          if(anima[N-2] == anima[0]){
            return true;
          }
        }else{
          if(anima[N-2] != anima[0]){
            return true;
          }
        }
      }else{
        if(anima[N-1] == 'S'){
          if(anima[N-2] != anima[0]){
            return true;
          }
        }else{
          if(anima[N-2] == anima[0]){
            return true;
          }
        }
      }
      return false;
    }

}