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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {          
    
    static int N;
    static char[] cs;    
    
    public static void main(String[] args){           
        
         Scanner sc = new Scanner(System.in);
   
         N = sc.nextInt();         
         
         String S = sc.next();
         
         cs = S.toCharArray();
    
         for(int i = 0;i < 2;i++){
            for(int j = 0;j < 2;j++){
                
                int a[] = new int[N];  
                
                a[0] = i;
                a[1] = j;
                 
                if(cal(a)){                                                                                    
                     for(int k = 0;k < N;k++){
                         if(a[k] == 1){
                             System.out.print("S");
                         }else{
                             System.out.print("W");                             
                         }
                     }
                     System.out.println();
                     return;
                }                                                   
                 
            }
         }           
         
         System.out.println(-1);
         
  }    
    
   static boolean cal(int[] a){
       
            for (int i = 2; i < N; i++) {
                if (cs[i - 1] == 'o') {
                    if (a[i - 1] == 1) {
                        a[i] = a[i - 2];
                    } else {
                        a[i] = a[i - 2] ^ 1;
                    }
                } else {
                    if (a[i - 1] == 1) {
                        a[i] = a[i - 2] ^ 1;
                    } else {
                        a[i] = a[i - 2];
                    }
                }
            }

            if (a[0] == 1) {
                if (cs[0] == 'o') {
                    if (a[1] != a[N - 1]) return false;
                }
                if (cs[0] == 'x') {
                    if (a[1] == a[N - 1]) return false;
                }
            } else {
                if (cs[0] == 'o') {
                    if (a[1] == a[N - 1]) return false;
                }
                if (cs[0] == 'x') {
                    if (a[1] != a[N - 1]) return false;
                }
            }

            // check n-1
            if (cs[N - 1] == 'o') {
                if (a[N - 1] == 1) {
                    return a[N - 2] == a[0];
                } else {
                    return a[N - 2] != a[0];
                }
            } else {
                if (a[N - 1] == 1) {
                    return a[N - 2] != a[0];
                } else {
                    return a[N - 2] == a[0];
                }
            }            
    }                              
}