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: Time Limit Exceeded)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    String s = sc.next();
    int p = -1;
    String[] ans = new String[n];
    for(int k = 0; k < 4; k++) {
      String[] temp = new String[n];
      if((k % 2) == 0) {
        temp[0] = "W";
      } else {
        temp[0] = "S";
      }
      k /= 2;
      if((k % 2) == 0) {
        temp[1] = "W";
      } else {
        temp[1] = "S";
      }
      for(int i = 1; i < (n - 1); i++) {
        if(s.charAt(i) == 'o') {
          if(temp[i].equals("W")) {
            if(temp[i - 1].equals("W")) {
              temp[i + 1] = "S";
            } else {
              temp[i + 1] = "W";
            }
          } else {
            temp[i + 1] = temp[i - 1];
          }
        } else {
          if(temp[i].equals("W")) {
            temp[i + 1] = temp[i - 1];
          } else {
            if(temp[i - 1].equals("W")) {
              temp[i + 1] = "S";
            } else {
              temp[i + 1] = "W";
            }
          }
        }
      }
      int q = 0;
      for(int i = 0; i < n; i++) {
        int a = i - 1;
        int b = i + 1;
        if(i == 0) a = (n - 1);
        if(i == (n - 1)) b = 0;
        if(s.charAt(i) == 'o') {
          if(temp[i].equals("W")) {
            if(temp[a] == temp[b]) q = 1;
          } else {
            if(temp[a] != temp[b]) q = 1;
          }
        } else {
          if(temp[i].equals("W")) {
            if(temp[a] != temp[b]) q = 1;
          } else {
            if(temp[a] == temp[b]) q = 1;
          }
        }
      }
      if(q == 0) {
        p = 0;
        ans = temp;
      } else {
        
      }
    }
    if(p == -1) {
      System.out.println(-1);
    } else {
      String str = "";
      for(int i = 0; i < n; i++) {
        str += ans[i];
      }
      System.out.println(str);
    }
  }
}