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.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

  char[] S;
  int N;

  private void solve(Scanner in, PrintWriter out) {
    N = in.nextInt();
    S = in.next().toCharArray();
    int[] sheep = new int[N];
    for (int s0 = 0; s0 <= 1; s0++) {
      for (int s1 = 0; s1 <= 1; s1++) {
        Arrays.fill(sheep, -1);
        sheep[0] = s0;
        sheep[1] = s1;
        if (check(sheep)) {
          for (int i = 0; i < N; i++) {
            out.print(sheep[i] == 1 ? "S" : "W");
          }
          out.println();
          return;
        } else {
          continue;
        }
      }
    }
    out.println(-1);
  }

  boolean check(int[] sheep) {
    for (int i = 2; i < N; i++) {
      int x;
      int prev = sheep[i - 2];
      if (S[i - 1] == 'o') {
        if (sheep[i - 1] == 1) {
          x = prev;
        } else {
          x = prev ^ 1;
        }
      } else {
        if (sheep[i - 1] == 1) {
          x = prev ^ 1;
        } else {
          x = prev;
        }
      }

      if (S[i - 1] == 'o') {
        if (sheep[i - 1] == 1) {
          if (x != prev) {
            return false;
          }
        } else {
          if (x == prev) {
            return false;
          }
        }
      } else {
        if (sheep[i - 1] == 1) {
          if (x == prev) {
            return false;
          }
        } else {
          if (x != prev) {
            return false;
          }
        }
      }
      sheep[i] = x;
    }
    if (S[N - 1] == 'o') {
      if (sheep[N - 1] == 1) {
        if (sheep[0] != sheep[N - 2]) {
          return false;
        }
      } else {
        if (sheep[0] == sheep[N - 2]) {
          return false;
        }
      }
    } else {
      if (sheep[N - 1] == 1) {
        if (sheep[0] == sheep[N - 2]) {
          return false;
        }
      } else {
        if (sheep[0] != sheep[N - 2]) {
          return false;
        }
      }
    }

    if (S[0] == 'o') {
      if (sheep[0] == 1) {
        if (sheep[1] != sheep[N - 1]) {
          return false;
        }
      } else {
        if (sheep[1] == sheep[N - 1]) {
          return false;
        }
      }
    } else {
      if (sheep[0] == 1) {
        if (sheep[1] == sheep[N - 1]) {
          return false;
        }
      } else {
        if (sheep[1] != sheep[N - 1]) {
          return false;
        }
      }
    }
    return true;
  }

  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    new Main().solve(in, out);
    in.close();
    out.close();
  }
}