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 <cstdio>

int main(void) {
  int N;
  scanf("%d", &N);
  char reply[N+2];
  scanf("%s", reply);
  reply[N] = reply[0]; reply[N+1] = reply[1];// reply N, N+1を忘れないように
  
  int animal[N+2];

  for (int initial = 0; initial < 4; initial++) {
    if (!(initial % 2)) { 
      animal[0] = 0;
      if (initial < 2) animal[1] = 0; else animal[1] = 1;
    } else {
      animal[0] = 1;
      if (initial < 2) animal[1] = 0; else animal[1] = 1;
    }
 

    for (int i = 0; i < N; i++) {
      if (animal[i+1] == 0) {
        if (reply[i+1] == 'o') animal[i+2] = animal[i]; 
        else animal[i+2] = 1-animal[i];
      } else {
        if (reply[i+1] == 'o') animal[i+2] = 1-animal[i];
        else animal[i+2] = animal[i];
      }
    }
    if (animal[0] == animal[N] && animal[1] == animal[N+1]) {
      for (int j = 0; j < N; j++) {
        if (animal[j] == 0) printf("S");
        else printf("W");
      }
      printf("\n");
      return 0;
    }
  }
  printf("-1\n");
  return 0;
}