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: Runtime Error)

#include <iostream>
#include <stdio.h>
#include <stdlib.h>

using namespace std;

char *search(char a, char b, char *s, int N) {
  char *ans = (char *)malloc(N + 1);
  ans[0] = a;
  ans[1] = b;
  for (int i = 0; i < N - 2; i++) {
    if (s[i + 1] == 'o' && ans[i + 1] == 'S') {
      ans[i + 2] = ans[i];
    } else if (s[i + 1] == 'x' && ans[i + 1] == 'W') {
      ans[i + 2] = ans[i];
    } else {
      if (ans[i] == 'S') {
        ans[i + 2] = 'W';
      } else {
        ans[i + 2] = 'S';
      }
    }
  }
  if (s[0] == 'o' && ans[0] == 'S') {
    ans[N] = ans[1];
  } else if (s[0] == 'x' && ans[0] == 'W') {
    ans[N] = ans[1];
  } else {
    if (ans[1] == 'S') {
      ans[N] = 'W';
    } else {
      ans[N] = 'S';
    }
  }
  if (ans[N - 1] == ans[N]) {
    ans[N] = '\0';
    return ans;
  } else {
    return NULL;
  }
  free(ans);
}

int main() {
  int N;
  char *s = (char *)malloc(N + 1);
  cin >> N >> s;

  char *epoch0 = search('S', 'S', s, N);
  // char *epoch1 = search('S', 'W', s, N);
  // char *epoch2 = search('W', 'S', s, N);
  // char *epoch3 = search('W', 'W', s, N);

  if (epoch0 != NULL) {
    cout << epoch0 << endl;
  } else {
    free(epoch0);
    char *epoch1 = search('S', 'W', s, N);
    if (epoch1 != NULL) {
      cout << epoch1 << endl;
    } else {
      free(epoch1);
      char *epoch2 = search('W', 'S', s, N);
      if (epoch2 != NULL) {
        cout << epoch2 << endl;
      } else {
        free(epoch2);
        char *epoch3 = search('W', 'W', s, N);
        if (epoch3 != NULL) {
          cout << epoch2 << endl;
        } else {
          free(epoch3);
          cout << -1 << endl;
        }
      }
    }
  }

  return 0;
}