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 <iostream>
#include <cmath>
#include <algorithm>
#include <deque>
#include <vector>

typedef long long ll;
using namespace std;

int main(){
  int n;
  string str;
  int i, j, k;

  cin >> n;
  cin >> str;
  int sw[n];
  int tmp;


  sw[0] = 1; sw[1] = -1;
  if(str[0]=='o'){
    tmp = -1;
  }else{
    tmp = 1;
  }
  for(i = 1; i < n-1; i++){
    if(str[i] == 'o'){
      if(sw[i] == 1){
        sw[i+1] = sw[i-1];
      }else{
        sw[i+1] = sw[i-1] * -1;
      }
    }else{
      if(sw[i] == 1){
        sw[i+1] = sw[i-1] * -1;
      }else{
        sw[i+1] = sw[i-1];
      }
    }
  }
  if(sw[n-1] == tmp && ((str[n-1] == 'o' && sw[0] * sw[n-2] * sw[n-1] == 1) || (str[n-1] == 'x' && sw[0] * sw[n-2] * sw[n-1] == -1)) ){
    for(i = 0; i < n; i++){
      if(sw[i] == 1){
        cout << 'S';
      }else{
        cout << 'W';
      }
    }
    cout << endl;
    return 0;
  }

  sw[0] = -1; sw[1] = 1;
  if(str[0]=='o'){
    tmp = -1;
  }else{
    tmp = 1;
  }
  for(i = 1; i < n-1; i++){
    if(str[i] == 'o'){
      if(sw[i] == 1){
        sw[i+1] = sw[i-1];
      }else{
        sw[i+1] = sw[i-1] * -1;
      }
    }else{
      if(sw[i] == 1){
        sw[i+1] = sw[i-1] * -1;
      }else{
        sw[i+1] = sw[i-1];
      }
    }
  }
  if(sw[n-1] == tmp && ((str[n-1] == 'o' && sw[0] * sw[n-2] * sw[n-1] == 1) || (str[n-1] == 'x' && sw[0] * sw[n-2] * sw[n-1] == -1)) ){
    for(i = 0; i < n; i++){
      if(sw[i] == 1){
        cout << 'S';
      }else{
        cout << 'W';
      }
    }
    cout << endl;
    return 0;
  }

  sw[0] = 1; sw[1] = 1;
  if(str[0]=='o'){
    tmp = 1;
  }else{
    tmp = -1;
  }
  for(i = 1; i < n-1; i++){
    if(str[i] == 'o'){
      if(sw[i] == 1){
        sw[i+1] = sw[i-1];
      }else{
        sw[i+1] = sw[i-1] * -1;
      }
    }else{
      if(sw[i] == 1){
        sw[i+1] = sw[i-1] * -1;
      }else{
        sw[i+1] = sw[i-1];
      }
    }
  }
  if(sw[n-1] == tmp && ((str[n-1] == 'o' && sw[0] * sw[n-2] * sw[n-1] == 1) || (str[n-1] == 'x' && sw[0] * sw[n-2] * sw[n-1] == -1)) ){
    for(i = 0; i < n; i++){
      if(sw[i] == 1){
        cout << 'S';
      }else{
        cout << 'W';
      }
    }
    cout << endl;
    return 0;
  }

  sw[0] = -1; sw[1] = -1;
  if(str[0]=='o'){
    tmp = 1;
  }else{
    tmp = -1;
  }
  for(i = 1; i < n-1; i++){
    if(str[i] == 'o'){
      if(sw[i] == 1){
        sw[i+1] = sw[i-1];
      }else{
        sw[i+1] = sw[i-1] * -1;
      }
    }else{
      if(sw[i] == 1){
        sw[i+1] = sw[i-1] * -1;
      }else{
        sw[i+1] = sw[i-1];
      }
    }
  }
  if(sw[n-1] == tmp && ((str[n-1] == 'o' && sw[0] * sw[n-2] * sw[n-1] == 1) || (str[n-1] == 'x' && sw[0] * sw[n-2] * sw[n-1] == -1)) ){
    for(i = 0; i < n; i++){
      if(sw[i] == 1){
        cout << 'S';
      }else{
        cout << 'W';
      }
    }
    cout << endl;
    return 0;
  }

  cout << -1 << endl;



  return 0;
}