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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int main(){
  int n,i,flag=0,j;
  char b;
  char s[100001];
  char a[8][100001];
  scanf("%d",&n);
  scanf("%s",s);
  a[0][0]=a[1][0]=a[2][0]=a[3][0]=a[0][1]=a[0][n-1]=a[2][n-1]=a[3][1]=a[4][n-1]=a[5][1]=a[6][1]=a[6][n-1]='S';
  a[1][1]=a[1][n-1]=a[2][1]=a[3][n-1]=a[4][0]=a[4][1]=a[5][0]=a[5][n-1]=a[6][0]=a[7][0]=a[7][1]=a[7][n-1]='W';
  for(i=0;i<8;i++){
    if(s[0]=='o'&&(i==0||i==1||i==4||i==5)){
      for(j=1;j<n-1;j++){
        if((a[i][j-1]=='S'&&a[i][j]=='S'&&s[j]=='o')||(a[i][j-1]=='W'&&a[i][j]=='S'&&s[j]=='x')||(a[i][j-1]=='S'&&a[i][j]=='W'&&s[j]=='x')||(a[i][j-1]=='W'&&a[i][j]=='W'&&s[j]=='o')){
          b='S';
          if(j!=n-2)
            a[i][j+1]=b;
          else{
            if(b==a[i][n-1]){
              printf("%s\n",a[i]);
              return 0;
            }
          }
        }
        else{
          b='W';
          if(j!=n-2)
            a[i][j+1]=b;
          else{
            if(b==a[i][n-1]){
              printf("%s\n",a[i]);
              return 0;
            }
          }
        }
      }
    }
    else if(s[0]=='x'&&(i==2||i==3||i==6||i==7)){
      for(j=1;j<n-1;j++){
        if((a[i][j-1]=='S'&&a[i][j]=='S'&&s[j]=='o')||(a[i][j-1]=='W'&&a[i][j]=='S'&&s[j]=='x')||(a[i][j-1]=='S'&&a[i][j]=='W'&&s[j]=='x')||(a[i][j-1]=='W'&&a[i][j]=='W'&&s[j]=='o')){
          b='S';
          if(j!=n-2)
            a[i][j+1]=b;
          else{
            if(b==a[i][n-1]){
              printf("%s\n",a[i]);
              return 0;
            }
          }
        }
        else{
          b='W';
          if(j!=n-2)
            a[i][j+1]=b;
          else{
            if(b==a[i][n-1]){
              printf("%s\n",a[i]);
              return 0;
            }
          }
        }
      }
    }
  }
  printf("-1\n");
}