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>
#include<stdlib.h>
#include<string.h>
#include<stdbool.h>

char makeSandW(char A,char B,int N);
char check(char back,char foward,char middle);


char t[100010],s[100010];

int main(void){
  int N,i;
  char ans[100010];
  scanf("%d",&N);
  scanf("%s",s);
  if(makeSandW('S','S',N)=='S' && check(t[N-1],t[1],t[0])==s[0]){
    t[N]='\0';
    printf("%s\n",t);
  }else if(makeSandW('S','W',N)=='S' && check(t[N-1],t[1],t[0])==s[0]){
    //strncpy(ans,t,N);
    t[N]='\0';
    printf("%s\n",t);
  }else{
    puts("-1");
  }
  return 0;
}

char makeSandW(char A,char B,int N){
  int i;
  t[0]=A;
  t[1]=B;
  for(i=1;i<N;i++){
    if(s[i]=='o' && t[i]=='S'){
      if(t[i-1]=='S'){
        t[i+1]='S';
      }else{
        t[i+1]='W';
      }
    }else if(s[i]=='x' && t[i]=='S'){
      if(t[i-1]=='S'){
        t[i+1]='W';
      }else{
        t[i+1]='S';
      }
    }else if(s[i]=='o' && t[i]=='W'){
      if(t[i-1]=='S'){
        t[i+1]='W';
      }else{
        t[i+1]='S';
      }
    }else if(s[i]=='x' && t[i]=='W'){
      if(t[i-1]=='S'){
        t[i+1]='S';
      }else{
        t[i+1]='W';
      }
    }
  }
  return t[N];
}

char check(char back,char foward,char middle){
  if(middle == 'S'){
    if(back == foward){
      return 'o';
    }else{
      return 'x';
    }
  }else{
    if(back == foward){
      return 'x';
    }else{
      return 'o';
    }
  }
}