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,d[1000010],i,j,k;
  char s[100010];
  scanf("%d %s",&n,s);
  for(i=0;s[i];i++){
    if(s[i]-s[(i+1)%n])break;
  }
  if(s[i]==0){
    for(i=0;i<n;i++)printf("%c",s[i]=='o'?'S':'W');
    printf("\n");
    return 0;
  }      //printf("%d\n",i);
  for(k=0;k<4;k++){
    d[i]=k/2;
    d[(i+1)%n]=k%2;
    for(j=1;j<n;j++){
      if(d[(i+j)%n]==0){
	if(s[(i+j)%n]=='o')d[(i+j+1)%n]=  d[(i+j-1+n)%n];
	else               d[(i+j+1)%n]=1-d[(i+j-1+n)%n];
      }
      else{
	if(s[(i+j)%n]=='x')d[(i+j+1)%n]=  d[(i+j-1+n)%n];
	else               d[(i+j+1)%n]=1-d[(i+j-1+n)%n];
      }
    }
    if(d[(i+j)%n]==k/2){
      for(j=0;j<n;j++)printf("%c",d[j]?'W':'S');
      printf("\n");
      return 0;
    }
  }
  printf("-1\n");
  return 0;
}