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 (Clang 3.8.0) (judge verdict: Wrong Answer)

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

int main()
{
unsigned long long N;
char animalans[200000];
char animal[4][200002];
int A=0;
unsigned long long i;
unsigned long long j;

scanf("%llu",&N);
scanf("%s",animalans);
if(animalans[0]=='x')
{
 animal[0][N+1]='S';
 animal[0][0]='W';
 animal[0][1]='S';

 animal[1][N+1]='W';
 animal[1][0]='W';
 animal[1][1]='W';

 animal[2][N+1]='W';
 animal[2][0]='S';
 animal[2][1]='S';

 animal[3][N+1]='S';
 animal[3][0]='S';
 animal[3][1]='W';
}else{
 animal[0][N+1]='S';
 animal[0][0]='W';
 animal[0][1]='S';

 animal[1][N+1]='S';
 animal[1][0]='W';
 animal[1][1]='W';

 animal[2][N+1]='S';
 animal[2][0]='S';
 animal[2][1]='S';

 animal[3][N+1]='W';
 animal[3][0]='S';
 animal[3][1]='W';
}
for( i=1; i<N; i++)
{
 if(animalans[i]=='x')
 {
  for( j=0; j<4; j++)
  {
    if((animal[j][i-1]=='W')&(animal[j][i]=='S')) animal[j][i+1]='S';
    if((animal[j][i-1]=='W')&(animal[j][i]=='W')) animal[j][i+1]='W';
    if((animal[j][i-1]=='S')&(animal[j][i]=='S')) animal[j][i+1]='W';
    if((animal[j][i-1]=='S')&(animal[j][i]=='W')) animal[j][i+1]='S';
   }
 }else{
  for( j=0; j<4; j++)
  {
    if((animal[j][i-1]=='W')&(animal[j][i]=='S')) animal[j][i+1]='W';
    if((animal[j][i-1]=='W')&(animal[j][i]=='W')) animal[j][i+1]='S';
    if((animal[j][i-1]=='S')&(animal[j][i]=='S')) animal[j][i+1]='S';
    if((animal[j][i-1]=='S')&(animal[j][i]=='W')) animal[j][i+1]='W';
  }
 }
}
A=-1;
for(j=0; j<4; j++)
{
 if((animal[j][N+1]==animal[j][N-1])&(animal[j][N]==animal[j][0])){
         A=j;
         break;
 }
}

if(A==-1)
{
 printf("%d",A);
}else{
 for(i=0; i<N; i++) printf("%c",animal[A][i]);
}

return 0;
}