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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
int main(){
  int n,i;
  scanf("%d",&n);
  char s[n+1],ans[n+2];
  scanf("%*c%s",s);
  ans[0]='S';
  ans[1]='S';
  for(i=1;i<=n;i++){
    if(ans[i]=='S'){
      if(s[i-1]=='o')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
    else{
      if(s[i-1]=='x')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
  }
  if(ans[0]==ans[n] && ans[1]==ans[n+1]){
    for(i=1;i<=n;i++)
      printf("%c",ans[i]);
    puts("");
    return 0;
  }
  ans[0]='S';
  ans[1]='W';
  for(i=1;i<=n;i++){
    if(ans[i]=='S'){
      if(s[i-1]=='o')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
    else{
      if(s[i-1]=='x')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
  }
  if(ans[0]==ans[n] && ans[1]==ans[n+1]){
    for(i=1;i<=n;i++)
      printf("%c",ans[i]);
    puts("");
    return 0;
  }
  ans[0]='W';
  ans[1]='S';
  for(i=1;i<=n;i++){
    if(ans[i]=='S'){
      if(s[i-1]=='o')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
    else{
      if(s[i-1]=='x')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
  }
  if(ans[0]==ans[n] && ans[1]==ans[n+1]){
    for(i=1;i<=n;i++)
      printf("%c",ans[i]);
    puts("");
    return 0;
  }
  ans[0]='W';
  ans[1]='W';
  for(i=1;i<=n;i++){
    if(ans[i]=='S'){
      if(s[i-1]=='o')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
    else{
      if(s[i-1]=='x')
        ans[i+1]=ans[i-1];
      else if(ans[i-1]=='S')
        ans[i+1]='W';
      else
        ans[i+1]='S';
    }
  }
  if(ans[0]==ans[n] && ans[1]==ans[n+1]){
    for(i=1;i<=n;i++)
      printf("%c",ans[i]);
    puts("");
    return 0;
  }
  puts("-1");
  return 0;
}