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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>

#define t(a) ((a == 's') ? (0) : (1))

using namespace std;

int N;
char S[100001];
char ans[100001];
char sw[3] = "sw";
bool f1 = true;

char dp(short int b, short int t, char r);

int main(){

  scanf("%d", &N);
  scanf("%s", S);

  for(int l = 0; l < 4 && f1; l++){
    ans[0] = sw[l/2];//ssww
    ans[1] = sw[l%2];//swsw
    for(int m = 1; m <= N-1 && f1; m++){
      if(m < N-1 ){
        ans[m+1] = dp(t(ans[m-1]), t(ans[m]), S[m]);
      }else if(ans[0] == dp(t(ans[N-2]), t(ans[N-1]), S[N-1])){//m = N-1
        f1 = false;
      }
    }
  }

  if(f1){
    printf("-1");
  }else{
    printf("%s", ans);
  }

  return 0;

}

char dp(short int b, short int t, char r){

  if((b+t)%2 == 0){
    if(r == 'o'){
      return 's';
    }else{//r == 'x'
      return 'w';
    }
  }else{//(a+b)%2 == 1
    if(r == 'o'){
      return 'w';
    }else{//r == 'x'
      return 's';
    }
  }

  return '\0';

}