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 N;
char s[100010];
char a[100010];

int judge (int i, char a[100010]) {
  int ans;
  if(i>1 && i <N){
    if((a[i-1]=='S' && s[i-1]=='o') || (a[i-1]=='W' && s[i-1]=='x')){
      if(a[i-2]==a[i]){
	ans = 1;
      } else {
	ans = 0;
      }
    } else {
      if(a[i-2]!=a[i]){
	ans = 1;
      } else {
	ans = 0;
      }
    }
  } else if(i==1){
    if((a[0]=='S' && s[0]=='o') || (a[0]=='W' && s[0]=='x')){
      if(a[N-1]==a[1]){
	ans = 1;
      } else {
	ans = 0;
      }
    } else {
      if(a[N-1]!=a[1]){
	ans = 1;
      } else {
	ans = 0;
      }
    }
  } else if(i==N){
    if((a[N-1]=='S' && s[N-1]=='o') || (a[N-1]=='W' && s[N-1]=='x')){
      if(a[N-2]==a[0]){
	ans = 1;
      } else {
	ans = 0;
      }
    } else {
      if(a[N-2]!=a[0]){
	ans = 1;
      } else {
	ans = 0;
      }
    }
  } 
  return ans;
}


int dfs (int i, char a[100010]) {
  //int ans;
  if(i==N){
    if(judge(N,a)){
      return 1;
    } else {
      return 0;
    }
  } else {
    a[i-1] = 'S';
    if(judge(i-1,a)){
      return dfs(i+1,a);
    } else {
      a[i-1] = 'W';
      if(judge(i-1,a)){
	return dfs(i+1,a);
      } else {
	return 0;
      }
    }
  }

  //return 0;
}


int main (void) {
  scanf("%d",&N);
  scanf("%s",s);
  a[0] = 'S';
  a[N-1] = 'S';
  if(dfs(2,a)){
    printf("%s\n",a);
  } else {
    a[0] = 'S';
    a[N-1] = 'W';
    if(dfs(2,a)){
      printf("%s\n",a);
    } else {
      a[0] = 'W';
      a[N-1] = 'S';
      if(dfs(2,a)){
	printf("%s\n",a);
      } else {
	a[0] = 'W';
	a[N-1] = 'W';
	if(dfs(2,a)){
	  printf("%s\n",a);
	} else {
	  printf("-1\n");
	}
      }
    }
  }
  return 0;
}