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: Wrong Answer)

#include<stdio.h>

int judge(char *a,char *b,int n){
    int i=0;
    while(i<n-2){
        if(*(a+i+1)=='o'){
            if(*(b+i)=='S'&&*(b+i+1)=='S'){
                *(b+i+2)='S';
            }else if(*(b+i)=='S'&&*(b+i+1)=='W'){
                *(b+i+2)='W';
            }else if(*(b+i)=='W'&&*(b+i+1)=='S'){
                *(b+i+2)='W';
            }else if(*(b+i)=='W'&&*(b+i+1)=='W'){
                *(b+i+2)='S';
            }
        }else{
            if(*(b+i)=='S'&&*(b+i+1)=='S'){
                *(b+i+2)='W';
            }else if(*(b+i)=='S'&&*(b+i+1)=='W'){
                *(b+i+2)='S';
            }else if(*(b+i)=='W'&&*(b+i+1)=='S'){
                *(b+i+2)='S';
            }else if(*(b+i)=='W'&&*(b+i+1)=='W'){
                *(b+i+2)='W';
            }
        }
        i++;
    }

    int sp=0;
    if(*(a+n-1)=='o'){
        if(*(b+n-1)=='S'){
            if(*(b+n-2)=='S'&&*b=='S'){
                sp++;
            }else if(*(b+n-2)=='W'&&*b=='W'){
                sp++;
            }
        }else{
            if(*(b+n-2)=='S'&&*b=='W'){
                sp++;
            }else if(*(b+n-2)=='W'&&*b=='S'){
                sp++;
            }
        }
    }else{
        if(*(b+n-1)=='S'){
            if(*(b+n-2)=='S'&&*b=='W'){
                sp++;
            }else if(*(b+n-2)=='W'&&*b=='S'){
                sp++;
            }
        }else{
            if(*(b+n-2)=='S'&&*b=='S'){
                sp++;
            }else if(*(b+n-2)=='W'&&*b=='W'){
                sp++;
            }
        }
    }
    return sp;
}

int main(){
    long long int n;
    scanf("%lld",&n);
    char s[n];
    scanf("%s",s);

    char t[n],u[n],v[n],w[n];
    t[0]='S';
    t[1]='S';
    int st=judge(s,t,n);
    u[0]='S';
    u[1]='W';
    int su=judge(s,u,n);
    v[0]='W';
    v[1]='S';
    int sv=judge(s,v,n);
    w[0]='W';
    w[1]='W';
    int sw=judge(s,w,n);

    if(st>0){
        for(int i=0;i<n;i++){
            printf("%c",t[i]);
        }
    }else if(su>0){
        for(int i=0;i<n;i++){
            printf("%c",u[i]);
        }
    }else if(sv>0){
        for(int i=0;i<n;i++){
            printf("%c",v[i]);
        }
    }else if(sw>0){
        for(int i=0;i<n;i++){
            printf("%c",w[i]);
        }
    }else{
        printf("-1\n");
    }
    return 0;
}