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 main(){
	int n;
	int a=0;
	scanf("%d",&n);
	char s[100005],sw[100005]={0},ss[100005]={0},ws[100005]={0},ww[100005]={0};
	sw[0]='S';sw[1]='W';ss[0]='S';ss[1]='S';ww[0]='W';ww[1]='W';ws[0]='W';ws[1]='S';
	getchar();
	for(int i=0;i<n;i++){
		scanf("%c",&s[i]);
	}
	for(int i=0;i<4;i++){
		if(i==0){
			for(int j=1;j<n;j++){
				if(j!=n-1){
					if(s[j]=='o'){
						if(ss[j-1]=='S'&&ss[j]=='S'){
							ss[j+1]='S';
						}
						else if(ss[j-1]=='S'&&ss[j]=='W'){
							ss[j+1]='W';
						}
						else if(ss[j-1]=='W'&&ss[j]=='S'){
							ss[j+1]='W';
						}
						else if(ss[j-1]=='W'&&ss[j]=='W'){
							ss[j+1]='S'; 
						}
					}
					else{
						if(ss[j-1]=='S'&&ss[j]=='S'){
							ss[j+1]='W';
						}
						else if(ss[j-1]=='S'&&ss[j]=='W'){
							ss[j+1]='S';
						}
						else if(ss[j-1]=='W'&&ss[j]=='S'){
							ss[j+1]='S';
						}
						else if(ss[j-1]=='W'&&ss[j]=='W'){
							ss[j+1]='W';
						}
					}
				}
				else{
					if(s[j]=='o'){
						if(ss[j-1]=='S'&&ss[j]=='S'){
							if(ss[0]=='S'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='W'&&ss[j]=='S'){
							if(ss[0]=='W'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='S'&&ss[j]=='W'){
							if(ss[0]=='W'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='W'&&ss[j]=='W'){
							if(ss[0]=='S'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
					}
					else{
						if(ss[j-1]=='S'&&ss[j]=='S'){
							if(ss[0]=='W'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='W'&&ss[j]=='S'){
							if(ss[0]=='S'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='S'&&ss[j]=='W'){
							if(ss[0]=='S'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
						else if(ss[j-1]=='W'&&ss[j]=='W'){
							if(ss[0]=='W'){
								printf("%s",ss);
								a=1;
								break;
							}
						}
					}
				}	
			} 
			if(a=1){
				break;
			}
		}
		else if(i==1){
			for(int j=1;j<n;j++){
				if(j!=n-1){
					if(s[j]=='o'){
						if(sw[j-1]=='S'&&sw[j]=='S'){
							sw[j+1]='S';
						}
						else if(sw[j-1]=='S'&&sw[j]=='W'){
							sw[j+1]='W';
						}
						else if(sw[j-1]=='W'&&sw[j]=='S'){
							sw[j+1]='W';
						}
						else if(sw[j-1]=='W'&&sw[j]=='W'){
							sw[j+1]='S'; 
						}
					}
					else{
						if(sw[j-1]=='S'&&sw[j]=='S'){
							sw[j+1]='W';
						}
						else if(sw[j-1]=='S'&&sw[j]=='W'){
							sw[j+1]='S';
						}
						else if(sw[j-1]=='W'&&sw[j]=='S'){
							sw[j+1]='S';
						}
						else if(sw[j-1]=='W'&&sw[j]=='W'){
							sw[j+1]='W';
						}
					}
				}
				else{
					if(s[j]=='o'){
						if(sw[j-1]=='S'&&sw[j]=='S'){
							if(sw[0]=='S'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='W'&&sw[j]=='S'){
							if(sw[0]=='W'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='S'&&sw[j]=='W'){
							if(sw[0]=='W'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='W'&&sw[j]=='W'){
							if(sw[0]=='S'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
					}
					else{
						if(sw[j-1]=='S'&&sw[j]=='S'){
							if(sw[0]=='W'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='W'&&sw[j]=='S'){
							if(sw[0]=='S'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='S'&&sw[j]=='W'){
							if(sw[0]=='S'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
						else if(sw[j-1]=='W'&&sw[j]=='W'){
							if(sw[0]=='W'){
								printf("%s",sw);
								a=1;
								break;
							}
						}
					}
				}	
			}
			if(a=1){
				break;
			}
		}
		else if(i==2){
			for(int j=1;j<n;j++){
				if(j!=n-1){
					if(s[j]=='o'){
						if(ww[j-1]=='S'&&ww[j]=='S'){
							ww[j+1]='S';
						}
						else if(ww[j-1]=='S'&&ww[j]=='W'){
							ww[j+1]='W';
						}
						else if(ww[j-1]=='W'&&ww[j]=='S'){
							ww[j+1]='W';
						}
						else if(ww[j-1]=='W'&&ww[j]=='W'){
							ww[j+1]='S'; 
						}
					}
					else{
						if(ww[j-1]=='S'&&ww[j]=='S'){
							ww[j+1]='W';
						}
						else if(ww[j-1]=='S'&&ww[j]=='W'){
							ww[j+1]='S';
						}
						else if(ww[j-1]=='W'&&ww[j]=='S'){
							ww[j+1]='S';
						}
						else if(ww[j-1]=='W'&&ww[j]=='W'){
							ww[j+1]='W';
						}
					}
				}
				else{
					if(s[j]=='o'){
						if(ww[j-1]=='S'&&ww[j]=='S'){
							if(ww[0]=='S'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='W'&&ww[j]=='S'){
							if(ww[0]=='W'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='S'&&ww[j]=='W'){
							if(ww[0]=='W'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='W'&&ww[j]=='W'){
							if(ww[0]=='S'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
					}
					else{
						if(ww[j-1]=='S'&&ww[j]=='S'){
							if(ww[0]=='W'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='W'&&ww[j]=='S'){
							if(ww[0]=='S'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='S'&&ww[j]=='W'){
							if(ww[0]=='S'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
						else if(ww[j-1]=='W'&&ww[j]=='W'){
							if(ww[0]=='W'){
								printf("%s",ww);
								a=1;
								break;
							}
						}
					}
				}	
			}
			if(a=1){
				break;
			}
		}
		else if(i==3){
			for(int j=1;j<n;j++){
				if(j!=n-1){
					if(s[j]=='o'){
						if(ws[j-1]=='S'&&ws[j]=='S'){
							ws[j+1]='S';
						}
						else if(ws[j-1]=='S'&&ws[j]=='W'){
							ws[j+1]='W';
						}
						else if(ws[j-1]=='W'&&ws[j]=='S'){
							ws[j+1]='W';
						}
						else if(ws[j-1]=='W'&&ws[j]=='W'){
							ws[j+1]='S'; 
						}
					}
					else{
						if(ws[j-1]=='S'&&ws[j]=='S'){
							ws[j+1]='W';
						}
						else if(ws[j-1]=='S'&&ws[j]=='W'){
							ws[j+1]='S';
						}
						else if(ws[j-1]=='W'&&ws[j]=='S'){
							ws[j+1]='S';
						}
						else if(ws[j-1]=='W'&&ws[j]=='W'){
							ws[j+1]='W';
						}
					}
				}
				else{
					if(s[j]=='o'){
						if(ws[j-1]=='S'&&ws[j]=='S'){
							if(ws[0]=='S'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='W'&&ws[j]=='S'){
							if(ws[0]=='W'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='S'&&ws[j]=='W'){
							if(ws[0]=='W'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='W'&&ws[j]=='W'){
							if(ws[0]=='S'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
					}
					else{
						if(ws[j-1]=='S'&&ws[j]=='S'){
							if(ws[0]=='W'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='W'&&ws[j]=='S'){
							if(ws[0]=='S'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='S'&&ws[j]=='W'){
							if(ws[0]=='S'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
						else if(ws[j-1]=='W'&&ws[j]=='W'){
							if(ws[0]=='W'){
								printf("%s",ws);
								a=1;
								break;
							}
						}
					}
				}	
			}
			if(a=1){
				break;
			}
		}
	}
	if(a!=1){
		printf("-1");
	}
}