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 "bits/stdc++.h"
using namespace std;

int main(){
	int n;
	cin>>n;
	string s;
	cin>>s;
	
	string x(n,'0');
	
	x[0]='S';
	x[1]='S';
	
	for(int i=1;i<n-1;i++){
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='W';
	}
	
	bool f=true;
	
	if(s[n-1]=='o'){
		if(x[n-1]=='S'&&x[n-2]==x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]!=x[0])f&=true;
	}else{
		if(x[n-1]=='S'&&x[n-2]!=x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]==x[0])f&=true;
	}
	
	if(s[0]=='o'){
		if(x[0]=='S'&&x[n-1]==x[1])f&=true;
		if(x[0]=='W'&&x[n-1]!=x[1])f&=true;
	}else{
		if(x[0]=='S'&&x[n-1]!=x[1])f&=true;
		if(x[0]=='W'&&x[n-1]==x[1])f&=true;
	}
	
	if(f){
		cout<<x<<endl;
		return 0;
	}
	
	x[0]='S';
	x[1]='W';
	
	for(int i=1;i<n-1;i++){
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='W';
	}
	
	f=true;
	
	if(s[n-1]=='o'){
		if(x[n-1]=='S'&&x[n-2]==x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]!=x[0])f&=true;
	}else{
		if(x[n-1]=='S'&&x[n-2]!=x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]==x[0])f&=true;
	}
	
	if(s[0]=='o'){
		if(x[0]=='S'&&x[n-1]==x[1])f&=true;
		if(x[0]=='W'&&x[n-1]!=x[1])f&=true;
	}else{
		if(x[0]=='S'&&x[n-1]!=x[1])f&=true;
		if(x[0]=='W'&&x[n-1]==x[1])f&=true;
	}
	
	if(f){
		cout<<x<<endl;
		return 0;
	}
	
	x[0]='W';
	x[1]='S';
	
	for(int i=1;i<n-1;i++){
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='W';
	}
	
	f=true;
	
	if(s[n-1]=='o'){
		if(x[n-1]=='S'&&x[n-2]==x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]!=x[0])f&=true;
	}else{
		if(x[n-1]=='S'&&x[n-2]!=x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]==x[0])f&=true;
	}
	
	if(s[0]=='o'){
		if(x[0]=='S'&&x[n-1]==x[1])f&=true;
		if(x[0]=='W'&&x[n-1]!=x[1])f&=true;
	}else{
		if(x[0]=='S'&&x[n-1]!=x[1])f&=true;
		if(x[0]=='W'&&x[n-1]==x[1])f&=true;
	}
	
	if(f){
		cout<<x<<endl;
		return 0;
	}
	
	x[0]='W';
	x[1]='W';
	
	for(int i=1;i<n-1;i++){
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='o'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='o'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='S')x[i+1]='W';
		if(s[i]=='x'&&x[i]=='S'&&x[i-1]=='W')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='S')x[i+1]='S';
		if(s[i]=='x'&&x[i]=='W'&&x[i-1]=='W')x[i+1]='W';
	}
	
	f=true;
	
	if(s[n-1]=='o'){
		if(x[n-1]=='S'&&x[n-2]==x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]!=x[0])f&=true;
	}else{
		if(x[n-1]=='S'&&x[n-2]!=x[0])f&=true;
		if(x[n-1]=='W'&&x[n-2]==x[0])f&=true;
	}
	
	if(s[0]=='o'){
		if(x[0]=='S'&&x[n-1]==x[1])f&=true;
		if(x[0]=='W'&&x[n-1]!=x[1])f&=true;
	}else{
		if(x[0]=='S'&&x[n-1]!=x[1])f&=true;
		if(x[0]=='W'&&x[n-1]==x[1])f&=true;
	}
	
	if(f){
		cout<<x<<endl;
		return 0;
	}
	
	cout<<-1<<endl;
	
}