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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.Set;

public class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.nextLine());
        char[] ans = sc.nextLine().toCharArray();
        final char[][] init = {
            {'S', 'S'}, {'S', 'W'}, {'W', 'S'}, {'W', 'W'}
        };
        boolean can=false;
        char[] animals = new char[n];
        for(char[] initSet:init){
            animals = new char[n];
            animals[0]=initSet[0];
            animals[1]=initSet[1];
            if(animals[0]=='S'){
                animals[n-1] = (ans[0]=='o')? animals[1] : revAnimal(animals[1]);
            }else{
                animals[n-1] = (ans[0]=='o')? revAnimal(animals[1]) : animals[1];
            }

            for(int i=1;i<n-2;i++){
                if(animals[i]=='S'){
                    animals[i+1] = (ans[i]=='o')? animals[i-1] : revAnimal(animals[i-1]);
                }else{
                    animals[i+1] = (ans[i]=='o')? revAnimal(animals[i-1]) : animals[i-1];
                }
                animals[i+1] = nextAnimal(animals[i], animals[i-1], ans[i]);
            }
            
            char constrain = nextAnimal(animals[n-2], animals[n-3], ans[n-2]);
            if(constrain==animals[n-1]){
                if(animals[n-1]=='S'){
                    if(ans[n-1]=='o'){
                        can = (animals[0]==animals[n-2]);
                    }else{
                        can = (animals[0]!=animals[n-2]);
                    }
                }else{
                    if(ans[n-1]=='o'){
                        can = (animals[0]!=animals[n-2]);
                    }else{
                        can = (animals[0]==animals[n-2]);
                    }
                }
            }else{
                continue;
            }
            break;
        }
        if(can){
            String str = new StringBuilder().append(animals).toString();
            System.out.println(str);
        }else{
            System.out.println(-1);
        }
    }
    public static char revAnimal(char animal){
        if(animal=='S'){
            return 'W';
        }else{
            return 'S';
        }
    }

    public static char nextAnimal(char animal, char prevAnimal, char ans){
        char next;
        if(animal=='S'){
            next = (ans=='o')? prevAnimal : revAnimal(prevAnimal);
        }else{
            next = (ans=='o')? revAnimal(prevAnimal) : prevAnimal;
        }
        return next;
    }
}