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: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		String s = sc.next();
		boolean[] o = new boolean[n];
		
		for(int i = 0; i < n; i++)
		{
			o[i] = s.charAt(i) == 'o';
		}
		
		int[] fill = new int[n]; //1 sheep 2 wolf
		for(int a = 1; a <= 2; a++)
		{
			for(int b = 1; b <= 2; b++)
			{
				fill[0] = a;
				fill[1] = b;
				//0: a, 1: b
//				System.out.println(a + " " + b);
				
				//assign last fill
				boolean same;
				if(fill[0]==2)same = !o[0];
				else same = o[0];
				if(same)fill[n-1] = b;
				else fill[n-1] = 3-b;
//				System.out.println("Assign last with " + fill[n-1]);
				
				for(int i = 2; i < n-1; i++)
				{ //fill spot i
					if(fill[i-1]==2)same = !o[i-1];
					else same = o[i-1];
					if(same)fill[i] = fill[i-2];
					
					else fill[i] = 3-fill[i-2];
					
//						System.out.println("Fill " + i + " with: " + fill[i]);
//						System.out.println("Deb " + a + " " + b);
//						System.out.println("Fill " + i + " with: " + (fill[i]==1?'S':'W'));
//						System.out.println("Reason: " + (fill[i-1]==2) + " xor " + o[i-1] + " makes " + same);
				}
				
				//check last claim to 0
				int mustbe;
				if(fill[n-1]==2)same = !o[n-1];
				else same = o[n-1];
				if(same)mustbe = fill[n-2];
				else mustbe = 3-(fill[n-2]);
				
				if(fill[0] != mustbe)
				{
//					System.out.println("LS ERROR: " + fill[n-2] + " and " + fill[0] + ", mustbe " + mustbe);
//					System.out.println("Cause " + fill[n-1] + ", " + o[n-1]);
					continue;
				}
				
				
				//reassign last fill with n-2
				if(fill[n-2]==2)same = !o[n-2];
				else same = o[n-2];
				if(same)mustbe = fill[n-3];
				else mustbe = 3-(fill[n-3]);
				
				if(fill[n-1] != mustbe)
				{
					continue;
				}
				else
				{
					StringBuilder sb = new StringBuilder();
					for(int i = 0; i < n; i++)
					{
						if(fill[i] == 1)sb.append('S');
						else if(fill[i] == 2 )sb.append('W');
						else System.out.println("ERRROR!");
					}
					System.out.println(sb);
					return;
				}
				
				
			}
			
			
		}
		System.out.println(-1);

	}

}