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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var N = int.Parse(Console.ReadLine());
			string s = Console.ReadLine();
			var array = new bool[N];
			for (int i = 0; i < N; i++)
			{
				array[i] = s[i] == 'o';
			}
			var result = new bool[][] { new[] { true, true }, new[] { true, false }, new[] { false, true }, new[] { false, false } };
			for (int i = 0; i < 4; i++)
			{
				if(GetString(result[i], array, N) != "-1")
				{
					Console.WriteLine(GetString(result[i], array, N));
					return;
				}
			}
			Console.WriteLine("-1");
		}
		static string GetString(bool[] K,bool[] s, int N)
		{
			var answer = new bool[N+1];
			answer[0] = K[0];
			answer[1] = K[1];
			for (int i = 1; i < N; i++) answer[i+1] = answer[i] == answer[i - 1] ?s[i]:!s[i];
			return answer[0] == answer[N] && ((s[0] == answer[0] == answer[1] == answer[N - 1]) || (!s[0] == !(answer[0] == answer[1] == answer[N - 1]))) ? string.Join("", answer.Take(N).Select(z => z ? "S" : "W")) : "-1";
		}
	}
}