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: Wrong Answer)

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();
			string[] hoge = new string[] { "SS", "SW", "WS", "WW" };
			string[] result = new string[4];
			for (int i = 0; i < 4; i++)
			{
				switch (hoge[i])
				{
					case "SS": result[i] = GetString("SS", s, N); break;
					case "SW": result[i] = GetString("SW", s, N); break;
					case "WS": result[i] = GetString("WS", s, N); break;
					case "WW": result[i] = GetString("WW", s, N); break;
				}
				if (result[i] != "-1")
				{
					Console.WriteLine(result[i]);
					return;
				}
			}
			Console.WriteLine("-1");
		}
		static string GetString(string K,string s, int N)
		{
			string answer = K;
			for (int i = 1; i <= N - 1; i++)
			{
				if (answer[i] == 'S' && answer[i - 1] == 'S')
				{
					if (s[i] == 'x')
					{
						answer += 'W';
					}
					else
					{
						answer += 'S';
					}
				}
				else if (answer[i] == 'W' && answer[i - 1] == 'S')
				{
					if (s[i] == 'x')
					{
						answer += 'S';
					}
					else
					{
						answer += 'W';
					}
				}
				else if (answer[i] == 'S' && answer[i - 1] == 'W')
				{
					if (s[i] == 'x')
					{
						answer += 'S';
					}
					else
					{
						answer += 'W';
					}
				}
				else if (answer[i] == 'W' && answer[i - 1] == 'W')
				{
					if (s[i] == 'x')
					{
						answer += 'W';
					}
					else
					{
						answer += 'S';
					}
				}
			}
			if (answer[N] == answer[0])
			//if ((answer[N-1] == 'S' && ((answer[N - 2] == 'W' && s[N - 1] == 'x')|| (answer[N - 2] == 'S' && s[N - 1] == 'o')))
			//|| (answer[N-1] == 'W'&& ((answer[N - 2] == 'S' && s[N - 1] == 'x')||(answer[N-2] =='W' && s[N-1] == 'o'))))
			{
				answer = answer.Remove(N);
				return answer;
			}
			else
			{
				return "-1";
			}
		}
	}
}