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.Numerics;

public class Program {
	public static void Main() {
		new Calc().calc();
	}
	public class Calc {
		public Calc() { }
		public void calc() {
			long N = long.Parse(Console.ReadLine());
			bool[] s = Console.ReadLine().Select(_ => _ == 'o' ? true : false).ToArray();
			bool[,] line = new bool[4,N+1];
			line[0, 0] = true; line[0, 1] = true;
			line[1, 0] = true; line[1, 1] = false;
			line[2, 0] = false; line[2, 1] = true;
			line[3, 0] = false; line[3, 1] = false;
			int detectIndex=-1;
			for (int i = 0; i < 4; i++) {
				line[i, N] = false;
				for (int n = 1; n < N - 1; n++) {
					line[i, n + 1] = find(s[n], line[i, n - 1], line[i, n]);
				}
				if (line[i,0]==find(s[N-1],line[i,N-2],line[i,N-1])) { line[i, N] = true;detectIndex = i; break; }
			}
			if (detectIndex!=-1) {
				string foo = "";
				for (int i = 0; i < N; i++) {
					foo += line[detectIndex, i] ? "S" : "W";
				}
				Console.WriteLine(foo);
			} else {
				Console.WriteLine(-1);
			}
			return;
		}
		private bool check(bool self,bool l,bool r,bool ox) {
			if (self && ox&& l == r) return true;
			if (!self && !ox && l == r) return true;
			if (self && !ox && l != r) return true;
			if (!self && ox && l != r) return true;
			return false;
		}
		private bool find(bool ox_self,bool l,bool self) {
			if (self && !ox_self) return !l;
			if (!self && ox_self) return !l;
			return l;
		}
	}
}