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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public class Hello
{
    public static void Main()
    {
        Console.WriteLine(program(new string[] { Console.ReadLine(), Console.ReadLine() }));
    }
    
    private static string program(string[] args)
    {
        var n = int.Parse(args[0]);
        var s = args[1].ToCharArray();
        
        var animalPattern = new List<Tuple<char, char>>() { Tuple.Create('S', 'S'), Tuple.Create('S', 'W'), Tuple.Create('W', 'S'), Tuple.Create('W', 'W') }; // Item1:1番目の動物, Item2:N番目の動物
        
        return animalPattern.Select(animals => s.Aggregate(animals.Item2.ToString() + animals.Item1.ToString(),
            (t, elem) => t + (isXor(t[t.Length-1], elem) ? not(t[t.Length-2]) : t[t.Length-2]).ToString()))
        .FirstOrDefault(result => result.Substring(0, 2) == result.Substring(result.Length-2, 2))?.Substring(1, n) ?? "-1";
    }

    private static bool isXor(char animal, char ans) => animal == 'S' && ans == 'x' || animal == 'W' && ans == 'o';
    
    private static char not(char animal) => animal == 'S' ? 'W' : 'S';
}