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.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Text;
 
public class Program
{
    public void Proc() {
        Reader.IsDebug = false;
        int totalCount = int.Parse(Reader.ReadLine());
        this.IsSame = Reader.ReadLine().Select(a=>a=='o').ToArray();
        List<Nullable<bool>[]> list = new List<Nullable<bool>[]>();
        list.Add(new Nullable<bool>[totalCount]);
        list[0][0] = false;
        list[0][1] = false;
        list.Add(new Nullable<bool>[totalCount]);
        list[1][0] = false;
        list[1][1] = true;
        list.Add(new Nullable<bool>[totalCount]);
        list[2][0] = true;
        list[2][1] = false;
        list.Add(new Nullable<bool>[totalCount]);
        list[3][0] = true;
        list[3][1] = true;

        foreach(Nullable<bool>[] l in list) {
            string ans = this.GetAns(l);
            if(ans.Length > 0) {
                Console.WriteLine(ans);
                return;
            }
        }
        Console.WriteLine("-1");
    }

    private bool[] IsSame;
    private string GetAns(Nullable<bool>[] isWolf) {
        for(int i=2; i<isWolf.Length; i++) {
            if(isWolf[i-1].Value) {
                if(IsSame[i-1]) {
                    isWolf[i] = !isWolf[i-2].Value;
                } else {
                    isWolf[i] = isWolf[i-2].Value;
                }
            } else {
                if(IsSame[i-1]) {
                    isWolf[i] = isWolf[i-2].Value;
                } else {
                    isWolf[i] = !isWolf[i-2].Value;
                }
            }
        }
        if(isWolf[0].Value) {
            if(IsSame[0]) {
                if(isWolf[1].Value == isWolf.Last().Value) {
                    return string.Empty;
                }
            } else {
                if(isWolf[1].Value != isWolf.Last().Value) {
                    return string.Empty;
                }                
            }
        } else {
            if(IsSame[0]) {
                if(isWolf[1].Value != isWolf.Last().Value) {
                    return string.Empty;
                }
            } else {
                if(isWolf[1].Value == isWolf.Last().Value) {
                    return string.Empty;
                }                
            }
        }
        StringBuilder ans = new StringBuilder();
        for(int i=0; i<isWolf.Length; i++) {
            if(isWolf[i].Value) {
                ans.Append("W");
            } else {
                ans.Append("S");
            }
        }
        return ans.ToString();
    }


    public class Reader {
        public static bool IsDebug = true;
        private static System.IO.StringReader SReader;
        private static string InitText = @"



10
oxooxoxoox




";
        public static string ReadLine() {
            if(IsDebug) {
                if(SReader == null) {
                    SReader = new System.IO.StringReader(InitText.Trim());
                }
                return SReader.ReadLine();
            } else {
                return Console.ReadLine();
            }
        }
    }
    public static void Main(string[] args)
    {
        Program prg = new Program();
        prg.Proc();
    }
}