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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Runtime.InteropServices;
using System.Runtime.Remoting.Messaging;
using System.Security.Principal;
using System.Text;
class Simple
{
    int N;
    string S;
    void Solve() {
        //input
        N = io.Int;
        S = io.String;
        //cal
        var sArr = S.Select(c => c.ToString()).ToArray();
        var sw = new string[] { "S", "W" };
        var ring = new string[0];
        Func<string, string> rev = (a) => a == "S" ? "W" : "S";
        Func<int, bool> isHonest = (index) => ring[index] == "S";
        Func<int, bool> isSaySame = (index) => sArr[index] == "o";
        Action<int> setSame = (index) => ring[index + 1] = ring[index - 1];
        Action<int> setDiff = (index) => ring[index + 1] = rev(ring[index - 1]);
        Func<bool> isOK1 = () => ring[N - 2] == ring[0];
        Func<bool> isOK2 = () => ring[N - 1] == ring[1];
        Func<bool> isValid = () => {
            var f1 = false;
            var f2 = false;
            if (isHonest(N - 1))
                if (isSaySame(N - 1))  f1= isOK1();
                else                           f1= !isOK1();
            else
                if (isSaySame(N - 1))  f1=!isOK1();
            else                               f1= isOK1();
            if (isHonest(0))
                if (isSaySame(0))       f2 = isOK2();
                else                           f2 = !isOK2();
            else
                if (isSaySame(0))       f2 = !isOK2();
            else                               f2 = isOK2();
            return f1 && f2;
        };
        for (int n0 = 0; n0 < sw.Length; ++n0) {
            for (int n1 = 0; n1 < sw.Length; ++n1) {
                ring = new string[N];
                ring[0] = sw[n0];
                ring[1] = sw[n1];
                for (int i = 1; i < N - 1; ++i) {
                    if (isHonest(i))
                        if (isSaySame(i))
                            setSame(i);
                        else
                            setDiff(i);
                    else
                        if (isSaySame(i))
                        setDiff(i);
                    else
                        setSame(i);
                }
                if (isValid()) {
                    //ret
                    Console.WriteLine(string.Join("", ring));
                    return;
                }
            }
        }
        //ret
        Console.WriteLine(-1);

    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    void Stream() {
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        System.Console.SetIn(exStdIn);
        Solve();
        io.writeFlush();
    }
}
class SimpleIO
{
    string[] nextBuffer;
    int BufferCnt;
    char[] cs = new char[] { ' ' };
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    public SimpleIO() {
        nextBuffer = new string[0];
        BufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        BufferCnt = 0;
        return nextBuffer[BufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void writeFlush() { Console.Out.Flush(); }
}