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;
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
        bool ans = false;
        var ring = new string[N];
        Func<string, string> rev = (str) => str == "S" ? "W" : "S";
        Func<string, bool> isHonest = (str) => str == "S";
        Func<char, bool> isSame = (cha) => cha == 'o';
        Action<string> initSame = (str) => ring[1] = ring[N - 1] = str;
        Action<string> initDiff = (str) => ring[1] = rev(ring[N - 1] = str);
        Action<int, string> same = (index, str) => ring[index + 1] = ring[index - 1];
        Action<int, string> diff = (index, str) => ring[index + 1] = rev(ring[index - 1]);
        Action f = () => {
            for (int i = 1; i < N - 1; ++i) {
                if (isHonest(ring[i])) {
                    if (isSame(S[i])) {
                        same(i, ring[i]);
                    } else {
                        diff(i, ring[i]);
                    }
                } else {
                    if (isSame(S[i])) {
                        diff(i, ring[i]);
                    } else {
                        same(i, ring[i]);
                    }
                }
            }
        };
        Func<bool> finIsSame = () => ring[N - 2] == ring[0];
        Func<bool> finIsDiff = () => !finIsSame();
        Func<bool> isValid = () => {
            if (isHonest(ring[N - 1])) {
                if (isSame(S[N - 1])) {
                    return finIsSame();
                } else {
                    return finIsDiff();
                }
            } else {
                if (isSame(S[N - 1])) {
                    return finIsDiff();
                } else {
                    return finIsSame();
                }
            }
        };
        //羊スタート
        //初回            
        ring[0] = "S";
        if (isSame(S[0])) {
            initSame(ring[0]);
        } else {
            initDiff(ring[0]);
        }
        //中間
        f();
        //最終チェック
        if (isValid()) {
            ans = true;
        }
        //狼スタート
        //初回        
        ring = new string[N];
        ring[0] = "W";
        if (isSame(S[0])) {
            initDiff(ring[0]);
        } else {
            initSame(ring[0]);
        }
        //中間
        f();
        //最終チェック
        if (isValid()) {
            ans = true;
        }
        
       //ret
        if (ans) {
            for (int i = 0; i < N; ++i) {
                Console.Write(ring[i]);
            }
            Console.WriteLine("");
        } else {
            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(); }
}