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: Accepted)

using System;
using System.Collections.Generic;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("6");
            WillReturn.Add("ooxoox");
            //SSSWWS
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3");
            WillReturn.Add("oox");
            //-1
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("10");
            WillReturn.Add("oxooxoxoox");
            //SSWWSSSWWS
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static string s;
    static int N;

    static void Main()
    {
        List<string> InputList = GetInputList();
        N = int.Parse(InputList[0]);
        s = InputList[1];

        string Wariate1 = DeriveWariate("SS");
        string Wariate2 = DeriveWariate("SW");
        string Wariate3 = DeriveWariate("WS");
        string Wariate4 = DeriveWariate("WW");

        if (Wariate1 != "-1") { Console.WriteLine(Wariate1); return; }
        if (Wariate2 != "-1") { Console.WriteLine(Wariate2); return; }
        if (Wariate3 != "-1") { Console.WriteLine(Wariate3); return; }
        if (Wariate4 != "-1") { Console.WriteLine(Wariate4); return; }
        Console.WriteLine(-1);
    }

    //最初の2匹を引数として、各動物の割り当てを返す
    static string DeriveWariate(string pSaisyo2)
    {
        int UB = N - 1;
        char[] WariateArr = new char[UB + 1];
        WariateArr[0] = pSaisyo2[0];
        WariateArr[1] = pSaisyo2[1];

        for (int I = 1; I <= UB - 1; I++) {
            char Prev = WariateArr[I - 1];
            char Curr = WariateArr[I];
            char Hatugen = s[I];

            char NextAnimal = DeriveNextAnimal(Prev, Curr, Hatugen);
            WariateArr[I + 1] = NextAnimal;
        }

        //最初の2匹が矛盾していないかチェック
        if (WariateArr[0] !=
            DeriveNextAnimal(WariateArr[UB - 1], WariateArr[UB], s[UB])) {
            return "-1";
        }
        if (WariateArr[1] !=
            DeriveNextAnimal(WariateArr[UB], WariateArr[0], s[0])) {
            return "-1";
        }

        return new string(WariateArr);
    }

    //前とカレントの動物と、カレントの動物の発言を引数として、カレントの次の動物を返す
    static char DeriveNextAnimal(char pPrev, char pCurr, char pHatugen)
    {
        if (pPrev == 'S' && pCurr == 'S') {
            if (pHatugen == 'o') return 'S';
            if (pHatugen == 'x') return 'W';
        }
        if (pPrev == 'S' && pCurr == 'W') {
            if (pHatugen == 'o') return 'W';
            if (pHatugen == 'x') return 'S';
        }
        if (pPrev == 'W' && pCurr == 'S') {
            if (pHatugen == 'o') return 'W';
            if (pHatugen == 'x') return 'S';
        }
        if (pPrev == 'W' && pCurr == 'W') {
            if (pHatugen == 'o') return 'S';
            if (pHatugen == 'x') return 'W';
        }
        return '\0';
    }
}