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;

class p
{
    static string t;

    //i,i+1文字目からi-1文字目を決めて返す
    static char backChar(string s,string temp,int i)
    {
        if (temp[i] == 'S')//i文字目が羊
        {
            if (s[i] == 'o')//羊かつ〇なら両側が同じ
                return temp[i + 1];
            else //羊かつ×なら両側が異なる
            {
                if (temp[i + 1] == 'S') return 'W';
                else return 'S';
            }
        }
        else //i文字目が狼
        {
            if (s[i] == 'x')//狼かつ×なら両側が同じ
                return temp[i + 1];
            else //狼かつ〇なら両側が異なる
            {
                if (temp[i + 1] == 'S') return 'W';
                else return 'S';
            }
        }
    }

    //i-1,i文字目からi+1文字目を決めて返す
    static char nextChar(string s,string temp,int i)
    {
        if (temp[i] == 'S')//i文字目が羊
        {
            if (s[i] == 'o')//羊かつ〇なら両側が同じ
                return temp[i - 1];
            else //羊かつ×なら両側が異なる
            {
                if (temp[i - 1] == 'S') return 'W';
                else return 'S';
            }
        }
        else //i文字目が狼
        {
            if (s[i] == 'x')//狼かつ×なら両側が同じ
                return temp[i - 1];
            else //狼かつ〇なら両側が異なる
            {
                if (temp[i - 1] == 'S') return 'W';
                else return 'S';
            }
        }
    }

    static void Main(string[] a)
    {
        int N = int.Parse(Console.ReadLine());
        string s = Console.ReadLine();
        //s は o と x のみからなる長さ N の文字列
        t = "-1";
        //t は長さ N で S と W のみからなる文字列;解がない場合の-1を代入
        string temp = "";
        //１，２文字目を仮定してシミュレーションするための文字列temp
        char lastNext;
        char firstBack;

        string[] strarray = { "SS", "SW", "WS", "WW" };

        foreach (string str in strarray)
        {
            if (t != "-1") break;
            temp = str;
            for (int i = 1; i < N - 1; i++)
            {
                temp += nextChar(s, temp, i);
            }
            lastNext = nextChar(s, temp, N - 1);
            firstBack = backChar(s, temp, 0);
            if (lastNext == temp[0] && firstBack == temp[N - 1]) t = temp;
        }

        Console.WriteLine(t);

    }
}