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;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;

class Prog
{
    public Prog() { }
    public static int Main()
    {
        new Prog().calc();
        return 0;
    }

    Scanner cin;
    int N;
    string s;

    public void calc()
    {
        cin = new Scanner();
        N = cin.nextInt();
        s = cin.next();

        string ans;

        ans = create("SS");
        if (ans != "") { Console.WriteLine(ans); return; }

        ans = create("SW");
        if (ans != "") { Console.WriteLine(ans); return; }

        ans = create("WS");
        if (ans != "") { Console.WriteLine(ans); return; }

        ans = create("WW");
        if (ans != "") { Console.WriteLine(ans); return; }

        Console.WriteLine("-1");

    }

    string create(string start2)
    {
        var ans = new char[N];
        ans[0] = start2[0];
        ans[1] = start2[1];

        for (int i = 1;i<N-1;i++)
        {
            ans[i + 1] = addchar(ans[i - 1], ans[i], i);
        }

        if (!eval(ans[N - 1], ans[0], ans[1], s[0])) return "";
        if (!eval(ans[N - 2], ans[N - 1], ans[0], s[N - 1])) return "";
        return new string(ans);
    }



    char addchar(char c0,char c1,int n)
    {
        if (s[n] == 'o')
        {
            if (c1 == 'S')
            {
                if (c0 == 'S') return 'S';
                return 'W';
            }
            if (c0 == 'S') return 'W';
            return 'S';
        }
        if (c1 == 'S')
        {
            if (c0 == 'S') return 'W';
            return 'S';
        }
        if (c0 == 'S') return 'S';
        return 'W';

    }

    bool eval(char a,char b,char c,char ox)
    {
        if (ox == 'o')
        {
            if (b == 'S') return a == c;
            return a != c;
        }
        if (b == 'S') return a != c;
        return a == c;
    }
}




class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }

}