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;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    public struct Pair { public int x, y; public Pair(int x, int y) { this.x = x; this.y = y; } }
    public static void Solve()
    {
        int N = NextInt();
        string s = NextString();
        //決め打ちでどうにかする
        if (Menagerie(s, N, 1, 1)) return;
        if (Menagerie(s, N, 1, -1)) return;
        if (Menagerie(s, N, -1, 1)) return;
        if (Menagerie(s, N, -1, -1)) return;
        Console.WriteLine(-1);
    }
    public static bool Menagerie(string s, int N, int a, int b)
    {
        int[] ans = new int[N + 1];
        ans[0] = a;
        ans[1] = b;
        for (int i = 1; i < N; i++)
        {
            if (ans[i] == 1)
            {
                if (s[i] == 'o') ans[i + 1] = ans[i - 1];
                else ans[i + 1] = -ans[i - 1];
            }
            else
            {
                if (s[i] == 'o') ans[i + 1] = -ans[i - 1];
                else ans[i + 1] = ans[i - 1];
            }
        }
        for (int i = 0; i < N; i++)
        {
            int n0 = (i - 1 + N) % N;
            int n1 = (i + 1 + N) % N;
            if (ans[i] == 1)
            {
                if (s[i] == 'o' && ans[n0] != ans[n1]) return false;
                else if (s[i] == 'x' && ans[n0] == ans[n1]) return false;
            }
            else
            {
                if (s[i] == 'o' && ans[n0] == ans[n1]) return false;
                else if (s[i] == 'x' && ans[n0] != ans[n1]) return false;
            }
        }
        if (ans[0] == ans[N])
        {
            for (int i = 0; i < N; i++) Console.Write(ans[i] == 1 ? "S" : "W");
            Console.WriteLine();
            return true;
        }
        else return false;
    }
    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}