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 System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Mod(int a, int b)
        {
            return (a % b + b) % b;
        }
        static int[] Convert(string s)
        {
            return s.Select(c => (c == 'S') ? 1 : -1).ToArray();
        }
        static int[] Solve(int N, int[] S)
        {
            foreach (int[] t in new[] { new[] { -1, -1 }, new[] { -1, 1 },new[] { 1, -1 }, new[] { 1, 1 } })
            {
                int[] ans = new int[N];
                Array.Copy(t, ans, 2);
                for (int i = 2; i < N; ++i)
                {
                    int a0 = Mod(i - 2, N);
                    int a1 = Mod(i - 1, N);
                    int a2 = Mod(i - 0, N);
                    ans[a2] = ans[a0] * ans[a1] * S[a1];
                }
                if (Enumerable.Range(0, N).All(i =>
                {
                    int a0 = Mod(i - 1, N);
                    int a1 = Mod(i, N);
                    int a2 = Mod(i + 1, N);
                    return (ans[a0] * ans[a2] == ans[a1] * S[a1]);
                }))
                {
                    return ans;
                }
            }
            return null;
        }
        static void Main(string[] args)
        {
            int N = ReadInt();
            string s = Read();
            int[] ans = Solve(N, s.Select(c => (c == 'o') ? 1 : -1).ToArray());
            Console.WriteLine((ans != null) ? new string(Array.ConvertAll(ans, n => (n == 1) ? 'S' : 'W')) : "-1");
        }
    }
}