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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;



namespace VS_TopCoder
{



    class Program
    {

        static void Main(string[] args)
        {
            Test();

            int number = int.Parse(Console.ReadLine());
            string marubatsu = Console.ReadLine();

            string SW;
            var cond = new string[] { "SS", "SW", "WS", "WW" };

            for (int j = 0; j < cond.Length; j++)
            {
                SW = cond[j];


                for (int i = 1; i < marubatsu.Length; i++)
                {
                    if (marubatsu[i] == 'o' && SW[i] == 'S')
                    {
                        SW += SW[i - 1];
                    }
                    else if (marubatsu[i] == 'x' && SW[i] == 'S')
                    {
                        if (SW[i - 1] == 'S')
                        {
                            SW += 'W';
                        }
                        else
                        {
                            SW += 'S';
                        }


                    }
                    else if (marubatsu[i] == 'o' && SW[i] == 'W')
                    {
                        if (SW[i - 1] == 'S')
                        {
                            SW += 'W';
                        }
                        else
                        {
                            SW += 'S';
                        }
                    }
                    else if (marubatsu[i] == 'x' && SW[i] == 'W')
                    {
                        SW += SW[i - 1];
                    }


                }

                bool chk=false;
                //最後にNと0を評価する
                if (SW[0] == SW[marubatsu.Length])
                {

                    if (marubatsu[0] == 'o' && SW[0] == 'S' && SW[marubatsu.Length - 1] == SW[1])
                    {
                        chk = true;
                    }
                    else if (marubatsu[0] == 'x' && SW[0] == 'S' && SW[marubatsu.Length - 1] != SW[1])
                    {
                        chk = true;


                    }
                    else if (marubatsu[0] == 'o' && SW[0] == 'W' && SW[marubatsu.Length -1] != SW[1])
                    {
                        chk = true;
                    }
                    else if (marubatsu[0] == 'x' && SW[0] == 'W' && SW[marubatsu.Length - 1] == SW[1])
                    {
                        chk = true;
                    }

                    if (chk)
                    {
                        Console.WriteLine(SW.Substring(0, marubatsu.Length));
                        return;
                    }
                }
            }





            Console.WriteLine(-1);


        }


        static List<string> Readlines()
        {
            List<string> answer = new List<string>();

            do
            {
                var item = Console.ReadLine();
                if (item == null)
                {
                    break;
                }
                else
                {
                    answer.Add(item);
                }
            } while (true);

            return answer;
        }

        static List<string[]> Readlines2D(string divider)
        {
            List<string[]> answer = new List<string[]>();

            do
            {
                var item = Console.ReadLine();
                if (item == null)
                {
                    break;
                }
                else
                {
                    answer.Add(item.Split(Convert.ToChar(divider)));
                }
            } while (true);

            return answer;
        }

        //priority queue


        [Conditional("DEBUG")]
        static private void Test()
        {
            Console.SetIn(new System.IO.StreamReader(@"c:\users\user\documents\visual studio 2015\Projects\VS TopCoder\VS TopCoder\Test.txt"));
        }
    }
    class PriorityQueue<T>
    {
        private readonly List<T> heap;
        private readonly Comparison<T> compare;
        private int size;
        public PriorityQueue() : this(Comparer<T>.Default) { }
        public PriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) { }
        public PriorityQueue(Comparison<T> comparison) : this(16, comparison) { }
        public PriorityQueue(int capacity, Comparison<T> comparison)
        {
            heap = new List<T>(capacity);
            compare = comparison;
        }
        public void Enqueue(T item)
        {
            heap.Add(item);
            var i = size++;
            while (i > 0)
            {
                var p = (i - 1) >> 1;
                if (compare(this.heap[p], item) <= 0)
                    break;
                this.heap[i] = heap[p];
                i = p;
            }
            this.heap[i] = item;

        }
        public T Dequeue()
        {
            var ret = this.heap[0];
            var x = this.heap[--size];
            var i = 0;
            while ((i << 1) + 1 < size)
            {
                var a = (i << 1) + 1;
                var b = (i << 1) + 2;
                if (b < size && compare(heap[b], heap[a]) < 0) a = b;
                if (compare(heap[a], x) >= 0)
                    break;
                heap[i] = heap[a];
                i = a;

            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }

        public T Peek() { return heap[0]; }
        public int Count { get { return size; } }
        public bool Any() { return size > 0; }



    }


}