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.Text;

namespace AtTest.ForBlue.ABC_055
{
    class AtTemplate
    {
        static int n;
        static string pattern;

        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            n = int.Parse(Console.ReadLine());
            pattern = Console.ReadLine();

            var result = new char[n];

            result[0] = 'S';
            result[1] = 'S';
            if (OK(ref result))
            {
                Console.WriteLine(result);
                return;
            }
            result[0] = 'S';
            result[1] = 'W';
            if (OK(ref result))
            {
                Console.WriteLine(result);
                return;
            }
            result[0] = 'W';
            result[1] = 'S';
            if (OK(ref result))
            {
                Console.WriteLine(result);
                return;
            }
            result[0] = 'W';
            result[1] = 'W';
            if (OK(ref result))
            {
                Console.WriteLine(result);
                return;
            }

            Console.WriteLine(-1);
        }

        static bool OK(ref char[] result)
        {
            var firstResult = result[0];
            for (int i = 1; i < n; i++)
            {
                int nextNo = (i + 1) % n;
                if (pattern[i] == 'o')
                {
                    if (result[i - 1] == 'S')
                    {
                        result[nextNo] = result[i] == 'S' ? 'S' : 'W';
                    }
                    else
                    {
                        result[nextNo] = result[i] == 'S' ? 'W' : 'S';
                    }
                }
                else
                {
                    if (result[i - 1] == 'S')
                    {
                        result[nextNo] = result[i] == 'S' ? 'W' : 'S';
                    }
                    else
                    {
                        result[nextNo] = result[i] == 'S' ? 'S' : 'W';
                    }
                }
            }

            if (result[0] == firstResult)
            {
                if (pattern[0] == 'o')
                {
                    if (result[0] == 'S')
                    {
                        return result[1] == result[n - 1];
                    }
                    else
                    {
                        return result[1] != result[n - 1];
                    }
                }
                else
                {
                    if (result[0] == 'S')
                    {
                        return result[1] != result[n - 1];
                    }
                    else
                    {
                        return result[1] == result[n - 1];
                    }
                }
            }
            else
            {
                return false;
            }
        }
    }
}