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: Wrong Answer)

// dryしたいがまず提出

using System;

namespace AtCoder {
    class CircleList<T> {
        T[] circle_list;

        public int Length {
            get {
                return circle_list.Length;
            }
        }

        public CircleList(int length){
            circle_list = new T[length];
        }

        public CircleList(T[] char_array) {
            circle_list = char_array;
        }

        public T this[int index] {
            get {
                return circle_list[index % Length];
            }
            set {
                circle_list[index % Length] = value;
            }
        }

        public void Print() {
            foreach (T t in circle_list) Console.Write(t);
            Console.WriteLine();
        }
    }



    class Program {
        static void Main() {
            string input = Console.ReadLine();
            int count = int.Parse(input);
            input = Console.ReadLine();

            CircleList<char> declares = new CircleList<char>(input.ToCharArray());
            CircleList<char>  animals = new CircleList<char>(declares.Length);


            // 最初の２頭をSSと仮定
            animals[0] = 'S';
            animals[1] = 'S';
            Solve(declares, animals);

            // 最初の２頭をSWと仮定
            animals[0] = 'S';
            animals[1] = 'W';
            Solve(declares, animals);

            // 最初の２頭をWSと仮定
            animals[0] = 'W';
            animals[1] = 'S';
            Solve(declares, animals);

            // 最初の２頭をWWと仮定
            animals[0] = 'W';
            animals[1] = 'W';
            Solve(declares, animals);

            Console.WriteLine(-1);
        }

        static void Solve(CircleList<char> declares, CircleList<char> animals) {
            for (int i = 2; i < animals.Length * 2; i++) {
                animals[i] = GuessNextAnimal(animals[i - 1], declares[i - 1], animals[i - 2]);
            }
            if (CheckValidity(declares, animals)) {
                animals.Print();
                return;
            }
        }
                
        static char GuessNextAnimal(char current_animal, char current_declare, char previous_animal) {
            switch (current_animal) {
                case 'S':
                    switch (current_declare) {
                        case 'o':
                            switch (previous_animal) {
                                case 'S':
                                    return 'S';
                                case 'W':
                                    return 'W';
                            }
                            break;
                        case 'x':
                            switch (previous_animal) {
                                case 'S':
                                    return 'W';                                    
                                case 'W':
                                    return 'S';
                            }
                            break;
                    }
                    break;
                case 'W':
                    switch (current_declare) {
                        case 'o':
                            switch (previous_animal) {
                                case 'S':
                                    return 'W';
                                case 'W':
                                    return 'S';
                            }
                            break;
                        case 'x':
                            switch (previous_animal) {
                                case 'S':
                                    return 'S';
                                case 'W':
                                    return 'W';
                            }
                            break;
                    }
                    break;
            }
            return ' ';
        }

        static bool CheckValidity(CircleList<char> declares, CircleList<char> animals) {
            for(int i = 1; i <= declares.Length + 1; i++) {
                if(animals[i + 1] == GuessNextAnimal(animals[i], declares[i], animals[i - 1])){
                    // trueなら何もしない
                } else {
                    return false;
                }
            }
            return true;
        }
    }
}