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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.*;

import static java.lang.System.*;

// https://atcoder.jp/contests/abc055/tasks/arc069_b
// 12:30-  ２つを固定すると4パターンしかないので全探索。O(n)
public class Main {

    static final char sheep = 'S';
    static final char wolf = 'W';

    static final char same = 'o';
    static final char diff = 'x';

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        char[] statements = sc.next().toCharArray();

        solver(N, statements);
    }

    public static void solver(int N, char[] statements) {

        char[] animals = new char[]{sheep, wolf};
        for (char a1 : animals) {
            for (char a2 : animals) {
                char[] ans = existPattern(a1, a2, N, statements);
                if (ans != null) {
                    out.println(String.valueOf(ans));
                    return;
                }
            }
        }
        out.println("-1");
    }

    // 与えれれた条件（1番目・2番目の動物、発言）から動物のパターンが存在するかチェックする
    // 存在する場合は、存在するパターンを返却する。なければNullを返却する
    public static char[] existPattern(char first_animal, char second_animal, int N, char[] statements){

        char[] ans = new char[N];
        ans[0] = first_animal;
        ans[1] = second_animal;

        char left_ani = first_animal;
        char center_ani = second_animal;
        char right_ani;

        // パターンを列挙
        for(int n=2; n<N; n++){
            char center_statement = statements[n-1];
            right_ani = rightAnimal(left_ani, center_ani, center_statement);
            ans[n] = right_ani;
            left_ani = center_ani;
            center_ani = right_ani;
        }

        //out.println(ans);

        // 1週回ったところで矛盾するかチェック
        // まだチェックしていない1番目と最後の動物の発言をチェック

        char last_before_animal = ans[N-2];
        char last_animal = ans[N-1];

        char first_statement = statements[0];
        char last_statement = statements[N-1];

        if (rightAnimal(last_animal, first_animal, first_statement) == second_animal &&
                rightAnimal(last_before_animal, last_animal, last_statement) == first_animal){
            return ans;
        }

        return null;
    }

    public static char rightAnimal(char left_ani, char center_ani, char center_statement){
        char right_ani;
        switch (center_ani) {
            case (sheep):
                switch (center_statement){
                    case (same):
                        right_ani = left_ani;
                        break;
                    default:
                        right_ani = diffAnimal(left_ani);
                }
                break;

            default:    // wolf
                switch (center_statement){
                    case(same):
                        right_ani = diffAnimal(left_ani);
                        break;
                    default:
                        right_ani = left_ani;
                }
        }
       return right_ani;
    }

    public static char diffAnimal(char animal){
        if(animal == sheep){
            return wolf;
        }
        return sheep;
    }
}