We will say that two integer sequences of length N, x_1, x_2, ..., x_N and y_1, y_2, ..., y_N, are similar when |x_i - y_i| \leq 1 holds for all i (1 \leq i \leq N).

In particular, any integer sequence is similar to itself.

You are given an integer N and an integer sequence of length N, A_1, A_2, ..., A_N.

How many integer sequences b_1, b_2, ..., b_N are there such that b_1, b_2, ..., b_N is similar to A and the product of all elements, b_1 b_2 ... b_N, is even?

Constraints

* 1 \leq N \leq 10
* 1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the number of integer sequences that satisfy the condition.

Examples

Input

2
2 3


Output

7


Input

3
3 3 3


Output

26


Input

1
100


Output

1


Input

10
90 52 56 71 44 8 13 30 57 84


Output

58921
import java.util.Scanner;

class Main {

    private static int count;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int N = Integer.parseInt(scanner.next());

        int[] A = new int[N];

        for (int i = 0; i < N; i++) {
            A[i] = Integer.parseInt(scanner.next());
        }

        calculate(A, N, 0);
        System.out.println(count);
    }

    private static void calculate(int[] A, int N, int i) {
        if (i == N) {
            int num = 1;
            for (int j = 0; j < N; j++) {
                num *= A[j];
            }
            if (num % 2 == 0) {
                count++;
            }
        } else {
            for (int j = 0; j < 3; j++) {
                int tmp = A[i];
                A[i] = tmp - 1 + j;
                calculate(A, N, i+1);
                A[i] = tmp;
            }
        }
    }
}