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

		int n = sc.nextInt();

		int cntEven = 0;
		for (int i = 0; i < n; i++) {
			int tmp = sc.nextInt();
			if (tmp % 2 == 0)
				cntEven++;
		}

		int ans = (int) Math.pow(3, n) - (1 << cntEven);

		System.out.println(ans);

		sc.close();
	}

}
