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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) {
        try {
            // 標準入力
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            int n = Integer.parseInt(br.readLine());
            String str[] = br.readLine().split(" ");
            int ans = 3;
            int minus = 1;
            for (int i = 0; i < str.length; i++) {
                int temp = Integer.parseInt(str[i]);
                if (temp % 2 == 0) {
                    minus = minus * 2;
                }
                if (i != 0) {
                    ans = ans * 3;
                }
            }
            System.out.println(ans - minus);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}
