Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

2
2 3

Sample Output 1

7

There are seven integer sequences that satisfy the condition:

1, 2

1, 4

2, 2

2, 3

2, 4

3, 2

3, 4

Sample Input 2

3
3 3 3

Sample Output 2

26

Sample Input 3

1
100

Sample Output 3

1

Sample Input 4

10
90 52 56 71 44 8 13 30 57 84

Sample Output 4

58921

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

class Main {

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

        int n = scanner.nextInt();

        int[] a = new int[n];

        for (int i = 0; i < a.length; i++) {
            a[i] = scanner.nextInt();
        }

        System.out.println(enumerate(a, 0));
    }

    private static int enumerate(int[] a, int index){
        if (index == a.length - 1) return a[index] % 2 == 0?1:2;
        int even = a[index] % 2 == 0?1:2;
        return even*(int) Math.pow(3, a.length - index - 1) + (3 - even)*enumerate(a, index + 1);
    }
}