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 Python (3.8.2) (judge verdict: Accepted)

ans = 0
number = set()
def exsearch(s, i, N, A):
    if i == N:
        global ans
        mul = 1
        for i in range(N):
            if s[i] == "0":
                mul *= A[i]

            elif s[i] == "1":
                    mul *= (A[i] - 1)

            elif s[i] == "2":
                    mul *= (A[i] + 1)

        if mul % 2 == 0:
            ans += 1

    else:
        for c in ["0", "1", "2"]:
            exsearch(s + c, i + 1, N, A)

def main():
    N = int(input())
    A = [int(a) for a in input().split()]

    exsearch("", 0, N, A)

    print(ans)

if __name__ == "__main__":
    main()