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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn dfs(ans: &mut i64, a: &[i64], b: &mut Vec<i64>) {
    if b.len() == a.len() {
        let mut y = 1_i64;
        for &b_i in b.iter() {
            y *= b_i;
        }
        if y % 2 == 0 {
            *ans += 1;
        }
        return;
    }
    let i = b.len();
    for &d in [-1, 0, 1].iter() {
        b.push(a[i] + d);
        dfs(ans, a, b);
        b.pop();
    }
}

fn main() {
    input! {
        n: usize,
        a: [i64; n],
    };
    let mut ans = 0;
    dfs(&mut ans, &a, &mut vec![]);
    println!("{}", ans);
}