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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

int n, a[105];
ll dp[105][2];

int main()
{
    ios_base::sync_with_stdio(false);

    cin >> n;
    dp[0][1] = 1;
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
        if (a[i] % 2 == 0) {
            dp[i][0] += dp[i - 1][0] + dp[i - 1][1];

            dp[i][0] += 2 * dp[i - 1][0];
            dp[i][1] += 2 * dp[i - 1][1];
        } else {
            dp[i][0] += 2 * (dp[i - 1][0] + dp[i - 1][1]);

            dp[i][0] += dp[i - 1][0];
            dp[i][1] += dp[i - 1][1];
        }
    }
    cout << dp[n][0] << endl;

    return 0;
}