Contest Duration: - (local time) (120 minutes)
B - Similar Arrays /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

2 つの長さ N の整数列 x_1, x_2, ..., x_Ny_1, y_2, ..., y_N が「似ている」とは、 任意の i (1 \leq i \leq N) に対して |x_i - y_i| \leq 1 が成り立つことをいうものとします。

とくに、どの整数列もその数列自身と似ていると考えます。

A と似ている整数列 b_1, b_2, ..., b_N であって、すべての項の積 b_1 b_2 ... b_N が偶数となるものはいくつあるか求めてください。

### 制約

• 1 \leq N \leq 10
• 1 \leq A_i \leq 100

### 入力

N
A_1 A_2 ... A_N


### 入力例 1

2
2 3


### 出力例 1

7


• 1, 2
• 1, 4
• 2, 2
• 2, 3
• 2, 4
• 3, 2
• 3, 4

### 入力例 2

3
3 3 3


### 出力例 2

26


### 入力例 3

1
100


### 出力例 3

1


### 入力例 4

10
90 52 56 71 44 8 13 30 57 84


### 出力例 4

58921


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