Similar Arrays

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.

Examples

Input

2 2 3

Output

7

Input

3 3 3 3

Output

26

Input

1 100

Output

1

Input

10 90 52 56 71 44 8 13 30 57 84

Output

58921

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

Print the number of integer sequences that satisfy the condition.

Examples

Input

2 2 3

Output

7

Input

3 3 3 3

Output

26

Input

1 100

Output

1

Input

10 90 52 56 71 44 8 13 30 57 84

Output

58921

样例

10
90 52 56 71 44 8 13 30 57 84

58921