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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

main = do
  li <- getLine
  let n = read li
  li <- getLine
  let as = map read $ words li
  let ans = compute n as
  print ans

{-
整数列に対して、似た整数列は、それぞれの要素が-1,+-0,+1の3バリエーションがある。
長さNならば、全部で3^N個ある。
積は、全てが奇数のとき奇数、どれか一つでも偶数があると偶数になる。
aiが奇数のとき、奇数はそれだけ。1つ。aiが偶数のとき、a-1とa+1が奇数。可能性2つ。
それの積が、奇数な似た整数列の個数。これを引けばよい。
-}

compute :: Int -> [Int] -> Int
compute n as = 3^n - product (map f as)

f n
  | even n = 2
  | True   = 1