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
import java.util.*;


public class Main {
	int n;
	int [] data;
	long ans;
	
	private void dfs(int ind, long sum){
		if(ind == n){
			if(sum%2 == 0)ans++;
			return;
		}
		
		int now = data[ind];
		dfs(ind+1, sum * (now -1));
		dfs(ind+1, sum * now);
		dfs(ind+1, sum * (now+1));
	}
	
	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			n = sc.nextInt();
			data = new int[n];
			for(int i =0 ; i < n; i++){
				data[i] = sc.nextInt();
			}
			ans = 0;
			dfs(0, 1);
			System.out.println(ans);
		}
	}



	private void debug(Object... o) {
		System.out.println("debug = " + Arrays.deepToString(o));
	}

	public static void main(String[] args) {
		new Main().doit();
	}

}
