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.Map;
import java.util.Scanner;

public class Main {

    /**
     * 本処理を実行します。
     */
    public static void execute() {
        Scanner sc = new Scanner(System.in);

        int n = nextInt(sc);

        int odd = 0;
        int even = 0;

        for (int i = 0; i < n; i++) {
            int a = nextInt(sc);
            if ((a & 1) == 1) {
                // 奇数
                odd++;
            } else {
                // 偶数
                even++;
            }

        }

        if (odd == n) {
            out((int)Math.pow(3, n) - 1);
        } else if (even == n) {
            out((int)Math.pow(3, n) - (int)Math.pow(2, n));
        } else {
            out ((int)Math.pow(3, n) - (int)Math.pow(2, even));
        }
    }

    /**
     * 次の標準入力をintで受け取ります。
     * @return 標準入力値(int)
     */
    public static int nextInt(Scanner sc) {
        return sc.nextInt();
    }

    /**
     * 次の標準入力をStringで受け取ります。
     * @return 標準入力値(String)
     */
    public static String nextString(Scanner sc) {
        return sc.next();
    }

    /**
     * 次の標準入力を指定回数分intで受け取ります。
     * @param n 取得回数
     * @return 取得した標準入力値の配列(int)
     */
    public static int[] nextInts(Scanner sc, int n) {
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            arr[i] = nextInt(sc);
        }

        return arr;
    }

    /**
     * 標準出力にオブジェクトを出力します。
     * @param o 出力対象
     */
    public static void out(Object o) {
        System.out.println(o);
    }

    public static void main(String[] args) {
        execute();
    }

    public static void putCountMap(Map<Integer, Integer> map, int value) {
        if (map.containsKey(value)) {
            map.put(value, map.get(value) + 1);
        } else {
            map.put(value, 1);
        }
    }
}

