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.io.*;
import java.util.*;
import static java.lang.Math.*;

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

    int[] array;
    int N ;
    long count = 0;
    public void solve(String[] args) {
        MyScanner scanner = new MyScanner();
        N = scanner.nextInt();
        array = new int[N];
        for (int i = 0; i < N; i++) {
            array[i] = scanner.nextInt();
        }
        dfs(0, 1);
        System.out.println(count);
    }

    private void dfs(int depth, long v) {
        if (depth == N) {
            if (v % 2 == 0) {
                count++;
            }
            return;
        }
        for (int i = -1; i < 2; i++) {
            dfs(depth+1, v * (array[depth] + i));
        }
    }

    private class MyScanner {
        String[] s;
        int i;
        BufferedReader br;
        String reg = " ";

        MyScanner () {
            s = new String[0];
            i = 0;
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {
            try {
                if (i < s.length) return s[i++];
                String line = br.readLine();
                while (line.equals("")) {
                    line = br.readLine();
                }
                s = line.split(reg, 0);
                i = 0;
                return s[i++];
            } catch (Exception e) {
                e.printStackTrace();
            }
            return null;
        }

        public int nextInt() {
            try {
                return Integer.parseInt(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }

        public double nextDouble() {
            try {
                return Double.parseDouble(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }

        public long nextLong()  {
            try {
                return Long.parseLong(next());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return -1;
        }
    }
}
