N people are standing in a queue, numbered 1, 2, 3, ..., N from front to back. Each person wears a hat, which is red, blue, or green.

The person numbered i says:

* "In front of me, exactly A_i people are wearing hats with the same color as mine."



Assuming that all these statements are correct, find the number of possible combinations of colors of the N people's hats.

Since the count can be enormous, compute it modulo 1000000007.

Constraints

* 1 \leq N \leq 100000
* 0 \leq A_i \leq N-1
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 A_3 ... A_N


Output

Print the number of possible combinations of colors of the N people's hats, modulo 1000000007.

Examples

Input

6
0 1 2 3 4 5


Output

3


Input

3
0 0 0


Output

6


Input

54
0 0 1 0 1 2 1 2 3 2 3 3 4 4 5 4 6 5 7 8 5 6 6 7 7 8 8 9 9 10 10 11 9 12 10 13 14 11 11 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17


Output

115295190
import java.util.Scanner;

public class Main {
	static final long mod = 1000000007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long ans = 0;
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		int[] color = new int[3];

		if(a[0] == 0) {
			ans = 3;
			color[0] = 1;
			int x = 0;
			boolean flag = true;
			for (int i = 1; i < n; i++) {
				x = 0;
				flag = true;
				for(int j = 0; j < 3; j++) {
					if(color[j] == a[i]) {
						x++;
						if(flag) {
							color[j]++;
							flag = false;
						}
					}
				}
				ans = (x*ans)%mod;
			}

		}else {
			ans = 0;
		}

		System.out.println(ans);
		sc.close();
	}
}