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 int first = -1;
	static int second = -1;
	static int third = -1;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long result = 1;
		for (int i = 0; i < n; i++) {
			int a = sc.nextInt();
			long mul = countNum(a);
			addNum(a);
			result = result * mul % 1000000007;
		}
		System.out.println(result);
	}

	public static int countNum(int num) {
		int count = 0;
		if (first == num - 1) {
			count++;
		}
		if (second == num - 1) {
			count++;
		}
		if (third == num - 1) {
			count++;
		}
		return count;
	}

	public static void addNum(int num) {
		if (first == num - 1) {
			first++;
			return;
		}
		if (second == num - 1) {
			second++;
			return;
		}
		if (third == num - 1) {
			third++;
		}
	}
}