Problem:
Score: 500 points

Problem Statement

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.

Sample Input 1

6
0 1 2 3 4 5

Sample Output 1

3

We have three possible combinations, as follows:

Red, Red, Red, Red, Red, Red

Blue, Blue, Blue, Blue, Blue, Blue

Green, Green, Green, Green, Green, Green

Sample Input 2

3
0 0 0

Sample Output 2

6

Sample Input 3

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

Sample Output 3

115295190

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
public class Main {
	
	public static void main(String[] args) {
		
		int mod = (int)1e9+7; 
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int A[] = new int[N];
		for(int i=0;i<N;i++)A[i]=sc.nextInt();
		sc.close();
		
		int memo[] = new int[N];
		long ans = 1;
		for(int i=0;i<N;i++) {
			if(A[i]==0) {
				ans *= (3 - memo[A[i]]);
			}else {
				ans *= (memo[A[i]-1]-memo[A[i]]);
			}
			ans %= mod;
			memo[A[i]]++;
		}
		System.out.println(ans);
	}
}