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: Wrong Answer)

import java.util.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	final int MOD = 1000000007;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;
	final int LEN = 0;

	int a[];
	
	void doIt() {
		int n = sc.nextInt();
		long ans = 1;
		int num[] = new int[n];
		a = new int[n];
		for(int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		for(int i = 0; i < n; i++) {
			if(a[i] != 0) {
				ans = ans * (num[a[i] - 1] - num[a[i]]);
			}
			num[a[i]] ++;
		}
		System.out.println(ans  * 6 %MOD);
	}
	
	long dfs(int _num[], int dps, int n) {
		if(dps == n) return 1L;
		int num[] = _num.clone();
		long ans = 0;
		for(int i = 0; i < 3; i++) {
			if(num[i] == a[dps]) {
				num[i]++;
				ans = (ans + dfs(num, dps + 1, n)) % MOD;
				num = _num.clone();
			}
		}
		System.out.println(dps +" "+ ans);
		return ans;
	}

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