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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		long[]A = new long[N];
		string[] str = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = long.Parse(str[i]);
		}
		long mod = 1000000007;
		long ans = 0;
		if(A[0]==0){
			ans = 3;
			int a1 = 1;
			int a2 = 0;
			int a3 = 0;
			for(var i=1;i<N;i++){
				if(A[i]==a1){
					if(A[i]==a2){
						if(A[i]==a3){
							ans = ans * 3 % mod;
							a1++;
						} else {
							ans = ans * 2 % mod;
							a1++;
						}
					} else {
						if(A[i]==a3){
							ans = ans * 2 % mod;
							a1++;
						} else {
							ans = ans * 1 % mod;
							a1++;
						}
					}
				} else {
					if(A[i]==a2){
						if(A[i]==a3){
							ans = ans * 2 % mod;
							a2++;
						} else {
							ans = ans * 1 % mod;
							a2++;
						}
					} else {
						if(A[i]==a3){
							ans = ans * 1 % mod;
							a3++;
						} else {
							ans = 0;
						}
					}
				}
              	//Console.Error.WriteLine(ans+" "+a1+" "+a2+" "+a3);
			}
		}
		Console.WriteLine(ans);
	}
}