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;

namespace E
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            long MOD = 1000000007;

            long result = 1;
            var colorCount = new int[3];
            for (int i = 0; i < N; i++)
            {
                if (A[i] == colorCount[0] && A[i] == colorCount[1] && A[i] == colorCount[2])
                {
                    result *= 3;
                    result %= MOD;
                    colorCount[0]++;
                }
                else if (A[i] == colorCount[0] && A[i] == colorCount[1])
                {
                    result *= 2;
                    result %= MOD;
                    colorCount[0]++;
                }
                else if (A[i] == colorCount[1] && A[i] == colorCount[2])
                {
                    result *= 2;
                    result %= MOD;
                    colorCount[1]++;
                }
                else if (A[i] == colorCount[0])
                {
                    colorCount[0]++;
                }
                else if (A[i] == colorCount[1])
                {
                    colorCount[1]++;
                }
                else if (A[i] == colorCount[2])
                {
                    colorCount[2]++;
                }
                else result = 0;
            }
            Console.WriteLine(result);
        }
    }
}