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;
using System.Linq;

namespace AtCoderCs
{
    class Program
    {
        static void Main()
        {

            var Num = int.Parse(Console.ReadLine());
            var Comment = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var Result = 1L;
            var Mod = 1000000007L;
            var Buffer = new int[3] { 0, 0, 0 };

            for (int i = 0; i < Num; i++)
            {

                Result *= Buffer.Count(x => x == Comment[i]);
                if (Buffer[0] == Comment[i]) Buffer[0]++;
                else if (Buffer[1] == Comment[i]) Buffer[1]++;
                else Buffer[2]++;

                if (Result == 0) break;
                while (Mod < Result)
                {
                    Result -= Mod;
                }

            }

            Console.WriteLine(Result);

        }


    }
}