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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using static System.Math;using static System.Console;using System.Collections.Generic;using System.Linq;using System;using System.Collections;
using System.Runtime.Serialization;
using System.Collections.Specialized;
using System.Security.Cryptography;
using System.Globalization;

class Program
{
    #region Reader
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine());
    static int[] ReadInts => Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine());
    static long[] ReadLongs => Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    #endregion
    #region Method
    const int mod = 1000000007;
    public static int Mod(int a,int mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    public static long Mod(long a, long mod = mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    #endregion


    static void Main()
    {
        int N = ReadInt;
        int[] As = ReadInts;
        long ans = 1;

        int[] d = { 0, 0, 0 };


        //0番目は任意
        d[0]++;
        ans *= 3;

        for (int i = 1; i < N; i++)
        {
            int options = 0;
            int color = -1;

            if(As[i] == d[0])
            {
                options++;
                color = 0;
            }
            if (As[i] == d[1])
            {
                options++;
                color = 1;
            }
            if (As[i] == d[2])
            {
                options++;
                color =2;
            }
            if(color == -1)
            {
                options++;
                color = 2;
            }

            ans *= options;
            ans %= mod;
            d[color]++;
        }
        WriteLine(ans);

    }

}