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: Accepted)

import java.util.Scanner;

public class Main {
    static final int COLORS = 3;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        for(int i=0; i<n; i++) {
            a[i] = in.nextInt();
        }
        long c = 1;
        int[] h = new int[COLORS];
        for(int i=0; i<COLORS; i++) {
            h[i] = -1;
        }
        for(int i=0; i<n; i++) {
            int temp = 0;
            boolean added = false;
            for(int j=0; j<COLORS; j++) {
                if(h[j] == a[i]-1) {
                    temp++;
                    if(!added) {
                        added = true;
                        h[j] = a[i];
                    }
                }
            }
            c *= temp;
            if(temp == 0) {
                break;
            }
            if(c%1000000007 > 1) {
                c = c % 1000000007;
            }
        }

        System.out.println(c % 1000000007);
    }
}