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: Wrong Answer)

import java.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map.Entry;

import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	
	public static void main(String[] args) throws IOException {	
		try(final Scanner sc = new Scanner(System.in)){
			final int N = sc.nextInt();
			final long MOD = 1000000007;
			
			int fst = -1, snd = -1, thd = -1;

			long answer = 1;
			
			for(int i = 0; i < N; i++) {
				final int val = sc.nextInt();
				
				if(val == 0) {
					if(fst == -1) { fst = 1; }
					else if(snd == -1) { snd = 1; }
					else if(thd == -1) { thd = 1; }
				}else {
					if(fst == val && snd == val && thd == val) {
						fst += 1; answer *= 3; answer %= MOD;
					}else if(fst == val && snd == val) {
						fst += 1; answer *= 2; answer %= MOD;
					}else if(snd == val && thd == val) {
						snd += 1; answer *= 2; answer %= MOD;
					}else if(thd == val && fst == val) {
						fst += 1; answer *= 2; answer %= MOD;
					}else if(fst == val) {
						fst += 1;
					}else if(snd == val) {
						snd += 1;
					}else if(thd == val) {
						thd += 1;
					}
				}
			}
			
			//System.out.println(fst + " " + snd + " " + thd);
			
			if(snd < 0 && thd < 0) {
				answer *= 3; answer %= MOD;
			}else if(thd < 0) {
				answer *= 6; answer %= MOD;
			}else {
				answer *= 6; answer %= MOD;
			}
			
			System.out.println(answer);
			
		}
	}

	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() throws IOException {
			while(!hasNext()){
				tok = new StringTokenizer(br.readLine());
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}

		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}

		public void close() throws IOException {
			br.close();
		}
	}
}