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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
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.LinkedList;
import java.util.Map;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {

    private static PrintWriter out;

    private static void mprintln(Object... ar) {
        for (Object i : ar) {
            out.print(i + " ");
        }
        out.println();
    }

    private static void mprint(Object... ar) {
        for (Object i : ar) {
            out.print(i + " ");
        }
    }

    public static void main(String[] args) throws FileNotFoundException {

        /* Input from file */

        // File inputFile = new File("JavaFile.txt");
        // File outputFile = new File("JavaOutputFile.txt");
        // FileReader fileReader = new FileReader(inputFile);

        /* Here it ends */

        MyScanner sc = new MyScanner(); // Input from console.
        // MyScanner sc = new MyScanner(fileReader); // Input from file.

        out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console.
        // out = new PrintWriter(new PrintStream(outputFile)); // Output to file.

        int t = 1;
        for (int test = 1; test <= t; ++test)
            getAns(sc);

        out.close();
    }

    /**
     * Don't use built-in function (Math.ceil).
     */
    private static void getAns(MyScanner sc) {
        int n = sc.ni();
        Integer[] ar = sc.niArr0(n);

        long[] dp = new long[n];
        final long MOD = (long) (1e9 + 7);

        HashMap<Integer, Integer>[] map = new HashMap[n];
        for (int i = 0; i < n; i++) map[i] = new HashMap<>();

        for (int i = n - 2; i >= 0; --i) {
            map[i] = (HashMap<Integer, Integer>) map[i + 1].clone();
            map[i].put(ar[i + 1], 1 + map[i].getOrDefault(ar[i + 1], 0));
        }

//        Arrays.stream(map).forEach(out::println);

        dp[n - 1] = 3;

        for (int i = n - 2; i >= 0; --i) {
            long temp = map[i].getOrDefault(ar[i] + 1, 3) - map[i].getOrDefault(ar[i], 0);
            dp[i] = temp;
        }

//        out.println(Arrays.toString(dp));

        long ans = 1;

        for (long cur: dp) ans = (ans * cur) % MOD;

        out.println(ans);
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        MyScanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

        MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nn() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String ans = "";
            try {
                ans = br.readLine();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return ans;
        }

        char nc() {
            return nn().charAt(0);
        }

        int ni() {
            return Integer.parseInt(nn());
        }

        long nl() {
            return Long.parseLong(nn());
        }

        double nd() {
            return Double.parseDouble(nn());
        }

        Integer[] niArr0(int n) {
            Integer[] ar = new Integer[n];
            for (int i = 0; i < n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        Integer[] niArr1(int n) {
            Integer[] ar = new Integer[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        Long[] nlArr0(int n) {
            Long[] ar = new Long[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nl();
            }
            return ar;
        }

        Long[] nlArr1(int n) {
            Long[] ar = new Long[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = nl();
            }
            return ar;
        }
    }
}