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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
define('MOD', pow(10, 9) + 7);
fscanf(STDIN, "%d", $N);
$a = array_map('intval', explode(' ', trim(fgets(STDIN))));
$x[0] = 3;
$ans = 1;
for ($i = 0; $i < $N; $i++) {
    if (!isset($x[$a[$i]]) || $x[$a[$i]] === 0) {
        $ans = 0;
        break;
    } else {
        $ans *= $x[$a[$i]];
        $x[$a[$i]]--;
        if (!isset($x[$a[$i] + 1])) {
            $x[$a[$i] + 1] = 1;
        } else {
            $x[$a[$i] + 1]++;
        }
    }
    $ans %= MOD;
}
printf("%d", $ans);