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 PHP (7.4.4) (judge verdict: Accepted)

<?php
define('MOD', 10 ** 9 + 7);
list($n) = ints();
$a = ints();
// 先頭を赤に固定して考える
$cnt = [0, 0, 0];
$ans = 1;
for ($i = 0; $i < $n; ++$i) {
    $tmp = 0;
    for ($k = 0; $k < 3; ++$k) {
        if ($a[$i] === $cnt[$k]) {
            $tmpk = $k;
            ++$tmp;
        }
    }
    ++$cnt[$tmpk];
    $ans = ($ans * $tmp) % MOD;
}
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}