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: Wrong Answer)

<?php
  # 2WAがとれず。。。。。

  
  $n = intVal(trim(fgets(STDIN)));
  $s = array_map("intVal", explode(" ", trim(fgets(STDIN))));
  $color = 0;
  $ans = 1;
  $MOD = 1000000007;
  $cur = [-1, -1, -1];

  if($s[0] != 0){
    echo 0 . PHP_EOL;
    exit();
  }
  foreach($s as $c){
    if($c == 0){
      $cur[$color] = 0;
      $color += 1;
      $ans %= $MOD;
    }else{
      $x = 0;
      foreach($cur as $curn){
        if($curn == $c-1){
          $x += 1;
        }
      }
      if($x == 0){
        echo 0 . PHP_EOL;
        exit();
      }
      $ans *= $x;
      $ans %= $MOD;
      $idx = array_search($c-1, $cur);
      $cur[$idx] += 1;
    }
  }

  if($color == 1){
    $ans *= 3;
  }elseif($color == 2){
    $ans *= 6;
  }
  $ans %= $MOD;
  echo $ans . PHP_EOL;
?>