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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input) {
    input = input.trim().split("\n").map(function(x) { return x.split(" ")});    
    var N = parseInt(input[0][0], 10);
    var RGBWithoutOrder = [1, 0, 0];
    var tmp1, tmp2, flag;
    var ans = 3;
    for (var i = 1; i < N; i++){
        tmp2 = 0;
        tmp1 = parseInt(input[1][i], 10);
        for (var x of RGBWithoutOrder){
            if (x === tmp1) tmp2 ++;
        }
        ans *= tmp2;
        ans %= (1e+9 + 7);

        for (var j = 0; j < 3; j++){
            if (RGBWithoutOrder[j] === tmp1){
                RGBWithoutOrder[j] ++;
                break;
            }
        }
    }
    console.log(ans);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));