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 Rust (1.15.1) (judge verdict: Accepted)

const MOD: i64 = 1000000007;

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	s.next().unwrap();
	let (ans, _) = s.fold((1, [0; 3]), |r, a|{
		let a = a.parse::<i64>().unwrap();
		let (f, c) = {
			let mut f = -1;
			let mut c = 0;
			for i in 0..3 {
				if a == r.1[i] {
					if f < 0 { f = i as i64; }
					c += 1;
				}
			}
			(f, c)
		};
		(r.0 * c % MOD, match f {
			0 => [r.1[0] + 1, r.1[1], r.1[2]],
			1 => [r.1[0], r.1[1] + 1, r.1[2]],
			2 => [r.1[0], r.1[1], r.1[2] + 1],
			_ => [-1, -1, -1]
		})
	});
	println!("{}", ans);
}