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)

use std::io::stdin;

fn main() {
    let mo:i64 = 1000000007;
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let n = st.trim().parse::<i32>().unwrap();
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let a:Vec<_> = st.trim().split(" ").map(|x| x.parse::<i32>().unwrap()).collect();
    let mut r:Vec<i32> = [-1,-1,-1].to_vec();
    let mut result:i64 = 1;
    let mut c:i64 = 0;
    let mut num = 0;
    let mut p = 0;
    for i in 0..n {
        p = a[i as usize];
        for j in 0..3 {
            let t = j as usize;
            if p == &r[t]+1 {
                c += 1;
                num = t;
            }
        }
        r[num] += 1;
        result *= c;
        result %= mo;
        c = 0;
        num = 0;
    };
    println!("{}", result);
}