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 input::*;
use std::cmp::*;
use std::io::*;
use std::num::*;
use std::str::*;

mod input {
    use super::*;
    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }
    pub fn string() -> String {
        read()
    }
    pub fn int() -> i64 {
        read()
    }
    pub fn char() -> char {
        read::<String>().pop().unwrap()
    }
    pub fn vecchar() -> Vec<char> {
        string().chars().collect()
    }
    pub fn vecint(n: i64) -> Vec<i64> {
        let mut vec = Vec::new();
        for i in 0..n {
            vec.push(int())
        }
        vec
    }
}
fn main() {
    let n = int();
    let a = vecint(n);
    let mut cur = vec![0i64, 0, 0];

    let MOD = 1_000_000_007;
    let mut ans = 1;
    for v in a {
        let count = cur.iter().filter(|x| **x == v).count();
        ans = ans * count % MOD;
        //dbg!(count, v, ans, &cur);
        for i in 0..3 {
            if cur[i] == v {
                cur[i] = v + 1;
                break;
            }
        }
    }
    println!("{}", ans)
}