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: Wrong Answer)

fn main() {
    let n = read::<usize>();
    let v = read_vec::<u64>();
    let div: u64 = 1000000007;

    let mut dp = vec![0u64; n + 1];
    let mut kind = vec![0u64; 3];
    let mut ans = 0;

    for i in 0..n {
        if i == 0 {
            dp[i] = 1;
            kind[0] = 1;
            continue;
        }

        if v[i] == 0 {
            if kind[1] == 0 {
                kind[1] = 1;
            } else {
                kind[2] = 1;
            }

            dp[i] = dp[i-1];
        } else {
            let count = kind.iter().filter(|&x| *x==v[i]).count();
            dp[i] = dp[i-1] * count as u64;

            for k in 0..3 {
                if kind[k] == v[i] {
                    kind[k] += 1;
                    break;
                }
            }
        }
    }

    let colors_count = kind.iter().filter(|&x| *x>0).count();
    if colors_count == 1 {
        ans = dp[n-1] * 3 % div;
    } else if colors_count == 2 {
        ans = dp[n-1] * 3 % div;
    } else if colors_count == 3 {
        ans = dp[n-1] * 6 % div;
    }
    println!("{}", ans);
}

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("1");
    } else {
        println!("0");
    }
}