Problem:
Score : 400 points

Problem Statement

You are given an integer N. Among the divisors of N! (= 1 \times 2 \times ... \times N), how many Shichi-Go numbers (literally "Seven-Five numbers") are there?

Here, a Shichi-Go number is a positive integer that has exactly 75 divisors.

Note

When a positive integer A divides a positive integer B, A is said to a divisor of B.
For example, 6 has four divisors: 1, 2, 3 and 6.

Constraints

1 \leq N \leq 100

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of the Shichi-Go numbers that are divisors of N!.

Sample Input 1

9

Sample Output 1

0

There are no Shichi-Go numbers among the divisors of 9! = 1 \times 2 \times ... \times 9 = 362880.

Sample Input 2

10

Sample Output 2

1

There is one Shichi-Go number among the divisors of 10! = 3628800: 32400.

Sample Input 3

100

Sample Output 3

543

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn is_prime(n: usize) -> bool {
    if n <= 1 {
        return false;
    }
    let mut k = 2;
    while k * k <= n {
        if n % k == 0 {
            return false;
        }
        k += 1;
    }
    true
}

fn calc(a: &Vec<usize>, k: usize, n: usize) -> usize {
    if n == 1 {
        return 1;
    }
    if k >= a.len() {
        return 0;
    }
    let mut res = calc(a, k + 1, n);
    for d in 2..(n + 1) {
        if n % d == 0 && d <= a[k] + 1 {
            res += calc(a, k + 1, n / d);
        }
    }
    res
}

fn run() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let n: usize = s.trim().parse().unwrap();
    let mut a = vec![];
    for i in 2..(n + 1) {
        if is_prime(i) {
            let mut c = 0;
            let mut t = n;
            while t >= i {
                c += t / i;
                t /= i;
            }
            a.push(c);
        }
    }
    let ans = calc(&a, 0, 75);
    println!("{}", ans);
}

fn main() {
    run();
}