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)

pub 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()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn f(k: usize, v: &mut Vec<usize>) {
    for i in 2..k + 1 {
        if k % i == 0 {
            v[i] += 1;
            f(k / i, v);
            break;
        }
    }
}

fn main() {
    let n: usize = read();
    let mut prime_cnt = vec![0; 100];
    for k in 2..n + 1 {
        f(k, &mut prime_cnt);
    }
    let mut c2: u32 = 0;
    let mut c4: u32 = 0;
    let mut c14: u32 = 0;
    let mut c24: u32 = 0;
    let mut c74: u32 = 0;
    for i in 0..n {
        if prime_cnt[i] >= 2 {
            c2 += 1;
            if prime_cnt[i] >= 4 {
                c4 += 1;
                if prime_cnt[i] >= 14 {
                    c14 += 1;
                    if prime_cnt[i] >= 24 {
                        c24 += 1;
                        if prime_cnt[i] >= 74 {
                            c74 += 1;
                        }
                    }
                }
            }
        }
    }
    let mut ans = 0;
    ans += (c2 - 2) * c4 * (c4 - 1) / 2;
    ans += (c2 - 1) * c24;
    ans += (c4 - 1) * c14;
    ans += c74;
    println!("{}", ans);
}