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)

use std::collections::HashMap;

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()
}

fn main() {
    let n: usize = read();
    let mut primes = Vec::new();
    for i in 2..n + 1 {
        let mut is_prime = true;
        for j in 2..i {
            if i % j == 0 {
                is_prime = false;
                break;
            }
        }
        if is_prime {
            primes.push(i);
        }
    }

    let mut factors = HashMap::new();
    for i in 1..n + 1 {
        let mut i = i;
        for p in primes.iter() {
            while i % *p == 0 {
                (*factors.entry(p).or_insert(1)) += 1;
                i /= *p;
            }
        }
    }
    // println!("{:?}", factors);

    let mut over3 = 0;
    let mut over5 = 0;
    let mut over15 = 0;
    let mut over25 = 0;
    let mut over75 = 0;
    for v in factors.values() {
        if *v >= 75 {
            over75 += 1;
        }
        if *v >= 25 {
            over25 += 1;
        }
        if *v >= 15 {
            over15 += 1;
        }
        if *v >= 5 {
            over5 += 1;
        }
        if *v >= 3 {
            over3 += 1;
        }
    }
    // println!("{:?}", (over3, over5, over15, over25, over75));

    let mut ans = over75;
    ans += over25 * std::cmp::max(over3 - 1, 0);
    ans += over15 * std::cmp::max(over5 - 1, 0);
    ans += over5 * std::cmp::max(over5 - 1, 0) * std::cmp::max(over3 - 2, 0) / 2;
    println!("{:?}", ans);
}