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::io::*;
use std::str::FromStr;

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

fn main() {
    let n: usize = read();
    let mut vec: Vec<usize> = vec![0; 110];
    let mut prime: Vec<usize> = Vec::new();
    for i in 2..n + 1 {
        if prime_check(i) {
            prime.push(i);
            vec[i] += 1;
        } else {
            for j in &prime {
                let mut po = i;
                while po % *j == 0 {
                    vec[*j] += 1;
                    po /= *j;
                }
            }
        }
    }
    let mut value: Vec<i64> = vec![0; 110];
    for i in 2..n + 1 {
        value[vec[i]] += 1;
    }
    for i in 1..n {
        value[n - i - 1] += value[n - i];
    }
    let mut ans = 0;
    if value[4] >= 2 && value[2] >= 3 {
        ans += value[4] * (value[4] - 1) / 2 * (value[2] - 2);
    }
    if value[24] >= 1 && value[2] >= 2 {
        ans += value[24] * (value[2] - 1);
    }
    if value[74] >= 1 {
        ans += value[74];
    }
    if value[14] >= 1 && value[4] >= 2 {
        ans += value[14] * (value[4] - 1);
    }
    println!("{}", ans);
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}