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::str::FromStr;
use std::fmt::Debug;
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}


fn get_num(table: &Vec<u32>, n: u32) -> usize{
    (*table).iter().filter(|x| **x > n-2).collect::<Vec<&u32>>().len()
}

fn main(){
    let n: u32 = read_as_vec()[0];

    let mut table = vec![0;(n+1) as usize];

    
    for i in 2..n+1{
        let mut target = i;
        for j in 2..i+1{
            while target % j == 0{
                target /= j;
                table[j as usize] += 1;
            }
        }
    }
    
    let ans = get_num(&table, 75)
        + get_num(&table, 15) * (get_num(&table, 5) -1)
        + get_num(&table, 25) * (get_num(&table, 3) -1)
        + get_num(&table, 5) * (get_num(&table, 5) -1)* (get_num(&table, 3)-2)/2;
    println!("{}", ans);
        
}