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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

#[proconio::fastout]
fn main() {
    input! {
        N: usize
    }
    let mut count = [0u128; 100 * 100 + 1];
    for x in 1..=N {
        let mut i = 2;
        let mut temp = x;
        while i * i <= temp {
            while temp % i == 0 {
                count[i] += 1;
                temp /= i;
            }
            i += 1;
        }
        count[temp] += 1;
    }
    let primes = &count[2..];
    let two = primes.iter().filter(|x| **x >= 2).count() as i128;
    let four = primes.iter().filter(|x| **x >= 4).count() as i128;
    let fourteen = primes.iter().filter(|x| **x >= 14).count() as i128;
    let twenty_four = primes.iter().filter(|x| **x >= 24).count() as i128;
    let seventy_four = primes.iter().filter(|x| **x >= 74).count() as i128;

    let two_four_four = four * (four - 1) * (two - 2) / 2;
    let four_fourteen = fourteen * (four - 1);
    let two_24 = twenty_four * (two - 1);
    println!("{}", seventy_four + two_four_four + four_fourteen + two_24);
}