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)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize,
    }

    let mut primes = HashMap::new();
    for mut i in 2..=n {
        for p in 2..=n {
            let mut count = 0;
            while i % p == 0 {
                count += 1;
                i /= p;
            }
            if count > 0 {
                *primes.entry(p).or_insert(0) += count;
            }
        }
    }

    let mut ans = 0;
    ans += primes.values().filter(|v| **v >= 74).count();
    
    let v1 = primes.values().filter(|v| **v >= 24).count();
    let v2 = primes.values().filter(|v| **v >= 2).count() - 1;
    ans += v1 * v2;
    
    let v1 = primes.values().filter(|v| **v >= 14).count();
    let v2 = primes.values().filter(|v| **v >= 4).count() - 1;
    ans += v1 * v2;

    let v1 = primes.values().filter(|v| **v >= 4).count();
    let v1 = v1 * (v1 - 1) / 2;
    let v2 = primes.values().filter(|v| **v >= 2).count() - 2;
    ans += v1 * v2;
    println!("{}", ans);
}