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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let primes = get_primes(n);
    let mut dict = HashMap::new();
    for i in 1..n + 1 {
        let factors = factorize(i, &primes);
        for (&fact, &value) in factors.iter() {
            *dict.entry(fact).or_insert(1) += value;
        }
    }
    let mut over75 = 0;
    let mut over25 = 0;
    let mut over15 = 0;
    let mut over5 = 0;
    let mut over3 = 0;

    for &count in dict.values() {
        if count >= 3 {
            over3 += 1;
        }
        if count >= 5 {
            over5 += 1;
        }
        if count >= 15 {
            over15 += 1;
        }
        if count >= 25 {
            over25 += 1;
        }
        if count >= 75 {
            over75 += 1;
        }
    }
    debug!(over3);
    debug!(over5);
    debug!(dict);
    let mut ans = over75;
    ans += over25 * (over3 - 1);
    ans += over15 * (over5 - 1);
    ans += over5 * (over5 - 1) * max(over3 - 2, 0) / 2;
    println!("{}", ans);
}

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 read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn get_primes(n: usize) -> Vec<usize> {
    let mut is_prime = vec![true; n + 1];
    let mut primes = Vec::new();
    is_prime[0] = false;
    is_prime[1] = false;

    for i in 2..n + 1 {
        if is_prime[i] {
            primes.push(i);
            let mut j = 2 * i;
            while j < n {
                is_prime[j] = false;
                j += i;
            }
        }
    }
    primes
}

fn factorize(mut num: usize, primes: &Vec<usize>) -> std::collections::HashMap<usize, usize> {
    // max_primes >= (num)^(1/2)
    let mut dict = std::collections::HashMap::new();
    for &p in primes.iter() {
        while num % p == 0 {
            *dict.entry(p).or_insert(0) += 1usize;
            num /= p;
        }
        if num == 1 {
            break;
        }
    }
    if num != 1 {
        dict.insert(num, 1);
    }
    dict
}