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 std::io;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::BTreeMap;

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn prime_factors(n: u64) -> HashMap<u64, u64> {
    let mut n = n; 
    let mut prime_numbers: HashMap<u64, u64> = HashMap::new();
    let mut candidate = 2;

    while n > 1 {
        while n % candidate == 0 {
            let val = prime_numbers.entry(candidate).or_insert(0);
            *val += 1;
            n /= candidate;
        }
        candidate += 1;
    }
    return prime_numbers;
}

fn main() {
    let n: u64 = input();
    let mut factors: BTreeMap<u64, u64> = BTreeMap::new();
    for i in 1..(n+1) {
        // println!("{:?}", prime_factors(i));
        for (k, v) in prime_factors(i) {
            let num = factors.entry(k).or_insert(0);
            *num += v;
        }
    }
    let mut count = 0;
    let entries: Vec<_> = factors.iter().collect();
    for entry in &entries {
        if *entry.1 + 1 >= 75 {
            count += 1;
        } else {
            break;
        }
    }
    if entries.len() < 1 {
        println!("{}", count);
        return;
    }
    for i in 0..entries.len()-1 {
        for j in (i+1)..entries.len() {
            if entries[i].1 + 1 >= 25 && entries[j].1 + 1 >= 3 {
                count += 1;
            }
            if entries[i].1 + 1 >= 15 && entries[j].1 + 1 >= 5 {
                count += 1;
            }
            if entries[j].1 + 1 >= 25 && entries[i].1 + 1 >= 3 {
                count += 1;
            }
            if entries[j].1 + 1 >= 15 && entries[i].1 + 1 >= 5 {
                count += 1;
            }
        }
    }
    if entries.len() < 2 {
        println!("{}", count);
        return;
    }
    for i in 0..entries.len()-2 {
        for j in (i+1)..entries.len()-1 {
            for k in (j+1)..entries.len() {
                if entries[i].1 + 1 >= 5 && entries[j].1 + 1 >= 5 && entries[k].1 + 1 >= 3 {
                    // println!("{:?}, {:?}, {:?}", entries[i], entries[j], entries[k]);
                    count += 1;
                }
                if entries[j].1 + 1 >= 5 && entries[k].1 + 1 >= 5 && entries[i].1 + 1 >= 3 {
                    // println!("{:?}, {:?}, {:?}", entries[i], entries[j], entries[k]);
                    count += 1;
                }
                if entries[k].1 + 1 >= 5 && entries[i].1 + 1 >= 5 && entries[j].1 + 1 >= 3 {
                    // println!("{:?}, {:?}, {:?}", entries[i], entries[j], entries[k]);
                    count += 1;
                }
            }
        }
    }
    println!("{}", count);
}