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)

//
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
//
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

//
// solution 
//
#[allow(unused_mut)]
#[allow(non_snake_case)]
fn main() {
    input!{
        N: usize,
    }

    if N < 10 {
        println!("0");
        return;
    }

    let mut num_primes = vec![0_usize; N+1];
    for n in 2..N+1 {
        let mut num = n;
        while num > 1 {
            if num % 2 == 0 {
                num_primes[2] += 1;
                num /= 2;
            } else if num % 3 == 0 {
                num_primes[3] += 1;
                num /= 3;
            } else if num % 5 == 0 {
                num_primes[5] += 1;
                num /= 5;
            } else if num % 7 == 0 {
                num_primes[7] += 1;
                num /= 7;
            } else {
                num_primes[num] += 1;
                num /= num;
            }
        }
    }

    // (2, 4, 4) or (4, 14) or (2, 24) or 74 を探す
    let num4 = num_primes.iter().filter(|a| **a >= 4).count();
    let num2 = num_primes.iter().filter(|a| **a >= 2).count();
    let num14 = num_primes.iter().filter(|a| **a >= 14).count();
    let num24 = num_primes.iter().filter(|a| **a >= 24).count();
    let num74 = num_primes.iter().filter(|a| **a >= 74).count();

    let num_4_4_1 = 
        if num4 >= 2 {
            num4 * (num4 - 1) / 2 * (num2 - 2) 
        } else {
            0
        };
    let num_4_14 = 
        if num4 >= 2 {
            num14 * (num4 - 1)
        } else {
            0
        };
    let num_2_24 =
        if num2 >= 2 {
            num24 * (num2 - 1)
        } else {
            0
        };

    println!("{}", num_4_4_1 + num_4_14 + num_2_24 + num74);
}