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)]

#[macro_use]
mod _input {
    use std::fmt;
    use std::io::{self, Read};
    use std::str::{self, FromStr};

    macro_rules! input {
        ($($name:ident : $t:tt),*,) => {
            input!($($name: $t),*)
        };
        ($($name:ident : $t:tt),*) => {
            let mut _scanned = ::_input::Scanned::new(::std::io::stdin(), 1024);
            $(
                let $name = _read_value!(_scanned, $t);
            )*
        };
    }

    macro_rules! _read_value {
        ($scanned:expr, ($($t:tt),*)) => {
            ($(_read_value!($scanned, $t)),*)
        };
        ($scanned:expr, [$t:tt; $n:expr]) => {
            (0..$n).map(|_| _read_value!($scanned, $t)).collect::<Vec<_>>()
        };
        ($scanned:expr, _bytes) => {
            _read_value!($scanned, String).into_bytes()
        };
        ($scanned:expr, _index) => {
            _read_value!($scanned, usize) - 1
        };
        ($scanned:expr, $t:ty) => {
            $scanned.next::<$t>()
        };
    }

    #[derive(Default)]
    pub struct Scanned {
        buf: Vec<u8>,
        pos: usize,
    }

    impl Scanned {
        pub fn new<R: Read>(mut input: R, estimated: usize) -> Self {
            let mut buf = Vec::with_capacity(estimated);
            let _ = io::copy(&mut input, &mut buf).unwrap();
            if buf.last() != Some(&b'\n') {
                buf.push(b'\n'); // input may not end with '\n'
            }
            // https://doc.rust-lang.org/src/core/char/methods.rs.html#906-908
            // assert!(str::from_utf8(&buf).unwrap().bytes().all(|c| u32::from(c) <= 0x7F));
            Scanned { buf: buf, pos: 0 }
        }

        #[inline]
        pub fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: fmt::Debug,
        {
            let mut start = None;
            loop {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
        }
    }
}

#[allow(dead_code)]
mod output {
    use std::io::{self, BufWriter, StdoutLock, Write as _Write};

    pub fn with_stdout<F: FnMut(&mut BufWriter<StdoutLock>)>(mut f: F) {
        let stdout = io::stdout();
        let mut stdout = BufWriter::new(stdout.lock());
        f(&mut stdout);
        stdout.flush().unwrap();
    }
}

use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::Write;
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
};
use std::str::{self, FromStr};
use std::{char, cmp, f32, f64, fmt, i16, i32, i64, i8, thread, u16, u32, u64, u8};

fn main() {
    input! {
        n: u64,
    }
    let mut c = vec![1; 98];
    for mut m in 2..n + 1 {
        for f in 2..m + 1 {
            while m % f == 0 {
                c[f as usize] += 1;
                m /= f;
            }
        }
    }
    // 75 = 3 * 5^2
    // 75, 5 * 15, 3 * 25, 3 * 5 * 5
    let k1 = c.iter().filter(|&&k| k >= 75).count() as u64;
    let k2 = c.iter().filter(|&&k| k >= 25).count() as u64;
    let k3 = c.iter().filter(|&&k| k >= 15).count() as u64;
    let k4 = c.iter().filter(|&&k| k >= 5).count() as u64;
    let k5 = c.iter().filter(|&&k| k >= 3).count() as u64;
    let r1 = k1;
    let r2 = k2 * (cmp::max(k5, 1) - 1);
    let r3 = k3 * (cmp::max(k4, 1) - 1);
    let r4 = if k4 > 0 && k5 > 1 {
        k4 * (k4 - 1) * (k5 - 2) / 2
    } else {
        0
    };
    println!("{}", r1 + r2 + r3 + r4);
}