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)

#[macro_use]
#[allow(dead_code)]
mod template {
    macro_rules! debug {
        ($($a:expr),*) => {{
            use ::std::io::Write;
            writeln!(&mut ::std::io::stderr(), concat!($(stringify!($a), " = {:?}, "),*), $($a),*).unwrap();
        }}
    }

    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut scanner = ::template::BufScanner::new($s.as_bytes());
            input_inner!{scanner, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = ::std::io::stdin();
            let mut scanner = ::template::BufScanner::new(stdin.lock());
            input_inner!{scanner, $($r)*}
        };
    }

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

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

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

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

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

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

        ($scanner:ident, $t:ty) => {
            ($scanner).next::<$t>()
        };
    }

    pub struct BufScanner<R: ::std::io::BufRead> {
        br: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl<R: ::std::io::BufRead> BufScanner<R> {
        pub fn new(br: R) -> Self {
            BufScanner {
                br: br,
                buf: Vec::new(),
                pos: 0usize,
            }
        }
        fn fill_line(&mut self) {
            self.buf.clear();
            self.pos = 0;
            self.br
                .read_until(b'\n', &mut self.buf)
                .expect("Read a line");
            if let Some(&b'\n') = self.buf.last() {
                self.buf.pop();
                if let Some(&b'\r') = self.buf.last() {
                    self.buf.pop();
                }
            }
        }
        fn skip_space(&mut self) {
            loop {
                for i in self.pos..self.buf.len() {
                    if self.buf[i] != b' ' {
                        self.pos = i;
                        return;
                    }
                }
                self.fill_line();
            }
        }
        pub fn read_token(&mut self) -> &str {
            self.skip_space();
            let start = self.pos;
            while self.pos < self.buf.len() && self.buf[self.pos] != b' ' {
                self.pos += 1;
            }
            let ret = unsafe { ::std::str::from_utf8_unchecked(&self.buf[start..self.pos]) };
            self.pos += 1; // skip the last space (or len() + 1 which is fine)
            return ret;
        }
        pub fn next<T: ::std::str::FromStr>(&mut self) -> T {
            self.read_token().parse::<T>().ok().expect("Parse")
        }
    }
}

fn eratosthenes(n: usize) -> (Vec<usize>, Vec<usize>) {
    let mut ps = Vec::new();
    let mut divisor: Vec<_> = (0..n).map(|i| i).collect();
    for i in 2..n {
        if divisor[i] == i {
            ps.push(i);
        }
        for p in ps.iter() {
            let m = i * *p;
            if m >= n {
                break;
            }
            divisor[m] = *p;
        }
    }
    return (ps, divisor);
}

fn main() {
    input! {
        n: usize
    }
    let n: usize = n + 1;

    let (_, divisor) = eratosthenes(n + 100);

    let mut exponents: Vec<_> = (0..n).map(|_| 0).collect();

    const K: usize = 100;
    for t in 1..n {
        let mut tmp = t;
        while tmp != 1 {
            let p = divisor[tmp];
            exponents[p] += 1;
            tmp /= p;
        }
    }
    let mut dp: Vec<usize> = (0..K).map(|_| 0).collect();
    dp[1] = 1;
    for i in 0..n {
        let mut qb: Vec<usize> = (0..K).map(|_| 0).collect();

        for e in 0..(exponents[i] + 1) {
            for num_divisors in 0..K {
                let next_num_divisors = num_divisors * (e + 1);
                if next_num_divisors < K {
                    qb[next_num_divisors] += dp[num_divisors];
                }
            }
        }
        dp = qb;
    }
    println!("{}", dp[75]);
}