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)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;

#[fastout]
fn main() {
    input! {
    n: usize
    }
    let mut d =  vec![0; n + 1];
    let mut dp =  vec![vec![0; 76]; n + 1];
    dp[1][1] = 1;
    for i in 1..=n {
        for j in divisor(i) {
            d[j] += 1;
        }
    }
    for i in 1..n {
        for j in 0..=75 {
            for k in 0..=d[i + 1] {
                if j * (k + 1) <= 75 {
                    dp[i + 1][j * (k + 1)] += dp[i][j];
                }
            }
        }
    }
    println!("{}", dp[n][75]);
}

fn divisor(m: usize) -> Vec<usize> {
    let mut l = Vec::new();
    let mut m = m;
    for i in 2.. {
        if i * i > m {break}
        while m % i == 0 {
            l.push(i);
            m /= i;
        }
    }
    if m > 1 {
        l.push(m);
    }
    l
}