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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function main(input) {
  const inputs = input.split("\n").filter(x => x !== "");
  let N = Number(inputs[0]);

  function resolve(n) {
    let result = Array(n + 1).fill(0);
    for (let i = 2; i <= n; i++) {
      let cur = i;
      for (let j = 2; j <= i; j++) {
        while (cur % j === 0) {
          result[j] += 1;
          cur = cur / j;
        }
      }
    }
    return result;
  }

  function findLargerThan(num, array) {
    return array.filter(element => element >= num).length;
  }

  function combination(numA, numB) {
    let result = 1;
    for (let i = numA; i > numA - numB; i = i - 1) {
      result = result * i;
    }

    for (let i = numB; i > 0; i = i - 1) {
      result = result / i;
    }
    return result;
  }

  let result = resolve(N);

  let l74 = findLargerThan(74, result);
  let l24 = findLargerThan(24, result);
  let l14 = findLargerThan(14, result);
  let l4 = findLargerThan(4, result);
  let l2 = findLargerThan(2, result);

  let r5x5x3 = (l4 * (l4 - 1) * (l2 - 2)) / 2;
  let r15x5 = l14 * (l4 - 1);
  let r25x3 = l24 * (l2 - 1);
  let r75 = l74;

  console.log(
    l74 + l24 * (l2 - 1) + l14 * (l4 - 1) + (l4 * (l4 - 1) * (l2 - 2)) / 2
  );
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));