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 Ruby (2.3.3) (judge verdict: Runtime Error)

# frozen_string_literal: true

require 'prime'

n = gets.to_i
factorial = (1..n).inject(:*)

def calc_divisors(n)
  return [1] if n == 1

  powered = n.prime_division.map! {|base, exponent| (0..exponent).map {|e| base ** e } }
  powered[0].product(*powered[1..-1]).map! {|numbers| numbers.inject(:*) }
end

answer = calc_divisors(factorial).select {|number| calc_divisors(number).size == 75 }.size
puts answer