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)

input = gets.to_i

if input == 1
  puts 0
  exit
end

require 'prime'

prime_division_list = (2..input).map do |i|
  h = i.prime_division.to_h
  a = [2,3,5,7].map do |p|
    h.delete(p).to_i
  end
  if h.length == 0 then a else nil end
end.compact

r = (1..prime_division_list.length).map do |i|
  prime_division_list.combination(i).select do |c|
    [
      [0,0,0,74],
      [0,0,2,24],
      [0,0,4,14],
      [0,2,4,4],
    ].include?([0,0,0,0].zip(*c).map(&:sum).sort)
  end.length
end.sum

puts r