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: Accepted)

require 'prime'
N = gets.to_i
prime_division = Prime.prime_division((1..N).reduce { |acc, n| acc * n })
el = prime_division.map { |_, v| v }
def e_gt_n(el, n)
  el.count { |e| e >= n }
end
answer = (
  e_gt_n(el, 74) +
  e_gt_n(el, 24) * (e_gt_n(el, 2) - 1) +
  e_gt_n(el, 14) * (e_gt_n(el, 4) - 1) +
  e_gt_n(el, 4) * (e_gt_n(el, 4) - 1) * (e_gt_n(el, 2) - 2) / 2
)
puts answer