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.chomp.to_i

def fact(n)
  return 1 if n <= 1
  n * fact(n-1)
end

def num_div(d, divs)
  num_divs = []
  begin
    divs.each_index { |i| num_divs.push(d.select { |e| e >= divs[i] - 1 }.size - i) }
    if divs == [5, 5, 3]
      num_divs.reduce(1) { |mul, e| mul * e } / 2
    else
      num_divs.reduce(1) { |mul, e| mul * e }
    end
  rescue NoMethodError
    0
  end
end

f = fact(n)
count = 0
d = f.prime_division.map { |e| e.last }
[[75], [25, 3], [15, 5], [5, 5, 3]].each do |divs|
  n = num_div(d, divs)
  count += n
end
puts count