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

h = {}

(2..n).each{|x| x.prime_division.each{|x,y| h[x] ||= 0; h[x] += y}}

r = 0

(2..n).each do |i|
  next unless h[i]
  (i+1..n).each do |j|
    next unless h[j]
    (j+1..n).each do |k|
      next unless h[k]
      r += 1 if h[i] >= 2 && h[j] >= 4 && h[k] >= 4
      r += 1 if h[i] >= 4 && h[j] >= 2 && h[k] >= 4
      r += 1 if h[i] >= 4 && h[j] >= 4 && h[k] >= 2
    end
  end
end

(2..n).each do |i|
  next unless h[i]
  (i+1..n).each do |j|
    next unless h[j]
    r += 1 if h[i] >= 14 && h[j] >= 4
    r += 1 if h[i] >= 4 && h[j] >= 14

    r += 1 if h[i] >= 24 && h[j] >= 2
    r += 1 if h[i] >= 2 && h[j] >= 24
  end
end

(2..n).each do |i|
  next unless h[i]
  r += 1 if h[i] >= 74
end

puts r