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

def factorial(n)
  return 1 if n == 0
  n * factorial(n-1)
end

num = factorial(n)
primes = num.prime_division.select{|a| a[1] >= 2}.map{|a| a[1]}

ans = 0

primes.size.times do |i|
  if primes[i] >= 74
    ans += 1
  else
    break
  end
end

primes.size.times do |i|
  if primes[i] >= 24 
    primes.size.times do |j|
      if i == j
        next
      end
      if primes[j] >= 2
        ans += 1
      end
    end
  else
    break
  end
end

primes.size.times do |i|
  if primes[i] >= 14 
    primes.size.times do |j|
      if i == j
        next
      end
      if primes[j] >= 4
        ans += 1
      end
    end
  else
    break
  end
end

primes.size.times do |i|
  if primes[i] >= 4
    primes.size.times do |j|
      if i >= j
        next
      end
      if primes[j] >= 4
        primes.size.times do |k|
          if i == k || j == k
            next
          end
          if primes[k] >= 2
            ans += 1
          end
        end
      end
    end
  else
    break
  end
end

puts ans