output_description: Print the number of the Shichi-Go numbers that are divisors of N!.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: from collections import defaultdict
  
  primes = list(range(2, 101))
  for i in range(len(primes)):
      if primes[i]:
          j = i
          j += primes[i]
          while j < len(primes):
              primes[j] = None
              j += primes[i]
  primes = [p for p in primes if p]
  N = int(input())
  fact = defaultdict(int)
  for p in primes:
      i = p
      while i <= N:
          fact[p] += N // i
          i *= p
  f2 = set()
  f4 = set()
  f14 = set()
  f24 = set()
  f74 = set()
  for p in fact:
      if fact[p] >= 2:
          f2.add(p)
      if fact[p] >= 4:
          f4.add(p)
      if fact[p] >= 14:
          f14.add(p)
      if fact[p] >= 24:
          f24.add(p)
      if fact[p] >= 74:
          f74.add(p)
  ans = 0
  ans += len(f74)
  ans += len(f24) * (len(f2) - 1)
  ans += len(f14) * (len(f4) - 1)
  ans += (len(f2) - 2) * len(f4) * (len(f4) - 1) // 2
  print(ans)
  
problem_description: 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.
samples: [{"input": "9", "output": "0\n    \n\nThere are no Shichi-Go numbers among the divisors of 9! = 1 \\times 2 \\times\n... \\times 9 = 362880.\n\n* * *"}, {"input": "10", "output": "1\n    \n\nThere is one Shichi-Go number among the divisors of 10! = 3628800: 32400.\n\n* * *"}, {"input": "100", "output": "543"}]