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: def primesbelow(N):
      # http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
      # """ Input N>=6, Returns a list of primes, 2 <= p < N """
      correction = N % 6 > 1
      N = {0: N, 1: N - 1, 2: N + 4, 3: N + 3, 4: N + 2, 5: N + 1}[N % 6]
      sieve = [True] * (N // 3)
      sieve[0] = False
      for i in range(int(N**0.5) // 3 + 1):
          if sieve[i]:
              k = (3 * i + 1) | 1
              sieve[k * k // 3 :: 2 * k] = [False] * (
                  (N // 6 - (k * k) // 6 - 1) // k + 1
              )
              sieve[(k * k + 4 * k - 2 * k * (i % 2)) // 3 :: 2 * k] = [False] * (
                  (N // 6 - (k * k + 4 * k - 2 * k * (i % 2)) // 6 - 1) // k + 1
              )
      return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N // 3 - correction) if sieve[i]]
  
  
  n = int(input())
  primes = primesbelow(n)
  factor = {}
  
  
  def val(n, d):
      ans = 0
      t = d
      while t <= n:
          ans += n // t
          t *= d
      return ans
  
  
  g2 = 0
  g4 = 0
  g24 = 0
  g14 = 0
  g74 = 0
  for i in primes:
      k = val(n, i)
      if k >= 4:
          g4 += 1
      if k >= 2:
          g2 += 1
      if k >= 24:
          g24 += 1
      if k >= 14:
          g14 += 1
      if k >= 74:
          g74 += 1
  
  a = (g2 - 2) * ((g4 * (g4 - 1)) // 2)
  b = g24 * (g2 - 1)
  c = g14 * (g4 - 1)
  d = g74
  print(a + b + c + d)
  
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"}]