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, Counter
  
  
  def primes(x):
      d = {}
      i = 2
      while i <= x:
          count = 0
          while x % i == 0 and x > 0:
              count += 1
              x //= i
          if count > 0:
              d[i] = count
          i += 1
      return d
  
  
  if __name__ == "__main__":
      n = int(input())
      d = {}
      for i in range(2, n + 1):
          d1 = primes(i)
          for j, v in d1.items():
              if j not in d:
                  d[j] = v
              else:
                  d[j] += v
      counter = Counter(d.values())
      d2 = {3: 0, 5: 0, 15: 0, 25: 0, 75: 0}
      for count, v in counter.items():
          if count >= 74:
              d2[75] += v
          if count >= 24:
              d2[25] += v
          if count >= 14:
              d2[15] += v
          if count >= 4:
              d2[5] += v
          if count >= 2:
              d2[3] += v
      ans = (
          d2[75]
          + d2[25] * (d2[3] - 1)
          + d2[15] * (d2[5] - 1)
          + d2[5] * (d2[5] - 1) * (d2[3] - 2) // 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"}]