output_description: Print the number of the positive divisors of N!, modulo 10^9+7.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N
attempt: import numpy as np
  
  primes = np.array(
      [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19,
          23,
          29,
          31,
          37,
          41,
          43,
          47,
          53,
          59,
          61,
          67,
          71,
          73,
          79,
          83,
          89,
          97,
          101,
          103,
          107,
          109,
          113,
          127,
          131,
          137,
          139,
          149,
          151,
          157,
          163,
          167,
          173,
          179,
          181,
          191,
          193,
          197,
          199,
          211,
          223,
          227,
          229,
          233,
          239,
          241,
          251,
          257,
          263,
          269,
          271,
          277,
          281,
          283,
          293,
          307,
          311,
          313,
          317,
          331,
          337,
          347,
          349,
          353,
          359,
          367,
          373,
          379,
          383,
          389,
          397,
          401,
          409,
          419,
          421,
          431,
          433,
          439,
          443,
          449,
          457,
          461,
          463,
          467,
          479,
          487,
          491,
          499,
          503,
          509,
          521,
          523,
          541,
          547,
          557,
          563,
          569,
          571,
          577,
          587,
          593,
          599,
          601,
          607,
          613,
          617,
          619,
          631,
          641,
          643,
          647,
          653,
          659,
          661,
          673,
          677,
          683,
          691,
          701,
          709,
          719,
          727,
          733,
          739,
          743,
          751,
          757,
          761,
          769,
          773,
          787,
          797,
          809,
          811,
          821,
          823,
          827,
          829,
          839,
          853,
          857,
          859,
          863,
          877,
          881,
          883,
          887,
          907,
          911,
          919,
          929,
          937,
          941,
          947,
          953,
          967,
          971,
          977,
          983,
          991,
          997,
      ],
      dtype=np.int64,
  )
  n = int(input())
  div = primes[primes <= n]
  mod = 10**9 + 7
  
  
  def divide(p, n):
      if n < p:
          return 0
      return divide(p, n // p) + n // p
  
  
  ans = 1
  for p in div:
      ans *= divide(p, n) + 1
      ans %= mod
  print(ans)
  
problem_description: Statement
  
  You are given an integer N. Find the number of the positive divisors of N!,
  modulo 10^9+7.
samples: [{"input": "3", "output": "4\n    \n\nThere are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.\n\n* * *"}, {"input": "6", "output": "30\n    \n\n* * *"}, {"input": "1000", "output": "972926972"}]