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: N = int(input())
  if N == 1:
      print(1)
  # calculate primes by sieve
  primes = list(range(2, N + 1))
  prime_index = 0
  n = primes[prime_index]
  while n**2 <= N:
      primes = list(filter(lambda x: x == n or x % n != 0, primes))
      prime_index += 1
      n = primes[prime_index]
  # calculate exponents
  exponents = [0 for _ in range(len(primes))]
  for n in range(2, N + 1):
      for prime_index, prime in enumerate(primes):
          exponent = 0
          tmp = n
          while tmp % prime == 0:
              tmp //= prime
              exponent += 1
          exponents[prime_index] += exponent
  # calculate answer
  const = 10**9 + 7
  answer = 1
  for e in exponents:
      answer = answer * (e + 1)
      answer %= const
  print(answer)
  
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"}]