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: # prime_number?
  
  n = int(input())
  
  from math import sqrt
  from random import randint
  
  
  def isprime(num):  # O(sqrt(n))
      root = int(sqrt(n))
      for i in range(2, root + 1):
          if num % i == 0:
              return False
      return True
  
  
  def isprime_(num, n=1):  # O(k+n)未満 (ミラー・ラビンテスト)
      q = num
      if q == 2:
          return True
      if q == 1 or q & 1 == 0:
          return False
      d = (q - 1) >> 1
      while d & 1 == 0:
          d >>= 1
      for i in range(n):
          a = randint(1, q - 1)
          t = d
          y = pow(a, t, q)
          while t != q - 1 and y != 1 and y != q - 1:
              y = pow(y, 2, q)
              t <<= 1
          if y != q - 1 and t & 1 == 0:
              return False
      return True
  
  
  def dividers(num, sort=True):
      root = int(sqrt(n))
      l = []
      m = []
      for i in range(1, root + 1):
          if num % i == 0:
              l.append(i)
              if i < root:
                  m.append(int(num / i))
      if sort:
          l.extend(sorted(m))
          return l
      else:
          l.extend(m)
          return l
  
  
  def decomposit(num):
      root = int(sqrt(n))
      l = []
      i = 2
      while i < root + 1:
          if num % i == 0:
              j = 0
              while num % i == 0:
                  j += 1
                  num = num / i
              l.append([i, j])
              root = int(sqrt(n))
          i += 1
      if num != 1:
          l.append([int(num), 1])
      return l
  
  
  l = {}
  for i in range(n + 1):
      if isprime_(i):
          l[i] = 0
  
  for i in range(1, n + 1):
      for j in decomposit(i):
          l[j[0]] += j[1]
  
  d = 1
  for i in l.values():
      d *= i + 1
  
  d %= 10**9 + 7
  print(d)
  
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"}]