Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Python (3.4.3) (judge verdict: Runtime Error)

import math
from sympy import sieve
N=int(input())

num = math.factorial(N)
primeNum=[]

for i in range(2,1000):
  flag=False  
  for j in range(2,i):
    if i%j==0:
      flag=True
      break
  if flag==False:
    primeNum.append(i)
    

# primeNum = [i for i in sieve.primerange(1,1000)]
# print(primeNum)
resulNum=[0]*len(primeNum)
result=1

j=0
flag=False
for i in primeNum:
  while num % i == 0 :
    num = num // i
    resulNum[j]+=1
    flag=True
  
  if flag==True:
    result*=(resulNum[j]+1)
    result %= 10**9+7
  j+=1
  flag=False

print(result)