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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from math import sqrt, ceil
N = int(input())
x = [1]*N
for i in range(2,N+1):
  for j in range(2,int(ceil(sqrt(N)))):
    while i%j == 0:
      i //= j;
      x[j-1] += 1
answer = 1
for i in x:
  answer *= i+1
  answer %= 1000000007
print(answer)