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.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
import math

N = int(input())

f = math.factorial(N)
i = 2
ans = 1
cnt = 0

while f != 1:
    if f % i == 0:
        f //= i
        cnt += 1
    else:
        ans *= (cnt + 1)
        cnt = 0
        i += 1


print(ans * (cnt + 1) % (10 ** 9 + 7))