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
from math import factorial

N = factorial(int(input()))

i = 2
check = 1
ans = 1
while N != 1:
    if N % i == 0:
        N //= i
        check += 1
    else:
        ans *= check
        check = 1
        i += 1
print((ans*check)%(10**9+7))