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 = int(input())
mod = 10**9+7
fn = factorial(N)

ans = 1
for i in range(2, N+1):
    count = 1
    while fn % i == 0:
        count += 1 
        fn //= i 
    ans *= count
print(ans%mod)