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())
N = math.factorial(N) 

i = 2 
num = 1
ans = 1

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

print(ans)