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())
N = factorial(N)

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