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())

F = factorial(N)
result = 1
for i in range(2, N + 1):
    count = 1
    while F % i == 0:
        F //= i
        count += 1
    result *= count

print(result % (10 ** 9 + 7))