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 as fact
ans = 1
n = int(input())
m = fact(n)
for i in range(2, n+1):
    tmp = 1
    while m%i==0:
        m //= i
        tmp += 1
    ans *= tmp
print(ans%(10**9+7))