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 collections import defaultdict
import math
n = math.factorial(int(input()))
i = 2
factors = defaultdict(int)
ans = 1
while i**2 <= n:
    while n%i==0:
        n //= i
        factors[i] += 1
    i += 1
if n > 1:
    factors[n] += 1
for k,v in factors.items():
    ans = (ans*(v+1))%(10**9+7)
print(ans)