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 collections
n = int(input())
li = []
for k in range(2, n+1):
  for i in range(2, int(k**0.5)+1):
    while k % i == 0:
      k //= i
      li.append(i)
  if k != 1:
    li.append(k)
c = collections.Counter(li)
ans = 1
for k, v in c.items():
  ans *= (v+1)
print(ans%(10**9+7))
    