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 math
n = int(input())
d = {}
       
for i in range(2,n+1):
  for j in range(2,i+1):
    while i%j == 0:
      i /= j
      if j in d:
        d[j] += 1
      else:
        d[j] = 2
ans = 1
for i in list(d.values()):
  ans *= i
print(ans%(10**9+7))