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())
m = math.factorial(N)
arr = 1000*[1]

for n in range(2,1001):
  while m%n==0:
    m//=n
    arr[n]+=1

ans = 1
for n in arr:
  ans*=n

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