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=[1]*1000
for i in range(2,1001):
  while m%i==0:
    m//=i
    arr[i]+=1
ans=1
for i in arr:
  ans*=i
print(ans%(10**9+7))