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())
l=[2]
for i in range(3,n+1):
    for p in l:
        if i%p==0:break
    else: l.append(i)
a=1
for p in l:
    s=0
    for i in range(1,int(math.log(n,p))+1):
        s+=n//p**i
    a=a*(s+1)%(10**9+7)
print(a)