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