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 
insu=[[0]*1001 for i in range(1001)]
for i in range(1, 1001):
    n=i
    for j in range(2, 1001):
        while n%j==0:
            n=n//j
            insu[i][j]+=1
n=int(input())
new=[1]*1001
for i in range(1,n+1):
    for j in range(1001):
        new[j]+=insu[i][j]
ans=1
for n in new:
    ans*=n
print(ans%(10**9+7))