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())
mod=10**9+7
ans=1
cnt=[0]*1000
for i in range(2,n+1):
    x=i
    for j in range(2,int(math.sqrt(n))+1):
        while x%j==0:
            cnt[j]+=1
            x/=j
    if x!=1:
        cnt[int(x)]+=1
for i in cnt:
    if i!=0:
        ans*=(i+1)
        ans%=mod
print(int(ans))