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
x=int(raw_input())

prime=[True]*(x+1)
prime[0:2]=[False]*2
for i in range(2,x+1):
    if prime[i]:
        for j in range(i*2,x+1,i):
            prime[j]=False

prime_num=[0]*(x+1)

for i in range(0,x+1):
    if prime[i]:
        j=i
        while True:
            prime_num[i]+=x/j
            j*=i
            if j>x:
                break


print reduce(lambda p,x:p*(x+1),prime_num,1)%(10**9+7)

