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())
s=math.factorial(n)
mod=10**9+7
i=2
cnt=0
ans=1
while s!=1:
	if s%i==0:
		cnt+=1
		s//=i
	else:
		ans*=(cnt+1)
		cnt=0
		i+=1
print(ans*(cnt+1)%mod)

