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

def is_prime(n):
	if n == 1:
		return False
	
	for k in range(2, int(math.sqrt(n)) + 1):
		if n%k == 0:
			return False
	return True

p = []
for i in range(1,n+1):
	if is_prime(i):
		p.append(i)
ans = 1
for i in p:
	s = 0
	x = i
	while x <= n:
		s += n//x
		x *= i
	ans *= (s+1)
	ans %= mod
print (ans)
