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
from collections import defaultdict
import math

n = math.factorial(int(input()))
i = 2
f = defaultdict(int)
a = 1
while i ** 2 <= n:
    while n%i==0:
        n //= i
        f[i] += 1
    i += 1
if n > 1:
    f[n] += 1
for n,m in f.items():
    a = (a*(m+1)) % (10**9+7)
print(a)