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
import collections

N = int(input())
a = math.factorial(N)
check = []
ans = 1
i = 2

while a != 1:
    if a % i == 0:
        a //= i
        check.append(i)
    else:
        i += 1
        
check = collections.Counter(check).values()
for i in check:
    ans *= (i+1)
    ans %= 10**9+7
print(ans)