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 sys
sys.setrecursionlimit(10**9)

n = int(input())

def factorial(n):
    if n == 1:
        return 1
    return n * factorial(n-1)

num = factorial(n)

ans = 1
for i in range(2, n+1):
    count = 0
    while num % i == 0:
        count += 1
        num = num // i
    ans *= (count + 1)

print(ans % (10 ** 9 + 7))