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 collections
import itertools
import functools
import math

s = set([])
if __name__ == "__main__":
    n = int(input())
    m = math.factorial(n)
    res = 1
    for j in range(2, n + 1):
        tmp = 1
        while m % j == 0:
            m = m//j
            tmp += 1
        res *= tmp
    print(res % (10**9 + 7))