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 functools import reduce
N = int(input())

prime_table = [1] * (N+1)

for x in range(2, N+1):
    for t in range(2, x+1):
        while x % t == 0:
            prime_table[t] += 1
            x //= t
print(reduce(lambda x, y: x * y % (int(1e9) + 7), prime_table))