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
N = int(input())
plist = [2]
for i in range(3, N + 1):
    for prime in plist:
        if i % prime == 0:
            break
    else:
        plist.append(i)
ans = 1
for prime in plist:
    s = 0
    for i in range(1, int(math.log(N, prime)) + 1):
        s += N // (prime ** i)
    ans = ans * (s + 1) % (10 ** 9 + 7)
print(ans)
