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())
ans = 1
q = [1 for i in range(N + 1)]
for i in range(2,N + 1):
    k = i
    for i2 in range(2,i + 1):
        while k % i2 == 0:
            k /= i2
            q[i2] += 1
            
for i in range(N + 1):
    ans *= q[i]
    ans %= 10 ** 9 + 7

print(ans)