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
mod = 10 ** 9 + 7
n = int(input())

def nprf(n):
    E = [0] * (n + 1)
    for i in range(2, n + 1):
        for j in range(2, i + 1):
            while i % j == 0:
                E[j] += 1
                i //= j
    return E

ans = 1
for i in nprf(n):
    ans *= i + 1
    
print(ans % mod)