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
def factor(n):
    for i in range(2, n+1):
        if n % i == 0:
            l = factor(n // i)
            l.append(i)
            return l
    return []

from collections import Counter
N = int(input())
c = Counter()
for i in range(1, N+1):
    c += Counter(factor(i))
p = 1
for _, i in c.items():
    p *= (i+1)
    p %= 1000000007
print(p)


