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 collections import Counter
N = int(raw_input())
d = Counter()

for i in range(1, N+1):
    n = i
    for p in range(2, i+1):
        while n % p == 0:
            n /= p
            d[p] += 1
ans = 1
for p in d:
    ans *= d[p] + 1
    ans %= 10 ** 9 + 7
print ans
