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 defaultdict

N = int(input())
factors = defaultdict(int)
for n in range(2, N+1):
    for i in range(2,int(n**.5)+1):
        while n % i == 0:
            n //= i
            factors[i] += 1
    if n > 1:
        factors[n] += 1

ans = 1
for c in factors.values():
    ans *= c + 1
    ans %= 1000000007
print(ans)