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
N = int(input())
ans = 1
divine = [1 for _ in range(N+1)]

for i in range(1, N+1):
    for j in range(2, i+1):
        while i%j== 0:
            i //= j
            divine[j] += 1

for k in divine:
    ans *= k

print(ans%1000000007)