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
pr = [True] * 1001
n = int(input())
ans = 1
MOD = 10 ** 9 + 7
 
for i in range(2, n + 1):
    if pr[i]:
        for j in range(i * 2, n + 1, i):
            pr[j] = False
        cnt = 0
        now = n
        while now:
            cnt += now // i
            now //= i
        ans = ans * (cnt + 1) % MOD
 
print(ans)