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
import math
from collections import defaultdict

N = int(input())
MOD = 10**9+7

d = defaultdict(int)
d[1] = 0

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

ans = 1
for i in d.values():
    ans = (ans*(i+1)) % MOD
print(ans)
