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(input())
div = []
for i in range(2,N+1):
    while i != 1:
        for d in range(2,i+1):
            while i%d==0:
                i = i//d
                div.append(d)
C = Counter(div).most_common()
Ans = 1
for k,v in C:
    Ans = Ans*(v+1) % (10**9+7)

print(Ans)
