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
d={}
for i in range(int(input())+1):
  for j in d:
    while i>1 and i%j<1: d[j]+=1; i//=j
  if i>1: d[i]=2
a=1
for v in d.values(): a=a*v%(10**9+7)
print(a)