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 sys
n=int(input())
lis=[0for i in range(n)]
for i in range(2,n+1):
  ib=i
  for j in range(2,ib+1):
    while(ib%j==0):
      lis[j-1]+=1
      ib=ib//j
pat=1
for i in lis:pat*=(i+1)
print(pat%(10**9+7))