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
mod=10**9+7
import math
n=int(input())
ans=1
l=[0]*n
for ii in range(2,n+1):
  i=ii
  for j in range(2,int(math.sqrt(i))+1):
    if i%j==0:
      cnt=0
      while  i%j==0:
        cnt+=1;i//=j
      l[j-1]+=cnt
  if i!=1:
    l[i-1]+=1
for i in l:
  ans*=(i+1)
  ans%=mod
print(ans)
