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 defaultdict
n=int(input())
mod=10**9+7
d=defaultdict(int)
for i in range(2,n+1):
  c=i
  for j in range(2,c+1):
    if c%j==0:
      cnt=0
      while c%j==0:
        cnt+=1
        c//=j
      d[j]+=cnt
ans=1
for v in d.values():
  ans=(ans*(v+1))%mod
print(ans)