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
mp = defaultdict(int)
for i in range(2, N+1) :
  x = i
  for j in range(2, x+1): 
    while x%j == 0:
      x /= j
      mp[j] += 1
      
ans = 1
for v in mp.values():
  ans = (ans * (v+1)) % MOD
print(ans)