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 Counter
import math

N = input()
PRIMES = [2,3,5,7,11,13,17,19,23,27,29,31] # < sqrt(1000)
factors = []
for n in range(2,N+1):
  tmp = n
  for prime in PRIMES:
    while tmp % prime == 0:
      factors.append(prime)
      tmp /= prime
    if tmp == 1:
      break
  if tmp > math.sqrt(n):
    factors.append(tmp)

count = 1
for v in Counter(factors).values():
  count *= (v+1)
count = count % (10**9+7)
print count 