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 math
N = int(raw_input())
count = [0 for i in xrange(N)]
def prime_decomposition(n):
  i = 2
  table = []
  while i * i <= n:
    while n % i == 0:
      n /= i
      table.append(i)
    i += 1
  if n > 1:
    table.append(n)
  return table

for n in xrange(2,N+1):
  table = prime_decomposition(n)
  for t in table:
    count[t-2]+=1

C = 1
for c in count:
  if c!=0:
    C*=(c+1)
print C%1000000007