Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun abc052c (n)
  (let ((ex (make-array (1+ n) :initial-element 0)))
    (loop for i from 1 to n do
	  (loop for (p . e) in (prime-factorization i) do
		(setf (aref ex p)
		      (+ (aref ex p) e))))
    (rem (reduce #'*
	    (map 'list #'1+ ex))
	 (+ (expt 10 9) 7))))
 
(let ((n (read)))
   (princ (abc052c n))(terpri))