Problem:
Score : 400 points

Problem Statement

Given is a positive integer N. Consider repeatedly applying the operation below on N:

First, choose a positive integer z satisfying all of the conditions below:

z can be represented as z=p^e, where p is a prime number and e is a positive integer;

z divides N;

z is different from all integers chosen in previous operations.

Then, replace N with N/z.

Find the maximum number of times the operation can be applied.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum number of times the operation can be applied.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Runtime Error)

;;(declaim (optimize (speed 0) (safety 3) (debug 3)))
(declaim (optimize (speed 3) (safety 0) (debug 0)))

(declaim (type (integer 1 1000000000000) *n*))
(defvar *n* (read))
;;(defvar *n* 10)
(declaim (type (simple-array bit (*)) *sieve*))
(defvar *sieve* (make-array (1+ *n*)
			    :initial-element 1
			    :element-type 'bit))

(loop for p fixnum = 2 then (position 1 *sieve* :start (1+ p))
      while (< p (1+ (sqrt *n*))) do
      (loop for q fixnum = (+ p p) then (+ q p)
	    while (<= q *n*) do
	    (setf (aref *sieve* q) 0)))
(declaim (type (array fixnum (*)) *primes*))
(defvar *primes* (make-array (ash *n* -2)
			     :element-type 'fixnum
			     :adjustable t
			     :fill-pointer 0))

(loop for i from 2 to *n* do
      (if (= 1 (aref *sieve* i))
	  (vector-push-extend i *primes*)))


(defun rev-tri (n)
  (loop for i from 0 do
	(when (> (ash (* i (1+ i)) -1) n)
	  (return (1- i)))))
(defun divisible-times (p n)
  (loop for i from 0
	for rem = (rem n p)
	when (/= rem 0) do (return i)
	do
	(setf n (floor n p))))

(princ (loop for p across *primes* summing
	     (rev-tri (divisible-times p *n*))))