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 Python (3.8.2) (judge verdict: Wrong Answer)

N = int(input())

p = [2]
count = 0
for i in range(2,N):
  if N % i == 0:
    flag = 1
    if i % 2 == 0:
      flag = 0
    else:
      for j in range(p[-1],int(i/2)):	# 素数判定
        if i % j == 0:
          flag = 0
          break
    if flag == 1:	# 素数である場合
      #print('sosuu:',i)
      p.append(i)
      N /= i
      count+=1
    elif flag == 0:	# 素数でないが、素数の冪乗である場合(2は例外)
      for j in range(len(p)):
        if i % p[j] == 0:
          #print(i)
          N /= i
          count+=1
          break
  if N == 1:
    break
#print(p)
print(count)