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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextLong()
    println(problem169d(n))
}

fun problem169d(n: Long): Int {
    if (n == 1L) return 0

    /**
     * 素因数分解
     * 対象の値が1になるまで素数で順番に割っていき割った数を列挙する
     */
    fun computePrimeFactorList(n: Long): List<Long> {
        val p = mutableListOf<Long>()
        var primeFactor = n
        for (i in 2..n) {
            while (primeFactor % i == 0L) {
                primeFactor /= i
                p.add(i)
            }
        }
        return p
    }

    val used = mutableSetOf<Long>()
    var count = 0
    var n2 = n
    while (true) {
        val prev = n2
        for (i in 2..10000L) {
            if (used.contains(i)) continue
            if (computePrimeFactorList(i).isEmpty()) continue
            if (n2 % i != 0L) {
                continue
            }
            n2 /= i
            used.add(i)
            break
        }
        if (prev == n2) break
        count++
    }

    return Math.max(count, 1)
}