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.

Examples

Input

24


Output

3


Input

1


Output

0


Input

64


Output

3


Input

1000000007


Output

1


Input

997764507000


Output

7

import java.util.*;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		long n = Long.parseLong(sc.next());

		// nが1だったら答えは0で確定
		if (n == 1) {
			System.out.println(0);
			return;
		}

		// nを素因数分解
		HashMap<Long, Long> map = primeFactorize(n);

		// 素因数分解の結果表示
		for (long key : map.keySet()) {
			// System.out.println(key + "^" + map.get(key));
		}

		// 結果を求めて出力
		int result = 0;
		for (long key : map.keySet()) {
			long z = map.get(key);
			for (int j = 1; j < 10000; j++) {
				if (j <= z) {
					z -= j;
					result++;
				} else {
					break;
				}
			}
		}

		System.out.println(result);

	}

	// nを素因数分解して、結果用mapに素因数と指数のペアを入れて返す関数。
	public static HashMap<Long, Long> primeFactorize(long n) {

		long input = n;
		HashMap<Long, Long> map = new HashMap<Long, Long>();

		// nが0以下だったらnullを返す
		if (n <= 0) {
			return null;
		}

		// nが1だったら素因数分解結果は1^1
		if (n == 1) {
			map.put(1L, 1L);
			return map;
		}

		// 素因数分解していく。計算量はO(√n)
		for (long i = 2; i * i <= input; i++) {
			long j = 0;
			while (true) {
				if (n % i == 0) {
					j++;
					map.put(i, j);
					n /= i;
				} else {
					break;
				}
			}
		}

		// 最後に残った数も忘れずに入れる
		if (n != 1) {
			map.put(n, 1L);
		}

		return map;
	}
}