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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {
    public static void main(final String[] args) {
        final FastScanner scanner = new FastScanner(System.in);
        final long n = scanner.nextLong();
        final Map<Long, Long> map = primeFactorization(n);
        long all = 0;
        for (final long value : map.values()) {
            for (long tmp = 1; ; tmp++) {
                if (tmp * (tmp + 1) / 2 > value) {
                    all += tmp - 1;
                    break;
                }
            }
        }
        System.out.println(all);
    }

    private static Map<Long, Long> primeFactorization(long n) {
        final double sqrt = Math.sqrt(n);
        final Map<Long, Long> countMap = new HashMap<>();
        for (long i = 2; i <= sqrt; i++) {
            if (n % i == 0) {
                countMap.compute(i, (k, v) -> v = v == null ? 1 : v + 1);
                n /= i;
                i--;
            }
        }

        if (n != 1) {
            countMap.compute(n, (k, v) -> v = v == null ? 1 : v + 1);
        }

        return countMap;
    }

    private static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(final InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }
    }
}
