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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Spandan Mishra
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DDivGame solver = new DDivGame();
        solver.solve(1, in, out);
        out.close();
    }

    static class DDivGame {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long n = in.readLong();

            if (n == 1)
                System.out.println(0);

            else {
                long tmp = n;
                long ans = 0;
                for (long i = 2; i * i <= n; i++) {
                    long pow = i;
                    while (tmp % pow == 0) {
                        tmp /= pow;
                        ans++;
                        pow *= i;
                    }
                    while (tmp % i == 0) {
                        tmp /= i;
                    }
                }

                System.out.println(tmp > 1 ? ++ans : ans);
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new RuntimeException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

