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.*; 
import java.io.*;
 
public class Main {
		
	public static void solve(InputReader in) {
		long n = in.readLong();
		ArrayList<Long> list = new ArrayList<>();  
		long temp = n; 
		for(long i = 2; i*i <= temp; i++) {
			if(n%i == 0) {
				long count = 0;
				while(n % i == 0) {
					n/=i; 
					count++; 
				}
				list.add(count); 
			}
		}
		if(n > 1) list.add(1L); 
		long sum = 0;
		for(Long i : list) {
			long beg = 0; long end = i; long ans = 0;  
			while( beg <= end) {
				long med = (beg + end)/2;
				if(med*(med + 1)/2 <= i) {
					ans = med; 
					beg = med + 1; 
				}
				else
					end = med - 1; 
			}
			sum += ans; 
		}
		System.out.println(sum); 
	}

    public static void main(String[] args) {
    	InputReader in = new InputReader(System.in); 
    	int t = 1;
    	while(t-- > 0) {
    		solve(in); 
    	}
    }
}

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

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

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

    public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

    public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

    public long readLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9') {
				throw new InputMismatchException();
			}
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	
    public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

    public String next() {
		return readString();
	}

    public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
