JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:

  * mul x: multiplies n by x (where x is an arbitrary positive integer). 
  * sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer). 



You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?

Apparently, no one in the class knows the answer to this problem, maybe you can help them?

Input

The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.

Output

Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.

Examples

Input

20


Output

10 2

Input

5184


Output

6 4

Note

In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.

In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.

Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
import java.io.*;
import java.util.*;
 
public class Main {
    
    static MyScanner sc = new MyScanner();

    static boolean sqrt(int n) {
        int n1 = (int)Math.sqrt(n);
        return n1 * n1 == n;
    }
    
    public static void main(String[] args) {
        
        int n = sc.nextInt();
        int count = 0;
        int c = 0;

        if(n == 1)
            out.println(n + " 0");

        else {

            while(sqrt(n)) 
            {
                n = (int)Math.sqrt(n);
                count++;
            }
            
            for(int i = (int)Math.sqrt(n); i > 1; i--) {
                while(n % (i * i) == 0) {
                    n /= i;
                    c = 1;
                    count++;
                }
            }

            out.println(n + " " + (count + c));
        }
        
        out.close();
 
    }
    
    
/********************************************************************************************************************/
    
    // array of int type taking input
    public static int[] init(int n) {
        
        int[] arr = new int[n];
        
        for(int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();
            
        return arr;
    }
    
    //return gcd of two numbers
    public static int gcd(int a, int b) {
        
        if(a == 0)
            return b;
            
        return gcd(b % a, a);
    }

    public static int lcm(int a, int b) {

        return (a * b) / gcd(a,b);
    }
    
    
    //checks whether a number is prime or not
    public static boolean prime(int n) {
        
        if(n < 2)
            return false;
        
        for(int i = 2; i * i <= n; ++i)
            if(n % i == 0)
                return false;
                
        return true;
    }

// Pair Class
static class Pair<S extends Comparable<S>, T extends Comparable<T>> implements Comparable<Pair<S, T>> {
        
        S first;
        T second;
        
        public Pair(){}
        
        Pair(S f, T s) {
            first = f;
            second = s;
        }
        
        public S getX(){return this.first;}
        public T getY(){return this.second;}
    
        @Override
        public int compareTo(Pair<S, T> o) {
            int t = first.compareTo(o.first);
            if (t == 0) return second.compareTo(o.second);
            return t;
        }
        
        public void show() {
            System.out.println("[" + this.getX() + " , " + this.getY() + "]");
        }
        
        @Override
        public int hashCode() {
            return (31 + first.hashCode()) * 31 + second.hashCode();
        }
        
        @Override
        public boolean equals(Object o) {
            if (!(o instanceof Pair)) return false;
            if (o == this) return true;
            Pair p = (Pair) o;
            return first.equals(p.first) && second.equals(p.second);
        }
        
        @Override
        public String toString() {
            return "Pair{" + first + ", " + second + "}";
        }
    }
    
/*******************************************************************************************************************/
    
                        /****        Fast I/O        ****/
    
    
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}