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.

/**
 * Date: 14 Nov, 2018
 * Link: http://codeforces.com/contest/1062/problem/A
 *
 * @author Prasad-Chaudhari
 * @linkedIn: https://www.linkedin.com/in/prasad-chaudhari-841655a6/
 * @git: https://github.com/Prasad-Chaudhari
 */
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;

public class A_Prank_1062_A {

    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        FastIO in = new FastIO();
        int n = in.ni();
        if (n == 1) {
            System.out.println("1 0");
        } else {
            int primes[] = Primes.getPrimes(1000001);
            int nop = primes.length;
            int freq[] = new int[nop];
            int temp = n;
            for (int i = 0; i < nop; i++) {
                while (temp % primes[i] == 0) {
                    temp /= primes[i];
                    freq[i]++;
                }
            }
            int max = 0;
            for (int i : freq) {
                max = Math.max(max, i);
            }
            int count = 0;
            boolean p = false;
            if (max != 1) {
                for (int i = 1; i < 30; i++) {
                    if (max <= Math.pow(2, i)) {
                        if (max < Math.pow(2, i)) {
                            count++;
                        } else {
                            p = true;
                        }
                        max = (int) Math.pow(2, i);
                        break;
                    }
                }
            }
            if (p) {
                for (int i = 0; i < nop; i++) {
                    if (freq[i] > 0) {
                        if (freq[i] != max) {
                            count++;
                            break;
                        }
                    }
                }
            }
//            System.out.println(max);
            while (max > 1) {
                max /= 2;
                count++;
            }
            int pro = 1;
            for (int i = 0; i < nop; i++) {
                if (freq[i] != 0) {
                    pro *= primes[i];
                }
            }
            System.out.println(pro + " " + count);
        }
    }

    static class Primes {

        public static int[] getPrimes(int n) {
            boolean[] c = new boolean[n + 1];
            int nop = 0;
            int root = (int) (Math.sqrt(n) + 1);
            for (int i = 2; i <= root; i++) {
                if (!c[i]) {
                    for (int j = i * i; j <= n; j = j + i) {
                        c[j] = true;
                    }
                }
            }
            for (int i = 2; i < n; i++) {
                if (!c[i]) {
                    nop++;
                }
            }
            int[] primes = new int[nop];
            nop = 0;
            for (int i = 2; i < n; i++) {
                if (!c[i]) {
                    primes[nop++] = i;
                }
            }
            return primes;
        }
    }

    static class FastIO {

        private final BufferedReader br;
        private final BufferedWriter bw;
        private String s[];
        private int index;
        private StringBuilder sb;

        public FastIO() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            bw = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
            s = br.readLine().split(" ");
            sb = new StringBuilder();
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = nl();
            }
            return a;
        }

        public int[][] gg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public void print(String s) throws IOException {
            bw.write(s);
        }

        public void println(String s) throws IOException {
            bw.write(s);
            bw.newLine();
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }

    static class Data implements Comparable<Data> {

        int a, b;

        public Data(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Data o) {
            if (a == o.a) {
                return Integer.compare(b, o.b);
            }
            return Integer.compare(a, o.a);
        }

        public static void sort(int a[]) {
            Data d[] = new Data[a.length];
            for (int i = 0; i < a.length; i++) {
                d[i] = new Data(a[i], 0);
            }
            Arrays.sort(d);
            for (int i = 0; i < a.length; i++) {
                a[i] = d[i].a;
            }
        }
    }
}
