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.
    //    A Computer is Like a mischievous genie.
    //    It will give you exactly what you ask for,
    //    but not always what you want
    //    A code by Rahul Verma


    import java.io.BufferedOutputStream;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.io.PrintWriter;
    import java.math.BigInteger;
    import java.util.ArrayList;
    import java.util.Arrays;
    import java.util.Collections;
    import java.util.Comparator;
    import java.util.HashMap;
    import java.util.HashSet;
    import java.util.LinkedHashSet;
    import java.util.LinkedList;
    import java.util.List;
    import java.util.PriorityQueue;
    import java.util.Queue;
    import java.util.Set;
    import java.util.Stack;
    import java.util.StringTokenizer;
    import java.util.TreeMap;
    import java.util.TreeSet;


    public class Main {


        static class Clock {

            protected long start, stop;

            public void start() {

                start = System.currentTimeMillis();
            }

            public void stop() {
                stop = System.currentTimeMillis();
            }

            public String getTime() {

                return ((stop - start) + " ms");
            }
        }


        public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        static class FastReader {

            BufferedReader br;
            StringTokenizer st;

            public FastReader() {
                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[] nextSArray() {
                String sr[] = null;
                try {
                    sr = br.readLine().trim().split(" ");
                } catch (IOException e) {
                    e.printStackTrace();
                }
                return sr;
            }

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

                return str;
            }
        }


        static long powmodulo(long a, long p) {
            if (p == 0) {
                return 1 % mod;
            }
            if (p == 1) {
                return a % mod;
            }
            long ans = 1;
            while (p > 0) {
                if ((p & 1) > 0) {
                    ans = (ans * a) % mod;
                }
                a = (a * a) % mod;
                p = p >> 1;
            }
            return ans % mod;
        }


        static long mod = 1000000007;

        static long gcd(long a, long b) {
            if (a == 0) {
                return b;
            }
            return gcd(b % a, a);
        }

        static long fast_powerNumbers(long a, long n) {
            if (n == 1) {
                return a;
            }
            long ans = fast_powerNumbers(a, n / 2);
            if (n % 2 == 0) {
                return (ans * ans);
            } else {
                return ((ans * ans) * (a));
            }
        }


        static void dfs_helper(int[][] arr, int i, int j, int team, int n, int m) {
            arr[i][j] = team;
            if (i - 1 >= 0 && arr[i - 1][j] == 1) {
                dfs(arr, i - 1, j, team, n, m);
            }
            if (j - 1 >= 0 && arr[i][j - 1] == 1) {
                dfs(arr, i, j - 1, team, n, m);
            }
            if (i + 1 < n && arr[i + 1][j] == 1) {
                dfs(arr, i + 1, j, team, n, m);
            }
            if (j + 1 < m && arr[i][j + 1] == 1) {
                dfs(arr, i, j + 1, team, n, m);
            }

        }

        static void dfs(int[][] arr, int i, int j, int team, int n, int m) {
            dfs_helper(arr, i, j, team, n, m);

        }
        public static int arr[];


        static void seive(int n) {
            // 1 is not prime
            arr = new int[n + 1];
            arr[0] = arr[1] = 1;
            for (int i = 4; i <= n; i = i + 2) {
                arr[i] = 1;
            }
            for (int i = 3; i * i <= n; i = i + 2) {
                if (arr[i] == 0) {
                    for (int j = i * i; j <= n; j = j + i) {
                        arr[j] = 1;
                    }

                }
            }
        }


        public static HashMap<Integer,Integer> primefac(int n)
        {
            HashMap<Integer,Integer>hm=new HashMap<>();
            //int x = (int) Math.sqrt(n);
            for (int i = 2; i <=n; i++) {
                int x=0;
                while(n%i==0)
                {
                    n=n/i;
                    ++x;
                }
                if(x!=0)
                {
                    hm.put(i,x);
                }
            }
            return hm;
        }



        public static void main(String[] args) throws Exception {
            FastReader sc = new FastReader();

            Clock clock = new Clock();

            clock.start();
           int n = sc.nextInt();
           HashMap<Integer,Integer>hm = primefac(n);
           int x=1;
           ArrayList<Integer>poww=new ArrayList<>();
            for (int i = 0; i < 31; i++) {
                poww.add(x);
                x=x<<1;
            }
            int mul=0;
            int max=0;
            //System.out.println(hm);
            if(hm.containsKey(n))
            {
                System.out.println(n+" "+0);
                return;
            }
            int ans=1;
            for(Integer ele: hm.keySet())
            {
                ans=ans*ele;
                int  p =hm.get(ele);
                if((p&(p-1))!=0 || p==1)
                {
                    mul=1;
                }
                int ii = Collections.binarySearch(poww,p);
                if(ii<0)
                    ii = -ii -1;
                if(ii==0)
                    ++ii;
                max=Math.max(max , ii);
            }
            if(ans==n)
            {
                System.out.println(ans+" "+0);
            }
            else
            System.out.println(ans+" "+(max+mul));



        }
    }


    class Pair{

        int a,b;
        Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
        }
    }
    class DSU
    {
        int parent[];
        int rank[];

        long sum[] ;
        DSU(int n)
        {
            this.parent=new int[n];
            this.rank=new int[n];
            sum=new long[n];
            Arrays.fill(parent,-1);
            Arrays.fill(rank,1);

        }

        int find(int s1)
        {
            if(parent[s1]==-1)
                return s1;
            return parent[s1]=find(parent[s1]);
        }

        void unite(int s1,int s2)
        {
            int p1=this.find(s1);
            int p2=this.find(s2);
            if(p1==p2)
                return;
            if(rank[p1]>rank[p2])
            {
                parent[p2]=p1;
                rank[p1]+=rank[p2];
                // System.out.println(arr[p2]);

                sum[p1]+=sum[p2];
                //sum[p2]+=sum[p1];

            }
            else
            {
                parent[p1]=p2;
                rank[p2]+=rank[p1];
                //System.out.println(arr[p1]);
                sum[p2]+=sum[p1];
                //sum[p1]+=sum[p2];
            }
        }


    }

    class Gaph {

        HashMap<Integer, ArrayList<Integer>> hm;

        Gaph() {
            hm = new HashMap<>();
        }

        Gaph(int n) {

            hm = new HashMap<>();
            for (int i = 0; i < n; i++) {
                hm.put(i, new ArrayList<Integer>());
            }
        }

        // function for adding an edge.................................................
        public void addEdge(int a, int b, boolean isDir) {
            if (isDir) {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }
            } else {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else if (!hm.containsKey(a)) {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }

                if (hm.containsKey(b)) {
                    hm.get(b).add(a);
                } else if (!hm.containsKey(b)) {
                    hm.put(b, new ArrayList<>(Arrays.asList(a)));
                }
            }
        }


    }

    // out.println(al.toString().replaceAll("[\\[|\\]|,]",""));