Problem: There were n types of swords in the theater basement which had been used during the plays. Moreover there were exactly x swords of each type. y people have broken into the theater basement and each of them has taken exactly z swords of some single type. Note that different people might have taken different types of swords. Note that the values x, y and z are unknown for you.

The next morning the director of the theater discovers the loss. He counts all swords — exactly a_i swords of the i-th type are left untouched.

The director has no clue about the initial number of swords of each type in the basement, the number of people who have broken into the basement and how many swords each of them have taken.

For example, if n=3, a = [3, 12, 6] then one of the possible situations is x=12, y=5 and z=3. Then the first three people took swords of the first type and the other two people took swords of the third type. Note that you don't know values x, y and z beforehand but know values of n and a.

Thus he seeks for your help. Determine the minimum number of people y, which could have broken into the theater basement, and the number of swords z each of them has taken.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^{5}) — the number of types of swords.

The second line of the input contains the sequence a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{9}), where a_i equals to the number of swords of the i-th type, which have remained in the basement after the theft. It is guaranteed that there exists at least one such pair of indices (j, k) that a_j ≠ a_k.

Output

Print two integers y and z — the minimum number of people which could have broken into the basement and the number of swords each of them has taken.

Examples

Input


3
3 12 6


Output


5 3


Input


2
2 9


Output


1 7


Input


7
2 1000000000 4 6 8 4 2


Output


2999999987 2


Input


6
13 52 0 13 26 52


Output


12 13

Note

In the first example the minimum value of y equals to 5, i.e. the minimum number of people who could have broken into the basement, is 5. Each of them has taken 3 swords: three of them have taken 3 swords of the first type, and two others have taken 3 swords of the third type.

In the second example the minimum value of y is 1, i.e. the minimum number of people who could have broken into the basement, equals to 1. He has taken 7 swords of the first type.

Solution (in JAVA):

Solution:
//import com.sun.org.apache.xpath.internal.operations.String;

import java.io.*;
import java.util.*;


public class scratch_25 {
    // int count=0;
    //static long count=0;
    static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

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

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

    public static class Graph{
        public static class Vertex{
            HashMap<Integer,Integer> nb= new HashMap<>();     // for neighbours of each vertex
        }

        public static HashMap<Integer,Vertex> vt;   // for vertices(all)

        public Graph(){
            vt= new HashMap<>();
        }

        public static int numVer(){
            return vt.size();
        }

        public static boolean contVer(int ver){
            return vt.containsKey(ver);
        }

        public static void addVer(int ver){
            Vertex v= new Vertex();
            vt.put(ver,v);
        }

        public static int numEdg(){
            int count=0;
            ArrayList<Integer> vrtc= new ArrayList<>(vt.keySet());
            for (int i = 0; i <vrtc.size() ; i++) {
                count+=(vt.get(vrtc.get(i))).nb.size();
            }
            return count/2;
        }

        public static boolean contEdg(int ver1, int ver2){
            if(vt.get(ver1)==null || vt.get(ver2)==null){
                return false;
            }

            Vertex v= vt.get(ver1);
            if(v.nb.containsKey(ver2)){
                return true;
            }
            return false;
        }

        public static void addEdge(int ver1, int ver2, int weight){
            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }
            Vertex v1= vt.get(ver1);
            Vertex v2= vt.get(ver2);
            v1.nb.put(ver2,weight);                                 // if previously there is an edge, then this replaces that edge
            v2.nb.put(ver1,weight);
        }

        public static void delEdge(int ver1, int ver2){

            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }

            vt.get(ver1).nb.remove(ver2);
            vt.get(ver2).nb.remove(ver1);

        }

        public static void delVer(int ver){
            if(!vt.containsKey(ver)){
                return;
            }
            Vertex v1= vt.get(ver);
            ArrayList<Integer> arr= new ArrayList<>(v1.nb.keySet());
            for (int i = 0; i <arr.size() ; i++) {
                int s= arr.get(i);
                vt.get(s).nb.remove(ver);
            }
            vt.remove(ver);
        }

        public class Pair{
            int vname;
            ArrayList<Integer> psf= new ArrayList<>();       // path so far
            int dis;
            int col;
        }









        public HashMap<Integer,Integer> bfs(int src){
            HashMap<Integer, Boolean> prcd= new HashMap<>();    // jo jo ho chuke hain unke liye

            HashMap<Integer, Integer> ans= new HashMap<>();

            LinkedList<Pair> queue= new LinkedList<>();      // for bfs queue

            Pair strtp= new Pair();

            strtp.vname= src;

            ArrayList<Integer> ar= new ArrayList<>();
            ar.add(src);

            strtp.psf= ar;
            strtp.dis=0;

            queue.addLast(strtp);

            while(!queue.isEmpty()){

                Pair rp =  queue.removeFirst();

                if(prcd.containsKey(rp.vname)){
                    continue;
                }
                prcd.put(rp.vname,true);
                ans.put(rp.vname,rp.dis);

//                if(contEdg(rp.vname,dst)){
//                    return true;
//                }

                Vertex a= vt.get(rp.vname);
                ArrayList<Integer> arr= new ArrayList<>(a.nb.keySet());
                for (int i = 0; i <arr.size() ; i++) {
                    int s= arr.get(i);
                    if(!prcd.containsKey(s)){
                        Pair np = new Pair();
                        np.vname= s;
                        np.dis+=rp.dis+a.nb.get(s);
                        np.psf.addAll(rp.psf);
                        np.psf.add(s);
//                        np.psf.add(s);
//                         np.psf= rp.psf+" "+s;
                        queue.addLast(np);
                    }

                }
            }
            return ans;

            //   return false;
        }








        public HashMap<Integer,Integer> dfs(int src){
            HashMap<Integer, Boolean> prcd= new HashMap<>();    // jo jo ho chuke hain unke liye

            HashMap<Integer, Integer> ans= new HashMap<>();

            LinkedList<Pair> stack= new LinkedList<>();      // for bfs queue

            Pair strtp= new Pair();

            strtp.vname= src;

            ArrayList<Integer> ar= new ArrayList<>();
            ar.add(src);

            strtp.psf= ar;
            strtp.dis=0;

            stack.addFirst(strtp);

            while(!stack.isEmpty()){

                Pair rp =  stack.removeFirst();

                if(prcd.containsKey(rp.vname)){
                    continue;
                }
                prcd.put(rp.vname,true);
                ans.put(rp.vname,rp.dis);

//                if(contEdg(rp.vname,dst)){
//                    return true;
//                }

                Vertex a= vt.get(rp.vname);
                ArrayList<Integer> arr= new ArrayList<>(a.nb.keySet());
                for (int i = 0; i <arr.size() ; i++) {
                    int s= arr.get(i);
                    if(!prcd.containsKey(s)){
                        Pair np = new Pair();
                        np.vname= s;
                        np.dis+=rp.dis+a.nb.get(s);
                        np.psf.addAll(rp.psf);
                        np.psf.add(s);
//                        np.psf.add(s);
//                         np.psf= rp.psf+" "+s;
                        stack.addFirst(np);
                    }

                }
            }
            return ans;

            //   return false;
        }






        public boolean isCycle(){
            HashMap<Integer, Boolean> prcd= new HashMap<>();    // jo jo ho chuke hain unke liye

            //   HashMap<Integer, Integer> ans= new HashMap<>();

            LinkedList<Pair> queue= new LinkedList<>();      // for bfs queue



            ArrayList<Integer> keys = new ArrayList<>(vt.keySet());
            for (int i = 0; i <keys.size(); i++) {
                int cur= keys.get(i);
                if(prcd.containsKey(cur)){
                    continue;
                }

                Pair sp = new Pair();
                sp.vname= cur;
                ArrayList<Integer> as= new ArrayList<>();
                as.add(cur);
                sp.psf= as;

                queue.addLast(sp);

                while(!queue.isEmpty()){




                    Pair rp= queue.removeFirst();
                    if(prcd.containsKey(rp.vname)){
                        return true;
                    }

                    prcd.put(rp.vname,true);




                    Vertex v1= vt.get(rp.vname);
                    ArrayList<Integer> nbrs= new ArrayList<>(v1.nb.keySet());
                    for (int j = 0; j <nbrs.size() ; j++) {
                        int u= nbrs.get(j);
                        Pair np= new Pair();
                        np.vname= u;
                        queue.addLast(np);
                    }
                }

            }
            return false;
        }






        public  ArrayList<ArrayList<Integer>> genConnctdComp(){
            HashMap<Integer, Boolean> prcd= new HashMap<>();    // jo jo ho chuke hain unke liye

            ArrayList<ArrayList<Integer>> ans= new ArrayList<>();

            //   HashMap<Integer, Integer> ans= new HashMap<>();

            LinkedList<Pair> queue= new LinkedList<>();      // for bfs queue

            //  int con=-1;

            ArrayList<Integer> keys = new ArrayList<>(vt.keySet());
            for (int i = 0; i <keys.size(); i++) {
                int cur= keys.get(i);
                if(prcd.containsKey(cur)){
                    //return true;
                    continue;
                }
                int count=0;
                ArrayList<Integer> fu= new ArrayList<>();
                fu.add(cur);


                Pair sp = new Pair();
                sp.vname= cur;
                ArrayList<Integer> as= new ArrayList<>();
                as.add(cur);
                sp.psf= as;

                queue.addLast(sp);

                while(!queue.isEmpty()){




                    Pair rp= queue.removeFirst();
                    if(prcd.containsKey(rp.vname)){
                        //return true;
                        continue;
                    }

                    prcd.put(rp.vname,true);
                    fu.add(rp.vname);



                    Vertex v1= vt.get(rp.vname);
                    ArrayList<Integer> nbrs= new ArrayList<>(v1.nb.keySet());
                    for (int j = 0; j <nbrs.size() ; j++) {
                        int u= nbrs.get(j);
                        if(!prcd.containsKey(u)){
                            count++;
                            Pair np= new Pair();
                            np.vname= u;
                            queue.addLast(np);
                        }
                    }}
                fu.add(count);
                ans.add(fu);

            }
            //return false;
            return ans;

        }

        public boolean isBip(int src){                       // only for connected graph

            HashMap<Integer,Integer> clr= new HashMap<>();
            // colors are 1 and -1


            LinkedList<Integer>q = new LinkedList<Integer>();
            clr.put(src,1);
            q.add(src);


            while(!q.isEmpty()){

                int u = q.getFirst();
                q.pop();

                ArrayList<Integer> arr= new ArrayList<>(vt.keySet());

                for (int i = 0; i <arr.size() ; ++i) {

                    int x= arr.get(i);

                    if(vt.get(u).nb.containsKey(x) && !clr.containsKey(x)){

                        if(clr.get(u)==1){
                            clr.put(x,-1);
                        }
                        else{
                            clr.put(x,1);
                        }
                        q.push(x);
                    }

                    else if(vt.get(u).nb.containsKey(x) && (clr.get(x)==clr.get(u))){
                        return false;
                    }

                }
            }
            return true;
        }

















        public static void printGr() {
            ArrayList<Integer> arr= new ArrayList<>(vt.keySet());
            for (int i = 0; i <arr.size() ; i++) {
                int ver= arr.get(i);
                Vertex v1= vt.get(ver);
                ArrayList<Integer> arr1= new ArrayList<>(v1.nb.keySet());
                for (int j = 0; j <arr1.size() ; j++) {
                    System.out.println(ver+"-"+arr1.get(j)+":"+v1.nb.get(arr1.get(j)));
                }

            }
        }
    }

    static class Cus implements Comparable<Cus>{
        int size;
        int mon;
        int num;
        public Cus(int size,int mon,int num){
            this.size=size;
            this.mon=mon;
            this.num=num;
        }
        @Override
        public int compareTo(Cus o){
            if(this.mon!=o.mon){
                return this.mon-o.mon;}

            else{
                return o.size-this.size;
            }

        }



    }

    static class Table implements Comparable<Table>{
        int go;
      //  int cum;
        int cost;
        public Table(int go,int cost){
            this.go=go;
        //    this.cum=cum;
            this.cost=cost;
        }
        @Override
        public int compareTo(Table o){
           
            return this.cost-o.cost;

        }


    }
    static class Table1 implements Comparable<Table1>{
        int go;
        //int cum;
        int cost;
        public Table1(int go,int cost){
            this.go=go;
          //  this.cum=cum;
            this.cost=cost;
        }
        @Override
        public int compareTo(Table1 o){
            return this.cost-o.cost;


        }}

    public static class DisjointSet{
        HashMap<Integer,Node> mp= new HashMap<>();

        public static class Node{
            int data;
            Node parent;
            int rank;
        }


        public void create(int val){
            Node nn= new Node();
            nn.data=val;
            nn.parent=nn;
            nn.rank=0;
            mp.put(val,nn);
        }

        public int find(int val){

            return findn(mp.get(val)).data;

        }


        public Node findn(Node n){
            if(n==n.parent){
                return n;
            }
            Node rr= findn(n.parent);
            n.parent=rr;
            return rr;
        }



        public void union(int val1, int val2){                                                                               // can also be used to check cycles

            Node n1= findn(mp.get(val1));
            Node n2= findn(mp.get(val2));


            if(n1.data==n2.data) {
                return;
            }



            if(n1.rank<n2.rank){
                n1.parent=n2;
            }

            else if(n2.rank<n1.rank){
                n2.parent=n1;
            }

            else {
                n2.parent=n1;
                n1.rank++;
            }

        }
    }









    public static void main(String[] args)  throws IOException {
        Reader.init(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int n= Reader.nextInt();
        long arr[]= new long[n];
        long max=0;
        for (int i = 0; i <n ; i++) {
            arr[i]= Reader.nextLong();
            max=Math.max(max, arr[i]);
        }
        long gcd= max-arr[0];
        for (int i = 0; i <n ; i++) {
            if(arr[i]!=max){
            gcd= gcd(gcd, max-arr[i]);
        }}
        long ans=0;
        for (int i = 0; i <n ; i++) {
            ans+=(max-arr[i])/gcd;
        }
        System.out.println(ans+" "+gcd);























    }

    static long pow(long x, long y){
        long res=1;
        if(x==0){
            return 0;
        }
        while(y>0){
            if((y & 1)==1)
                res = (res * x) ;

            // y must be even now
            // y = y / 2
            y = y >> 1;
            x = (x * x) ;
        }
        return res;

















    }



















    static int countDivisibles(int A, int B, int M)
    {
        // Add 1 explicitly as A is divisible by M
        if (A % M == 0)
            return (B / M) - (A / M) + 1;

        // A is not divisible by M
        return (B / M) - (A / M);
    }


    public static void df(int x, int y,int n, int m, char[][]ar, int l){
        boolean done[][]= new boolean[n][m];
        int count=0;
        LinkedList<int[]> stk= new LinkedList<>();
        int a[]= {x,y};
        stk.addFirst(a);
        while(!stk.isEmpty() && count<l){
            //  count++;
            int b[]=stk.removeFirst();
            if( done[b[0]][b[1]]){
                continue;
            }
            count++;

            done[b[0]][b[1]]=true;
            ar[b[0]][b[1]]='@';
            int arr[][]={{1,0},{-1,0},{0,1},{0,-1}};
            for (int i = 0; i <arr.length ; i++) {
                if(!(b[0]+arr[i][0]>=n || b[1]+arr[i][1]>=m || b[0]+arr[i][0]<0 || b[1]+arr[i][1]<0 ||  ar[b[0]+arr[i][0]][b[1]+arr[i][1]]=='#')){
                    int r[]= {b[0]+arr[i][0], b[1]+arr[i][1]};
                    stk.addFirst(r);
                    // continue;



                }
            }}


        for (int i = 0; i <n ; i++) {
            for (int j = 0; j <m ; j++) {
                if(ar[i][j]=='.'){
                    System.out.print('X');
                }
                else if(ar[i][j]=='@'){
                    System.out.print('.');
                }
                else{
                    System.out.print(ar[i][j]);
                }
            }
            System.out.println();
        }
























    }











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



    static long gcd1(long a, long b)
    {

        // Everything divides 0
        if (a == 0)
            return b;
        if (b == 0)
            return a;

        // base case
        if (a == b)
            return a;

        // a is greater
        //count++;
        if (a > b){
            return gcd(a-b, b);

        }
        return gcd(a, b-a);
    }





    // method to return LCM of two numbers
    static long lcm(long a, long b)
    {
        return (a*b)/gcd(a, b);
    }

    // Driver method

    static int partition(long arr[],long arr1[], int low, int high)
    {
        long pivot = arr[high];
        int i = (low-1); // index of smaller element
        for (int j=low; j<high; j++)
        {
            // If current element is smaller than the pivot
            if (arr[j] < pivot)
            {
                i++;

                // swap arr[i] and arr[j]
                long temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
                long temp1=arr1[i];
                arr1[i]=arr1[j];
                arr1[j]=temp1;

            }
        }

        // swap arr[i+1] and arr[high] (or pivot)
        long temp = arr[i+1];
        arr[i+1] = arr[high];
        arr[high] = temp;
        long temp1= arr1[i+1];
        arr1[i+1]=arr1[high];
        arr1[high]= temp1;

        return i+1;
    }


    /* The main function that implements QuickSort()
      arr[] --> Array to be sorted,
      low  --> Starting index,
      high  --> Ending index */
    static void sort(long arr[],long arr1[], int low, int high)
    {
        if (low < high)
        {
            /* pi is partitioning index, arr[pi] is
              now at right place */
            int pi = partition(arr,arr1, low, high);

            // Recursively sort elements before
            // partition and after partition
            sort(arr,arr1, low, pi-1);
            sort(arr,arr1, pi+1, high);
        }
    }







































































    public static ArrayList<Integer> Sieve(int n) {
        boolean arr[]= new boolean [n+1];
        Arrays.fill(arr,true);
        arr[0]=false;
        arr[1]=false;
        for (int i = 2; i*i <=n ; i++) {
            if(arr[i]){
                for (int j = 2; j <=n/i ; j++) {
                    int u= i*j;
                    arr[u]=false;
                }}
        }
        ArrayList<Integer> ans= new ArrayList<>();
        for (int i = 0; i <n+1 ; i++) {
            if(arr[i]){
                ans.add(i);
            }
        }
        return ans;










    }





}