Pashmak decided to give Parmida a pair of flowers from the garden. There are n flowers in the garden and the i-th of them has a beauty number bi. Parmida is a very strange girl so she doesn't want to have the two most beautiful flowers necessarily. She wants to have those pairs of flowers that their beauty difference is maximal possible!

Your task is to write a program which calculates two things:

  1. The maximum beauty difference of flowers that Pashmak can give to Parmida. 
  2. The number of ways that Pashmak can pick the flowers. Two ways are considered different if and only if there is at least one flower that is chosen in the first way and not chosen in the second way. 

Input

The first line of the input contains n (2 ≤ n ≤ 2·105). In the next line there are n space-separated integers b1, b2, ..., bn (1 ≤ bi ≤ 109).

Output

The only line of output should contain two integers. The maximum beauty difference and the number of ways this may happen, respectively.

Examples

Input

2
1 2


Output

1 1

Input

3
1 4 5


Output

4 1

Input

5
3 1 2 3 1


Output

2 4

Note

In the third sample the maximum beauty difference is 2 and there are 4 ways to do this:

  1. choosing the first and the second flowers; 
  2. choosing the first and the fifth flowers; 
  3. choosing the fourth and the second flowers; 
  4. choosing the fourth and the fifth flowers. 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;

import java.lang.management.MemoryType;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.function.Function;


public class Main {
    static final int INF = Integer.MAX_VALUE;

    static int mergeSort(int[] a,int [] c, int begin, int end)
    {
        int inversion=0;
        if(begin < end)
        {
            inversion=0;
            int mid = (begin + end) >>1;
            inversion+= mergeSort(a,c, begin, mid);
            inversion+=mergeSort(a, c,mid + 1, end);
            inversion+=merge(a,c, begin, mid, end);
        }
        return inversion;
    }


    static int  merge(int[] a,int[]c, int b, int mid, int e)
    {
        int n1 = mid - b + 1;
        int n2 = e - mid;
        int[] L = new int[n1+1], R = new int[n2+1];
        int[] L1 = new int[n1+1], R1 = new int[n2+1];


        //inversion
        int inversion=0;

        for(int i = 0; i < n1; i++) {
            L[i] = a[b + i];
            L1[i] = c[b + i];
            //  L2[i] = w[b + i];
        }
        for(int i = 0; i < n2; i++)  {
            R[i] = a[mid + 1 + i];
            R1[i] = c[mid + 1 + i];
            //R2[i] = w[mid + 1 + i];
        }
        L[n1] = R[n2] = INF;

        for(int k = b, i = 0, j = 0; k <= e; k++)
            if(L[i] <= R[j]){
                a[k] = L[i];
                c[k] = L1[i];
                ++i;
                //  w[k]=L2[i++];
            }

            else
            {
                a[k] = R[j];
                c[k] = R1[j];
                //w[k] = R2[j++];
                ++j;

                inversion=inversion+(n1-i);

            }
        return inversion;

    }

    static int []c;

    static int[] v;
    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    public class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode(int x) { val = x; }

    }
    int ans;
    void  dfs(TreeNode node,int L,int R){
        if (node !=null&&node.val>=L&&node.val<=R){
            ans+=node.val;
            if (node.val>L&&node.left!=null)dfs(node.left,L,R);
            if (node.val<R&&node.right!=null)dfs(node.right,L,R);
        }
    }

    static int bs(Pair []a,Pair item,int e){
        int r=e,l=0,mid=0,ans=-1;
        while (r>=l){
            mid=(r+l)>>1;
            if (a[mid].first<item.first){
                if (a[mid].second>item.second){
                    return mid;
                }else r=mid-1;
            }else r=mid-1;

        }
        return ans;
    }




    int rangeSumBST(TreeNode root, int L, int R) {
        if (root!=null)dfs(root,L,R);
        return ans;
    }





    public static void main (String[]args) throws IOException {
        Scanner in = new Scanner(System.in);
        try(PrintWriter or = new PrintWriter(System.out)) {
            int n = in.nextInt();
         long [] a= new long[n];
         long min=Integer.MAX_VALUE,max=Integer.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                a[i]=in.nextLong();
                max=Math.max(max,a[i]);
                min=Math.min(min,a[i]);
            }
            or.print((max-min)+" ");
            long cmax=0,cmin=0;
            for (int i = 0; i <n ; i++) {
                if (a[i]==min)++cmin;
                else if (a[i]==max)++cmax;
            }
            or.println(min==max?Math.max(cmin-1,cmax-1)*(Math.max(cmin,cmax))/2:cmax*cmin);

            




        }

    }
    static int getlen(int r,int l,int a){
        return (r-l+1+1)/(a+1);
    }






    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++) {
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec) {
                        f *= 10;
                    }
                }
            }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}

class Pair implements Comparable<Pair> {
    int first, second;

    public Pair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public int compareTo(Pair o) {
        return first - o.first;
    }


}

class Tempo {

    int num;
    int index;

    public Tempo(int num, int index) {
        this.num = num;
        this.index = index;
    }
}