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.*;
import java.util.*;

import static java.lang.Math.*;

/**
 * @author master_j
 * @version 0.4
 * @since May 3, 2014
 */
public class Main {
    private void solve() throws IOException {
        long n = io.nI();
        long min = Integer.MAX_VALUE, max = Integer.MIN_VALUE, minNum = 0, maxNum = 0;
        for(int i = 0; i < n;  i++){
            int t = io.nI();

            if(t < min){
                minNum = 0;
                min = t;
            }
            if(t == min)
                minNum++;

            if(max < t){
                maxNum = 0;
                max = t;
            }
            if(t == max)
                maxNum++;
        }

        if(min < max)
            io.wf("%d %d\n", max - min, maxNum * minNum);
        else
            io.wf("%d %d\n", max - min, minNum * (minNum - 1) / 2);
    }//2.2250738585072012e-308

    public static void main(String[] args) throws IOException {
        IO.launchSolution(args);
    }

    Main(IO io) throws IOException {
        this.io = io;
        solve();
    }

    private final IO io;
}

class IO {
    static final String _localArg = "master_j";
    private static final String _problemName = "";
    private static final IO.Mode _inMode = Mode.STD_;
    private static final IO.Mode _outMode = Mode.STD_;
    private static final boolean _autoFlush = false;

    static enum Mode {STD_, _PUT_TXT, PROBNAME_}

    private final StreamTokenizer st;
    private final BufferedReader br;
    private final Reader reader;

    private final PrintWriter pw;
    private final Writer writer;

    static void launchSolution(String[] args) throws IOException {
        boolean local = (args.length == 1 && args[0].equals(IO._localArg));
        IO io = new IO(local);

        long nanoTime = 0;
        if (local) {
            nanoTime -= System.nanoTime();
            io.wln("<output>");
        }

        io.flush();
        new Main(io);
        io.flush();

        if(local){
            io.wln("</output>");
            nanoTime += System.nanoTime();
            final long D9 = 1000000000, D6 = 1000000, D3 = 1000;
            if(nanoTime >= D9)
                io.wf("%d.%d seconds\n", nanoTime/D9, nanoTime%D9);
            else if(nanoTime >= D6)
                io.wf("%d.%d millis\n", nanoTime/D6, nanoTime%D6);
            else if(nanoTime >= D3)
                io.wf("%d.%d micros\n", nanoTime/D3, nanoTime%D3);
            else
                io.wf("%d nanos\n", nanoTime);
        }

        io.close();
    }

    IO(boolean local) throws IOException {
        if(_inMode == Mode.PROBNAME_ || _outMode == Mode.PROBNAME_)
            if(_problemName.length() == 0)
                throw new IllegalStateException("You imbecile. Where's my <_problemName>?");

        if(_problemName.length() > 0)
            if(_inMode != Mode.PROBNAME_ && _outMode != Mode.PROBNAME_)
                throw new IllegalStateException("You imbecile. What's the <_problemName> for?");

        Locale.setDefault(Locale.US);

        if (local) {
            reader = new FileReader("input.txt");
            writer = new OutputStreamWriter(System.out);
        } else {
            switch (_inMode) {
                case STD_:
                    reader = new InputStreamReader(System.in);
                    break;
                case PROBNAME_:
                    reader = new FileReader(_problemName + ".in");
                    break;
                case _PUT_TXT:
                    reader = new FileReader("input.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _inMode.");
            }
            switch (_outMode) {
                case STD_:
                    writer = new OutputStreamWriter(System.out);
                    break;
                case PROBNAME_:
                    writer = new FileWriter(_problemName + ".out");
                    break;
                case _PUT_TXT:
                    writer = new FileWriter("output.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _outMode.");
            }
        }

        br = new BufferedReader(reader);
        st = new StreamTokenizer(br);

        pw = new PrintWriter(writer, _autoFlush);

        if(local && _autoFlush)
            wln("Note: auto-flush is on.");
    }

    void wln()          {pw.println(); }
    void wln(boolean x) {pw.println(x);}
    void wln(char x)    {pw.println(x);}
    void wln(char x[])  {pw.println(x);}
    void wln(double x)  {pw.println(x);}
    void wln(float x)   {pw.println(x);}
    void wln(int x)     {pw.println(x);}
    void wln(long x)    {pw.println(x);}
    void wln(Object x)  {pw.println(x);}
    void wln(String x)  {pw.println(x);}

    void wf(String f, Object...o){pw.printf(f, o);}

    void w(boolean x)   {pw.print(x);}
    void w(char x)      {pw.print(x);}
    void w(char x[])    {pw.print(x);}
    void w(double x)    {pw.print(x);}
    void w(float x)     {pw.print(x);}
    void w(int x)       {pw.print(x);}
    void w(long x)      {pw.print(x);}
    void w(Object x)    {pw.print(x);}
    void w(String x)    {pw.print(x);}

    int nI() throws IOException    {st.nextToken(); return (int)st.nval;}
    double nD() throws IOException {st.nextToken(); return st.nval;}
    float nF() throws IOException  {st.nextToken(); return (float)st.nval;}
    long nL() throws IOException   {st.nextToken(); return (long)st.nval;}
    String nS() throws IOException {st.nextToken(); return st.sval;}

    void wc(String x){ wc(x.toCharArray()); }
    void wc(char c1, char c2){for(char c = c1; c<=c2; c++)wc(c);}
    void wc(char x[]){
        for(char c : x)
            wc(c);
    }
    void wc(char x){st.ordinaryChar(x); st.wordChars(x, x);}

    public boolean eof() {return st.ttype == StreamTokenizer.TT_EOF;}
    public boolean eol() {return st.ttype == StreamTokenizer.TT_EOL;}

    void flush(){pw.flush();}
    void close() throws IOException{reader.close(); br.close(); flush(); pw.close();}
}