Everybody knows what an arithmetic progression is. Let us remind you just in case that an arithmetic progression is such sequence of numbers a1, a2, ..., an of length n, that the following condition fulfills: 

a2 - a1 = a3 - a2 = a4 - a3 = ... = ai + 1 - ai = ... = an - an - 1.

For example, sequences [1, 5], [10], [5, 4, 3] are arithmetic progressions and sequences [1, 3, 2], [1, 2, 4] are not.

Alexander has n cards containing integers. Arthur wants to give Alexander exactly one more card with a number so that he could use the resulting n + 1 cards to make an arithmetic progression (Alexander has to use all of his cards).

Arthur has already bought a card but he hasn't written a number on it. Help him, print all integers that you can write on a card so that the described condition fulfilled.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of cards. The next line contains the sequence of integers — the numbers on Alexander's cards. The numbers are positive integers, each of them doesn't exceed 108.

Output

If Arthur can write infinitely many distinct integers on the card, print on a single line -1.

Otherwise, print on the first line the number of integers that suit you. In the second line, print the numbers in the increasing order. Note that the numbers in the answer can exceed 108 or even be negative (see test samples).

Examples

Input

3
4 1 7


Output

2
-2 10


Input

1
10


Output

-1


Input

4
1 3 5 9


Output

1
7


Input

4
4 3 4 5


Output

0


Input

2
2 4


Output

3
0 3 6
import java.io.*;
import java.math.*;
import java.util.*;
import java.lang.*;

public class Main2{ 

    public static InputStream inputStream = System.in;
    public static OutputStream outputStream = System.out;
    public static FastReader in = new FastReader(inputStream);
    public static PrintWriter out = new PrintWriter(outputStream);


    public static void main(String[] args)throws java.lang.Exception{
        new Main2().run();
        out.close();
    }
    
    void run()throws java.lang.Exception{
        int n = in.nextInt();
        long[] a = new long[n];
        boolean allSame = true;
        for(int i=0; i<n; i++){
            a[i] = in.nextLong();
            if(i!=0 && a[i]!=a[i-1]){
                allSame = false;
            }
        }
        if(n==1){
            System.out.println(-1);
            System.exit(0);
        }
        Arrays.sort(a);
        if(allSame){
            System.out.println(1);
            System.out.println(a[0]);
            System.exit(0);
        }
        if(n==2){
            if((a[0]+a[1]) %2==0){
                System.out.println(3);
                long d = a[1]-a[0];
                System.out.println((a[0]-d) + 
                        " " + (a[0]+a[1])/2 + " " 
                        + (a[1]+d));
            }else{
                System.out.println(2);
                long d = a[1]-a[0];
                System.out.println((a[0]-d) + " " + (a[1]+d));
            }
        }else{
            long d = a[1]-a[0];
            boolean ap = true;
            for(int i=1; i<n; i++){
                if(a[i]-a[i-1] != d){
                    ap = false;
                    break;
                }
            }
            if(ap){
                System.out.println(2);
                System.out.println((a[0]-d) + " " + (a[n-1]+d));
            }else{
                HashMap<Long, Integer> map = new HashMap<Long, Integer>();
                for(int i=1; i<n; i++){
                    long dif = a[i]-a[i-1];
                    if(map.containsKey(dif)){
                        map.put(dif, map.get(dif)+1);
                    }else{
                        map.put(dif, 1);
                    }
                }
                if(map.size()>=3){
                    System.out.println(0);
                    System.exit(0);
                }else{
                    long x1 = Integer.MAX_VALUE;
                    long x2 = -1;
                    for(Long xx : map.keySet()){
                        if(x1!=Integer.MAX_VALUE){
                            x2 = xx;
                        }else{
                            x1 = xx;
                        }
                    }
//                  System.out.println(x1 + " " + x2 + " are diffs");
                    long hi = Math.max(x1, x2);
                    long lo = Math.min(x1, x2);
                    if(map.get(hi)!=1){
                        System.out.println(0);
                    }else if(hi==lo*2){
                        System.out.println(1);
                        for(int i=1; i<n; i++){
                            long dif = a[i]-a[i-1];
                            if(dif==hi){
                                System.out.println((a[i-1]+dif/2));
                            }
                        }
                    }else{
                        System.out.println(0);
                    }
                }
            }
        }
    }
}

class FastReader{
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastReader(InputStream stream){
        this.stream = stream;
    }

    public int read(){
        if (numChars == -1){
            throw new InputMismatchException ();
        }
        if (curChar >= numChars){
            curChar = 0;
            try{
                numChars = stream.read (buf);
            } catch (IOException e){
                throw new InputMismatchException ();
            }
            if (numChars <= 0){
                return -1;
            }
        }
        return buf[curChar++];
    }

    public int peek(){
        if (numChars == -1){
            return -1;
        }
        if (curChar >= numChars){
            curChar = 0;
            try{
                numChars = stream.read (buf);
            } catch (IOException e){
                return -1;
            }
            if (numChars <= 0){
                return -1;
            }
        }
        return buf[curChar];
    }

    public int nextInt(){
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-'){
            sgn = -1;
            c = read ();
        }
        int res = 0;
        do{
            if(c==','){
                c = read();
            }
            if (c < '0' || c > '9'){
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }

    public long nextLong(){
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-'){
            sgn = -1;
            c = read ();
        }
        long res = 0;
        do{
            if (c < '0' || c > '9'){
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }

    public String nextString(){
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        StringBuilder res = new StringBuilder ();
        do{
            res.appendCodePoint (c);
            c = read ();
        } while (!isSpaceChar (c));
        return res.toString ();
    }

    public boolean isSpaceChar(int c){
        if (filter != null){
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }

    public static boolean isWhitespace(int c){
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0(){
        StringBuilder buf = new StringBuilder ();
        int c = read ();
        while (c != '\n' && c != -1){
            if (c != '\r'){
                buf.appendCodePoint (c);
            }
            c = read ();
        }
        return buf.toString ();
    }

    public String nextLine(){
        String s = readLine0 ();
        while (s.trim ().length () == 0)
            s = readLine0 ();
        return s;
    }

    public String nextLine(boolean ignoreEmptyLines){
        if (ignoreEmptyLines){
            return nextLine ();
        }else{
            return readLine0 ();
        }
    }

    public BigInteger nextBigInteger(){
        try{
            return new BigInteger (nextString ());
        } catch (NumberFormatException e){
            throw new InputMismatchException ();
        }
    }

    public char nextCharacter(){
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        return (char) c;
    }

    public double nextDouble(){
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-'){
            sgn = -1;
            c = read ();
        }
        double res = 0;
        while (!isSpaceChar (c) && c != '.'){
            if (c == 'e' || c == 'E'){
                return res * Math.pow (10, nextInt ());
            }
            if (c < '0' || c > '9'){
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        }
        if (c == '.'){
            c = read ();
            double m = 1;
            while (!isSpaceChar (c)){
                if (c == 'e' || c == 'E'){
                    return res * Math.pow (10, nextInt ());
                }
                if (c < '0' || c > '9'){
                    throw new InputMismatchException ();
                }
                m /= 10;
                res += (c - '0') * m;
                c = read ();
            }
        }
        return res * sgn;
    }

    public boolean isExhausted(){
        int value;
        while (isSpaceChar (value = peek ()) && value != -1)
            read ();
        return value == -1;
    }

    public String next(){
        return nextString ();
    }

    public SpaceCharFilter getFilter(){
        return filter;
    }

    public void setFilter(SpaceCharFilter filter){
        this.filter = filter;
    }

    public interface SpaceCharFilter{
        public boolean isSpaceChar(int ch);
    }
}