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.awt.*;
import java.awt.geom.Arc2D;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.List;
import static java.lang.Math.sqrt;


public class Question {

    public static void main(String[] args) {
        new Question(System.in, System.out);

/*        for (int i = 0; i < 10; i++)
            System.out.println("i : " + i + ", (ch) I : " + ((char) i));*/
    }

    static  class Solver {
        int n;

        InputReader in;
        PrintWriter out;



        void solve() throws IOException {
            n = in.nextInt();
            List<Integer> arr = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                arr.add(in.nextInt());
            }
            Collections.sort(arr);
            if(n==1){
                System.out.println("-1");
            }
            else if(n==2){
                int d =   arr.get(1) - arr.get(0);
                if(d%2==0){
                    if(d==0) {
                        System.out.println(1);
                        System.out.println(arr.get(0));
                    }else {
                        System.out.println(3);
                        System.out.print(arr.get(0) - d + " ");
                        System.out.print(arr.get(0) + d / 2 + " ");
                        System.out.print(arr.get(1) + d + " ");
                    }
                }
                else{
                    System.out.println(2);
                    System.out.print(arr.get(0) - d + " ");
                    System.out.print(arr.get(1) + d + " ");
                }

            }
            else {
                boolean flag = true;
                int d1=-1 , d2 = -1,i1=-1,i2=-1,noOfd1=0,noOfd2=0;
                for (int i = 1; i < n ; i++) {
                    int d =   arr.get(i) - arr.get(i-1);
                    if(d1 == -1){
                        d1  = d;
                        i1  = i;
                    }
                    else if(d!=d1 && d2==-1){
                        d2 = d;
                        i2 =i;
                    }
                    else if(d!=d1 && d!=d2){
                        flag = false;
                        break;
                    }
                    if(d==d1)noOfd1++;
                    else if(d==d2)noOfd2++;
                }
                func(arr,d1,d2,noOfd1,noOfd2,i1,i2,flag);
            }
        }
        public  void func(List<Integer> arr,int d1,int d2,int noOfd1,int noOfd2,int i1,int i2,boolean flag){
            if(flag == false){
                System.out.println("0");
            }
            else{
                if(d2==-1){
                    if(d1 == 0){
                        System.out.println(1);
                        System.out.println(arr.get(0));
                    }
                    else{
                        System.out.println(2);
                        System.out.print(arr.get(0)-d1 + " ");
                        System.out.println(arr.get(arr.size()-1)+d1);
                    }
                }
                else{
                    if(noOfd1==1 && noOfd2==1){
                        if(d1%2==0 && d1/2==d2){
                            System.out.println(1);
                            System.out.println(arr.get(i1)-d2);
                        }
                        else if(d2%2==0 && d2/2==d1){
                            System.out.println(1);
                            System.out.println(arr.get(i2)-d1);
                        }
                        else{
                            System.out.println("0");
                        }
                    }
                    else if(noOfd1==1 || noOfd2==1){
                        if(noOfd1==1){
                            if(d1%2==0 && d1/2==d2){
                                System.out.println(1);
                                System.out.println(arr.get(i1)-d2);
                            }
                            else{
                                System.out.println("0");
                            }

                        }
                        else if(noOfd2==1){
                            if(d2%2==0 && d2/2==d1){
                                System.out.println(1);
                                System.out.println(arr.get(i2)-d1);
                            }
                            else{
                                System.out.println("0");
                            }
                        }
                    }
                    else{
                        System.out.println("0");
                    }
                }
            }
        }
        Solver(InputReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        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 nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];

            for (int i = 0; i < arraySize; i++)
                array[i] = nextInt();

            return array;
        }

        public long nextLong() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sign = 1;

            if (c == '-') {
                sign = -1;

                c = read();
            }

            long result = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                result *= 10;
                result += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return result * sign;
        }

        public long[] nextLongArray(int arraySize) {
            long array[] = new long[arraySize];

            for (int i = 0; i < arraySize; i++)
                array[i] = nextLong();

            return array;
        }

        public float nextFloat() {
            float result, div;
            byte c;

            result = 0;
            div = 1;
            c = (byte) read();

            while (c <= ' ')
                c = (byte) read();

            boolean isNegative = (c == '-');

            if (isNegative)
                c = (byte) read();

            do {
                result = result * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');

            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    result += (c - '0') / (div *= 10);

            if (isNegative)
                return -result;

            return result;
        }

        public double nextDouble() {
            double ret = 0, div = 1;
            byte c = (byte) read();

            while (c <= ' ')
                c = (byte) read();

            boolean neg = (c == '-');

            if (neg)
                c = (byte) read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');

            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);

            if (neg)
                return -ret;

            return ret;
        }

        public String next() {
            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) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String nextLine() {
            int c = read();

            StringBuilder result = new StringBuilder();

            do {
                result.appendCodePoint(c);

                c = read();
            } while (!isNewLine(c));

            return result.toString();
        }

        public boolean isNewLine(int c) {
            return c == '\n';
        }

        public void close() {
            try {
                stream.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

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

    }

    Question(InputStream inputStream, OutputStream outputStream) {
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver(in, out);

        try {
            solver.solve();
        } catch (IOException e) {
            e.printStackTrace();
        }
        in.close();
        out.flush();
        out.close();
    }

}