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.util.*;
import java.math.*;
public class Main {

    /**
     * @param args
     */
    public static void main(String args[]) throws IOException {
        // TODO Auto-generated method stub
        InputStream inputstream = System.in;
        OutputStream outputstream = System.out;
        InputReader in = new InputReader(inputstream);
        OutputWriter out = new OutputWriter(outputstream);
        mysolver mysol = new mysolver();
        mysol.solve(in, out);
        out.close();

    }

}


class mysolver {
    public void solve(InputReader in,OutputWriter out) throws IOException
    {
            int n = in.readInt();
            int A[] = new int[n];
            for(int i=0;i<n;i++)
            {
                A[i] = in.readInt();
            }
            Arrays.sort(A);
            
            if(n==1)
            {
                System.out.println("-1");
            }
            else if(n==2)
            {
                if(A[0]==A[1])
                {
                    System.out.println("1");
                    System.out.println(A[0]);
                }
                else if((A[1]-A[0])%2==0)
                {
                    System.out.println("3");
                    int v1 = A[0] - (A[1]-A[0]);
                    int v2 = A[0] + (A[1]-A[0])/2;
                    int v3 = A[1] + (A[1]-A[0]);
                    System.out.println(v1+" "+v2+" "+v3);
                }
                else
                {
                    System.out.println("2");
                    int v1 = A[0] - (A[1]-A[0]);
                    int v2 = A[1] + A[1]-A[0];
                    System.out.println(v1+" "+v2);
                }
            }
            else
            {
                
                TreeSet<Integer> ts = new TreeSet();
                
                int check=0;
                for(int i=0;i<n-1;i++)
                {
                    ts.add(A[i+1]-A[i]);
                    if(ts.size()>2)
                    {
                        check=1;
                        break;
                    }
                }
                
                if(check==1)
                {
                    System.out.println("0");
                }
                else
                {
                    if(ts.size()==1)
                    {
                        if(A[0]==A[1])
                        {
                            System.out.println("1");
                            System.out.println(A[0]);
                        }
                        else
                        {
                            System.out.println("2");
                            int v1 = A[0] - (A[1]-A[0]);
                            int v2 = A[n-1] + (A[1]-A[0]);
                            System.out.println(v1+" "+v2);
                        }
                    }
                    else
                    {
                        int diff1 = A[1]-A[0];
                        int diff2 =0;
                        int c1 =1;
                        int c2 =0;
                        for(int i=1;i<n-1;i++)
                        {
                            if(A[i+1]-A[i]==diff1)
                            {
                                c1++;
                            }
                            else
                            {
                                diff2 = A[i+1]-A[i];
                                c2++;
                            }
                        }
                        if(c1>1 && c2>1)
                        {
                            System.out.println("0");
                        }
                        else if(c1==1 && c2==1)
                        {
                            if(diff1==2*diff2)
                            {
                                int v1 = A[0] + (A[1]-A[0])/2;
                                System.out.println("1");
                                System.out.println(v1);
                            }
                            else if(diff2==2*diff1)
                            {
                                int v1 = A[1] + (A[1]-A[0]);
                                System.out.println("1");
                                System.out.println(v1);
                            }
                            else
                            {
                                System.out.println("0");
                            }
                        }
                        else if(c1==1)
                        {
                            if(diff1==2*diff2)
                            {
                                int v1 = A[0] + diff2;
                                System.out.println("1");
                                System.out.println(v1);
                            }
                            else
                            {
                                System.out.println("0");
                            }
                        }
                        else
                        {
                           // System.out.println(":::");
                            if(diff2==2*diff1)
                            {
                                int j=0;
                                for(j=0;j<n-1;j++)
                                {
                                    if(A[j+1]-A[j]==diff2)
                                    {
                                        break;
                                    }
                                }
                                int v1 = A[j] + (A[j+1]-A[j])/2;
                                System.out.println("1");
                                System.out.println(v1);
                            }
                            else
                            {
                                System.out.println("0");
                            }
                        }
                    }
                }
            }
        }
}
class InputReader {
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private InputReader.SpaceCharFilter filter;
 
    public InputReader(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 readInt() {
        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 - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public String readString() {
        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;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}
 
class OutputWriter {
    private final PrintWriter writer;
 
    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }
 
    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }
 
    public void close() {
        writer.close();
    }
 
    public void printLine(int i) {
        writer.println(i);
    }
}
 
class IOUtils {
 
    public static void readIntArrays(InputReader in, int[]... arrays) {
        for (int i = 0; i < arrays[0].length; i++) {
            for (int j = 0; j < arrays.length; j++)
                arrays[j][i] = in.readInt();
        }
    }
 
    }