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.util.*;
import java.util.Map.*;
import java.awt.Point;
import java.io.*;
import java.math.BigInteger;

public class C1 
{
    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException 
    {
        int n     = in.nextInt();
        int mas[] = in.nextIntArray(n);
        
        if(n == 1)
            out.print(-1);
        else
        {
            Arrays.sort(mas);
            
            TreeMap<Integer, Integer> hm = new TreeMap<Integer, Integer>();
            
            for(int i = 1; i < mas.length; i++)
            {
                Integer dif = mas[i] - mas[i - 1];          
                
                Integer val = hm.get(dif);
                
                if(val == null)
                {
                    val = 0;
                }
                
                val++;
                
                hm.put(dif, val);
            }
            
            if(hm.size() > 2)
                out.print(0);
            else if(hm.size() == 1)
            {
                TreeSet<Integer> ts = new TreeSet<Integer>();
                
                if(hm.firstKey() % 2 == 0 && n == 2)
                    ts.add(mas[0] + hm.firstKey() / 2);
                
                ts.add(mas[0] - hm.firstKey());
                ts.add(mas[n - 1] + hm.firstKey());
                
                
                out.println(ts.size());
                for(Integer i : ts)
                {
                    out.print(i);
                    out.print(" ");
                }
            }
            else
            {
                int first = hm.firstKey();
                
                if(first == 0)
                    out.print(0);
                else
                {
                    Entry<Integer, Integer> entry = hm.lastEntry();
                    
                            
                    if(entry.getKey() % first == 0 && entry.getValue() == 1 && entry.getKey() / 2 == first)
                    {
                        for(int i = 1; i < mas.length; i++)
                        {
                            int dif = mas[i] - mas[i - 1];
                            
                            if(dif == entry.getKey())
                            {
                                out.println(1);
                                out.println(mas[i] - dif / 2);
                                break;
                                
                            }
                        }
                    }
                    else
                    {
                        out.print(0);
                    }
                }
            }
        }
            
        
        
    }

    public void run() {
        try {
            //in  = new FastScanner(new File("sum.in"));
            //out = new PrintWriter(new File("sum.out"));
            
            in  = new FastScanner();
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        FastScanner() {
            
            br = new BufferedReader(new InputStreamReader(System.in));
        
        }

        FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() 
        {
            return Integer.parseInt(next());
        }
        
        long nextLong() 
        {
            return Long.parseLong(next());
        }
        
        double nextDouble() 
        {
            return Double.parseDouble(next());
        }
        
        int[] nextIntArray(int size) 
        {
            int[] array = new int[size];
            
            for (int i = 0; i < size; i++){
                array[i] = nextInt();
            }
            
            return array;
        }
        
        long[] nextLongArray(int size) 
        {
            long[] array = new long[size];
            
            for (int i = 0; i < size; i++){
                array[i] = nextLong();
            }
            
            return array;
        }
        
        BigInteger nextBigInteger() 
        {
            return new BigInteger(next());
        }
        
        Point nextIntPoint()
        {
            int x = nextInt();
            int y = nextInt();
            return new Point(x, y);
        }
        
        Point[] nextIntPointArray(int size)
        {
            Point[] array = new Point[size];
            
            for (int index = 0; index < size; ++index){
                array[index] = nextIntPoint();
            }
            
            return array;
        }
        
        List<Integer>[] readGraph(int vertexNumber, int edgeNumber, boolean undirected)
        {
            List<Integer>[] graph = new List[vertexNumber];
                    
            for (int index = 0; index < vertexNumber; ++index)
            {
                graph[index] = new ArrayList<Integer>();
            }
                    
            while (edgeNumber-- > 0)
            {
                int from = nextInt() - 1;
                int to   = nextInt() - 1;
                        
                graph[from].add(to);
                if(undirected)
                    graph[to].add(from);
            }
                    
            return graph;
        }
    }

    public static void main(String[] arg) 
    {
        new C1().run();
    }
}