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
/*
 * Code Author: Jayesh Udhani
 * Institute  : DA-IICT 
 * 3rd year BTech ICT Student
 */

import java.io.*;
import java.util.*;
public class CF224C
{
	private static int[] input_array(InputReader in,int n)	
	{
		int[] a=new int[n];
		for(int i=0;i<n;i++)
			a[i]=in.nextInt();
		return a;
	}
	public static void main(String args[])
	{
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		int n=in.nextInt(),i=0,d;
		int[] a=input_array(in, n);
		if(n==1)
			System.out.println(-1);
		else 
		{
			Arrays.sort(a);
			if(n==2)
			{
				if(a[0]==a[1])
				{
					System.out.println("1\n"+a[0]);
					return ;
				}
				d=a[1]-a[0];
				if((d&1)==0)
				{
					System.out.println(3);
					System.out.println((a[0]-d)+" "+(a[0]+d/2)+" "+(a[1]+d));
				}
				else
				{
					System.out.println(2);
					System.out.println((a[0]-d)+" "+(a[1]+d));
				}
			}
			else
			{
				Map<Integer, Integer> map=new HashMap<>();
				for(i=1;i<n;i++)
				{
					if(map.containsKey(a[i]-a[i-1]))
						map.put(a[i]-a[i-1], map.get(a[i]-a[i-1])+1);
					else
						map.put(a[i]-a[i-1], 1);
				}
				if(map.size()==1)
				{
					d=a[1]-a[0];
					if(a[n-1]+d!=a[0]-d)
					{
						System.out.println(2);
						System.out.println((a[0]-d)+" "+(a[n-1]+d));
					}
					else
						System.out.println("1\n"+(a[n-1]+d));
				}
				else if(map.size()==2)
				{
					int[] b=new int[2];
					int[] c=new int[2];	// count
					i=0;
					for(Integer e:map.keySet())
					{
						b[i]=e;
						c[i]=map.get(e);
						i++;
					}
					if(c[0]==1 && b[0]==2*b[1])
					{
						for(i=1;i<n;i++)
						{
							if(a[i]-a[i-1]==b[0])
							{
								System.out.println("1\n"+(a[i-1]+b[1]));
								break;
							}
						}
					}
					else
					{
						if(c[1]==1 && b[1]==2*b[0])
						{
							for(i=1;i<n;i++)
							{
								if(a[i]-a[i-1]==b[1])
								{
									System.out.println("1\n"+(a[i-1]+b[0]));
									break;
								}
							}
						}
						else
							System.out.println(0);
					}
				}
				else
					System.out.println(0);
			}
		}
		out.close();
	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine(){
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}