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.io.*;
import java.lang.*;
import java.math.*;


public class cf3 implements Runnable {
	
	long gcd(long a,long b)
    {
    	if(a==0)
    		return b;
    	else
    		return gcd(b%a,a);
    }
	

	 long power(long x, long y, long p)
	    {
	       
	        long res = 1;     
	   
	        x=x % p; 
	     
	        while (y > 0)
	        {
	            
	            if((y & 1)==1)
	                res = ((res%p) * (x%p))% p;
	     
	            y =y >> 1; 
	            x =((x%p)*(x%p))%p; 
	        }
	        return res;
	    }
	 
	
		public void run(){
		
		
		
		InputReader in =  new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		int n=in.nextInt();
		int[] a=new int[n];
		
		for(int i=0;i<n;i++)
		{
			a[i]=in.nextInt();
		}
		
		if(n==1)
			w.println(-1);
		else
		{
			Arrays.sort(a);
			TreeSet<Integer> al=new TreeSet<>();
			
			int d=a[1]-a[0];
			
			if(n==2)
			{
				al.add(a[0]-d);
				al.add(a[1]+d);
				
				if(d%2==0)
					al.add(a[0]+(d/2));
				
				w.println(al.size());
				ArrayList<Integer> aa=new ArrayList<>(al);
				for(int s:al)
					w.print(s+" ");
			}
			else
			{
				TreeSet<Integer> ts=new TreeSet<>();
				d=a[1]-a[0];
				ts.add(d);
				
				for(int i=1;i<n-1;i++)
				{
					int d1=a[i+1]-a[i];
					ts.add(d1);
					
				}
				
				if(ts.size()==1)
				{
					al.add(a[0]-d);
					al.add(a[n-1]+d);
					
					w.println(al.size());
					ArrayList<Integer> aa=new ArrayList<>(al);
					for(int s:al)
						w.print(s+" ");
				}
				else if(ts.size()==2)
				{
					//w.println("ho");
					int rd=ts.first(); int cnt=0;
					//w.println("rd "+rd);
					int f=1;
					for(int i=0;i<n-1;i++)
					{
						int d1=a[i+1]-a[i];
						if(d1!=rd && cnt==0)
						{
							int d2=a[i+1]-(a[i]+rd);
							cnt++;
							//w.println("d2 "+d2);
							if(d2==rd)
							{
								al.add(a[i]+rd);
								//w.println("yes here");
							}
							else
							{
								f=0;
								//w.println("oh no");
								break;
							}
						}
						else if(d1!=rd && cnt>0)
						{
							f=0;
							break;
						}
					}
					
					if(f==0)
						w.println(0);
					else
					{
						w.println(al.size());
						ArrayList<Integer> aa=new ArrayList<>(al);
						for(int s:al)
							w.print(s+" ");
					}
				}
				else
					w.println(0);
			}
		}
		w.close();	
		
	}
	
	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private 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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		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 - '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 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 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 c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new cf3(),"cf3",1<<26).start();
	}
 }   