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.*;
/*
 * 	Heart beats fast
 * 		Colors and promises
 * 			How to be brave
 * 				How can I love when I am afraid to fall...
 */
public class Main 
{
	public static void main(String[] args) throws IOException
	{
		int n=ni();
		int a[]=nia(n);
		Arrays.sort(a);
		if(n==1)
			pr(-1);
		else if(n==2)
		{
			if(a[0]!=a[1])
			{
				if((a[1]+a[0])%2==0)
				{	
					pr(3);
					pr(2*a[0]-a[1]+" "+(a[0]+a[1])/2+" "+(2*a[1]-a[0]));
				}
				else
				{
					pr(2);
					pr((2*a[0]-a[1])+" "+(2*a[1]-a[0]));
				}
			}
			else
				pr("1\n"+a[0]);
		}
		else 
		{
			int d=a[1]-a[0];
			int mis=0;
			for(int i=2; i<n; i++)
				if(d!=a[i]-a[i-1])
					mis++;
			if(mis==n-2)
			{
				d=a[2]-a[1];
				mis=0;
				for(int i=1; i<n; i++)
					if(d!=a[i]-a[i-1])
						mis++;
			}
			if(d==0&&mis==0)
				pr("1\n"+a[0]);
			else if(n==3&&mis==1)
			{
				if(2*(a[1]-a[0])==a[2]-a[1])
				{
					pr(1);
					pr(2*a[1]-a[0]);
				}
				else if((a[1]-a[0])==2*(a[2]-a[1]))
				{
					pr(1);
					pr(a[0]+a[2]-a[1]);	
				}
				else
					pr(0);
			}
			else if(mis>1)
			{
				pr(0);
			}
			else if(mis==1)
			{
				for(int i=1; i<n; i++)
				{
					if(d!=a[i]-a[i-1])
					{
						if(2*d==a[i]-a[i-1])
							pr(1+"\n"+(a[i]+a[i-1])/2);
						else
							pr(0);
					}
				}
			}
			else
			{
				pr(2);
				pr(2*a[0]-a[1]+" "+(a[n-1]+a[1]-a[0]));
			}
		}
		System.out.println(ans);
	}
	static final int mod=1000000007;
	static final double eps=1e-8;
	static final long inf=100000000000000000L;
	static final boolean debug=true;
	static Reader in=new Reader();
	static StringBuilder ans=new StringBuilder();
	static long powm(long a, long b, long m)
	{
		long an=1;
		long c=a;
		while(b>0)
		{
			if(b%2==1)
				an=(an*c)%m;
			c=(c*c)%m;
			b>>=1;
		}
		return an;
	}
	static Random rn=new Random();
	static void pd(){if(debug)ans.append("hola");}
	static void pd(Object a){if(debug)ans.append(a+"\n");}
	static void pr(Object a){ans.append(a+"\n");}
	static void pr(){ans.append("\n");}
	static void p(Object a){ans.append(a);}
	static void sop(Object a){System.out.println(a);}
	static int ni(){return in.nextInt();}
	static int[] nia(int n){int a[]=new int[n];for(int i=0; i<n; i++)a[i]=ni();return a;}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static long nl(){return in.nextLong();}
	static String ns(){return in.next();}
	static double nd(){return in.nextDouble();}
	static String pr(String a, long b)
	{
		String c="";
		while(b>0)
		{
			if(b%2==1)
				c=c.concat(a);
			a=a.concat(a);
			b>>=1;
		}
		return c;
	}
	static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }
        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 int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
        	return Long.parseLong(next());
        }
        public double nextDouble() {
        	return Double.parseDouble(next());
        }
    }
	static class dyns 
	{
		dyns(long le,long ri)
		{
			lb=le;
			rb=ri;
		}
		dyns l,r;
		long val,lb,rb;
		void set(long te)
		{
			val++;
			if(lb!=te||rb!=te)
			{
				if((lb+rb)/2>=te)
				{
					if(l==null)
						l=new dyns(lb, (lb+rb)/2);
					l.set(te);
				}
				else
				{
					if(r==null)
						r=new dyns(((lb+rb)/2)+1,rb);
					r.set(te);
				}
			}
		}
		void reset(long a)
		{
			val--;
			if(val==0)
			{
				l=null;
				r=null;
				return;
			}
			if(lb!=a||rb!=a)
			{
				if((lb+rb)/2>=a)
					l.reset(a);
				else
					r.reset(a);
			}
		}
		long count(long le, long ri)
		{
			if(le<=lb&&ri>=rb)
				return val;
			if(le>rb)
				return 0;
			if(ri<lb)
				return 0;
			int a=0;
			if(l!=null)
				a+=l.count(le,ri);
			if(r!=null)
				a+=r.count(le,ri);
			return a;
		}
	}
}