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.BufferedReader;
import java.lang.*;
import java.math.BigInteger;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
 
public class Practice{
	
	
	 static class FastReader {
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public FastReader()
	        {
	            br = new BufferedReader(
	                new InputStreamReader(System.in));
	        }
	 
	        String next()
	        {
	            while (st == null || !st.hasMoreElements()) {
	                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());
	        }
	 
	        String nextLine()
	        {
	            String str = "";
	            try {
	                str = br.readLine();
	            }
	            catch (IOException e) {
	                e.printStackTrace();
	            }
	            return str;
	        }
	    }
	 
	 
	 static int  gcd(int a, int b) {


	    if (b == 0) {
	        return a;}
	    else {
	        return gcd(b, a % b);}}
	 
	 //for prime no
	  static boolean isPrime(int n) {
	        return BigInteger.valueOf(n).isProbablePrime(1);
	    }
	 
	    static boolean isPrime(long n) {
	        return BigInteger.valueOf(n).isProbablePrime(1);
	    }

	 static boolean[] seiveOfEratoSthenes(int n) {
		 boolean isPrime[]=new boolean[n+1];
		 Arrays.fill(isPrime, true);
		 isPrime[0]=false;
		 isPrime[1]=false;
		 for(int i=2;i<=Math.sqrt(n);i++) {
			 for(int j=2*i;j<=n;j+=i) {
				 isPrime[j]=false;
			 }
		 }
		 
		 return isPrime;
		 
	 }
	 
	 static long modulo(long a,long b,int n) {
		 long res=1;
		 
		 while(b>0) {
			 if((b&1)==1) {
				 res=(res*(a%n))%n;
			 }
			 a=((a%n)*(a%n))%n;
			 b=b>>1;
			 
		 }
		 return res;
	 }
	 
	 static class Pair  implements Comparable<Pair>{
		 int index;
		
		 int time;
		 
		 Pair(int time,int index){  
			 this.index=index;
			  
			 this.time=time;  
			 }  
		 public int compareTo(Pair st){  
			 if(time==st.time)  
			 return index-st.index;  
			 else if(time>st.time)  
			 return 1;  
			 else  
			 return -1;  
			 }  
	 } 
	 
	 static boolean isPalindrome(String s) {
	        int length = s.length();
	        for (int i = 0; i < length / 2; i++) {
	            if (s.charAt(i) != s.charAt(length - 1 - i)) {
	                return false;
	            }
	        }
	        return true;
	    }
	 
	 	static void reverseArray(int[] arr) {
	        for (int i = 0; i < arr.length / 2; i++) {
	            int temp = arr[i];
	            arr[i] = arr[arr.length - 1 - i];
	            arr[arr.length - 1 - i] = temp;
	        }
	    }
	 
	    static void reverseArray(String[] arr) {
	        for (int i = 0; i < arr.length / 2; i++) {
	            String temp = arr[i];
	            arr[i] = arr[arr.length - 1 - i];
	            arr[arr.length - 1 - i] = temp;
	        }
	    }
	 
	    static void reverseArray(char[] arr) {
	        for (int i = 0; i < arr.length / 2; i++) {
	            char temp = arr[i];
	            arr[i] = arr[arr.length - 1 - i];
	            arr[arr.length - 1 - i] = temp;
	        }
	    }

	    public static void main(String[] args)
	    {
	        FastReader sc = new FastReader();
	   
	        int n=sc.nextInt();
	       int arr[]=new int[n];
	       HashSet<Integer>set=new HashSet<>();
	        
	        for(int i=0;i<n;i++)
	        {
	        	arr[i]=sc.nextInt();
	        	
	        }	
	        if(n==1) {
	        	System.out.println(-1);
	        	return;
	        }
	        Arrays.sort(arr);
	        for(int i=1;i<n;i++)
	        {
	        	set.add(arr[i]-arr[i-1]);
	        	
	        }	
	        
	        
	        if(n==2) {
	        	
	        	int diff=arr[1]-arr[0];
	        	if(diff==0) {System.out.println(1);System.out.println(arr[0]);
	        	return;}
	        	if((diff&1)==0) {
	        	System.out.println(3);
	        	
	        	int ele=(arr[1]+arr[0])/2;
	        	arr[1]=arr[1]+diff;
	        	arr[0]=arr[0]-diff;
	        	System.out.println(arr[0]+" "+ele+" "+arr[1]);}
	        	else{
	        		System.out.println(2);
		        	
		        	arr[1]=arr[1]+diff;
		        	arr[0]=arr[0]-diff;
		        	System.out.println(arr[0]+" "+arr[1]);
	        	}
	        	return;
	        }
	        if(set.size()==1) {
	        	int diff=arr[1]-arr[0];
	        	if(diff==0) {
	        		System.out.println(1);System.out.println(arr[0]);
	        	return;}
	        	int el1=arr[0]-diff;
	        	int el2=arr[arr.length-1]+diff;
	        	System.out.println(2);
	        	System.out.println(el1+" "+el2);
	        }
	        else if(set.size()==2) {
	        	int err[]=new int[2];
	        	int i=0;
	        	for(int a:set) {
	        		err[i]=a;
	        		i++;
	        	}
	        	
	        	i=Math.min(err[0], err[1]);
	        	err[0]=Math.max(err[0], err[1]);
	        	if(i*2==err[0]) {
	        		boolean come=false;
	        		
	        		for(int j=1;j<n;j++) {
	        			if(arr[j]-arr[j-1]==i) {
	        				continue;
	        			}
	        			if(!come) {
	        				err[0]=arr[j-1]+i;
	        				come=true;
	        				continue;
	        				
	        			}
	        			if(come) {
	        				come=false;
	        				break;
	        			}
	        		}
	        		
	        		if(!come) {System.out.println(0);}
	        		else {System.out.println(1);
	        		System.out.println(err[0]);}
	        		
	        		
	        		
	        		
	        	}
	        	else {System.out.println(0);}
	        	
	        }
	        else {System.out.println(0);}
	    	
	        
	        		
	       }
	    
	
	 	static int binary(int start,int end,int arr[],int v ) {
	 		int Q=0;
	 	    if (end <= start) 
	 	        { Q=(v >= arr[start])?  start : (start-1); }
	 	    else{
	 	  
	 	    int mid = (start + end)/2; 
	 	  
	 	    if(v == arr[mid]) 
	 	       return mid; 
	 	  
	 	    if(v >arr[mid]) {
	 	        Q= binary( mid+1, end,arr, v); }
	 	    else if(v <arr[mid]){
	 	    Q= binary( start, mid-1,arr, v); }}
	 	    return Q;
	 	}
	        	 

	    }


	    
	     