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.math.*;

public class Practice 

{ 
	   static FastReader sc=new FastReader(); 
	   
		  public static void main(String[] args)
    {
			   int ttt =1;
			    	 //ttt=i();

	    	   PrintWriter out = new PrintWriter(System.out);
	    	   StringBuffer sb=new StringBuffer("");

		       outer: while (ttt-- > 0) 
				{
		    	   int n=i();
		    	   int A[]=input(n);
		    	   if(n==1) {
		    		   System.out.println("-1");
		    		   continue;
		    	   }
		    	   HashSet<Integer> set=new HashSet<Integer>();
		    	   for(int i : A)
		    		   set.add(i);
		    	   if(set.size()==1) {
		    		   System.out.println("1");
		    		   System.out.println(A[0]);
		    		   continue;
		    	   }
		    	   sort(A);
		    	   int d=A[1]-A[0];
		    	   boolean a=false;
		    	   for(int i=0;i<n-1;i++) {
		    		   if(A[i+1]-A[i]!=d) {
		    			   a=true;
		    			   break;
		    		   }
		    	   }
		    	   if(!a) {
		    		   if(n==2) {
		    			   if((A[0]+A[1])%2==0) {
		    				   System.out.println("3");
		    				   ArrayList<Integer> pp=new ArrayList<Integer>();
		    				   pp.add(A[0]-d);
		    				   pp.add(A[n-1]+d);
		    				   pp.add((A[0]+A[1])/2);
		    				   pp.sort(null);
		    				   System.out.println(pp.get(0)+" "+pp.get(1)+" "+pp.get(2));
		    				   continue;
		    			   }
		    		   }
		    		   System.out.println("2");
		    		   System.out.println((A[0]-d)+" "+(A[n-1]+d));
		    		   continue;
		    	   }
		    	  
		    	   HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
		    	   for(int i=0;i<n-1;i++) {
		    		  int diff=A[i+1]-A[i];
		    		  if(map.containsKey(diff))
		    			  map.put(diff, map.get(diff)+1);
		    		  else
		    			  map.put(diff, 1);
		    	   }
		    	   a=true;
		    	   if(map.size()>2) {
		    		   System.out.println("0");
		    		   continue;
		    	   }
		    	   ArrayList<Integer> l=new ArrayList<Integer>();
		    	   ArrayList<Integer> o=new ArrayList<Integer>();
		    	   for(int key : map.keySet()) {
		    		   l.add(key);
		    		   o.add(map.get(key));
		    	   }
		    	   if(o.get(0)>1 && o.get(1)>1) {
		    		   System.out.println("0");
		    		   continue;
		    	   }
		    	   //System.out.println(o.get(0)+" "+o.get(1));
		    	   if(o.get(0)==1 && o.get(1)!=1) {
		    		   for(int i=0;i<n-1;i++) {
		    			   int df=A[i+1]-A[i];
		    			   if(df==l.get(0)) {
		    			   int y=A[i+1]-l.get(1);
		    			   int u=A[i]+l.get(1);
		    			   if(y==u) {
		    				   System.out.println("1");

		    				   System.out.println(y);
		    				   continue outer;
		    			   }
		    		   }
		    		   }
		    		   System.out.println("0");
		    	   }
		    	   else if(o.get(0)!=1 && o.get(1)==1) {
		    		   for(int i=0;i<n-1;i++) {
		    			   int df=A[i+1]-A[i];
		    			   if(df==l.get(1)) {
		    			   int y=A[i+1]-l.get(0);
		    			   int u=A[i]+l.get(0);
		    			   if(y==u) {
		    				   System.out.println("1");

		    				   System.out.println(y);
		    				   continue outer;
		    			   }
		    		   }
		    		   }
		    		   System.out.println("0");   
		    	   }
		    	   else if(o.get(0)==1 && o.get(1)==1) {
		    		   for(int i=0;i<n-1;i++) {
		    			   int df=A[i+1]-A[i];
		    			   if(df==l.get(0)) {
		    			   int y=A[i+1]-l.get(1);
		    			   int u=A[i]+l.get(1);
		    			   if(y==u) {
		    				   System.out.println("1");

		    				   System.out.println(y);
		    				   continue outer;
		    			   }
		    		   }
		    	   }
		    		   for(int i=0;i<n-1;i++) {
		    			   int df=A[i+1]-A[i];
		    			   if(df==l.get(1)) {
		    			   int y=A[i+1]-l.get(0);
		    			   int u=A[i]+l.get(0);
		    			   if(y==u) {
		    				   System.out.println("1");

		    				   System.out.println(y);
		    				   continue outer;
		    			   }
		    		   }
		    		   }
		    		   System.out.println("0");
		    	   }
		    	   
		    	   
		    	   
		    	   
				}
			   
    }
static int[] input(int n) {
	int A[]=new int[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextInt();
	   }
	   return A;
   }
static long[] inputL(int n) {
	long A[]=new long[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextLong();
	   }
	   return A;
   }
static String[] inputS(int n) {
	String A[]=new String[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.next();
	   }
	   return A;
   }


static void input(int A[],int B[]) {
	   for(int i=0;i<A.length;i++) {
		   A[i]=sc.nextInt();
		   B[i]=sc.nextInt();
	   }
}
static int[][] input(int n,int m){
	int A[][]=new int[n][m];
	for(int i=0;i<n;i++) {
		for(int j=0;j<m;j++) {
			A[i][j]=i();
		}
	}
	return A;
}
static int max(int A[]) {
	int max=Integer.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static int min(int A[]) {
	int min=Integer.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long max(long A[]) {
	long max=Long.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static long min(long A[]) {
	long min=Long.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long mod(long x) {
	 int mod=1000000007;
	  return ((x%mod + mod)%mod);
}

     static int i() {
    	 return sc.nextInt();
     }
     static String s() {
    	 return sc.next();
     }
     static long l() {
    	 return sc.nextLong();
     }  
     static void sort(int[] A){
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
     }
     static void sort(long[] A){
	        int n = A.length;
	        Random rnd = new Random();
	        for(int i=0; i<n; ++i){
	            long tmp = A[i];
	            int randomPos = i + rnd.nextInt(n-i);
	            A[i] = A[randomPos];
	            A[randomPos] = tmp;
	        }
	        Arrays.sort(A);
	     }
  static String sort(String s) {
 	 Character ch[]=new Character[s.length()];
 	 for(int i=0;i<s.length();i++) {
 		 ch[i]=s.charAt(i);
 	 }
 	 Arrays.sort(ch);
 	 StringBuffer st=new StringBuffer("");
 	 for(int i=0;i<s.length();i++) {
 		 st.append(ch[i]);
 	 }
 	 return st.toString();
  }
     static boolean prime(int n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static boolean prime(long n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static int gcd(int a, int b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static long gcd(long a, long b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static class Pair implements Comparable<Pair>
     {
    	 int x;
    	 int y;
    	 Pair(int x,int y){
    		 this.x=x;
    		 this.y=y;
    	 }
		@Override
		public int compareTo(Pair o) {
			if(this.x>o.x) {
				return 1;
			}
			else if(this.x<o.x) {
				return -1;
			}
			else {
				if(this.y>o.y) {
					return 1;
				}
				else if(this.y<o.y) {
					return -1;
				}
			}
			return 0;
		}
     }
        
        
    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; 
        } 
    } 
} 
