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.math.*;
import java.util.*;

//Codeforces
public class MainCodeforces1 {
	private static MyScanner in;
	private static PrintStream out;
	private static boolean LOCAL_TEST = false;

	private static void solve() throws IOException
	{
		int n = in.nextInt();
		int[] x = new int[n];
		for (int i = 0; i < x.length; i++) {
			x[i] = in.nextInt();
		}
		int ans;
		ArrayList<Integer> ansList = new ArrayList<Integer>();
		if (n == 1) {
			out.println(-1);
			return;
		}
		else {
			HashSet<Integer> diffSet = new HashSet<Integer>();
			Arrays.sort(x);
			int minDiff = Integer.MAX_VALUE;
			if (n == 2) {
				if ((x[1] - x[0]) % 2 == 0) {
					minDiff = (x[1] - x[0]);
					ansList.add(x[0] - minDiff);
					if (minDiff > 0)
						ansList.add(x[0] + minDiff / 2);
					if (minDiff > 0)
						ansList.add(x[1] + minDiff);
				}
				else {
					minDiff = (x[1] - x[0]);
					ansList.add(x[0] - minDiff);
					ansList.add(x[1] + minDiff);
				}
			}
			else {
				for (int i = 1; i < x.length; i++) {
					int diff = x[i] - x[i - 1];
					diffSet.add(diff);
					minDiff = Math.min(diff, minDiff);
				}
				if (diffSet.size() == 1) {
					ansList.add(x[0] - minDiff);
					if (minDiff > 0)
						ansList.add(x[x.length - 1] + minDiff);
				}
				else if (diffSet.size() > 2) {
					out.println(0);
					return;
				}
				else {// if (diffSet.size() == 2) {
					if (minDiff == 0) {
						out.println(0);
						return;
					}

					boolean added = false;
					for (int i = 0; i < x.length - 1; i++) {
						if (x[i + 1] - x[i] == minDiff)
							continue;
						else if (x[i + 1] - x[i] == 2 * minDiff) {
							if (!added) {
								ansList.add(x[i] + minDiff);
								added = true;
							}
							else {
								out.println(0);
								return;
							}
						}
						else {
							out.println(0);
							return;
						}
					}
					ans = ansList.size();
				}
			}
		}
		out.println(ansList.size());
		for (int i = 0; i < ansList.size(); i++) {
			out.print(ansList.get(i));
			out.print(" ");
		}
	}

	public static void main(String[] args) throws IOException {
		// helpers for input/output
		out = System.out;
		try {
			String cname = System.getenv("COMPUTERNAME");
			if (!cname.equals(""))
				LOCAL_TEST = true;
		} catch (Exception e) {
		}
		if (LOCAL_TEST) {
			in = new MyScanner("E:\\zin.txt");
		}
		else {
			boolean usingFileForIO = false;
			if (usingFileForIO) {
				// using input.txt and output.txt as I/O
				in = new MyScanner("input.txt");
				out = new PrintStream("output.txt");
			}
			else {
				in = new MyScanner();
				out = System.out;
			}
		}

		solve();
	}

	// =====================================
	static class MyScanner {
		BufferedReader bufReader;
		StringTokenizer strTok;

		public MyScanner() throws IOException
		{
			bufReader = new BufferedReader(new InputStreamReader(System.in));
			strTok = new StringTokenizer("");
		}

		public MyScanner(String inputFile) throws IOException {
			bufReader = new BufferedReader(new InputStreamReader(new FileInputStream(
					inputFile)));
			strTok = new StringTokenizer("");
		}

		String GetNextToken() throws IOException {
			if (!strTok.hasMoreTokens())
				strTok = new StringTokenizer(bufReader.readLine());
			return strTok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.valueOf(GetNextToken());
		}

		public long nextLong() throws IOException {
			return Long.valueOf(GetNextToken());
		}

		public double nextDouble() throws IOException {
			return Double.valueOf(GetNextToken());
		}

		public String nextString() throws IOException {
			return GetNextToken();
		}

		public String nextLine() throws IOException {
			return bufReader.readLine();
		}

		public int countTokens() {
			return strTok.countTokens();
		}

		public boolean hasMoreTokens() {
			return strTok.hasMoreTokens();
		}
	}

}