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.*;

import static java.util.Arrays.*;

public class C {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();
	
	public void run() throws IOException {
		int n = io.nextInt();
		int[] x = io.nextIntArray(n);
		radixSort(x);
		if(n == 1) {
			io.out.println(-1);
			return;
		}
		
		if(x[0] == x[n-1]) {
			io.out.println(1);
			io.out.println(x[0]);
			return;
		}
		
		if(n == 2) {
			if((x[0] + x[1]) % 2 == 0) {
				io.out.println(3);
				io.out.print(x[0] - (x[1] - x[0]));
				io.out.print(" " + ((x[0] + x[1]) / 2));
				io.out.println(" " + (x[1] + (x[1] - x[0])));
			}
			else {
				io.out.println(2);
				io.out.print(x[0] - (x[1] - x[0]));
				io.out.println(" " + (x[1] + (x[1] - x[0])));
			}
			return;
		}
		Set<Integer> ans = new TreeSet<Integer>();
		LOOP: for(int j = 0; j < 2; j++) {
			int diff = x[j+1] - x[j];
			int num = Integer.MIN_VALUE;
			for(int i = 1, prev = x[0]; i < n; i++) {
				if(x[i] - prev != diff) {
					if(num != Integer.MIN_VALUE) {
						continue LOOP;
					}
					num = x[--i] + diff;
					prev = num;
				}
				else {
					prev = x[i];
				}
			}
			if(num == Integer.MIN_VALUE) {
				ans.add(x[0] - diff);
				ans.add(x[n-1] + diff);
			}
			else {
				ans.add(num);
			}
		}
		io.out.println(ans.size());
		List<Integer> ans2 = new ArrayList<Integer>(ans);
		for(int i = 0; i < ans2.size(); i++) {
			if(i != 0) io.out.print(" ");
			io.out.print(ans2.get(i));
		}
		io.out.println();
	}

	static void radixSort(int[] xs) {
		int[] cnt = new int[(1<<16)+1];
		int[] ys = new int[xs.length];
		
		for(int j = 0; j <= 16; j += 16) {
			Arrays.fill(cnt, 0);
			for(int x : xs) { cnt[(x>>j&0xFFFF)+1]++; }
			for(int i = 1; i < cnt.length; i++) { cnt[i] += cnt[i-1]; }
			for(int x : xs) { ys[cnt[x>>j&0xFFFF]++] = x; }
			{ final int[] t = xs; xs = ys; ys = t; }
		}
	}
	
	static void radixSort(long[] xs) {
		int[] cnt = new int[(1<<16)+1];
		long[] ys = new long[xs.length];
		
		for(int j = 0; j <= 48; j += 16) {
			Arrays.fill(cnt, 0);
			for(long x : xs) { cnt[(int)(x>>j&0xFFFF)+1]++; }
			for(int i = 1; i < cnt.length; i++) { cnt[i] += cnt[i-1]; }
			for(long x : xs) { ys[cnt[(int)(x>>j&0xFFFF)]++] = x; }
			{ final long[] t = xs; xs = ys; ys = t; }
		}
	}
	

	static void arrayIntSort(int[][] x, int... keys) {
		Arrays.sort(x, new ArrayIntsComparator(keys));
	}
	
	static class ArrayIntsComparator implements Comparator<int[]> {
		final int[] KEY;
		
		public ArrayIntsComparator(int... key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			for(int k : KEY) if(o1[k] != o2[k]) return o1[k] - o2[k];
			return 0;
		}
	}
	
	static class ArrayIntComparator implements Comparator<int[]> {
		final int KEY;
		
		public ArrayIntComparator(int key) {
			KEY = key;
		}
		
		@Override
		public int compare(int[] o1, int[] o2) {
			return o1[KEY] - o2[KEY];
		}
	}
	
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try {
			run();
		}
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}

	public static void main(String[] args) throws IOException {
		new C().main();
	}
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIO(String ins, String outs) throws IOException {
			in = new BufferedReader(new FileReader(ins));
			out = new PrintWriter(new FileWriter(outs));
		}

		//		private static final int BUFFER_SIZE = 50 * 200000;
		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; }
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public int read() throws IOException {
			if(pos >= readLen) {
				pos = 0;
				readLen = in.read(buffer);
				if(readLen <= 0) { throw new EndOfFileRuntimeException(); }
			}
			return buffer[pos++];
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(nextString());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(nextString());
		}

		public char nextChar() throws IOException {
			while(true) {
				final int c = read();
				if(!isSpace[c]) { return (char)c; }
			}
		}
		
		int reads(int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					
					if(str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					
					str[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}
		
		int reads(char[] cs, int len, boolean[] accept) throws IOException {
			try {
				while(true) {
					final int c = read();
					if(accept[c]) { break; }
					cs[len++] = (char)c;
				}
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return len;
		}

		public char[] nextLine() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isLineSep);
			
			try {
				if(str[len-1] == '\r') { len--; read(); }
			}
			catch(EndOfFileRuntimeException e) { ; }
			
			return Arrays.copyOf(str, len);
		}

		public String nextString() throws IOException {
			return new String(next());
		}

		public char[] next() throws IOException {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public int next(char[] cs) throws IOException {
			int len = 0;
			cs[len++] = nextChar();
			len = reads(cs, len, isSpace);
			return len;
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(nextString());
		}

		public long[] nextLongArray(final int n) throws IOException {
			final long[] res = new long[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public int[] nextIntArray(final int n) throws IOException {
			final int[] res = new int[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[][] nextIntArray2D(final int n, final int k) throws IOException {
			final int[][] res = new int[n][];
			for(int i = 0; i < n; i++) {
				res[i] = nextIntArray(k);
			}
			return res;
		}

		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException {
			final int[][] res = new int[n][k+1];
			for(int i = 0; i < n; i++) {
				for(int j = 0; j < k; j++) {
					res[i][j] = nextInt();
				}
				res[i][k] = i;
			}
			return res;
		}

		public double[] nextDoubleArray(final int n) throws IOException {
			final double[] res = new double[n];
			for(int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

	}

}
