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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Praney Rai
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CArithmeticProgression solver = new CArithmeticProgression();
        solver.solve(1, in, out);
        out.close();
    }

    static class CArithmeticProgression {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();
            Arrays.sort(a);
            if (n == 1) {
                out.println(-1);
                return;
            }
            if (n == 2) {
                if (a[0] == a[1]) {
                    out.println(1);
                    out.println(a[0]);
                } else {
                    long df = a[1] - a[0];
                    if (df % 2 == 0) {
                        out.println(3);
                        out.println((a[0] - df) + " " + (a[0] + df / 2) + " " + (a[1] + df));
                    } else {
                        out.println(2);
                        out.println((a[0] - df) + " " + (a[1] + df));
                    }
                }
                return;
            }
            TreeSet<Long> ts = new TreeSet<Long>();
            for (int i = 1; i < n; i++) {
                ts.add(a[i] - a[i - 1]);
            }
            if (ts.size() == 1) {
                long df = a[1] - a[0];
                if (df == 0) {
                    out.println(1);
                    out.println(a[0]);
                } else {
                    out.println(2);
                    out.println((a[0] - df) + " " + (a[n - 1] + df));
                }
            } else if (ts.size() == 2) {
                long v1 = ts.first();
                ts.remove(v1);
                long v2 = ts.first();
                if (v2 == 2 * v1) {
                    int cnt = 0;
                    int ind = 0;
                    for (int i = 1; i < n; i++) {
                        long df = a[i] - a[i - 1];
                        if (df == v2) {
                            ++cnt;
                            ind = i - 1;
                        }
                    }
                    if (cnt == 1) {
                        out.println(1);
                        out.println(a[ind] + v1);
                    } else {
                        out.println(0);
                    }
                } else {
                    out.println(0);
                }
            } else {
                out.println(0);
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

