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
//package codeforces;

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.ListIterator;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class A implements Closeable {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    A() throws IOException {
//        reader = new BufferedReader(new FileReader("input.txt"));
//        writer = new PrintWriter(new FileWriter("output.txt"));
    }

    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    private int MOD = 1000 * 1000 * 1000 + 7;

    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    int product(int a, int b) {
        return (int) (1l * a * b % MOD);
    }

    int pow(int x, int k) {
        int result = 1;
        while (k > 0) {
            if (k % 2 == 1) {
                result = product(result, x);
            }
            x = product(x, x);
            k /= 2;
        }
        return result;
    }

    int inv(int x) {
        return pow(x, MOD - 2);
    }

    void solve() throws IOException {
        final int n = nextInt();
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        if (n == 1) {
            writer.println(-1);
            return;
        }
        Arrays.sort(a);
        if (n == 2) {
            Collection<Integer> answer = new TreeSet<>();
            answer.add(2 * a[0] - a[1]);
            answer.add(2 * a[1] - a[0]);
            if ((a[1] - a[0]) % 2 == 0) {
                answer.add(a[0] + a[1] >> 1);
            }
            writer.println(answer.size());
            for (Integer x : answer) {
                writer.print(x + " ");
            }
            return;
        }
        final Collection<Integer> answer = new TreeSet<>();
        class Utils {
            void updateAnswer(int d) {
                if(a[n - 1] > a[0] + 1l * n * d) {
                    return;
                }
                if (d == 0) {
                    for (int i : a) {
                        if (i != a[0]) {
                            return;
                        }
                    }
                    answer.add(a[0]);
                    return;
                }
                long sum = 0;
                for (int i = 1; i < n; i++) {
                    int x = a[i];
                    int y = a[i - 1];
                    if (x - y != d && x - y != 2 * d) {
                        return;
                    }
                    sum += (x - a[0]) / d;
                }
                long x = 1l * n * (n + 1) / 2 - sum;
                if(x > n || x < 0) {
                    return;
                }
                answer.add(a[0] + (int) x * d);
                if (x == n) {
                    answer.add(a[0] - d);
                }
            }
        }
        Utils utils = new Utils();
        utils.updateAnswer(a[1] - a[0]);
        utils.updateAnswer(a[n - 1] - a[n - 2]);
        writer.println(answer.size());
        for (Integer x : answer) {
            writer.print(x + " ");
        }
    }

    public static void main(String[] args) throws IOException {
        try (A a = new A()) {
            a.solve();
        }
    }

    @Override
    public void close() throws IOException {
        reader.close();
        writer.close();
    }
}