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.*;

public class Main implements Runnable {

    public void solve() throws IOException {
        /*int a = nextInt();
         int b = nextInt();
         int w = nextInt();
         int x = nextInt();
         int c = nextInt();
         //1 0 2 1 2000000000 ans: 3999999998
         //System.out.println(a+" "+b+" "+w+" "+x+" "+c);
         //1 0 1000 999 2000000000
         //ans: 2149633283
         long t = 0;
         while (c > a) {
         if (b >= x) {
         //b -= x;
         int diff = b - x;
         int canSubtract = (diff + x) / x;
         int cdiff = c - a;
         int bestMin = Math.min(cdiff, canSubtract);
         c -= bestMin;
         c++;
         b -= bestMin * x;
         t += bestMin;
         t--;
         } else {
         int toadd = w - x;
         int diff = x - b;
         int canAdd = (diff + toadd) / toadd;
         int cdiff = c - a;
         int bestMin = Math.min(cdiff, canAdd);
         c -= bestMin;
         c++;
         a -= bestMin;
         b += bestMin * toadd;
         t += bestMin;
         t--;
         //--a;
         //b += (w - x);
         }
         c--;
         t++;
         //System.err.println(a + " " + b + " " + w + " " + x + " " + c + " " + t);
         }
         System.out.println(t);
         * */
        int n = nextInt();
        int[] arr = new int[n];
        int[][] diff = new int[n - 1][];
        for (int i = 0; i < n; i++) {
            arr[i] = nextInt();
        }
        Arrays.sort(arr);
        if (n == 1) {
            System.out.println("-1");
            return;
        }
        if (arr[0] == arr[n - 1]) {
            System.out.println(1);
            System.out.println(arr[0]);
            return;
        }
        for (int i = 1; i < n; i++) {
            diff[i - 1] = new int[]{arr[i] - arr[i - 1], i};
        }

        Arrays.sort(diff, new Comparator<int[]>() {
            public int compare(int[] a, int[] b) {
                return a[0] - b[0];
            }
        });
        Set<Integer> set = new TreeSet<Integer>();
        if (diff[0][0] == diff[n - 2][0]) {
            set.add(arr[0] - diff[0][0]);
            set.add(arr[n - 1] + diff[0][0]);
        }
        //print(arr);
        if (n - 2 == 0 || diff[n - 2][0] == diff[0][0] * 2 && diff[0][0] == diff[n - 3][0]) {
            if (diff[n - 2][0] % 2 == 0) {
                set.add(arr[diff[n - 2][1]] - (diff[n - 2][0] / 2));
            }
            //System.err.println(diff[n - 2][1] + " " + diff[0][0]);
        }
        StringBuffer ans = new StringBuffer("");
        for (int i : set) {
            ans.append(" " + i);
        }
        if (set.size() > 0) {
            System.out.println(set.size() + "\n" + ans.substring(1));
        } else {
            System.out.println(set.size());
        }
    }

    String[] check(String in) {
        String[] ret = new String[2];
        Arrays.fill(ret, "");
        int i = 0;
        for (i = 0; i < in.length(); i++) {
            if (in.charAt(i) == '|') {
                break;
            }
            ret[0] += in.charAt(i);
        }
        i++;
        for (; i < in.length(); i++) {
            //if(in.charAt(i)=='|')break;
            ret[1] += in.charAt(i);
        }
        return ret;
    }

    int answer(int[] a, int[] b) {
        int n = a.length;
        b = b.clone();
        a = a.clone();
        for (int i = 0; i < n; i++) {
            if (b[i] >= 0) {
                merge(a, i, b[i]);
            }
        }
        int cnt = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] < 0) {
                cnt++;
            }
        }
        return cnt;
    }

    void merge(int[] arr, int a, int b) {
        a = get(arr, a);
        b = get(arr, b);
        if (a != b) {
            if (arr[a] > arr[b]) {
                int t = a;
                a = b;
                b = t;
            }
            arr[a] += arr[b];
            arr[b] = a;
        }
    }

    int get(int[] arr, int a) {
        if (arr[a] < 0) {
            return a;
        }
        return arr[a] = get(arr, arr[a]);
    }

    void shuffle(int[] a) {
        int N = a.length;
        for (int i = 0; i < N / 2; i++) {
            int j = (int) (Math.random() * N);
            int t = a[i];
            a[i] = a[j];
            a[j] = t;
        }
    }

    void print(Object... obj) {
        for (Object o : obj) {
            System.out.println(o);
        }
    }

    void print(int[] a) {
        System.out.println();
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
    }

    void print(int[][] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }
    }

    void print(boolean[][] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }
    }

    boolean nextPermutation(int[] arr) {
        int f = -1;
        for (int i = arr.length - 2; i >= 0; i--) {
            if (arr[i + 1] > arr[i]) {
                f = i;
                break;
            }
        }
        if (f == -1) {
            return false;
        }
        int s = -1;
        for (int i = arr.length - 1; i >= 0; i--) {
            if (arr[i] > arr[f]) {
                s = i;
                break;
            }
        }
        int d = arr[f];
        arr[f] = arr[s];
        arr[s] = d;

        f++;
        int l = arr.length - 1;
        while (f < l) {
            d = arr[f];
            arr[f] = arr[l];
            arr[l] = d;
            f++;
            l--;
        }
        return true;
    }

    //-----------------------------------------------------------
    public static void main(String[] args) {
        new Main().run();
    }

    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            tok = null;
            solve();
            in.close();
        } catch (IOException e) {
            System.exit(0);
        }
    }

    public String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

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

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

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    BufferedReader in;
    StringTokenizer tok;
}

class Student {

    int idx;
    int level;
    int cost;

    public Student(int i, int l) {
        idx = i;
        level = l;
    }

    public String toString() {
        return idx + " " + level + " " + cost;
    }
    public static final Comparator<Student> byLevel = new Comparator<Student>() {
        public int compare(Student a, Student b) {
            if (a.level != b.level) {
                return b.level - a.level;
            }
            if (a.cost != b.cost) {
                return a.cost - b.cost;
            }
            return a.idx - b.idx;
        }
    };
    public static final Comparator<Student> byCost = new Comparator<Student>() {
        public int compare(Student a, Student b) {
            if (a.cost != b.cost) {
                return a.cost - b.cost;
            }
            if (a.level != b.level) {
                return b.level - a.level;
            }
            return a.idx - b.idx;
        }
    };
}

class Bug implements Comparable<Bug> {

    int idx;
    int level;

    public Bug(int idx, int level) {
        this.idx = idx;
        this.level = level;
    }

    public int compareTo(Bug other) {
        if (level != other.level) {
            return other.level - level;
        }
        return idx - other.idx;
    }

    public String toString() {
        return idx + " " + level;
    }
}
