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.util.*;
 
public class C382 {
 
    public static void main(String[] args) {
        IO io = new IO();

        int n = io.nextInt();
        long[] a = io.nLongA(n);


        Impl imp = new Impl();
        long[] solve = imp.solve(a);
        if (solve.length == 1 && (solve[0] == 0 || solve[0] == -1)) {
            io.write(solve, ' ');
        } else {
            io.write(solve.length);
            io.write(solve, ' ');
        }
    }

    static class Impl {
 
 
        public long[] solve(long[] a) {

            Arrays.sort(a);

            long[] r;

            if (a.length == 1) {
                r = new long[1];
                r[0] = -1;
                return r;
            }

            if (a.length == 2) {
                long diff = a[1] - a[0];


                if (diff == 0) {
                    r = new long[1];
                    r[0] = a[0];
                    return r;
                }

                if (diff % 2 != 0) {
                    r = new long[2];
                    r[0] = a[0] - diff;
                    r[1] = a[1] + diff;
                    return r;
                }

                r = new long[3];
                long d2 = diff/2;
                r[0] = a[0] - diff;
                r[1] = a[0] + d2;
                r[2] = a[1] + diff;
                return r;
            }


            long diff1 = -1;
            long dc = 0;
            int di = -1;
            long diff2 = -1;
            long d2c = 0;
            int d2i = -1;

            for (int i = 1; i < a.length; i++) {
                long d = a[i] - a[i-1];
                if (diff1 == -1) {
                    diff1 = d;
                    dc++;
                    di = i;
                } else if (diff1 == d) {
                    dc++;
                    di = -1;
                } else if (diff2 == -1) {
                    diff2 = d;
                    d2c++;
                    d2i = i;
                } else if (diff2 == d) {
                    d2c++;
                    d2i = -1;
                } else {
                    r = new long[1];
                    r[0] = 0;
                    return r;
                }
            }

            // 2 4 6

            if (dc > 1 && d2c == 0) { // all equal.
                if (diff1 == 0) {
                    r = new long[1];
                    r[0] = a[0];
                    return r;
                }
                r = new long[2];
                r[0] = a[0] - diff1;
                r[1] = a[a.length - 1]  + diff1;
                return r;
            } else if (dc > 1 && d2c == 1) { // 2 4 6 8 16 // one gt.
                if (diff2 % 2 == 0 && diff2/2 == diff1) {
                    r = new long[1];
                    r[0] = a[d2i] - diff1;
                    return r;
                } else {
                    r = new long[1];
                    r[0] = 0;
                    return r;
                }
            } else if (dc == 1 && d2c > 1) {
                if (diff1 % 2 == 0 && diff1/2 == diff2) {
                    r = new long[1];
                    r[0] = a[di] - diff2;
                    return r;
                } else {
                    r = new long[1];
                    r[0] = 0;
                    return r;
                }
            } else if (dc == 1 && d2c == 1) {

                if (diff1 > diff2 && diff1 % 2 == 0 && diff1/2 == diff2) {
                    r = new long[1];
                    r[0] = a[di] - diff2;
                    return r;
                } 

                if (diff2 > diff1 && diff2 % 2 == 0 && diff2/2 == diff1) {
                    r = new long[1];
                    r[0] = a[d2i] - diff1;
                    return r;
                } 

                if (diff1 == diff2) {
                    r = new long[2];
                    r[0] = a[0] - diff1;
                    r[1] = a[a.length-1] - diff1;
                    return r;
                }
            }


            r = new long[1];
            r[0] = 0;
            return r;

        }
    }
 
    static class IO {
        BufferedReader br;
        BufferedWriter bw;
        StringTokenizer st;
 
        public IO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void write(int length) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(length);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(boolean b, String truev, String falsv) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(b ? truev : falsv);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(int[] a, char sep) {
            try {
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i < a.length; i++) {
                   sb.append(a[i]);
                   sb.append(sep);
                }
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(long[] a, char sep) {
            try {
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i < a.length; i++) {
                   sb.append(a[i]);
                   sb.append(sep);
                }
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }
 
        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] nIntA(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public long[] nLongA(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        public double[] nDoubleA(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextDouble();
            }
            return a;
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}