Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Arithmetic Progression

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEverybody knows what an arithmetic progression is. Let us remind you just in case that an arithmetic progression is such sequence of numbers *a* _{1}, *a* _{2}, ..., *a* _{ n} of length *n*, that the following condition fulfills:

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* ≤ 10^{5}) — 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 10^{8}.

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 10^{8} 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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/15/2020 23:04:56 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|