Problem Description

Luka first wrote the numbers from $n$ license plates onto a piece of paper. Then, he tried to find an integer $m$ such that all the numbers on the paper leave the same remainder when divided by $m$.

Luka wants to find as many different values of $m$ as possible.

Write a program that, given Luka’s $n$ integers, determines all such $m$.

Note that you must ensure $m$ is a positive integer, i.e., $m > 1$.

Input Format

The first line contains a positive integer $n$, the number of integers.

In the next $n$ lines, each line contains an integer $a_i$, representing a number on the paper, and all $a_i$ are guaranteed to be distinct.

The testdata guarantees that there exists at least one $m$ that satisfies the requirement.

Output Format

Output all values of $m$ that satisfy the requirement in any order on the first line.

3
6
34
38 

2 4

5
5
17
23
14
83 

3

Hint

Sample #1 Explanation

All integers leave remainder $0$ when divided by $2$, and remainder $2$ when divided by $4$.

Constraints

• For $60\%$ of the testdata, $2 \le n \le 100$, $1 \le a_i \le 10^4$.
• For $100\%$ of the testdata, $2 \le n \le 100$, $1 \le a_i \le 10^9$.

Notes

• The full score for this problem is $50$ points.
• This problem enables the O2 optimization switch by default.
• Translated from COCI2007-2008 CONTEST #6 T3 GRANICA. Translator:
  https://www.luogu.com.cn/user/219791
• Thanks to
  https://www.luogu.com.cn/user/60864
  ing the checker, which you can download from the attachments.

Translated by ChatGPT 5