Same Remainder Divisors

Interview

Time limit1sMemory limit128 MB

Summary

Given N distinct integers, find all M greater than 1 for which all numbers share the same remainder mod M, output divisors of pairwise differences in increasing order.

Level: Medium4 of 10
Topics: Number theory, Math, Brute force
Solved: No attempts yet

Problem

You are given N distinct positive integers. Find every integer M greater than 1 such that all of the given numbers leave the same remainder when divided by M.

Input

The first line contains N, the number of integers written down. (2 <= N <= 100)

Each of the next N lines contains one integer. Every integer is at least 1 and at most 1,000,000,000, and no integer appears more than once.

The input is always chosen so that at least one valid M exists.

Output

Print all possible values of M on one line, separated by spaces. The values must be printed in increasing order.

Examples2

Example 1
Input
```
3
6
34
38
```
Expected output
```
2 4
```
Example 2
Input
```
5
5
17
23
14
83
```
Expected output
```
3
```