Finding All Valid Divisors

Luka writes down $n$ integers (from the numbers on license plates) on a piece of paper. Then he tries to find an integer $m$, with $m > 1$, such that when each of these numbers is divided by $m$, they all give the same remainder. In other words, for all given integers $a_i$, the condition [ a_i \equiv r \pmod{m} ] holds for some remainder $r$ (which might be different for different inputs), and $m$ must be greater than 1. Luka wants to find as many different values of $m$ as possible. Your task is to write a program that, given the $n$ integers, determines all possible $m$ values that satisfy the condition.

Note: Two numbers giving the same remainder modulo $m$ is equivalent to saying that $m$ divides the difference of any two of the numbers. Thus, if you compute the greatest common divisor ((g)) of all differences, then any divisor $m > 1$ of (g) will be a valid answer.

inputFormat

The first line of input contains an integer $n$ $(2 \le n \le 100)$, representing the number of integers. The second line contains $n$ space-separated integers. It is guaranteed that the integers are not all the same.

outputFormat

Output all valid integers $m$ (greater than 1) in increasing order, separated by a single space.

sample

3
38 6 34

2 4