All Tracks Math Number Theory Basic Number Theory-1 Problem

Help Oz
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Mathematics, Modular arithmetic, Number Theory

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Oz has a list arr[] of M integers. He has to find all integers K such that :

1) K > 1
2) arr[1]%K = arr[2]%K = arr[3]%K = ... = arr[M]%K where '%' is a modulus operator

Help Oz to find all such K's.

Input :
First line of input contains an integer M. Then M lines follow each containing one integer of the list. Input data is such that at least one integer K will always exist.

Output :
Output all possible integers K separated by space in increasing order.

Constraints :
- 2<= M <=100
- 1< value of each integer <109
- All integers will be distinct

SAMPLE INPUT
3
38
6
34
SAMPLE OUTPUT
2 4 
Time Limit: 3.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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