**Problem F: Reduced ID Numbers**

T. Chur teaches various groups of students at university U. Every U-student has a unique Student Identification Number (SIN). A SIN s is an integer in the range 0 ≤ s ≤ MaxSIN with MaxSIN = 106 − 1. T. Chur finds this range of SINs too large for identification within her groups. For each group, she wants to find the smallest positive integer m, such that within the group all SINs reduced modulo m are unique.

**Input**

On the first line of the input is a single positive integer N, telling the number of test cases (groups) to follow. Each case starts with one line containing the integer G (1 ≤ G ≤ 300): the number of students in the group. The following G lines each contain one SIN. The SINs

within a group are distinct, though not necessarily sorted.

**Output**

For each test case, output one line containing the smallest modulus m, such that all SINs

reduced modulo m are distinct.

*Sample input*

2

1

124866

3

124866

111111

987651

*Sample output*

1

8

----------------------------------------------------------------

This is NWERC's problem F. If you try to solve it by generating values for m starting with the number of students and checking you don't get repeated values for the reduced SINs you will get "Time Limit Exceded".

How can you solve this problem in a quicker way?

Thanks!