题目描述

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.

输入格式

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.

输出格式

For each test case, output one line containing the smallest modulus m, such that all SINs reduced modulo m are distinct.

样例 1

输入

2
1
124866
3
124866
111111
987651

输出

1
8

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题目来源：fps-zjgsu-1030-1039.xml；FPS 共享题包，题包内第 6 题。保留原作者与原赛事署名。