# Minimum Range

**Problem Statement**

In a sports club, there are 3 groups of players, say A, B and C. Each group has N players. You are the manager of the club and were asked to select 3 players

**(one from each group)**to represent your club in a team tournament. To do this you marked each player with an integer K, representing their compatibility with other players.

__The smaller the difference in K (between two players) the more compatible they are__, i.e. a player with K = 2 is more compatible with a player whose K = 3 or K = 1, than a player with K = 4.

**Now you want to select 3 players**

__(one from each group)__such that the range of K of those players in minimum.PS : Your club is very efficient so everyone in your club is equally skilled :P

**Input and Output Specifications**

First line of input will contain an integer T. T test cases follows.

First line of each test case contain N, the size of each array.

Next three lines contains N integers in

**increasing order.**

You have to output the minimum range of K possible.

You have to output the minimum range of K possible.

**Constrain**

```
```

T <= 100

N <= 1000

1 <= K <= 10^9

**Sample Input**

```
```

1

5

1 1 2 3 4

2 5 6 9 10

7 8 9 10 11

**Sample Output**

```
```

3

**Explanation**

4 is selected from first group, 5 or 6 from second and 7 from third. The range of K in this case is 3. Any other selection will result in larger range.

**Problem Source :**Flipkart Interview

**Problem Setter :**Pushkar Anand

**Problem Tester :**Jayant Mukherjee

**Languages:**Brain,C,C++,Java,Pascal,Perl,PHP,Python,Ruby,Text