You cannot submit for this problem because the contest is ended. You can click "Open in Problem Set" to view this problem in normal mode.

Time Limit: 4.0 s

Memory Limit: 256.0 MB

Description

You are given an array A[ ] and the length of the array is N.
You can rearrange this array A[ ]. After rearrange you can do following of the operations,

• Divide array A[ ] into maximum block.
• Each block has equal length
• Each block has at least two elements.
• Each block, different between Maximum and Minimum element should be equal for all. For example,
  A[] ={1,3,4,2}, we can divide it, two blocks : {1,3}, {4,2}.
  Different block {1,3} , Max element - Min element = 3 - 1 = 2 ;
  Different block {4,2} , Max element - Min element = 4 - 2 = 2 ;

Find the maximum block of the array after ful-fill the above conditions.

Input

• First Line T,(1 ≤ T ≤ 50) the number of test cases.
• In each test case,first line contain an integer N, (2 ≤ N ≤ 30), - length of the array.
• Second line, an array A[], ( 1 ≤ A[] ≤ \(10^5\)) with exactly N elements.

Output

In each test case, print the maximum block of the array.

Sample

3
6
8 3 7 3 8 7 
4
1 4 3 2
4
7 1 3 8 

3
2
1

First test case: