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Tasks
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Time limit  2 seconds 

Memory limit  256 megabytes 
Masha and Grisha like studying sets of positive integers.
One day Grisha has written a set A containing n different integers a_{i} on a blackboard. Now he asks Masha to create a set B containing n different integers b_{j} such that all n^{2} integers that can be obtained by summing up a_{i} and b_{j} for all possible pairs of i and j are different.
Both Masha and Grisha don't like big numbers, so all numbers in A are from 1 to 10^{6}, and all numbers in B must also be in the same range.
Help Masha to create the set B that satisfies Grisha's requirement.
Input format 
Input data contains multiple test cases. The first line contains an integer t — the number of test cases (1 ≤ t ≤ 100). Each test case is described in the following way: the first line of the description contains one integer n — the number of elements in A (1 ≤ n ≤ 100). The second line contains n integers a_{i} — the elements of A (1 ≤ a_{i} ≤ 10^{6}). 

Output format 
For each test first print the answer:

Examples 
Input data
3 3 1 10 100 1 1 2 2 4
Output data
YES 1 2 3 YES 1 YES 1 2 
