CF1857C Assembly via Minimums

Sasha has an array $ a $ of $ n $ integers. He got bored and for all $ i $ , $ j $ ( $ i < j $ ), he wrote down the minimum value of $ a_i $ and $ a_j $ . He obtained a new array $ b $ of size $ \frac{n\cdot (n-1)}{2} $ . For example, if $ a= $ \[ $ 2,3,5,1 $ \], he would write \[ $ \min(2, 3), \min(2, 5), \min(2, 1), \min(3, 5), \min(3, 1), min(5, 1) $ \] $ = $ \[ $ 2, 2, 1, 3, 1, 1 $ \]. Then, he randomly shuffled all the elements of the array $ b $ . Unfortunately, he forgot the array $ a $ , and your task is to restore any possible array $ a $ from which the array $ b $ could have been obtained. The elements of array $ a $ should be in the range $ [-10^9,10^9] $ .

The first line contains a single integer $ t $ ( $ 1\le t\le 200 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 2\le n\le 10^3 $ ) — the length of array $ a $ . The second line of each test case contains $ \frac{n\cdot (n-1)}{2} $ integers $ b_1,b_2,\dots,b_{\frac{n\cdot (n-1)}{2}} $ ( $ −10^9\le b_i\le 10^9 $ ) — the elements of array $ b $ . It is guaranteed that the sum of $ n $ over all tests does not exceed $ 10^3 $ and for each array $ b $ in the test, there exists an original array.

For each test case, output any possible array $ a $ of length $ n $ .

In the first sample, Sasha chose the array $ [1,3,3] $ , then the array $ b $ will look like $ [\min(a_1,a_2)=1, \min(a_1,a_3)=1, \min(a_2,a_3)=3] $ , after shuffling its elements, the array can look like $ [1,3,1] $ . In the second sample, there is only one pair, so the array $ [10,10] $ is suitable. Another suitable array could be $ [15,10] $ .