A16126. 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 $[15,10]$ .