1857C · Assembly via Minimums

Problem: 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 $[-10^9,10^9]$.

Input Format: 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.

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

Note: 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 $[15,10]$.