You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
A sequence of $$$n$$$ numbers is called permutation if it contains all integers from $$$1$$$ to $$$n$$$ exactly once. For example, the sequences [$$$3, 1, 4, 2$$$], [$$$1$$$] and [$$$2,1$$$] are permutations, but [$$$1,2,1$$$], [$$$0,1$$$] and [$$$1,3,4$$$] — are not.

Kristina had a permutation $$$p$$$ of $$$n$$$ elements. She wrote it on the whiteboard $$$n$$$ times in such a way that:

- while writing the permutation at the $$$i$$$-th ($$$1 \le i \le n)$$$ time she skipped the element $$$p_i$$$

For example, suppose Kristina had a permutation $$$p$$$ = $$$[4,2,1,3]$$$ of length $$$4$$$. Then she did the following:

1. Wrote the sequence $$$[2, 1, 3]$$$, skipping the element $$$p_1=4$$$ from the original permutation.
2. Wrote the sequence $$$[4, 1, 3]$$$, skipping the element $$$p_2=2$$$ from the original permutation.
3. Wrote the sequence $$$[4, 2, 3]$$$, skipping the element $$$p_3=1$$$ from the original permutation.
4. Wrote the sequence $$$[4, 2, 1]$$$, skipping the element $$$p_4=3$$$ from the original permutation.

You know all $$$n$$$ of sequences that have been written on the whiteboard, but you do not know the order in which they were written. They are given in arbitrary order. Reconstruct the original permutation from them.

For example, if you know the sequences $$$[4, 2, 1]$$$, $$$[4, 2, 3]$$$, $$$[2, 1, 3]$$$, $$$[4, 1, 3]$$$, then the original permutation will be $$$p$$$ = $$$[4, 2, 1, 3]$$$.

## Input Format
The first line of input data contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$3 \le n \le 100$$$).

This is followed by $$$n$$$ lines, each containing exactly $$$n-1$$$ integers and describing one of the sequences written out on the whiteboard.

It is guaranteed that all sequences could be obtained from some permutation $$$p$$$, and that the sum $$$n^2$$$ over all input sets does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, output on a separate line a permutation $$$p$$$ such that the given $$$n$$$ sequences could be obtained from it.

It is guaranteed that the answer exists and it is the only one. In other words, for each test case the required permutation is sure to exist.

## Examples
```input
5
4
4 2 1
4 2 3
2 1 3
4 1 3
3
2 3
1 3
1 2
5
4 2 1 3
2 1 3 5
4 2 3 5
4 1 3 5
4 2 1 5
4
2 3 4
1 3 4
1 2 3
1 2 4
3
2 1
1 3
2 3
```
```output
4 2 1 3 
1 2 3 
4 2 1 3 5 
1 2 3 4 
2 1 3
```

## Note
The first test case is described in the problem statement.

In the second test case, the sequences are written in the correct order.

Now solve the problem and return the code.