B. Three Sevens
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Lottery "Three Sevens" was held for $$$m$$$ days. On day $$$i$$$, $$$n_i$$$ people with the numbers $$$a_{i, 1}, \ldots, a_{i, n_i}$$$ participated in the lottery.

It is known that in each of the $$$m$$$ days, only one winner was selected from the lottery participants. The lottery winner on day $$$i$$$ was not allowed to participate in the lottery in the days from $$$i+1$$$ to $$$m$$$.

Unfortunately, the information about the lottery winners has been lost. You need to find any possible list of lottery winners on days from $$$1$$$ to $$$m$$$ or determine that no solution exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 50\,000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$m$$$ ($$$1 \le m \le 50\,000$$$) — the number of days in which the lottery was held.

Next, for each $$$i$$$ from $$$1$$$ to $$$m$$$, follows a two-line block of data.

The first line of each block contains a single integer $$$n_i$$$ ($$$1 \le n_i \le 50\,000$$$) — the number of lottery participants on day $$$i$$$.

The second line of the block contains integers $$$a_{i, 1}, \ldots, a_{i, n_i}$$$ ($$$1 \le a_{i, j} \le 50\,000$$$) — lottery participants on day $$$i$$$. It is guaranteed that all the numbers $$$a_{i, 1}, \ldots, a_{i, n_i}$$$ are pairwise distinct.

It is guaranteed that the sum of $$$n_i$$$ over all blocks of all test cases does not exceed $$$50\,000$$$.

Output

For each test case, if there is no solution, print a single integer $$$-1$$$.

Otherwise, print $$$m$$$ integers $$$p_1, p_2, \ldots, p_m$$$ ($$$1 \le p_i \le 50\,000$$$) — lottery winners on days from $$$1$$$ to $$$m$$$. If there are multiple solutions, print any of them.

Example
Input
3
3
4
1 2 4 8
3
2 9 1
2
1 4
2
2
1 2
2
2 1
4
4
1 2 3 4
1
1
1
4
1
3
Output
8 2 1 
-1
2 1 4 3
Note

In the first test case, one of the answers is $$$[8, 2, 1]$$$ since the participant with the number $$$8$$$ participated on day $$$1$$$, but did not participate on days $$$2$$$ and $$$3$$$; the participant with the number $$$2$$$ participated on day $$$2$$$, but did not participate on day $$$3$$$; and the participant with the number $$$1$$$ participated on day $$$3$$$. Note that this is not the only possible answer, for example, $$$[8, 9, 4]$$$ is also a correct answer.

In the second test case, both lottery participants participated on both days, so any possible lottery winner on the day $$$1$$$ must have participated on the day $$$2$$$, which is not allowed. Thus, there is no correct answer.

In the third test case, only one participant participated on days $$$2$$$, $$$3$$$, $$$4$$$, and on day $$$1$$$ there is only one participant who did not participate in the lottery on days $$$2, 3, 4$$$ — participant $$$2$$$, which means $$$[2, 1, 4, 3]$$$ is the only correct answer to this test case.