CF1798B.Three Sevens

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.

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 $50\,000$ .

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.

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.