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.

“三个七”彩票活动共举行了 $m$ 天。在第 $i$ 天，有 $n_i$ 人参与抽奖，他们的号码分别为 $a_{i, 1}, \ldots, a_{i, n_i}$。

已知在全部 $m$ 天中，每天恰好从当天的参与者中选出一名中奖者。且第 $i$ 天的中奖者不得再参加第 $i+1$ 天至第 $m$ 天的抽奖。

不幸的是，有关各日中奖者的信息已全部丢失。你需要找出一个可能的、从第 $1$ 天到第 $m$ 天的中奖者序列；若不存在满足条件的序列，则判定无解。

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 $50\,000$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 50\,000$）。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $m$（$1 \le m \le 50\,000$）—— 表示彩票举办的天数。

接下来，对每个 $i$（从 $1$ 到 $m$），给出一个两行的数据块。

每个数据块的第一行包含一个整数 $n_i$（$1 \le n_i \le 50\,000$）—— 表示第 $i$ 天的彩票参与者人数。

该数据块的第二行包含整数 $a_{i, 1}, \ldots, a_{i, n_i}$（$1 \le a_{i, j} \le 50\,000$）—— 表示第 $i$ 天的彩票参与者。保证所有数字 $a_{i, 1}, \ldots, a_{i, n_i}$ 两两互异。

保证所有测试用例中所有数据块的 $n_i$ 之和不超过 $50\,000$。

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.

对于每个测试用例，若无解，则输出单个整数 $-1$。

否则，输出 $m$ 个整数 $p_1, p_2, \ldots, p_m$（$1 \le p_i \le 50\,000$），表示第 $1$ 天到第 $m$ 天的彩票中奖者。若存在多个解，输出任意一个即可。

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.

在第一个测试用例中，一个可能的答案是 $[8, 2, 1]$，因为编号为 $8$ 的参与者仅在第 $1$ 天参与，而在第 $2$ 天和第 $3$ 天均未参与；编号为 $2$ 的参与者仅在第 $2$ 天参与，而在第 $3$ 天未参与；编号为 $1$ 的参与者在第 $3$ 天参与。注意，这并非唯一可能的答案，例如 $[8, 9, 4]$ 同样是一个正确答案。

在第二个测试用例中，两名抽奖参与者均在第 $1$ 天和第 $2$ 天都参与了抽奖，因此第 $1$ 天的任何可能中奖者都必然也在第 $2$ 天参与了抽奖，而这违反了题目要求。因此，该测试用例不存在正确答案。

在第三个测试用例中，仅有唯一一名参与者在第 $2$、$3$、$4$ 天均参与了抽奖；而在第 $1$ 天，仅有一名参与者未在第 $2$、$3$、$4$ 天参与抽奖——即参与者 $2$。这意味着 $[2, 1, 4, 3]$ 是该测试用例的唯一正确答案。