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.