A15863 · Three Sevens

题目描述

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.

输入 #1

输出 #1

8 2 1 
-1
2 1 4 3