Restore the Permutation by Sorted Segments

题意翻译

现有一个不确定的 $n$ 的全排列（即一个数列中 $1$ 到 $n$ 都恰好出现一次）$p$。给你 $n-1$ 个数列 $q$，每个 $q$ 为 $p$ 中一段区间 $[l,r]$ **排好序后**的数列（但 $l$ 和 $r$ 的值题目并未给出）。每个数列 $q$ 和一个 $r \in [2, n]$ 一一对应且满足 $l < r$。你要根据给定的 $n-1$ 个 $q$ 猜测出 $p$，题目保证有解。 **注意 $q$ 的给出顺序是随机的。**

题目描述

We guessed a permutation $ p $ consisting of $ n $ integers. The permutation of length $ n $ is the array of length $ n $ where each element from $ 1 $ to $ n $ appears exactly once. This permutation is a secret for you. For each position $ r $ from $ 2 $ to $ n $ we chose some other index $ l $ ( $ l < r $ ) and gave you the segment $ p_l, p_{l + 1}, \dots, p_r $ in sorted order (i.e. we rearranged the elements of this segment in a way that the elements of this segment are sorted). Thus, you are given exactly $ n-1 $ segments of the initial permutation but elements inside each segment are sorted. The segments are given to you in random order. For example, if the secret permutation is $ p=[3, 1, 4, 6, 2, 5] $ then the possible given set of segments can be: - $ [2, 5, 6] $ - $ [4, 6] $ - $ [1, 3, 4] $ - $ [1, 3] $ - $ [1, 2, 4, 6] $ Your task is to find any suitable permutation (i.e. any permutation corresponding to the given input data). It is guaranteed that the input data corresponds to some permutation (i.e. such permutation exists). You have to answer $ t $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Then $ t $ test cases follow. The first line of the test case contains one integer $ n $ ( $ 2 \le n \le 200 $ ) — the length of the permutation. The next $ n-1 $ lines describe given segments. The $ i $ -th line contains the description of the $ i $ -th segment. The line starts with the integer $ k_i $ ( $ 2 \le k_i \le n $ ) — the length of the $ i $ -th segment. Then $ k_i $ integers follow. All integers in a line are distinct, sorted in ascending order, between $ 1 $ and $ n $ , inclusive. It is guaranteed that the required $ p $ exists for each test case. It is also guaranteed that the sum of $ n $ over all test cases does not exceed $ 200 $ ( $ \sum n \le 200 $ ).

输出格式

For each test case, print the answer: n integers p1,p2,…,pn (1≤pi≤n, all pi should be distinct) — any suitable permutation (i.e. any permutation corresponding to the test case input).

输入输出样例

输入样例 #1

5
6
3 2 5 6
2 4 6
3 1 3 4
2 1 3
4 1 2 4 6
5
2 2 3
2 1 2
2 1 4
2 4 5
7
3 1 2 6
4 1 3 5 6
2 1 2
3 4 5 7
6 1 2 3 4 5 6
3 1 3 6
2
2 1 2
5
2 2 5
3 2 3 5
4 2 3 4 5
5 1 2 3 4 5

输出样例 #1

3 1 4 6 2 5 
3 2 1 4 5 
2 1 6 3 5 4 7 
1 2 
2 5 3 4 1 

题意翻译

现有一个不确定的 $n$ 的全排列（即一个数列中 $1$ 到 $n$ 都恰好出现一次）$p$。给你 $n-1$ 个数列 $q$，每个 $q$ 为 $p$ 中一段区间 $[l,r]$ **排好序后**的数列（但 $l$ 和 $r$ 的值题目并未给出）。每个数列 $q$ 和一个 $r \in [2, n]$ 一一对应且满足 $l < r$。你要根据给定的 $n-1$ 个 $q$ 猜测出 $p$，题目保证有解。 **注意 $q$ 的给出顺序是随机的。**