题目描述

Jay runs a small carnival that has various rides and attractions. Unfortunately, times are tough. A recent roller coaster accident, flooding in the restrooms, and an unfortunate clown incident have given Jay’s carnival a bad reputation with the public. With fewer paying customers and reduced revenue, he will need to cut some costs to stay in business.

One of the biggest carnival attractions is a large, confusing maze. It consists of a variety of circular rooms connected by narrow, twisting corridors. Visitors love getting lost in it and trying to map it out. It has come to Jay’s attention that some of the rooms might be effectively identical to each other. If that’s the case, he will be able to reduce its size without anyone noticing.

Two rooms $A$ and $B$ are effectively identical if, when you are dropped into either room $A$ or $B$ (and you know the map of the maze), you cannot tell whether you began in $A$ or $B$ just by exploring the maze. The corridor exits are evenly spaced around each room, and you cannot mark or leave anything in a room (in particular, you cannot tell whether you have previously visited it). The only identifying feature that rooms have is their number of exits. Corridors are also twisty enough to be indistinguishable from each other, but when you enter a room you know which corridor you came from, so you can navigate a little by using the order they appear around the room.

Jay has appealed to the Association for Carnival Mazery for help. That’s you! Write a program to determine all the sets of effectively identical rooms in the maze.

输入格式

The input consists of a single test case. The first line contains an integer $n$, the number of rooms in the maze ($1 \leq n \leq 100$). Rooms are numbered from 1 to $n$. Following this are $n$ lines, describing each room in order. Each line consists of an integer $k$, indicating that this room has $k$ corridors ($0 \leq k < 100$), and then $k$ distinct integers listing the rooms each corridor connects to (in clockwise order, from an arbitrary starting point). Rooms do not connect to themselves.

输出格式

Display one line for each maximal set of effectively identical rooms (ignoring sets of size 1) containing the room numbers in the set in increasing order. Order the sets by their smallest room numbers. If there are no such sets, display none instead.

题目大意

Jay经营着一家小型游乐场，其中有各种游乐设施和景点。不幸的是，由于顾客和收入的锐减，他将需要削减成本以维持业务。

一个大型迷宫是最大的景点之一，它由不同的圆形房间组成。这些房间通过狭窄且扭曲的走廊相连，而某些游客喜欢迷失在迷宫中并试图将其绘制出来。Jay已经注意到，有些房间可能一模一样。如果出现这样的情况，他就能减小迷宫的尺寸而不会被任何人发现。

当您进入AA或是BB房间（并且您知道迷宫的地图）时，两个房间AA和BB是相同的，那么您仅通过探索迷宫就无法分辨是从AA还是BB开始行动。走廊出口在每个房间周围均等分布，您不能在房间内标记或留下任何东西（您无法判断是否进入过该房间）。房间唯一的标识是出口数量。走廊很曲折，彼此之间无法区分，但是当您进入一个房间时，您会知道您来自哪个走廊，因此您可以通过它们在房间周围出现的顺序来指引方向。

Jay向你寻求帮助，请编写程序以找出迷宫中所有相同房间的集合。

Translated by EndlIa

13
2 2 4
3 1 3 5
2 2 4
3 1 3 6
2 2 6
2 4 5
2 8 9
2 7 9
2 7 8
2 11 13
2 10 12
2 11 13
2 10 12

2 4
5 6
7 8 9 10 11 12 13

6
3 3 4 5
0
1 1
1 1
2 1 6
1 5

none

提示

Time limit: 2000 ms, Memory limit: 1048576 kB.

International Collegiate Programming Contest (ACM-ICPC) World Finals 2014