# 2367. Sub-dictionary

In this problem, by the word “dictionary” we mean a list of alphabetically ordered words and their associated explanations in the same language. A dictionary must contain the definition for any word that appears in the explanation of another word. So you see, if a dictionary defines $N$ words, it has exactly $N$ distinct words in it. Also, we know that in a dictionary no word appears in the definition of itself.

A sub-dictionary is a collection of dictionary’s words and their definitions such that it can be published as an independent dictionary, obviously satisfying the mentioned condition. As a project of Computational Linguistics course, we are assigned to create a Lexical Knowledge Base which is the knowledge expressed by words. For this task we should create our knowledge foundation based on a dictionary.

It’s really hard for the computer to study words automatically. So, we decided to manually teach it some common words. We start from an appropriate sub-dictionary. By understanding its words, a computer could extend its knowledge to the whole dictionary word by word. For instance, a word “xyz” could be added to the computer’s understanding if computer knows the meaning of every words used in xyz’s definition. You are asked to write a program that can find the smallest extendable sub-dictionary for a specific dictionary.

### 输入格式

The input consists of multiple test cases. The first line of each test case is $n$ ($1 \le n \le 100$), the number of dictionary’s words. Each of the next $n$ lines contains a word and its definition (that has at most $30$ words). Words are separated by blanks and are made up of small English letters less than $25$ characters.

### 输出格式

For each test case, on the first line print the number of sub-dictionary’s words and on the second line write the alphabetically sorted list of words (separated by blanks).

### 样例

Input
5
aue oizer piqoi oizer
doy oizer hweqlo hweqlo
hweqlo piqoi aue
oizer piqoi
piqoi aue aue
0

Output
3
aue oizer piqoi


3 人解决，13 人已尝试。

3 份提交通过，共有 45 份提交。

9.3 EMB 奖励。