One Node is Gone

题意翻译

#### 题目描述 给定一个正整数$n(2\le n\le17)$ 我们将会先生成一个大小为$2^n-1$的完全二叉树，其有一个根 现在以某种规则删去了其中的一个非根节点，具体规则如下： 设删去点为$u$ 那么我们会删去所有$u$的出边，然后将其所有直系儿子与$u$的父亲连一条边，特别的，如果$u$是一个叶子节点，则不会连边. 现在给定一棵树，希望你求出其能否以上述规则通过删除完全二叉树的一个点后得到，如果可以，求出方案数并输出所有方案中$u$的父亲，你需要升序输出 #### 输入格式 第一行一个正整数$n$ 接下来$2^n-3$行，每行描述给定树的一条边 #### 输出格式 第一行输出方案数，若不为$0$，则第二行升序输出所有可能的父亲节点，否则不输出第二行

题目描述

You have an integer $ n $ . Let's define following tree generation as McDic's generation: 1. Make a complete and full binary tree of $ 2^{n} - 1 $ vertices. Complete and full binary tree means a tree that exactly one vertex is a root, all leaves have the same depth (distance from the root), and all non-leaf nodes have exactly two child nodes. 2. Select a non-root vertex $ v $ from that binary tree. 3. Remove $ v $ from tree and make new edges between $ v $ 's parent and $ v $ 's direct children. If $ v $ has no children, then no new edges will be made. You have a tree. Determine if this tree can be made by McDic's generation. If yes, then find the parent vertex of removed vertex in tree.

输入输出格式

输入格式

The first line contains integer $ n $ ( $ 2 \le n \le 17 $ ). The $ i $ -th of the next $ 2^{n} - 3 $ lines contains two integers $ a_{i} $ and $ b_{i} $ ( $ 1 \le a_{i} \lt b_{i} \le 2^{n} - 2 $ ) — meaning there is an edge between $ a_{i} $ and $ b_{i} $ . It is guaranteed that the given edges form a tree.

输出格式

Print two lines. In the first line, print a single integer — the number of answers. If given tree cannot be made by McDic's generation, then print $ 0 $ . In the second line, print all possible answers in ascending order, separated by spaces. If the given tree cannot be made by McDic's generation, then don't print anything.

输入输出样例

输入样例 #1

4
1 2
1 3
2 4
2 5
3 6
3 13
3 14
4 7
4 8
5 9
5 10
6 11
6 12

输出样例 #1

1
3

输入样例 #2

2
1 2

输出样例 #2

2
1 2

输入样例 #3

3
1 2
2 3
3 4
4 5
5 6

输出样例 #3

0

说明

In the first example, $ 3 $ is the only possible answer. In the second example, there are $ 2 $ possible answers. In the third example, the tree can't be generated by McDic's generation.