A12909 | One Node is Gone

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.

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.

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.