One Node is Gone

Description:

Input:

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.

Output:

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.

Sample Input:

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

Sample Output:

1
3

Sample Input:

2
1 2

Sample Output:

2
1 2

Sample Input:

3
1 2
2 3
3 4
4 5
5 6

Sample Output:

0

Note:

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.