Labeling the Tree with Distances

Description:

Input:

The first line contains one integer $$$n$$$ ($$$2\le n\le 2\cdot 10^5$$$) — the number of vertices in the tree.

The second line contains $$$n - 1$$$ integers $$$a_1,a_2,\ldots,a_{n-1}$$$ ($$$0\le a_i < n$$$) — the given list.

Then, $$$n−1$$$ lines follow. Each of them contains two integers $$$u$$$ and $$$v$$$ ($$$1\le u,v\le n$$$) denoting an edge between vertices $$$u$$$ and $$$v$$$. It is guaranteed that the edges form a tree.

Output:

In the first line print the number of good vertices.

In the second line, print the indices of all good vertices in ascending order.

Sample Input:

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

Sample Output:

2
2 4 

Sample Input:

5
1 2 1 2
1 2
3 2
3 4
5 4

Sample Output:

1
3 

Sample Input:

3
2 2
1 2
2 3

Sample Output:

0

Note:

This is the tree for the first example:

And these are two possible labelings with the elements on the list so that $$$2$$$ is a good vertex (left) and $$$4$$$ is a good vertex (right).

The square below each vertex represents its label. The black squares contain the numbers which were on the given list and the only white square contains the only number which was not on the given list.

In the second example, the only good vertex is vertex $$$3$$$.

In the third example, there are no good vertices.