A15865. Li Hua and Path

Li Hua has a tree of $n$ vertices and $n-1$ edges. The vertices are numbered from $1$ to $n$ .

A pair of vertices $(u,v)$ ( $u < v$ ) is considered cute if exactly one of the following two statements is true:

- $u$ is the vertex with the minimum index among all vertices on the path $(u,v)$ .
- $v$ is the vertex with the maximum index among all vertices on the path $(u,v)$ .

There will be $m$ operations. In each operation, he decides an integer $k_j$ , then inserts a vertex numbered $n+j$ to the tree, connecting with the vertex numbered $k_j$ .

He wants to calculate the number of cute pairs before operations and after each operation.

Suppose you were Li Hua, please solve this problem.

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

Next $n-1$ lines contain the edges of the tree. The $i$ -th line contains two integers $u_i$ and $v_i$ ( $1\le u_i,v_i\le n$ ; $u_i\ne v_i$ ) — the corresponding edge. The given edges form a tree.

The next line contains the single integer $m$ ( $1\le m\le 2\cdot 10^5$ ) — the number of operations.

Next $m$ lines contain operations — one operation per line. The $j$ -th operation contains one integer $k_j$ ( $1\le k_j < n+j$ ) — a vertex.

Print $m+1$ integers — the number of cute pairs before operations and after each operation.

The initial tree is shown in the following picture:

There are $11$ cute pairs — $(1,5),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,7),(6,7)$ .

Similarly, we can count the cute pairs after each operation and the result is $15$ and $19$ .