CF1797F 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 $ .