Tree with Maximum Cost

- 有一棵 $n$ 个节点的树，每个点有一个权值 $a_i$。 - 定义 $\operatorname{dist}(u,v)$ 为 $u,v$ 两点间距离。 - 您要找到一个点 $u$，使得 $$\sum_{i=1}^n\operatorname{dist}(i,u)\cdot a_i$$ 最大。您只需求出最大值。 - $1\le n,a_i\le 2\times 10^5$。

You are given a tree consisting exactly of $ n $ vertices. Tree is a connected undirected graph with $ n-1 $ edges. Each vertex $ v $ of this tree has a value $ a_v $ assigned to it. Let $ dist(x, y) $ be the distance between the vertices $ x $ and $ y $ . The distance between the vertices is the number of edges on the simple path between them. Let's define the cost of the tree as the following value: firstly, let's fix some vertex of the tree. Let it be $ v $ . Then the cost of the tree is $ \sum\limits_{i = 1}^{n} dist(i, v) \cdot a_i $ . Your task is to calculate the maximum possible cost of the tree if you can choose $ v $ arbitrarily.

The first line contains one integer $ n $ , the number of vertices in the tree ( $ 1 \le n \le 2 \cdot 10^5 $ ). The second line of the input contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 2 \cdot 10^5 $ ), where $ a_i $ is the value of the vertex $ i $ . Each of the next $ n - 1 $ lines describes an edge of the tree. Edge $ i $ is denoted by two integers $ u_i $ and $ v_i $ , the labels of vertices it connects ( $ 1 \le u_i, v_i \le n $ , $ u_i \ne v_i $ ). It is guaranteed that the given edges form a tree.

Print one integer — the maximum possible cost of the tree if you can choose any vertex as $ v $ .

8
9 4 1 7 10 1 6 5
1 2
2 3
1 4
1 5
5 6
5 7
5 8

121

1
1337

0

Picture corresponding to the first example:  You can choose the vertex $ 3 $ as a root, then the answer will be $ 2 \cdot 9 + 1 \cdot 4 + 0 \cdot 1 + 3 \cdot 7 + 3 \cdot 10 + 4 \cdot 1 + 4 \cdot 6 + 4 \cdot 5 = 18 + 4 + 0 + 21 + 30 + 4 + 24 + 20 = 121 $ . In the second example tree consists only of one vertex so the answer is always $ 0 $ .