F. Tree with Maximum Costtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint one integer — the maximum possible cost of the tree if you can choose any vertex as v.ExamplesInput
8
9 4 1 7 10 1 6 5
1 2
2 3
1 4
1 5
5 6
5 7
5 8
Output
121
Input
1
1337
Output
0
NotePicture 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.
8
9 4 1 7 10 1 6 5
1 2
2 3
1 4
1 5
5 6
5 7
5 8

121 
['dfs and similar', 'dp', 'trees', '*1900']