Tree with Maximum Cost
Description
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 $v$.
Input
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.
Output
Print one integer — the maximum possible cost of the tree if you can choose any vertex as $v$.
Samples
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
Note
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 $0$.