CF1324F.Maximum White Subtree

You are given a tree consisting of $n$ vertices. A tree is a connected undirected graph with $n-1$ edges. Each vertex $v$ of this tree has a color assigned to it ($a_v = 1$ if the vertex $v$ is white and $0$ if the vertex $v$ is black).

You have to solve the following problem for each vertex $v$: what is the maximum difference between the number of white and the number of black vertices you can obtain if you choose some subtree of the given tree that contains the vertex $v$? The subtree of the tree is the connected subgraph of the given tree. More formally, if you choose the subtree that contains $cnt_w$ white vertices and $cnt_b$ black vertices, you have to maximize $cnt_w - cnt_b$.

给你一棵包含 $n$ 个顶点的树。树是一种具有 $n-1$ 条边的连通无向图。该树的每个顶点 $v$ 均被赋予一种颜色（若顶点 $v$ 为白色，则 $a_v = 1$；若为黑色，则 $a_v = 0$）。

你需要对每个顶点 $v$ 求解如下问题：在所有包含顶点 $v$ 的子树中，白色顶点数与黑色顶点数之差（即 $cnt_w - cnt_b$）的最大值是多少？此处“子树”指原树的一个连通子图。更准确地说，若所选子树包含 $cnt_w$ 个白色顶点和 $cnt_b$ 个黑色顶点，则目标是最大化 $cnt_w - cnt_b$。

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

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 1$), where $a_i$ is the color of the $i$-th vertex.

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.

输入的第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）——树中顶点的数量。

输入的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 1$），其中 $a_i$ 表示第 $i$ 个顶点的颜色。

接下来的 $n-1$ 行每行描述树中的一条边。第 $i$ 条边由两个整数 $u_i$ 和 $v_i$ 表示，即该边所连接的两个顶点的编号（$1 \le u_i, v_i \le n$，且 $u_i \ne v_i$）。

保证所给的边构成一棵树。

Print $n$ integers $res_1, res_2, \dots, res_n$, where $res_i$ is the maximum possible difference between the number of white and black vertices in some subtree that contains the vertex $i$.

输出 $n$ 个整数 $res_1, res_2, \dots, res_n$，其中 $res_i$ 表示包含顶点 $i$ 的某个子树中白色顶点数量与黑色顶点数量之差的最大可能值。

The first example is shown below:

The black vertices have bold borders.

In the second example, the best subtree for vertices $2, 3$ and $4$ are vertices $2, 3$ and $4$ correspondingly. And the best subtree for the vertex $1$ is the subtree consisting of vertices $1$ and $3$.

第一个示例如下所示：

黑色顶点具有粗边框。

在第二个示例中，顶点 $2$、$3$ 和 $4$ 的最优子树分别为仅包含顶点 $2$、仅包含顶点 $3$、仅包含顶点 $4$ 的子树；而顶点 $1$ 的最优子树是由顶点 $1$ 和 $3$ 构成的子树。