CF1187E.Tree Painting

You are given a tree (an undirected connected acyclic graph) consisting of $n$ vertices. You are playing a game on this tree.

Initially all vertices are white. On the first turn of the game you choose one vertex and paint it black. Then on each turn you choose a white vertex adjacent (connected by an edge) to any black vertex and paint it black.

Each time when you choose a vertex (even during the first turn), you gain the number of points equal to the size of the connected component consisting only of white vertices that contains the chosen vertex. The game ends when all vertices are painted black.

Let's see the following example:

Vertices $1$ and $4$ are painted black already. If you choose the vertex $2$, you will gain $4$ points for the connected component consisting of vertices $2, 3, 5$ and $6$. If you choose the vertex $9$, you will gain $3$ points for the connected component consisting of vertices $7, 8$ and $9$.

Your task is to maximize the number of points you gain.

给你一棵树（一个无向、连通且无环的图），该树包含 $n$ 个顶点。你将在该树上进行一场游戏。

初始时，所有顶点均为白色。在游戏的第一轮中，你选择一个顶点并将其涂成黑色。随后，在每一轮中，你需选择一个与任意黑色顶点相邻（即通过一条边直接相连）的白色顶点，并将其涂成黑色。

每次当你选择一个顶点（包括第一轮）时，你将获得等于包含该顶点的、仅由白色顶点构成的连通分量的大小的分数。当所有顶点均被涂成黑色时，游戏结束。

我们来看如下示例：

顶点 $1$ 和 $4$ 已被涂成黑色。若你选择顶点 $2$，则你将获得 $4$ 分，对应由顶点 $2, 3, 5$ 和 $6$ 构成的白色连通分量；若你选择顶点 $9$，则你将获得 $3$ 分，对应由顶点 $7, 8$ 和 $9$ 构成的白色连通分量。

你的任务是最大化所获得的总分数。

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

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 indices 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.

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

接下来的 $n - 1$ 行每行描述树的一条边。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 one integer — the maximum number of points you gain if you will play optimally.

输出一个整数——如果你采取最优策略，所能获得的最大点数。

The first example tree is shown in the problem statement.

第一个示例树如题目陈述中所示。