CF622E.Ants in Leaves

Tree is a connected graph without cycles. A leaf of a tree is any vertex connected with exactly one other vertex.

You are given a tree with n vertices and a root in the vertex 1. There is an ant in each leaf of the tree. In one second some ants can simultaneously go to the parent vertex from the vertex they were in. No two ants can be in the same vertex simultaneously except for the root of the tree.

Find the minimal time required for all ants to be in the root of the tree. Note that at start the ants are only in the leaves of the tree.

树是无环的连通图。树的一个叶节点是指恰好与另一个顶点相连的任意顶点。

你被给定一棵含 $n$ 个顶点的树，其根节点为顶点 1。树的每个叶节点上都有一只蚂蚁。每秒钟，某些蚂蚁可以同时从当前所在顶点移动到其父节点。除树的根节点外，任意时刻不允许两只蚂蚁处于同一顶点。

求所有蚂蚁均到达树的根节点所需的最短时间。注意：初始时，蚂蚁仅位于树的所有叶节点上。

The first line contains integer n (2 ≤ n ≤ 5·105) — the number of vertices in the tree.

Each of the next n - 1 lines contains two integers x__i, y__i (1 ≤ x__i, y__i ≤ n) — the ends of the i-th edge. It is guaranteed that you are given the correct undirected tree.

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

接下来的 $n-1$ 行，每行包含两个整数 $x_i$、$y_i$（$1 \leq x_i, y_i \leq n$）——第 $i$ 条边的两个端点。保证所给的是一个合法的无向树。

Print the only integer t — the minimal time required for all ants to be in the root of the tree.

输出唯一的整数 $t$ —— 所有蚂蚁到达树根所需的最短时间。