Ants in Leaves

题意翻译

给定一棵 $n$ 个节点的树，根节点是 $1$。这棵树的每一个叶节点都有一只小蚂蚁。每过 $1$ 秒钟，可以选择让一些蚂蚁向父节点走一步。注意，两只蚂蚁不能同时在一个除去根节点的节点上。 问这些蚂蚁最少用多少秒的时间，使得所有蚂蚁都走到根节点。

题目描述

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.

输入输出格式

输入格式

The first line contains integer $ n $ ( $ 2<=n<=5·10^{5} $ ) — 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.

输出格式

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

输入输出样例

输入样例 #1

12
1 2
1 3
1 4
2 5
2 6
3 7
3 8
3 9
8 10
8 11
8 12

输出样例 #1

6

输入样例 #2

2
2 1

输出样例 #2

1