Tree Diameter

You are given an undirected tree with n nodes. A tree is an acyclic connected graph. The tree is provided in the form of edges. Your task is to compute the diameter of the tree. The diameter of a tree is defined as the number of edges in the longest path between any two nodes.

Note: The nodes are labeled from 0 to n-1.

Example:

Input:
7
0 1
0 2
1 3
1 4
2 5
2 6
Output:
4

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In the above tree, one of the longest paths is from node 3 to node 5 (or 3 to 6) via nodes 1, 0, and 2, which contains 4 edges.

inputFormat

The input is read from stdin and has the following format:

• The first line contains an integer n — the number of nodes in the tree.
• The next n-1 lines each contain two integers u and v, representing an undirected edge between nodes u and v.

It is guaranteed that the input forms a valid tree, and the nodes are numbered from 0 to n-1.

outputFormat

Output to stdout a single integer — the diameter of the tree (i.e. the number of edges in the longest path between any two nodes).

## sample

1

0