Diameter of a Tree

A tree is a connected undirected graph with no cycles. In a tree, there is exactly one simple path between any two nodes.

The length of a path between two nodes is the sum of the weights of the edges on that path. The diameter of a tree is the maximum path length among all pairs of nodes in the tree.

You are given a weighted tree whose nodes are numbered from 1 to n. The root is node 1, and each edge is described by its parent node, child node, and edge weight. Write a program that computes the diameter of the tree.

The first line contains the number of nodes n (1 ≤ n ≤ 10,000).

Each of the next n-1 lines contains information about one edge. Each line has three integers: the parent node number, the child node number, and the edge weight, in that order. Edge information is given in increasing order of parent node number; if the parent node numbers are the same, it is given in increasing order of child node number.

The root node is always node 1. Every edge weight is a positive integer not greater than 100.

Print the diameter of the tree on the first line.