18921번 - Cost Of Subtree 다국어

The valuable tree with $n$ vertices grows near Byteazar's house. Edge $i$ has cost $v_i$ assigned to it.

A subtree of the tree is defined as a non-empty connected subset of its edges.

The cost of a subtree is defined as the number of edges in the subtree multiplied by the lowest value of $v_i$ in it.

Byteazar wants to make some money by selling subtrees, so he wants to know the maximum cost of a subtree of his tree.

The first line contains a single integer $n$ ($2 \le n \le 10^5$) --- the number of vertices in the tree. Each of the following $n-1$ lines contains three integers $a_i$, $b_i$ and $v_i$ ($1 \le a_i, b_i \le n$; $a_i \ne b_i$; $1 \le v_i \le 10^9$) --- the vertices connected by the edge and its cost.

Print one integer --- the maximum cost of a subtree of the given tree.