[思维]Minimum Spanning Tree

In the mathematical discipline of graph theory, the line graph of a simple undirected weighted graph G is another simple undirected weighted graph L(G) that represents the adjacency between every two edges in G.

Precisely speaking, for an undirected weighted graph G without loops or multiple edges, its line graph L(G) is a graph such that:
·Each vertex of L(G) represents an edge of G.
·Two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G, and the weight of such edge between this two vertices is the sum of their corresponding edges‘ weight.
A minimum spanning tree(MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible.

Given a tree G, please write a program to find the minimum spanning tree of L(G).

The first line of the input contains an integer T(1≤T≤1000), denoting the number of test cases.

In each test case, there is one integer n(2≤n≤100000) in the first line, denoting the number of vertices of G.

For the next n−1 lines, each line contains three integers u,v,w(1≤u,v≤n,u≠v,1≤w≤109), denoting a bidirectional edge between vertex u and v with weight w.

It is guaranteed that ∑n≤106.

For each test case, print a single line containing an integer, denoting the sum of all the edges‘ weight of MST(L(G)).