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:
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 $u, v, w (1 <= u, v <= n, u eq.not v, 1 <= w <= 10^9)$, denoting a bidirectional edge between vertex $u$ and $v$ with weight $w$.
It is guaranteed that $sum n <= 10^6$.
For each test case, print a single line containing an integer, denoting the sum of all the edges' weight of $M S T (L (G))$.
## Input
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 $u, v, w (1 <= u, v <= n, u eq.not v, 1 <= w <= 10^9)$, denoting a bidirectional edge between vertex $u$ and $v$ with weight $w$.It is guaranteed that $sum n <= 10^6$.
## Output
For each test case, print a single line containing an integer, denoting the sum of all the edges' weight of $M S T (L (G))$.
[samples]
**Definitions**
Let $ T $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ denote the number of insertions.
- Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be a permutation of $ \{1, 2, \dots, n_k\} $, representing the sequence of values inserted into an initially empty 2-3-4 tree.
**Constraints**
1. $ 1 \le T \le 50 $
2. For each $ k \in \{1, \dots, T\} $:
- $ 1 \le n_k \le 5000 $
- $ A_k $ is a permutation of $ \{1, 2, \dots, n_k\} $
**Objective**
After inserting all elements of $ A_k $ into an initially empty 2-3-4 tree, output the tree structure in pre-order traversal, where each node is printed as a line containing its data elements in ascending order.