6446：Tree and Permutation

There are $N$ vertices connected by $N-1$ edges, each edge has its own length.
The set { $1, 2, 3, … , N$ } contains a total of $N!$ unique permutations, let’s say the $i$-th permutation is $P_i$ and $P_{i,j}$ is its $j$-th number.
For the $i$-th permutation, it can be a traverse sequence of the tree with $N$ vertices, which means we can go from the $P_{i,1}$-th vertex to the $P_{i,2}$-th vertex by the shortest path, then go to the $P_{i,3}$-th vertex ( also by the shortest path ) , and so on. Finally we’ll reach the $P_{i,N}$-th vertex, let’s define the total distance of this route as $D(P_i)$ , so please calculate the sum of $D(P_i)$ for all $N!$ permutations.

There are 10 test cases at most.
The first line of each test case contains one integer $N$ ( $1 ≤ N ≤ 10^5$ ) .
For the next $N-1$ lines, each line contains three integer $X$, $Y$ and $L$, which means there is an edge between $X$-th vertex and $Y$-th of length $L$ ( $1 ≤ X, Y ≤ N, 1 ≤ L ≤ 10^9$ ) .

For each test case, print the answer module $10^9+7$ in one line.