You are given a weighted tree with $N$ nodes and $N - 1$ edges. 

$E$ is defined as $\sum_\limits{i=1}^{i = N} \sum_\limits{j=i +1}^{j = N} F(i,j)$. Also, $F(i, j)$ is equal to = (Maximum value of the edge that is present on the simple path between node $i$ and $j$) $\times i \times j$ 

You are required to determine the value of $E$ modulo $10^9 + 7$.

Input format

• The first line contains an integer $N$ denoting the number of nodes in a tree.
• The next $N - 1$ lines contain three space-separated integers $u, v, w$ denoting an edge between node $u$ and $v$ with weight $w$.

Output format

Print the required value of $E$ modulo $10^9 + 7$.

Constraints

$1 \le N \le 2 \times 10^5 \\ 1 \le w \le 10^6 \\ 1 \le u, v \le N$