Triangle-Fruit Counting

Problem Description

Given a tree with $n$ nodes, a "triangle-fruit" is defined as a set of $3$ nodes whose pairwise shortest-path distances $a, b, c$ can form a triangle.

Count how many distinct triangle-fruits the tree has.

Note: two sets are the same if and only if $A \subseteq B$ and $B \subseteq A$.

Input Format

The first line contains a positive integer $n$, the number of nodes in the tree.

The next $n-1$ lines each contain three integers $u, v, w$, indicating an edge of weight $w$ between nodes $u$ and $v$.

Output Format

Output one integer: the answer.

Sample Input

7
1 2 1
1 3 1
2 4 1
2 5 1
3 6 1
3 7 1

Sample Output

8

Constraints

For all data: $1 \le n \le 10^5$, edge weight $1 \le w \le 10^5$, $1 \le u, v \le n$.