You are given a tree, consisting of $n$ vertices. Each edge has an integer value written on it.

Let $f(v, u)$ be the number of values that appear exactly once on the edges of a simple path between vertices $v$ and $u$.

Calculate the sum of $f(v, u)$ over all pairs of vertices $v$ and $u$ such that $1 \le v < u \le n$.

Input

The first line contains a single integer $n$ ($2 \le n \le 5 \cdot 10^5$) — the number of vertices in the tree.

Each of the next $n-1$ lines contains three integers $v, u$ and $x$ ($1 \le v, u, x \le n$) — the description of an edge: the vertices it connects and the value written on it.

The given edges form a tree.

Output

Print a single integer — the sum of $f(v, u)$ over all pairs of vertices $v$ and $u$ such that $v < u$.

见题面 Input 部分

见题面 Output 部分