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data structures

dfs and similar

divide and conquer

dp

dsu

trees

*2300

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F. Unique Occurrences

time limit per test

6 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard outputYou 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 $$$v < u$$$.

Examples

Input

3 1 2 1 1 3 2

Output

4

Input

3 1 2 2 1 3 2

Output

2

Input

5 1 4 4 1 2 3 3 4 4 4 5 5

Output

14

Input

2 2 1 1

Output

1

Input

10 10 2 3 3 8 8 4 8 9 5 8 5 3 10 7 7 8 2 5 6 6 9 3 4 1 6 3

Output

120

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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