# Unique Occurrences solution codeforces

## Unique Occurrences solution codeforces

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

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

Calculate the sum of f(v,u)f(v,u) over all pairs of vertices vv and uu such that 1v<un1≤v<u≤n.

Input

The first line contains a single integer nn (2n51052≤n≤5⋅105) — the number of vertices in the tree.

Each of the next n1n−1 lines contains three integers v,uv,u and xx (1v,u,xn1≤v,u,x≤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)f(v,u) over all pairs of vertices vv and uu such that v<uv<u.

Examples
input

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3
1 2 1
1 3 2

output

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4

input

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3
1 2 2
1 3 2

output

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2

input

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

output

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14

input

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2
2 1 1

output

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1

input

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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

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120