10041004 SUSTech Online Judge
Problem 1004 --Colorful Tree

1004: Colorful Tree

Time Limit: 3 Sec  Memory Limit: 128 MB
Submit: 10  Solved: 5
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There is a tree with n nodes, each of which has a type of color represented by an integer, where the color of node i is ci.

The path between each two different nodes is unique, of which we define the value as the number of different colors appearing in it.

Calculate the sum of values of all paths on the tree that has n(n−1)2 paths in total.


The input contains multiple test cases.

For each test case, the first line contains one positive integers n, indicating the number of node. (2≤n≤200000)

Next line contains n integers where the i-th integer represents ci, the color of node i(1≤ci≤n)

Each of the next n−1 lines contains two positive integers x,y (1≤x,y≤n,x≠y), meaning an edge between node x and node y.

It is guaranteed that these edges form a tree.


For each test case, output "Case #x: y" in one line (without quotes), where x indicates the case number starting from 1 and y denotes the answer of corresponding case.

Sample Input

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

Sample Output

Case #1: 6
Case #2: 29