2019CCPC-江西省赛 A-Cotree（树的重心）

链接：JXCPC A-Cotree

Avin has two trees which are not connected. He asks you to add an edge between them to make them connected while minimizing the function $$\sum _{i=1}^{n-1}\sum _{j=i+1}^{n}distance(i,j)$$, where dis(i, j) represents the number of edges of the path from i to j. He is happy with only the function value.

Input

The first line contains a number n (2<=n<=100000). In each of the following n−2 lines, there are two numbers u and v, meaning that there is an edge between u and v. The input is guaranteed to contain exactly two trees.

Output

Just print the minimum function value.

Sample Input

3
1 2

Sample Output

4

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题意：

给出两棵树（共n个结点，即n-2条边），加一条边连接两棵树使得得到的新树上结点两两距离和最小。即$$\sum _{i=1}^{n-1}$$