Three Trees

Description:

Input:

The first line contains three space-separated integers n₁, n₂, n₃ — the number of vertices in the first, second, and third trees, respectively. The following n₁ - 1 lines describe the first tree. Each of these lines describes an edge in the first tree and contains a pair of integers separated by a single space — the numeric labels of vertices connected by the edge. The following n₂ - 1 lines describe the second tree in the same fashion, and the n₃ - 1 lines after that similarly describe the third tree. The vertices in each tree are numbered with consecutive integers starting with 1.

The problem consists of two subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.

• In subproblem E1 (11 points), the number of vertices in each tree will be between 1 and 1000, inclusive.
• In subproblem E2 (13 points), the number of vertices in each tree will be between 1 and 100000, inclusive.

Output:

Print a single integer number — the maximum possible sum of distances between all pairs of nodes in the united tree.

Sample Input:

2 2 3
1 2
1 2
1 2
2 3

Sample Output:

56

Sample Input:

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

Sample Output:

151

Note:

Consider the first test case. There are two trees composed of two nodes, and one tree with three nodes. The maximum possible answer is obtained if the trees are connected in a single chain of 7 vertices.

In the second test case, a possible choice of new edges to obtain the maximum answer is the following:

• Connect node 3 from the first tree to node 1 from the second tree;
• Connect node 2 from the third tree to node 1 from the second tree.