We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies.
  1. Prepare
  2. Algorithms
  3. Graph Theory
  4. Tripartite Matching

Tripartite Matching

You are given unweighted, undirected graphs, , , and , with vertices each, where the graph has edges and the vertices in each graph are numbered from through . Find the number of ordered triples , where , , such that there is an edge in , an edge in , and an edge in .

Input Format

The first line contains single integer, , denoting the number of vertices in the graphs. The subsequent lines define , , and . Each graph is defined as follows:

  1. The first line contains an integer, , describing the number of edges in the graph being defined.
  2. Each line of the subsequent lines (where ) contains space-separated integers describing the respective nodes, and connected by edge .

Constraints

  • , and
  • Each graph contains no cycles and any pair of directly connected nodes is connected by a maximum of edge.

Output Format

Print a single integer denoting the number of distinct triples as described in the Problem Statement above.

Sample Input

3
2
1 2
2 3
3
1 2
1 3
2 3
2
1 3
2 3

Sample Output

3

Explanation

There are three possible triples in our Sample Input:

Thus, we print as our output.