Implement the Ford-Fulkerson algorithm and use it to solve the bipartite matching problem.

Use the following input file format to input a bipartite graph. The first number on each line is the number for a vertex in the left side of the bipartite graph. The rest of the numbers on each line ar evertices on the right side of the bipartite graph that the first vertex is adjacent to. For example:

1 10 11 12

2 11

3 10 12

Vertex 1 is adjacent to vertices 10, 11 and 10. Vertex 2 is adjacent to vertex 11. Vertex 3 is adjacent to vertices 10 and 12. All vertices in these graphs are adjacent to at least one other vertex.

Output the cardinality of a maximum matching and output the matching itself.