Maximum bipartite matching via max flow: implement Hopcroft-Karp-like algorithm.

In a social network, users can follow each other, and we want to find the maximum number of pairs of users where one user follows the other, but not vice versa. This can be modeled as a bipartite graph, where users are nodes, and a directed edge from user A to user B means A follows B. We need to implement an algorithm to find the maximum bipartite matching in this graph, which represents the maximum number of pairs of users with a one-way follow relationship.

Examples
Input: "test_input_1"
Output: "output_1"
Hints

Maximum bipartite matching via max flow: implement Hopcroft-Karp-like algorithm.

In a social network, users can follow each other, and we want to find the maximum number of pairs of users where one user follows the other, but not vice versa. This can be modeled as a bipartite graph, where users are nodes, and a directed edge from user A to user B means A follows B. We need to implement an algorithm to find the maximum bipartite matching in this graph, which represents the maximum number of pairs of users with a one-way follow relationship.