There are n teams T = {1, . . . , n} in a certain company, where team i has ai employees. The company wants to encourage teams to interact with each other, so they have arranged two group chat sessions. In each session, the employees are divided into m groups G = {1, . . . , m} where group j has at most bj employees. In the first session, each team must send all of their employees into different groups. In the second session, everyone must go to a different group, and at most 2 people in the same group from the first session can go to each group for the second session. (For the second session, it does not matter which teams the employees are from in each group.) The goal is to assign all employees to the groups in the two sessions, satisfying the given constraints. Formulate this as a maximum flow problem. You need to state the directed graph, the two nodes s and t, and the capacities of the arcs. Then draw a sketch of the formulation.