You are responsible for arranging a banquet for an agency. In the agency, some pairs of agents are enemies. A group of agents are called avengers, if and only if the number of agents in the group is odd and at least $3$, and it is possible to arrange all of them around a round table so that every two neighbors are enemies. You figure out a way to assign all agents to $11$ tables so that any two agents on the same tables are not enemies, and that’s the minimum number of tables you can get. Prove that there are at least $2^{10}-11$ avengers in the agency. This problem is adapted from 2015 IMO Shortlist C7.