A fighting game club has $2024$ members. One day, a game of Smash is played between some pairs of members such that every member has played against exactly $3$ other members. Each match has a winner and a loser. A member will be happy if they won in at least $2$ of the matches. What is the maximum number of happy members over all possible match-ups and all possible outcomes?

Let's think step by step and output the final answer within \boxed{}.
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