4. There are $24$ participants attended a meeting. Each two of them shook hands once or not. A total of $216$ handshakes occured in the meeting. For any two participants who have shaken hands, at most $10$ among the rest $22$ participants have shaken hands with exactly one of these two persons. Define a friend circle to be a group of $3$ participants in which each person has shaken hands with the other two. Find the minimum possible value of friend circles.
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