Antoine, Benoît, Claude, Didier, Étienne, and Françoise go to the cinema together to see a movie. The six of them want to sit in a single row of six seats. However, Antoine, Benoît, and Claude are mortal enemies and refuse to sit next to either of the other two. How many different seating arrangements are possible?

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