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Let the domain of discourse be the set S={1,2,3,4,5}S = \{1, 2, 3, 4, 5\}S={1,2,3,4,5}. How many distinct interpretations of a binary predicate P(x,y)P(x, y)P(x,y) on SSS satisfy the first-order sentence ∀x∃!yP(x,y)\forall x \exists! y P(x, y)∀x∃!yP(x,y) (where ∃!\exists!∃! denotes 'exists unique')?