One test is a multiple choice test with $5$ questions, each having $4$ options. There are $2000$ candidates, each choosing only one answer for each question. Find the smallest possible integer $n$ such that a student's answer sheet, labeled $n$, has the following property: The answer sheet contains four sheets, and any two of these four sheets have exactly the same three answers.

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