A huge group of people live a bizarre box based existence. Every day, everyone changes the box that they're in, and every day they share their box with exactly one person, and never share a box with the same person twice.

One of the people of the boxes gets sick. The illness is spread by co-box-itation. What is the minimum number of people who are ill on day n?

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**Additional information (not originally included in problem):**

Potentially relevant OEIS sequence: <http://oeis.org/A007843>