Find the largest integer \(n\) such that \(n, n+2016\), and \(n-2016\) are all perfect squares.

Enter 666 if you come to the conclusion that no such \(n\) exists.

**Bonus Question (very hard)**: Does there exist a rational number \(q\) such that \(q,q+2015\) and \(q-2015\) are all squares of rational numbers?

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