Question 3
For any positive integer $n$, define $f(n)$ as the sum of the squares of the digits of $n$ (in base ten). For example, $f(2012) = 2^2 + 0^2 + 1^2 + 2^2 = 9$. Find the greatest integer $n$ such that there exists a positive integer $d$ with $f(\underbrace{f(\cdots f(n)\cdots)}_{d \text{ times}}) = n$.