Weird natural numbers function problem

Question

So I came across with the following problem, of a Brazilian elementary number theory book, which did not came with the resolutions: "Let $f:\Bbb N^{*} \to \Bbb N^{*}$ a function such that $f(a)=f(1995)$, $f(a+1)=f(1996)$, $f(a+2)=f(1997)$ and $$f(a+n)=\frac{f(n)-1}{f(n)+1}$$ for $a∈\Bbb N$. Find the least possible value of $a$." I tried many calculations, but the result was always circular, and I'd like to see what you guys would try. I appreciate your help!