Putnam 1992 A1

Prove that $f(n) = 1-n$ is the only integer-valued function defined on the integers that satisfies the following conditions.

(i) $f(f(n)) = n$, for all integers $n$;

(ii) $f(f(n+2)+2) = n$ for all integers $n$;

(iii) $f(0) = 1$.