If $f: N\rightarrow N $ be such that $f(f(n))+f(n+1)=n+2$ for all $n\in N$ find $f(1)$ and $f(2)$.

Question

Putting $n=1$, we get $f(f(1))+f(2)=3$. Thus there are two possibilities. Either $f(f(1))=1, f(2)=2$ or $f(f(1))=2, f(2)=1$. Also, we observe that $f(f(n))=n+2-f(n+1)\leq n+1$ and $f(n+1)=n+2-f(f(n))\leq n+1$. How do we get the values of $f(1)$ and $f(2)$?