Let $f_1(x)=\sqrt{-x}$, and for integers $n\ge 2$, let $f_n(x)=f_{n-1}(\sqrt{n^2-x})$. If $N$ is the largest value of $n$ for which the domain of $f_n$ is nonempty, the domain of $f_N$ is $c$. What is $N+c$?