$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&S=0\text{ or }N=0\end{matrix}\right.$

$\left\{\begin{matrix}\\N=0\text{, }&\text{unconditionally}\\N\in \mathrm{C}\text{, }&S=0\text{ or }A=0\end{matrix}\right.$

$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&S=0\text{ or }N=0\end{matrix}\right.$

$\left\{\begin{matrix}\\N=0\text{, }&\text{unconditionally}\\N\in \mathrm{R}\text{, }&S=0\text{ or }A=0\end{matrix}\right.$