Let integers $$a,b \in [-3,3]$$ be such that $$a+b \neq 0$$. Then the number of all possible ordered pairs (a, b), for which $$\left|\frac{z-a}{z+b}\right| = 1$$ and $$\begin{vmatrix} z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega \end{vmatrix} = 1,\quad z \in \mathbb{C}$$, where $$\omega$$ and $$\omega^{2}$$ are the roots of $$x^{2} + x + 1 = 0$$, is equal to_________.