Cartesian plane challenge

In the Cartesian plane, $\triangle ABC (\angle A=90^{\circ})$ , $K$ is an inversion point of $A$ through $C$ , the line pass $K$ perpendicular to $BC$ at $E$ and cut $AB$ at $N(-1;3)$ . Let $\angle AEB=45^{\circ}$ , $(BK): 3x+y-15=0$ , $y_B>3$ . Find the sum of the coordinates of vertices $A,B,C$ .

Submit your answer to 3 decimal places.

Clarification : The sum of the coordinates is $x_A+y_A+x_B+y_B+x_C+y_C$ .