Three squares $ABB_1B_2,BCC_1C_2,CAA_1A_2$ are constructed in the exterior of a triangle $ABC$. In the exterior of these squares, another three squares $A_1B_2B_3B_4,B_1C_2C_3C_4,C_1A_2A_3A_4$ are constructed. Prove that the area of a triangle with sides $C_3A_4,A_3B_4,B_3C_4$ is $16$ times the area of $\triangle ABC$.