Let $ ABC$ be a triangle with area $ S$ and points $ D,E,F$ on the sides $ BC,CA,AB$. Perpendiculars at points $ D,E,F$ to the $ BC,CA,AB$ cut circumcircle of the triangle $ ABC$ at points $ (D_1,D_2), (E_1,E_2), (F_1,F_2)$. Prove that: $ |D_1B\cdot D_1C - D_2B\cdot D_2C| + |E_1A\cdot E_1C - E_2A\cdot E_2C| + |F_1B\cdot F_1A - F_2B\cdot F_2A| > 4S$