SHARYGIN 2020 Problem 5

Let $BB_1$ , $CC_1$ be the altitudes of triangle $ABC$ , and $AD$ be the diameter of its circumcircle. The lines $BB_1$ and $DC_1$ meet at point $E$ , the lines $CC_1$ and $DB_1$ meet at point $F$ . Prove that $\angle CAE = \angle BAF$ .