You informed me I failed to solve problem 8428 because I did not my move which leaded to winning rook on a1. Why not do more profitable (and shorter): 1.Qxa7 Qxc2+ 2.Kb5 and instead Qxb2+?? (recommended here) ... Qc5+!! and after 3.Ka4 (there is no other possibility) ...b5+! and after 4.Kb3 or Ka5 white queen is lost. I think it is much better than only a rook.