Which gets you first when you are falling into a black hole, the black hole singularity or the cosmic background radiation?

If you look up while you are falling into a black hole you see the universe blue shifted, that is, you see the universe moving quickly forward in time compared to your local time. Since this effect increases as you get closer to the singularity, a star aimed at you could blast you with a billion years of radiation in maybe a second. Of course, no star will be perfectly aligned for billions of years. On the other hand, there is lots of cosmic background radiation coming at you from everywhere in the sky and it will be blue shifted too. So, how bad is it? Would this radiation cook you before you hit the singularity?