This is random and 100% certain that it isn't the right answer, but I am thinking..
PxR=N+ Kg7 (forced)
and all they can really do is Qa1+ delaying Rg8#. I know it's wrong but I can't solve Mate in 4's in my head. Even though mine is mate in 5.
Edit: Typically, just after my post I've seen the Queen on c1 has the chance of taking the Rook on g5.