This is an extremely hard problem to solve. It haunted me for about a week until I finally got it. Without further ado, here are the nicely symmetrical solutions:
1 Bc1 Rb8 2 Qb7 bxc5 3 Qb2 d4 mate.
1 Rc1 Bh7 2 Qg6 d4 3 Qc2 bxc5 mate.
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