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1…Rc2+ 2.Ke3
( 2.Kd3 Qd1+ 3.Ke3 Rxe2+ 4.Kf3 Qf1+ 5.Qf2 Qxf2# )
2…Qc1+ 3.Kf3 g4+ 4.Kg2 Rxe2+ 5.Qf2 Qf1+ 6.Kh2 Rxf2#
1. Rc2+!
The longest I see is mate in 5. I see many shorter mates.
Rc2+ Ke3
Qg1+ Kd3
Qd1+ Ke3
Qxe2+ Kd4
Qxe4#
Rc2+ Ke3
Qg1+ Kf3
Qh1+ Kf2
Qh2+ etc