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I found alternate solution
Good puzzle but bad solution. Ba4 is much faster. I spent a good 20 min looking at this and was super confused when it rejected Ba4.
Kf7 after Ba4 just leads to Be8+ and Ng7#
That was very hard. It took me a long time to figure out which piece made the first move.
1. Nh6 f5+ Nf5 Kf7 Bd5+ e6 Ng5+ Kf6 Rd6 anything Re6# Or 4...Kg6 Rd6 anything Re6#
Note: I used black and hi-light it or quote it to see it.