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Puzzle solution (Nz4KC)

lichess.org/training/Nz4KC

Solution has mate in 4, but can mate in 3?! [numbering from initial puzzle position] -
1. Rh4 Kg8 2. Qh6... and 3. Qh8# or Qf8# depending on which Black bishop moves in mv2, or on White's whim if none does.

Or, more likely, what am i missing?