Solution:
1.Qd7!
1....Sh5 2.Sf7#
1....Se2 2.Sf7+ Kh5 3.Qh3#
1....Sf5 2.Sf7+ Kh5 3.Qd1#
1....Se4 or Sh1 2.Sf7+ Kh5 3.Qd1# or Qh3#
1....Sf~ 2.Sf7+ Kh5 3.Qh3#
1....Kh5 2.Qg4+ Kh6 3.Sf7#
1....Kg5 2.Qg4+ Kf6 3.Sd7#
2....Kh6 3.Sf7#
1....g5 2.Qg7+ Kh5 3.Qxh7#