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It is a mate in 4
1.Qb3+ Kd2
(1…Ke1 2.Qe5+ Re4 3.Qxe4+ Kd2 4.Qee3#)
(1…Ke2 2.Qe5+ Re4 3.Qxe4+ Kd2 4.Qee3#)
2.Qcc2+ Ke1
3.Qe3#
1Qb3+ Ke2 or Ke1
2Qe5+ Re4
3Qxe4+ Kd2
Qee3#
1. Qcde5
looks immediately like the strongest threat here.
Attacks one rook, binds the other, and threats the lady via Qe1+.
Well, the first move has to be Qb3 or Qf3+. I think both will suffice, but Qb3 is definitely clear to me, even without a chessboard:
1. Qb3 Ke1
If Ke2, white still plays 2.Qe5, and if Kd2, white plays 2.Qcc2, and 3.Qe3#. However, this mating motif can’t be avoided by black. Continuing:
2. Qe5 Re4
3. Qe4 Kd2
4. Qee3#