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bad puzzle

http://en.lichess.org/training/33484

The puzzle says the mating sequence starting with Qd2+ is the best mating sequence, but I think the sequence starting with Ng4+ is shorter:

Ng4+ Kg1 Qc5+ Kf1 Qf2#
Ng4+ Kf1 Qd1#
Ng4+ Ke1 Re8+ Ne5 Rxe5+ Kf1 Qd1#
Ng4+ Ke2 Re8+ Ne5 Rxe5+ Kf1 Qd1#
Oops, didn't see Ke1 followed by Be2... :)

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