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If it were Black's move she would easily win. In fact she has two different ways of checkmating White in three moves. One of them would be to take the Knight with the Rook, attacking the King and forcing White's Rook to recapture as the King has no square to go to; then to give check with the Queen on g3 forcing White's King to h1 and enabling the mate with the Queen on g2 or h2.
The other way would be to start with the check on g3. As White's Knight is pinned he cannot capture the Queen. Interposing the Rook on g2 would not help either as the Queen would simply take it at the same time checkmating the King. White's only move is, therefore, to play the King into the corner, and Black then mates by first taking the Knight and then moving the Queen to g2 or h2.
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