Hard Chess Puzzle: Two Rooks Against A Queen

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Here is a very hard chess puzzle where two White Rooks are managing to prevail over Black Queen only after a tough fight, all the time avoiding stalemate.

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Mario Matous, 1982
White is winning
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The puzzle in Forsyth-Edwards Notation (FEN):
7k/2q3pP/6P1/8/8/8/6Pp/2RR3K w – – 0 1
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