4 rooks in advent

Checkmate in Moves

Two white and two black rooks have come together for the endgame. But the main role is played by the white queen, which, as so often, tips the scales. Without her, the two white heavyweights would have a hard time reaching checkmate, although they do stack up quite threateningly next to the regent. And already after the first attempts to solve the problem, one thing quickly becomes clear, it would be quite simple - if there would be a fifth move! But it's Advent, so the question is, as it has been in previous years: First one, then two, then three, then four, then a king lies on the board? Netschach wishes a wonderful advent season!
Manual
Move for White with the best possible moves and achieve checkmate before the countdown expires. Black responds automatically and tries to prevent the checkmate.
Chesspuzzle: 162

Solution moves

Chess composer
Erich Brunner
Basler Nachrichten, 1934
Statistics
Fails: 3 // Checkmate: 2