Marinada '25

[lang=hr] Želimo postaviti $m$ polukraljica na šahovsku ploču dimenzija $1001 \times 1001$; one mogu napadati vodoravno, okomito ili po dijagonali prema dolje-desno/gore-lijevo (tj. u šest smjerova), a napadaju i polje na kojem se nalaze. Odredite najmanji $m$ takav da postoji raspored u kojem je svako polje na ploči napadnuto barem jednom polukraljicom. [/lang] [lang=en] We want to place \(m\) \emph{semi-queens} on a \(1001 \times 1001\) chessboard. A semi-queen can attack horizontally, vertically, and along the downward-right / upward-left diagonals (i.e., in six directions), and it also attacks the square it occupies. Determine the minimum \(m\) such that there exists an arrangement in which every square on the board is attacked by at least one semi-queen. [/lang]