Marinada '24

[lang=hr] Zarađenim novcem, Fran je odlučio kupiti novu farmu mahuna. Ona izgleda kao kvadratna mreža veličine $999 \times 999$. Fran ne poznaje toliko dobro zakone za ovako velike farme mahuna tako da je ovaj put u pomoć pozvao svog odvjetnika Saleta Dobroćudnog. Sale mu je kazao kako na nekim poljima treba, a na nekima ne smije posaditi mahune, ovisno o magičnom broju $T$. Broj $T$ se određuje kao broj uređenih trojki $(C_1, C_2, C_3)$ polja farme gdje su $C_1$ i $C_2$ u istom redu, a $C_2$ i $C_3$ u istom stupcu tako da su na $C_1$ i $C_3$ posađene mahune, a na $C_2$ ne. Sale je šapnuo Franu da ako želi da mu policija ne zaplijeni mahune, mora maksimizirati $T$. Pomognite Franu i odredite najveću moguću vrijednost magičnog broja. [/lang] [lang=en] With the money he earned, Fran decided to buy a new bean farm. It looks like a square grid of size $999 \times 999$. Fran isn't familiar with the laws for such large bean farms, so this time he called on his lawyer, Saul Goodman. Saul told him that in some fields, beans must be planted, while in others, they must not, depending on the magic number $T$. The number $T$ is defined as the number of ordered triples $(C_1, C_2, C_3)$ of farm fields where $C_1$ and $C_2$ are in the same row, and $C_2$ and $C_3$ are in the same column, such that beans are planted on $C_1$ and $C_3$, but not on $C_2$. Saul whispered to Fran that if he wants to avoid having his beans confiscated by the police, he must maximize $T$. Help Fran determine the maximum possible value of the magic number. [/lang]