Marinada '25

[lang=hr] u $7 \times 7$ ploču upisujemo brojeve $0$ i $1$ tako da suma svih brojeva po stupcu bude $1,2,3,4,5,6,7$ u nekom redoslijedu. Isto vrijedi i za sumu redaka. Na koliko načina možemo popuniti takvu tablicu? [/lang] [lang=en] We fill a $7 \times 7$ board with the numbers $0$ and $1$ so that the sum of all the numbers in each column is $1, 2, 3, 4, 5, 6, 7$ in some order. The same condition holds for the sums of the rows. In how many ways can we fill such a board? [/lang]