Kings all over the game

2500 chess kings have to be placed on a \(100 \times 100\) chessboard so that

(i) no king can capture any other one (i.e., no 2 kings are placed in two squares sharing a common vertex);

(ii) each row and each column consists exactly 25 kings.

Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.)

Image Credit: Flickr Darwyn

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