Selection and Training Session

2500 chess kings have to be placed on a $100\times 100$ chessboard so that 1) no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex); 2) each row and each column contains exactly $25$ kings; Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.) (IMO-2010 Shortlist, Problem C3)