According to the other problem, 2500 kin...

According to the other problem, 2500 king pieces of chess have to be placed on a `100xx100` 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.)

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