On a $2004\times 2004$ chessboard we place $2004$ white knights$^1$ in the upper row, and $2004$ black ones in the lowest row. After a finite number of regular chess moves$^2$ , we get the opposite situation where the black ones are on the top and the white ones on the bottom lines. In a turn we make a move with each of the pieces of a color. If you know that each square except those on which the knights originally lie, must not be used more than once in this process, and that after each turn no $2$ knights of the same color can be attacking each other$^3$ , determine the number of ways in which this can be accomplished. $^1$ also known as horses $^2$ the knight can be moved either one square horizontally and two vertically or two squares horizontally and one vertically, in any direction on both horizontal and vertical lines $^3$ a knight is attacking another knight, if in one chess move, the first one can be placed on the second one’s place