13 Color 8 small squares on a $4 \times 4$ chessboard black, such that each row and each column has exactly two black squares, then there are $\qquad$ different ways to do so. (Answer with a number)
(13) The first row can be colored with 2 black cells in $\mathrm{C}_{4}^{2}$ ways. After the first row is colored, there are the following three scenarios:
(1) The black cells in the second row are in the same columns as those in the first row, in which case there is only 1 way to color the remaining rows;
(2) The black cells in the second row are in different columns from those in the first row, in which case there are $\mathrm{C}_{4}^{2}$ ways to color the third row, and the coloring of the fourth row is then determined;
(3) The black cells in the second row have exactly one in the same column as a black cell in the first row, and there are 4 such coloring methods. After the first and second rows are colored, the black cells in the third row must have 1 in a different column from the black cells above, in which case there are 2 ways to color the third row, and the coloring of the fourth row is then determined.
Therefore, the total number of coloring methods is $6 \times(1+6+4 \times 2)=90$ (ways).