(10 pts) (Latin square) An n \times n Latin square (where n >= 1 is an integer) is an n \times n matrix
with entries being integers in {1, . . . , n}, such that no two entries in the same row are the same,
and no two entries in the same column are the same. We call n the order of the Latin square.
For example, this is a 3 \times 3 Latin square (of order 3):