You just need to create one specific latin square for each n. Looking at examples for n=1,2,3,4 might make clear a pattern that can be generalized. The tests only run to n=200, so performance is not a concern.

A latin square is an n × n array filled with the integers 1 to n, each occurring once in each row and column.

You can make it as random as you want as long as it's a Latin Square