We can say that an $n$-by-$n$ square is regular provided that:
Each of the integers from $0$ to $n^2 − 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is filled), and
If we express the entries in base-$n$ form, each base-$n$ digit occurs exactly once in the units’ position, and exactly once in the $n$’s position.
What is an example of a 4-by-4 filled, magic square which is not regular? The square should use the integers 0 to 15. Show the answer in both decimal and base-4 as well.