IMO P4/1997 in January Long 2020

I did not participate in this Long but I was going through the problems yesterday night and felt like had seen Doofish Matrix. Turns its a very slight variation of IMO P4/97.

DFMTRX asks to print a construction of a Doofish matrix given its order n whereas IMO P4/97 asks to show the existence of a Doofish Matrix for infinitely many n and showing that it doesn’t exist for n = 1997.
Most proofs characterize all those n for which the matrix exists and then give an explicit construction or atleast an algorithm for constructing for such a matrix.