KöMaL 2014 B4661

There are discs placed on some fields of a chessboard of $n$ columns and $k$ rows (at most one disc on each). Two discs are said to be adjacent if they lie in the same row or in the same column, and there is no other disc along the line segment connecting them. Each disc is adjacent to at most three others. What is the maximum possible number of discs on the chessboard?