Dutch Mathematical Olympiad

A chess board consists of $8\times 8$ squares. A knight is placed on a corner square. The knight makes jumps of either two squares horizontally and one square vertically, or two squares vertically and one square horizontally. On each square of the chess board, we write down how many jumps the knight needs to reach it. Which number did we write down most often? A) 2 B) 3 C) 4 D) 5 E) 6