OMM 2000 Problem 5

A board $n$ × $n$ is coloured black and white like a chessboard. The following steps are permitted: Choose a rectangle inside the board (consisting of entire cells)whose side lengths are both odd or both even, but not both equal to $1$ , and invert the colours of all cells inside the rectangle. Determine the values of $n$ for which it is possible to make all the cells have the same colour in a finite number of such steps.