BALKAN 2016 Problem 4

The plane is divided into unit squares by two sets of parallel lines, forming an infinite grid. Each unit square is coloured with one of 1201 colours so that no rectangle with perimeter 100 contains two squares of the same colour. Show that no rectangle of size $1 \times 1201$ or $1201 \times 1$ contains two squares of the same colour. Note: Any rectangle is assumed here to have sides contained in the lines of the grid.