Good Sets

Given an integer $n\geq2$ , suppose that there are $mn$ points on a circle. We paint the points in $n$ different colours so that there are $m$ points of each colour. Determine the least value of $M$ with the following property: for each $m\geq M$ , given any such colouring of the $mn$ points, there exists a set of $n$ points that contains one point of each colour, and with no two adjacent.