ZA-SAMO 2012 Problem 3

Sixty points, of which thirty are coloured red, twenty are coloured blue and ten are coloured green, are marked on a circle. These points divide the circle into sixty arcs. Each of these arcs is assigned a number according to the colours of its endpoints: an arc between a red and a green point is assigned a number $1$ , an arc between a red and a blue point is assigned a number $2$ , and an arc between a blue and a green point is assigned a number $3$ . The arcs between two points of the same colour are assigned a number $0$ . What is the greatest possible sum of all the numbers assigned to the arcs?