A kingdom has 2021 towns. All of the towns lie on a circle, and there is a one-way road going from every town to the next 101 towns in a clockwise order. Each road is colored in one color. Additionally, it is known that for any ordered pair of towns A and B it is possible to find a path from A to B so that no two roads of the path would have the same color. Find the minimal number of road colors in the kingdom. combinatoricsgraph theory