Game of Stones

Satkkeerthi has decided to participate in the Game of Stones. There are $n$ cities numbered $1$ to $n$ and $m$ $directed$ $roads$ between the cities. There is an infinitely large pile of stones in each city, of one particular colour. Each colour is described by a colour code, ai at the ith city. A player must choose a path starting from one city, and at every city along the path, he/she adds one