I think we need to make DAG with weights of edges 0/1. If u->v has weight 0 it means that a[v] >= a[u] + 0 and if u->v has weight 1 a[v] > a[i] (<=> a[v] >= a[u] + 1). If we have this graph it is easy to build the initial matrix. But i don't know how to build it and how to find out if there are no such graphs, so i also want to read the solution.