Maximum Difference Walk

Chef has a complete directed graph composed of N vertices. The graph contains a directed edge from every vertex i (1 ≤ i ≤ N) to every other vertex j (j != i) .We will denote such an edge by (i, j) and we will say that i is its starting vertex and j is its destination vertex. Thus, there are N(N-1) directed edges overall. Each of the directed edges has a unique cost in the range 1, 2, ... N(N-1).