Rainbow Graph

You are given an undirected compete graph with n nodes. Each edge can be one of n*(n-1)/2 +1 different colors. These colors are labeled from 0 to n*(n-1)/2, inclusive. But not all these n*(n-1)/2 +1 colors need to be used. ie. it is possible that two different edges could have the same color. Formally, let ci,j denote the color between the i-th and j-th nodes. (Note that these edges are undirected