BiCycles

Given a bipartite graph of N vertices in which every vertex has degree exactly 3, find a set of distinct simple cycles such that every edge belongs to exactly two cycles. The vertices are numbered from 1 to N. For the given constraints, it can be shown that such a set of cycles always exists. A simple cycle of length k (k must be at least 3) in the graph is a sequence of vertices v1, v2, .., vk,