Minimum Degree of a Connected Trio in a Graph

Given an undirected graph, find all connected trios (triangles) and compute each trio's degree — the number of edges with one endpoint in the trio and the other outside — then return the minimum such degree or -1 if no trio exists. The core challenge is efficiently enumerating triangles and counting their external edges (n ≤ 400 makes triangle enumeration via adjacency checks feasible).