Solution: Divide Nodes Into the Maximum Number of Groups

Statement

You are given an undirected graph with n nodes labeled from $1$ to n, and an edge list edges where each edges[i] connects two distinct nodes.

You want to partition all nodes into the maximum possible number of non empty groups, numbered consecutively from $1$ to k, such that for every edge connecting nodes u and v, the group indices of u and v differ by exactly $1$.

Return the maximum valid k. If no such grouping exists, return $-1$.

Constraints:

• $1 \leq$ n ...