Find Minimum Diameter After Merging Two Trees

Statement

You are given two undirected trees: one with $n$ nodes labeled from $0$ to $n - 1$, and another with $m$ nodes labeled from $0$ to $m - 1$. Their structures are defined by two $2D$ integer arrays—edges1 of length $n - 1$ for the first tree, and edges2 of length $m - 1$ for the second. Each element edges1[i] = [aᵢ, bᵢ] represents an edge between nodes $aᵢ$ and $bᵢ$ in the first tree, and similarly, edges2[i] = [uᵢ, vᵢ] represents an edge in the second tree.

Your task is to connect any node from the first tree to any node from the second tree using a single edge. Return the smallest possible diameter of the resulting combined tree.

Note: The diameter of a tree is the length of the longest path between any two nodes in it.

Constraints:

• $1 <= n, m <= 10^5$

• edges1.length $== n - 1$

• edges2.length $== m - 1$

• edges1[i].length $==$ edges2[i].length $== 2$

• edges1[i] = [ai, bi]

• $0 <= a_i, b_i < n$

• edges2[i] = [ui, vi]

• $0 <= u_i, v_i < m$

• The  edges1 and edges2 always represent valid trees.

Examples