Delete nodes from a tree to maximize remaining depth

Problem: Delete nodes in a rooted tree to maximize the remaining maximum depth You are given an undirected tree with n nodes rooted at node 1. You may delete any number of nodes (possibly none). Deleting a node removes all incident edges. After deletions, the remaining nodes must still contain the root 1 and the remaining graph must be connected (i.e., still a rooted tree). Output the maximum possible maximum depth (maximum number of edges from root to any remaining node) after such deletions. Input n n-1 edges u v Output One integer: the maximum achievable depth. Constraints 1 ≤ n ≤ 2e5 Note You must keep the root and maintain connectivity of remaining nodes. Examples See tests below. Example Input 5 1 2 1 3 3 4 4 5 Output 3