Problem Description

You are given a directed follows relationship representing a social graph. Each record (follower_id, followee_id) indicates that follower_id follows followee_id. This relationship should be treated as a directed graph.

Task

Implement a function that, given:

• A list of follow edges follows = [(follower_id, followee_id), ...]
• A starting user start_id

returns the maximum number of follow "layers" reachable from start_id by repeatedly following the next user. Formally, this means computing the length of the longest directed path starting at start_id.

• Layer 1: Users directly followed by start_id
• Layer 2: Users followed by those users (from Layer 1)
• ...

The function should return the maximum layer count reachable.

Requirements and Edge Cases

• The implementation must use recursion. Memoization is permitted and encouraged.
• The solution must correctly handle cycles (e.g., A→B→C→A) without resulting in infinite recursion.
• If start_id follows nobody, the function should return 0.

Example

Given the follow edges:

• 1→2
• 2→3
• 3→4

For start_id = 1, max_depth(1) should return 3 (layers: {2}, {3}, {4}).

Given the follow edges:

• 1→2
• 2→1

For start_id = 1, max_depth(1) should return 1 (due to the cycle, the path 1->2 has length 1, and 1->2->1 would be a cycle, so we don't count 1 again as a new layer).