class Solution:
    from collections import deque

    def numOfMinutes(self, n, headID, manager, informTime):
        # 1. Build Adjacency List (Manager -> subordinates)
        adj = [[] for _ in range(n)]
        for employee_id, mgr_id in enumerate(manager):
            if mgr_id != -1:
                adj[mgr_id].append(employee_id)
                
        # 2. BFS: (current_employee, cumulative_time_to_reach_them)
        queue = deque([(headID, 0)])
        max_time = 0
        
        while queue:
            curr_emp, curr_time = queue.popleft()
            
            # Update the total time needed
            max_time = max(max_time, curr_time)
            
            # For every subordinate, the time to reach them is 
            # current time + the time this manager takes to inform everyone
            for subordinate in adj[curr_emp]:
                queue.append((subordinate, curr_time + informTime[curr_emp]))
                
        return max_time