Minimum Project Completion Time

You are managing a large-scale software development project consisting of n distinct tasks, numbered from 1 to n. Each task requires a specific amount of time to complete, and some tasks depend on others—meaning certain tasks must be finished before others can begin.

You are provided with:

1. An integer n representing the total number of tasks.
2. A 2D integer array dependencies where each element dependencies[j] = [predecessor, successor] indicates that task predecessor must be completed before task successor can start.
3. A 0-indexed integer array duration where duration[i] specifies how many time units are required to complete task (i + 1).

Your team has unlimited capacity, meaning any number of tasks can be worked on simultaneously as long as all their prerequisite tasks have been completed.

Your goal is to determine the minimum total time required to finish all tasks.

Key Observations:

• If a task has no dependencies, you can start it immediately at time 0.
• If a task depends on multiple predecessors, you can only start it once all of its prerequisite tasks are finished.
• Tasks with no successors are the final deliverables of the project.
• The problem guarantees that the dependency graph forms a Directed Acyclic Graph (DAG), meaning there are no circular dependencies.

Note: The test inputs ensure that all tasks can be completed (i.e., the dependency structure is valid and acyclic).