Task Scheduling — Paid + Free Server

The data analysts of Hackerland want to schedule some long-running tasks on remote servers optimally to minimize the cost of running them locally. The analysts have two servers, a paid one and a free one. The free server can be used only if the paid server is occupied.

The iᵗʰ task is expected to take time[i] units of time to complete and the cost of processing the task on the paid server is cost[i]. The task can be run on the free server only if some task is already running on the paid server. The cost of the free server is 0 and it can process any task in 1 unit of time.

Find the minimum cost to complete all the tasks if tasks are scheduled optimally.