An assignment problem is solved to minimize the total processing time of four jobs ($1,2,3$ and $4$) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be $500$ minutes. Due to a change in design, the processing time of Job $4$ on each machine has increased by $20$ minutes. The revised minimum total processing time will be ___________________ minutes (in integer).