Task Scheduler: Minimum Execution Time

You are given a list of tasks represented by uppercase letters and a non-negative cooling interval n. Each task takes 1 unit of time to complete. However, the same task must be separated by at least n units of time. If there is no available task to execute during the cooling period, the CPU remains idle.

Formally, if the most frequent task appears f_max times and there are c tasks with this frequency, then the minimum time is:

[ \text{time} = \max(\text{totalTasks}, (f_{max} - 1) \times (n + 1) + c) ]

Determine the least number of units of time that the CPU will take to finish all the given tasks.

inputFormat

The input is given via standard input with three lines:

• First line: A single integer T denoting the number of tasks.
• Second line: T space-separated uppercase letters representing the list of tasks.
• Third line: An integer n representing the cooling interval.

outputFormat

Output a single integer representing the minimum number of time units required by the CPU to process all tasks.

## sample

6
A A A B B B
2

8

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