A company has n employees, uniquely identified with IDs from $0$ to n - 1. The head of the company has the ID headID.

Each employee i has a direct manager specified by manager[i]. The head of the company has no manager, so manager[headID] is equal to $-1$. The managerial structure forms a tree rooted at headID.

When an employee receives urgent news, they will inform all of their direct subordinates simultaneously. The time it takes for employee i to inform all of their direct subordinates is informTime[i] minutes.

Given n, headID, manager, and informTime, return the total number of minutes needed to inform all employees in the company.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ headID $<$ n

• manager.length $==$ n

• $0 \leq$ manager[i] $<$ n for all i where i $\neq$ headID

• manager[headID] $== -1$

• informTime.length $==$ n

• $0 \leq$ informTime[i] $\leq 1000$

• informTime[i] $== 0$ if employee i has no subordinates.

• It is guaranteed that all employees can be informed.

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