You are an event organizer at a university, and n companies would like to do a presentation about their company at your university on Career Day. However, each company has a tight schedule as to when it can come and present and how long it will present. For the ith company, starting from 0, they can present starting from minute starts[i] and they can present for durations[i] minutes. To give every student a chance to listen to every presentation, the University can allow only one company to present at a time. You would like to host as many presentations as possible, so given each company's schedule, find the maximum number of presentations that the university can hold.

starts: A list of integers with size n representing each company's starting time.

durations: A list of integers with size n representing the duration of the presentation for each company.

Result

The maximum number of presentations that the university can hold.

Example 1:

starts = [1, 3, 3, 5, 7]

durations = [2, 2, 1, 2, 1]

Output: 4

Explanation: Company 0 will present from minute 1~3, either company 1 present from minute 3~5 or company 2 present from minute 3~4. Then. company 3 and 4 can present without conflict. Therefore, a total of 4 companies can present.

Restrictions