Lecture Rooms

There are N lectures. For each lecture, its start time and end time are known. Assign all lectures using as few rooms as possible.

A room cannot host two or more lectures at the same time. However, if one lecture ends exactly when another lecture starts, those two lectures may use the same room.

Print the minimum number of lecture rooms needed for all lectures.

The first line contains the number of lectures N (1 <= N <= 100,000).

Each of the next N lines contains three integers in the form lecture number start time end time. Lecture numbers are from 1 to N. They may appear in any order in the input, but each number appears exactly once.

Start times and end times are integers between 0 and 1,000,000,000 inclusive, and each start time is less than its end time.

Print one integer: the minimum number of lecture rooms needed.