#!/usr/bin/env python3
from collections import namedtuple

Event = namedtuple('Event', 'type, time')


def get_key(e: Event) -> int:
    return e.time + 0.5 if e.type == 'out' else e.time


def pref_sum(xs):
    for i in range(1, len(xs)):
        xs[i] += xs[i-1]
    return xs


def intervals_to_events(intervals):
    events = []

    for in_time, out_time in intervals:
        events.append(Event('in', in_time))
        events.append(Event('out', out_time))

    return events


def max_overlap(intervals) -> int:
    events = intervals_to_events(intervals)
    events.sort(key=get_key)
    in_outs = list(map(lambda event: 1 if event.type == 'in' else -1, events))
    pref_sum(in_outs)
    return max(in_outs)


def main():
    _test()
    print("ok")


def _test():
    assert max_overlap([(30, 75), (0, 50), (60, 150)]) == 2


if __name__ == '__main__':
    main()