Peak Concurrent Solvers

Find the largest number of players who were solving today's challenge at the exact same moment.

Every player's attempt at today's challenge is logged as a (start_minute, end_minute) pair, showing when they opened the bracket and when they closed it, in minutes since midnight. Find the largest number of players who were solving the challenge at exactly the same moment, at any point in the day. A player who closes their bracket at the exact minute another player opens theirs is not counted as overlapping with them — the first player's session has already ended. Return that largest number as an integer.