Study Rooms Needed

medium

A library lets student groups book sessions, each [start, end] in minutes. Every concurrently running session needs its own room, and facilities wants the headcount: what is the minimum number of rooms that covers the whole day's sessions?

A session ending exactly when another starts can hand over its room — no extra room needed for that pair.

Example 1

in sessions = [[0, 30], [5, 10], [15, 20]]

out 2

[0, 30] runs throughout; [5, 10] and [15, 20] take turns in a second room.

Example 2

in sessions = [[7, 10], [2, 4]]

out 1

They never coexist — one room suffices.

Constraints

· 0 <= len(sessions) <= 2000
· 0 <= start < end <= 10^6