Restaurant customers

$n$ customers visited a restaurant: customer $i$ arrived at time $a_i$ and left at time $b_i$. A customer who leaves at time $b_i$ is not counted together with one who arrives at that same time. What was the maximum number of customers in the restaurant at the same time?

The first line contains $n$ ($1 \le n \le 2 \cdot 10^5$). The next $n$ lines contain $a_i$ and $b_i$ ($1 \le a_i < b_i \le 10^9$).

A single number — the maximum number of customers at the same time.

Sweep line: every customer gives two events — $(a_i, +1)$ and $(b_i, -1)$. Sort the events by time; on equal times a departure ($-1$) comes before an arrival ($+1$). Adding the events in order gives the current number of people in the restaurant — its maximum is the answer.

This is $O(n \log n)$. Checking every moment of time does not work with times up to $10^9$. In the example there are $2$ people from $3$ to $4$.

Source: CSES, problem 1619.