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# 0732. My Calendar III

<https://leetcode.com/problems/my-calendar-iii>

## Description

A `k`-booking happens when `k` events have some non-empty intersection (i.e., there is some time that is common to all `k` events.)

You are given some events `[start, end)`, after each given event, return an integer `k` representing the maximum `k`-booking between all the previous events.

Implement the `MyCalendarThree` class:

* `MyCalendarThree()` Initializes the object.
* `int book(int start, int end)` Returns an integer `k` representing the largest integer such that there exists a `k`-booking in the calendar.

**Example 1:**

```
**Input**
["MyCalendarThree", "book", "book", "book", "book", "book", "book"]
[[], [10, 20], [50, 60], [10, 40], [5, 15], [5, 10], [25, 55]]
**Output**
[null, 1, 1, 2, 3, 3, 3]
**Explanation**
MyCalendarThree myCalendarThree = new MyCalendarThree();
myCalendarThree.book(10, 20); // return 1, The first event can be booked and is disjoint, so the maximum k-booking is a 1-booking.
myCalendarThree.book(50, 60); // return 1, The second event can be booked and is disjoint, so the maximum k-booking is a 1-booking.
myCalendarThree.book(10, 40); // return 2, The third event [10, 40) intersects the first event, and the maximum k-booking is a 2-booking.
myCalendarThree.book(5, 15); // return 3, The remaining events cause the maximum K-booking to be only a 3-booking.
myCalendarThree.book(5, 10); // return 3
myCalendarThree.book(25, 55); // return 3
```

**Constraints:**

* `0 <= start < end <= 109`
* At most `400` calls will be made to `book`.

## ac

```java
```