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<p>A <code>k</code>-booking happens when <code>k</code> events have some non-empty intersection (i.e., there is some time that is common to all <code>k</code> events.)</p>
<p>You are given some events <code>[start, end)</code>, after each given event, return an integer <code>k</code> representing the maximum <code>k</code>-booking between all the previous events.</p>
<p>You are given some events <code>[startTime, endTime)</code>, after each given event, return an integer <code>k</code> representing the maximum <code>k</code>-booking between all the previous events.</p>
<p>Implement the <code>MyCalendarThree</code> class:</p>
<ul>
<li><code>MyCalendarThree()</code> Initializes the object.</li>
<li><code>int book(int start, int end)</code> Returns an integer <code>k</code> representing the largest integer such that there exists a <code>k</code>-booking in the calendar.</li>
<li><code>int book(int startTime, int endTime)</code> Returns an integer <code>k</code> representing the largest integer such that there exists a <code>k</code>-booking in the calendar.</li>
</ul>
<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>
<p><strong class="example">Example 1:</strong></p>
<pre>
<strong>Input</strong>
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<strong>Explanation</strong>
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(10, 20); // return 1
myCalendarThree.book(50, 60); // return 1
myCalendarThree.book(10, 40); // return 2
myCalendarThree.book(5, 15); // return 3
myCalendarThree.book(5, 10); // return 3
myCalendarThree.book(25, 55); // return 3
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>0 &lt;= start &lt; end &lt;= 10<sup>9</sup></code></li>
<li><code>0 &lt;= startTime &lt; endTime &lt;= 10<sup>9</sup></code></li>
<li>At most <code>400</code> calls will be made to <code>book</code>.</li>
</ul>