<p>You are implementing a program to use as your calendar. We can add a new event if adding the event will not cause a <strong>double booking</strong>.</p>

<p>A <strong>double booking</strong> happens when two events have some non-empty intersection (i.e., some moment is common to both events.).</p>

<p>The event can be represented as a pair of integers <code>start</code> and <code>end</code> that represents a booking on the half-open interval <code>[start, end)</code>, the range of real numbers <code>x</code> such that <code>start &lt;= x &lt; end</code>.</p>

<p>Implement the <code>MyCalendar</code> class:</p>

<ul>
	<li><code>MyCalendar()</code> Initializes the calendar object.</li>
	<li><code>boolean book(int start, int end)</code> Returns <code>true</code> if the event can be added to the calendar successfully without causing a <strong>double booking</strong>. Otherwise, return <code>false</code> and do not add the event to the calendar.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;MyCalendar&quot;, &quot;book&quot;, &quot;book&quot;, &quot;book&quot;]
[[], [10, 20], [15, 25], [20, 30]]
<strong>Output</strong>
[null, true, false, true]

<strong>Explanation</strong>
MyCalendar myCalendar = new MyCalendar();
myCalendar.book(10, 20); // return True
myCalendar.book(15, 25); // return False, It can not be booked because time 15 is already booked by another event.
myCalendar.book(20, 30); // return True, The event can be booked, as the first event takes every time less than 20, but not including 20.</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>At most <code>1000</code> calls will be made to <code>book</code>.</li>
</ul>