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

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

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

Implement the `MyCalendar` class:

- `MyCalendar()` Initializes the calendar object.
- `boolean book(int start, int end)` Returns `true` if the event can be added to the calendar successfully without causing a double booking. Otherwise, return `false` and do not add the event to the calendar.

Example 1:

    Input
    ["MyCalendar", "book", "book", "book"]
    [[], [10, 20], [15, 25], [20, 30]]
    Output
    [null, true, false, true]

    Explanation
    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.

Constraints:

- `0 <= start < end <= 109`
- At most `1000` calls will be made to `book`.