Overlapping Events

You are given a series of events, each with a start time and an end time. Your task is to determine whether any two events overlap.

An event is defined by a start time and an end time. Two events are considered to overlap if, after sorting the events by their start times, the end time of an event is greater than or equal to the start time of the next event. Note that if an event's end time is exactly equal to the next event's start time, they are also considered overlapping.

The input will be provided via standard input (stdin) and the result must be printed to standard output (stdout). If any overlap is found, print true; otherwise, print false.

inputFormat

The input begins with an integer N (1 ≤ N ≤ 10⁵), representing the number of events. The following N lines each contain two space-separated integers start and end (0 ≤ start, end ≤ 10⁹), which represent the start and end times of an event.

outputFormat

Output a single line containing true if any two events overlap, otherwise output false.

3
1 5
6 10
11 15

false