-----Description-----
This task requires writing a Lean 4 method that determines whether there are any intersections between chords on a circle. The method should return true if at least one pair of chords intersects, and false otherwise.

A chord is defined as a line segment connecting two distinct points on a circle. Two chords intersect if they cross each other inside the circle. The points are numbered from 1 to 2N in a clockwise direction, where N is the number of chords.

Constraints


- 2\leq N \leq 2\times 10^5
- 1\leq A_i,B_i \leq 2N
- A_1,\dots,A_N,B_1,\dots,B_N are all distinct
- All input values are integers

-----Input-----
The input consists of two parameters:
N: A natural number representing the number of chords (2 ≤ N ≤ 2×10^5).
chords: A list of N pairs of natural numbers, where each pair represents the endpoints of a chord. All endpoint values are distinct and range from 1 to 2N.

-----Output-----
The output is a boolean value:
- Returns true if there exists at least one pair of intersecting chords.
- Returns false if no chords intersect.

