The Skyline Problem

Compute the skyline of given rectangular buildings in a 2D city, eliminating hidden lines and forming the outer contour of the silhouette when viewed from a distance. Each building is described by its geometric information in the form of an array BUILDINGS[i] = [LEFT_i, RIGHT_i, HEIGHT_i].

Explanation:

• LEFT_i: x-coordinate of the left edge of the i-th building.
• RIGHT_i: x-coordinate of the right edge of the i-th building.
• HEIGHT_i: height of the i-th building.

It is assumed that all buildings are perfect rectangles grounded at height 0.

The skyline must be represented as a list of "key points" sorted by x-coordinate in the format [[x1, y1], [x2, y2], ...]. Each key point marks the left endpoint of a horizontal segment in the skyline, except for the last point, which always has y-coordinate 0 to indicate the skyline's termination.

Input:

The first line contains an integer N indicating the number of buildings.
Each of the following N lines contains three space-separated integers LEFT_i, RIGHT_i, and HEIGHT_i for each building.

Output:

Return a list of key points representing the skyline.
The format is [[x1, y1], [x2, y2], ...], with each point marking a key horizontal segment.

Example:

Input:
N = 2
BUILDINGS = [[2, 9, 10], [3, 7, 15]]

Output:
[[2, 10], [3, 15], [7, 10], [9, 0]]

Constraints:

• 1 <= |BUILDINGS| <= 10^4
• 0 <= LEFT_i < RIGHT_i <= 2^31 - 1
• 1 <= HEIGHT_i <= 2^31 - 1
• Time Limit: 1 sec

Note:

Ensure no consecutive horizontal segments of equal height in the output. If any, merge them into one.