A city's skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return the skyline formed by these buildings collectively .
The geometric information of each building is given in the array buildings where buildings[i] = [left _i , right _i , height _i ] :
left _i is the x coordinate of the left edge of the i ^th building.
right _i is the x coordinate of the right edge of the i ^th building.
height _i is the height of the i ^th building.
You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0 .
The skyline should be represented as a list of "key points" sorted by their x-coordinate in the form [[x _1 ,y _1 ],[x _2 ,y _2 ],...] . Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate 0 and is used to mark the skyline's termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline's contour.
Note: There must be no consecutive horizontal lines of equal height in the output skyline. For instance, [...,[2 3],[4 5],[7 5],[11 5],[12 7],...] is not acceptable; the three lines of height 5 should be merged into one in the final output as such: [...,[2 3],[4 5],[12 7],...]
1 <= buildings.length <= 10 ^40 <= left _i < right _i <= 2 ^31 - 11 <= height _i <= 2 ^31 - 1buildings is sorted by left _i in non-decreasing order.