Fail to solve the SkylineProblem on Leetcode with python

I write a solution to Skyline problem on Leetcode: http://ift.tt/1MpuepR But I always get a "Output Limit Exceeded" from online judge.

Here is my script:

class Solution:
def insort(self, point): # used to insert into sorted self.heights
    for i,height in enumerate(self.heights):
        if height[0] > point[1]:
            break
    self.heights.insert(i, (point[1], point[3]))

def remove(self, point): # used to remove from self.heights
    for i, height in enumerate(self.heights):
        if height[1] == point[3]:
            break
    del self.heights[i]

def getSkyline(self, buildings):
    buildings = sorted(buildings, cmp=lambda x,y: x[0]-y[0])

    # points is a list, with elements like 
    # (x_coordinate, y_coordinate, 
    # 'L'/'R' (building left/right side),
    # index_of_point_in_points)
    points = []

    # heights is a list of (point_height, point_index)
    self.heights = [(0,-1)]

    for i, building in enumerate(buildings):
        L, R, H = building
        points.append((L, H, 'L', i))
        points.append((R, H, 'R', i))

    # sort the points:
    # 1. First by x coordinate
    # 2. Then for points of same x, 
    #   put all L points after R points (descend -> ascend)
    # 3. For L points, sort by y, ascending
    # 4. For R points, sort by y, descending
    def point_cmp(x, y):
        if x[0] != y[0]:
            return x[0]-y[0]
        if x[2] != y[2]:
            return 1 if x[2]=='L' else -1
        if x[2] == 'L':
             return x[1]-y[1]
        else:
             return y[1]-x[1]

    points = sorted(points, cmp = point_cmp)

    results = []
    for point in points:
        if point[2] == 'L':
            # if higher than highest
            if point[1] > self.heights[-1][0]:
                # put at the top of stack
                self.heights.append((point[1], point[3]))
                # remove dups
                if results and point[0] == results[-1][0]:
                    results[-1][1] = point[1]
                else:
                    # add a point to result
                    results.append([point[0], point[1]])            
            else:
                self.insort(point)  
        else:
            if point[1] == self.heights[-1][0] and point[3] == self.heights[-1][1]:
                self.heights.pop()
                if results and point[0] == results[-1][0]:
                    results[-1][1] = self.heights[-1][0]
                else:
                    results.append([point[0], self.heights[-1][0]])
            else:
                self.remove(point)

    return results

It passes all my test cases, it must fail at some corner cases that I missed. I am really at my wit's end.

Could you help to find the bug with this script?