You are given an array heights representing the number of bricks in n consecutive towers. Your task is to remove some bricks to form a mountain-shaped tower arrangement. In this arrangement, the tower heights are non-decreasing, reaching a maximum peak value with one or multiple consecutive towers and then non-increasing. Return the maximum possible sum of heights of a mountain-shaped tower arrangement.
You are given an array maxHeights of n integers. Your task is to build n towers in the coordinate line where the height of the i-th tower is between 1 and maxHeights[i]. The configuration is beautiful if the heights form a mountain array, where heights increase to a peak and then decrease afterward. Return the maximum possible sum of the heights of a beautiful tower configuration.