Initialize two arrays prefix and suffix to store the prefix sum and suffix sum of heights, respectively.
Use a stack to find the previous smaller element for each tower and calculate the prefix sum.
Use another stack to find the next smaller element for each tower and calculate the suffix sum.
Iterate through each tower and calculate the sum of heights by adding the corresponding prefix and suffix sums and subtracting the height of the current tower.
Keep track of the maximum sum encountered during the iteration.