There is an $n \times n$ city represented by an integer matrix grid, where grid[r][c] denotes the height of the building located at row r and column c.

The skyline of the city is the outer contour formed by all buildings when viewed from the four cardinal directions:

• The skyline viewed from the north or south is the maximum value in each column.

• The skyline viewed from the east or west is the maximum value in each row.

You are allowed to increase the height of any number of buildings by any non negative amount, provided that the city skyline viewed from all four directions remains unchanged.

Return the maximum total sum by which the building heights can be increased.

Constraints:

• n $==$ grid.length

• n $==$ grid[r].length

• $2 \leq$ n $\leq 50$

• $0 \leq$ grid[r][c] $\leq 100$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.