You are given an n × n grid representing a three dimensional shape composed of $1 \times 1 \times 1$ cubes aligned with the coordinate axes.

Each value grid[i][j] represents the height of a tower of cubes placed at the grid cell (i, j).

A projection is the shadow cast by the shape onto a two dimensional plane. The shape is projected onto three planes:

• The top view (the $xy$ plane)

• The front view (the $yz$ plane)

• The side view (the $zx$ plane)

Return the total combined area of all three projections.

Constraints:

• n == grid.length == grid[i].length

• $1 \leq$ n $\leq 50$

• $0 \leq$ grid[i][j] $\leq 50$

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.