On aN*N grid, we place some1 * 1 * 1cubes that are axis-aligned with the x, y, and z axes.
Each valuev = grid[i][j]represents a tower ofvcubes placed on top of grid cell (i, j).
Now we view theprojectionof these cubesonto the xy, yz, and zx planes.
A projection is like a shadow, thatmaps our 3 dimensional figure to a 2 dimensional plane.
Here, we are viewing the "shadow" when looking at the cubes from the top, the front, and the side.
Return the total area of all three projections.
Example 1:
Input: [[2]]
Output: 5
Example 2:
Input: [[1,2],[3,4]]
Output: 17
Explanation:
Here are the three projections ("shadows") of the shape made with each axis-aligned plane.
Example 3:
Input: [[1,0],[0,2]]
Output: 8
Example 4:
Input: [[1,1,1],[1,0,1],[1,1,1]]
Output: 14
Example 5:
Input: [[2,2,2],[2,1,2],[2,2,2]]
Output: 21
Note:
- 1 <= grid.length = grid[0].length<= 50
- 0 <= grid[i][j] <= 50
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