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# 0883. Projection Area of 3D Shapes

<https://leetcode.com/problems/projection-area-of-3d-shapes>

## Description

You are given an `n x n` `grid` where we place some `1 x 1 x 1` cubes that are axis-aligned with the `x`, `y`, and `z` axes.

Each value `v = grid[i][j]` represents a tower of `v` cubes placed on top of the cell `(i, j)`.

We view the projection of these cubes onto the `xy`, `yz`, and `zx` planes.

A **projection** is like a shadow, that maps our **3-dimensional** figure to a **2-dimensional** plane. 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:**

![](https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/02/shadow.png)

```
**Input:** grid = [[1,2],[3,4]]
**Output:** 17
**Explanation:** Here are the three projections ("shadows") of the shape made with each axis-aligned plane.
```

**Example 2:**

```
**Input:** grid = [[2]]
**Output:** 5
```

**Example 3:**

```
**Input:** grid = [[1,0],[0,2]]
**Output:** 8
```

**Example 4:**

```
**Input:** grid = [[1,1,1],[1,0,1],[1,1,1]]
**Output:** 14
```

**Example 5:**

```
**Input:** grid = [[2,2,2],[2,1,2],[2,2,2]]
**Output:** 21
```

**Constraints:**

* `n == grid.length`
* `n == grid[i].length`
* `1 <= n <= 50`
* `0 <= grid[i][j] <= 50`

## ac

```java
```


---

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