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# 1739. Building Boxes

<https://leetcode.com/problems/building-boxes>

## Description

You have a cubic storeroom where the width, length, and height of the room are all equal to `n` units. You are asked to place `n` boxes in this room where each box is a cube of unit side length. There are however some rules to placing the boxes:

* You can place the boxes anywhere on the floor.
* If box `x` is placed on top of the box `y`, then each side of the four vertical sides of the box `y` **must** either be adjacent to another box or to a wall.

Given an integer `n`, return *the **minimum** possible number of boxes touching the floor.*

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/01/04/3-boxes.png)

```
**Input:** n = 3
**Output:** 3
**Explanation:** The figure above is for the placement of the three boxes.
These boxes are placed in the corner of the room, where the corner is on the left side.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/01/04/4-boxes.png)

```
**Input:** n = 4
**Output:** 3
**Explanation:** The figure above is for the placement of the four boxes.
These boxes are placed in the corner of the room, where the corner is on the left side.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/01/04/10-boxes.png)

```
**Input:** n = 10
**Output:** 6
**Explanation:** The figure above is for the placement of the ten boxes.
These boxes are placed in the corner of the room, where the corner is on the back side.
```

**Constraints:**

* `1 <= n <= 109`

## ac

```java
```