<p>You have a cubic storeroom where the width, length, and height of the room are all equal to <code>n</code> units. You are asked to place <code>n</code> boxes in this room where each box is a cube of unit side length. There are however some rules to placing the boxes:</p> <ul> <li>You can place the boxes anywhere on the floor.</li> <li>If box <code>x</code> is placed on top of the box <code>y</code>, then each side of the four vertical sides of the box <code>y</code> <strong>must</strong> either be adjacent to another box or to a wall.</li> </ul> <p>Given an integer <code>n</code>, return<em> the <strong>minimum</strong> possible number of boxes touching the floor.</em></p> <p> </p> <p><strong class="example">Example 1:</strong></p> <p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/3-boxes.png" style="width: 135px; height: 143px;" /></p> <pre> <strong>Input:</strong> n = 3 <strong>Output:</strong> 3 <strong>Explanation:</strong> 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. </pre> <p><strong class="example">Example 2:</strong></p> <p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/4-boxes.png" style="width: 135px; height: 179px;" /></p> <pre> <strong>Input:</strong> n = 4 <strong>Output:</strong> 3 <strong>Explanation:</strong> 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. </pre> <p><strong class="example">Example 3:</strong></p> <p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/10-boxes.png" style="width: 271px; height: 257px;" /></p> <pre> <strong>Input:</strong> n = 10 <strong>Output:</strong> 6 <strong>Explanation:</strong> 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.</pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= n <= 10<sup>9</sup></code></li> </ul>