Building Boxes

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 box y, then each side of the four vertical sides of 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.