You are given an integer n representing the total number of identical $1 imes 1 imes 1$ cubic boxes you must place in the corner of a room.

A placement of boxes is valid if it satisfies the following rules:

• Every box rests either directly on the floor or on top of another box.

• A box can be placed on top of another box only if the supporting box is surrounded on all $4$ of its vertical side faces by other boxes or room walls.

Return the minimum number of boxes that must touch the floor to place all n boxes in a valid arrangement.

Constraints:

• $1 \leq$ n $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.