An infinite two dimensional grid of unit cells starts completely uncolored. You are given a positive integer n.

During the first minute, exactly $1$ arbitrary cell is colored.

Every subsequent minute, every uncolored cell that shares an edge with at least $1$ already colored cell also becomes colored.

Return the total count of colored cells after n minutes have passed.

Constraints:

• $1 \leq$ n $\leq 10^5$

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.