You start at position $0$ on an infinite number line. On the $i$ th move, you must walk exactly $i$ steps, and you may choose to move either left or right.

Given an integer target, return the minimum number of moves required to land exactly on position target.

Constraints:

• $-10^9 \leq$ target $\leq 10^9$

• target $\neq 0$

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.