Given a string path, where each character represents a movement on a $2$D plane:

• 'N' moves $1$ unit north to $(x, y + 1)$

• 'S' moves $1$ unit south to $(x, y - 1)$

• 'E' moves $1$ unit east to $(x + 1, y)$

• 'W' moves $1$ unit west to $(x - 1, y)$

You start at the origin $(0, 0)$ on a $2$D plane and traverse the path specified by path.

Return true if the path crosses itself at any point (visiting any coordinate that has already been visited), and false otherwise.

Constraints:

• $1 \leq$ path.length $\leq 10^4$

• path[i] is either 'N', 'S', 'E', or 'W'.

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.