When you thought the plagiarism has ended, again.

I don't create this problem. All of the credits go to Trần Văn Tấn, Nguyễn Thị Thanh Thuỷ and Phạm Minh Phương for writing this problem, and the book in general.

The original problem is:

Solve the following system of equations:

$\large \left\{ \begin{aligned} \sqrt{x^2 + x + y + 1} + x + \sqrt{y^2 + y + x + 1} + y &= 18\\ \sqrt{x^2 + x + y + 1} - x + \sqrt{y^2 + y + x + 1} - y &= 2 \end{aligned} \right.$

If the number of real solutions to the system of equations is $n$ , submit your answer as $\large (x^2 + 2y + 1)^2 + (y^2 + 2x + 1)^2 - \sqrt x - \sqrt y - n$ .