Let \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), and \((x_4,y_4)\) be four distinct integer solutions to the equation

\[x^4+x^3y^3=y^4+xy\]

such that when connected, they form a square.

If this square is the second smallest possible square that can be made, then find the area of this square.

**Details and Assumptions**

The smallest square possible is made by the four solutions \((\pm 1, \pm 1)\). This square has area \(4\).

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