The two orthogonal parabolas
\[\begin{cases} y=(x+1)^2 \\ (y-2.5)^2=x+4 \end{cases}\]
intersect at four distinct points, \(A=(x_1,y_1), B=(x_2, y_2) \), \( C=(x_3, y_3)\) and \(D=(x_4, y_4)\). Let \(S=x_1+x_2+x_3+x_4\) and \(R=y_1+y_2+y_3+y_4\). Find the value of \(\lfloor{1000(R+S)}\rfloor\).

###### This problem is part of Curves... cut or touch?.

**Remark**: If the orthogonal parabolas intersect at four distinct points, then these four points are **always** on a same circle.

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