Above is the graph of the equation \[x^2+y^2-|2x+8|+2y=16\] If the area of the figure is denoted \(A\), then find \[\lfloor1000\{A\}\rfloor\]

**Details and Assumptions**

\(\{N\}\) denotes the fractional part of \(N\).

In other words, \(\{N\}=y\) where \(N=x+y\), \(x\) is an integer and \(0\le y < 1\).

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