Given the non-linear system:

\[ \begin{align} 3x_1-\cos(x_2x_3)&=\frac{1}{2},\\ x_1^2-81(x_2+0.1)^2+\sin x_3&=-1.06,\\ e^{-x_1x_2}+20x_3&=\frac{3-10\pi}{3}. \end{align} \]

Find the value of \(\lfloor\Omega\rceil\) where

\[ \Omega=1000\left|x_1-2x_2+3x_3\right|. \]

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