Overlapping braces

Question

I am trying to achieve a text where an over-brace is followed by an under-brace with a last digit overlapping, but couldn't able to do it, anyone help me to fix it, the example code is given.

\documentclass[12]{article}
\usepackage{amsmath}

\begin{document}

$$ . . . \overbrace{\times \times \times }^{\lbrace\pm 2x, \pm x, 0\rbrace} \underbrace{\times \times \times}_{\lbrace\pm 2x, \pm x, 0\rbrace} \overbrace{\times \times 0}^{\lbrace\pm 2x, \pm x, 0\rbrace}$$

\end{document}