If $\alpha = 1 + \sum\limits_{r = 1}^6 {{{( - 3)}^{r - 1}}} {\quad ^{12}}{{\rm{C}}_{2r - 1}}$, then the distance of the point $(12,\sqrt 3)$ from the line $\alpha x - \sqrt 3 y + 1 = 0$ is _____.
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