读取表格中的信息，解决问题．
\(n=1\) | \({{a}_{1}}=\sqrt{2}+2\sqrt{3}\) | \({{b}_{1}}=\sqrt{3}+2\) | \({{c}_{1}}=1+2\sqrt{2}\) |
\(n=2\) | \(a_{2}=b_{1}+2c_{1}\) | \(b_{2}=c_{1}+2a_{1}\) | \(c_{2}=a_{1}+2b_{1}\) |
\(n=3\) | \(a_{3}=b_{2}+2c_{2}\) | \(b_{3}=c_{2}+2a_{2}\) | \(c_{3}=a_{2}+2b_{2}\) |
\(…\) | \(…\) | \(…\) | \(…\) |
满足\(\dfrac{{{a}_{n}}+{{b}_{n}}+{{c}_{n}}}{\sqrt{3}+\sqrt{2}}\geqslant 2016\times (\sqrt{3}-\sqrt{2}+1)\)的\(n\)可以取得的最小整数是________．