When a 6-digit number $\overline{abcdef}$ is multiplied by 3, the result is $bcdef9$. \begin{equation} \begin{array}{cccccc} a & b & c & d & e & f \\ \times & & & & & 3 \\\hline b & c & d & e & f & 9 \end{array} \end{equation} Find the value of $\overline{abcdef}$.