\[ \Large \begin{array}{ccccc} & & & & & \color{red}{R} & \color{red}{E} &\color{red}{D} \\ \times & & & & \color{blue}{B} & \color{blue}{L} & \color{blue}{U} & \color{blue}{E} \\ \hline & & \color{gold}{Y} & \color{gold}{E} & \color{gold}{L} & \color{gold}{L} & \color{gold}{O} & \color{gold}{W} \\ \end {array} \]

The above expression represents a cryptarithm such that each letter represents a distinct single digit positive integer.

Calculate the 9-digit number \(\overline{BUYREDOWL}\).

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