\[ \begin{array}{ccccc} & & & & E&U\\ \times & & & & U & K \\ \hline & & N & O & P &E\\ \hline \end{array} \]

The above shows a cryptogram representing the product of two 2-digit integers to produce a 4-digit integer. Given that each letter representsâ€‹ distinct digits, and \(O =4\), what is the value of the 4-digit integer \(\overline{NOPE} \)?

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