\[ \begin{array}{ccccc} & & & X & Y&Z\\ + & & & X & Z & Y \\ \hline & & & Y & Z & X\\ \end{array} \]

Let \(X,Y\) and \(Z\) be three distinct single digits satisfying the cryptogram above with \(X\ne 0\). Find the value of the three digit integer, \(\overline{XYZ} \).

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