Scrambled Additions

Logic Level 2

XYZ+XZYYZX \begin{array}{ccccc} & & & X & Y&Z\\ + & & & X & Z & Y \\ \hline & & & Y & Z & X\\ \end{array}

Let X,YX,Y and ZZ be three distinct single digits satisfying the cryptogram above with X0X\ne 0. Find the value of the three digit integer, XYZ\overline{XYZ} .

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