2025 Fermat Problem 22

The triple (x, y, z) of integers satisfies the following system of equations: \begin{array}{r} 2^x + 2^y + 3^{z-1} = 2259 \\ 2^{x+y} + 3^z = 7073 \\ 2^x + 2^y + 3^z = 6633 \end{array} If P is equal to the product xyz, what is the integer formed by the rightmost two digits of P?

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