Sum of Powers is Perfect Square

QQ, XX, YY and ZZ are 44 positive integers where:

Q=3X+5Y+7ZQ={ 3 }^{ X }+{ 5 }^{ Y }+{ 7 }^{ Z }

QQ is a perfect square. Find X+Y+ZX+Y+Z, and QQ is the minimum possible perfect square in the sum above.

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