# Sum of Powers is Perfect Square

$$Q$$, $$X$$, $$Y$$ and $$Z$$ are $$4$$ positive integers where:

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

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

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