Let \(f\) be a real-valued function so that \(f(x) = a{ x }^{ 2 } + bx + c\) for any real \(x\), where \(a\), \(b\) and \(c\) are distinct non-zero real numbers. If \(f(a) = b\), \(f(b) = c\), and \(f(c) = a\), what is \(a + b + c?\)

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