Transcendental Dice Rolls

Three fair 6-sided dice each have their sides labeled \(0,1,e,\pi, i, \sqrt{2}\). If these dice are rolled, the probability that the product of all the numbers on the top face is real can be expressed as \( \frac {a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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