I want to fill in the eight circles below using each of the numbers 1, 2, 3, 4, 5, 6, 7, 8 **exactly once**. Additionally, consecutive numbers--e.g. \((1, 2)\) or \((5,6)\)-- **cannot** be placed in circles which are connected by a line segment.

Is this possible, and if so, what is the sum of the two numbers in the middle?

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