Is it possible to label each of the edges of a regular cube (see figure below) with distinct positive integers (i.e. > 0) in such a way that:
(a) the sum of the integers assigned to the three edges at any corner is the same for each of the eight corners; and
(b) the sum of the integers assigned to the four edges of any face is the same for each of the six faces.

If so, give a labeling with the smallest possible labels.

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