Workstation minimum price

A configurator prices a custom workstation. part_names lists every part on the shelf, part_groups[i] names the slot part i fills, for example case or board, and part_cents[i] is its price in cents. A build takes exactly one part from every slot that appears in part_groups. clashes holds pairs written as "case_mini|board_a", meaning those two parts cannot sit in the same build. A pair may be listed more than once and may be written in either order, it always names two different parts, and both names come from part_names. Return the lowest total price in cents of a build that fills every slot with no clash inside it. Return -1 when no such build exists, and 0 when the shelf is empty. Prices are never negative and there are at most 12 parts.