In assigning dormitory rooms, a college gives preference to pairs of students in this order: $$ A A, A B, A C, B B, B C, A D, C C, B D, C D, D D $$ in which $A A$ means two seniors, $A B$ means a senior and a junior, etc. Determine numerical values to assign to $A, B, C, D$ so that the set of numbers $A + A, A + B, A + C, B + B$, etc., corresponding to the order above will be in descending magnitude. Please provide the sum of A + B + C + D for the least positive integers that satisfy this condition.

Let's think step by step and output the final answer within \boxed{}.
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