Sums in a Grid

a---b---c---d---e---f
|   |   |   |   |   |
g---h---i---j---k---l
|   |   |   |   |   |
m---n---o---p---q---r
|   |   |   |   |   |
s---t---u---v---w---x
|   |   |   |   |   |
y---z---A---B---C---D
In a 4x5 grid of squares, the value in each square is determined by the sum of the digits placed at its four corners. Place any digit from 1-9 at each corner. The four corners of each square must be different. Try to achieve as many unique sums as possible.

Source: Original.


Solution
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