Is it the same as flipping every parenthesis to the other side of the number it's adjacent to, and then adding enough parentheses at the start and end?
For example,
(1 + 2) * (3 + 4)
becomes 1) + (2 * 3) + (4
and then we add the missing parentheses and it becomes (1) + (2 * 3) + (4)
which seems to achieve a similar goal and is pretty unambiguous.