A courtyard has the shape of a parallelogram $ABCD$. At the corners of the courtyard, there stand poles $AA'$, $BB'$, $CC'$, and $DD'$, each of which is perpendicular to the ground. The heights of these poles are $AA' = 68$ centimeters, $BB' = 75$ centimeters, $CC' = 112$ centimeters, and $DD' = 133$ centimeters. Find the distance in centimeters between the midpoints of $A'C'$ and $B'D'$.

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