Let $a,b,c,d,e,f$ be real numbers such that $a^2+b^2+c^2=14, d^2+e^2+f^2=77,$ and $ad+be+cf=32.$ Find $(bf-ce)^2+(cd-af)^2+(ae-bd)^2.$

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