Using each of the eight digits $1, 3, 4, 5, 6, 7, 8,$ and $9$ exactly once, form a three-digit number $A$, two two-digit numbers $B$ and $C$ (where $B < C$), and a one-digit number $D$. The numbers are such that $A + D = B + C = 143$. In how many ways can this be done?

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