Let $a,$ $b,$ and $c$ be real numbers such that $ab + ac + bc = 0$ and $(a + b + c + 1)^2 = abc.$  Find all possible values of
\[(ab - c)(ac - b)(bc - a).\]Enter the possible values, separated by commas.  For example, if you think the possible values are 3, 4, and 5, enter "3, 4, 5", without the quotation marks.

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