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.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
0
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.
train