Find the number of ordered pairs $(x,y)$ of real numbers that satisfy $ (x + y)^2 = (x + 1)(y - 1)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered pairs $(x,y)$ of real numbers that satisfy $ (x + y)^2 = (x + 1)(y - 1)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
Find the number of ordered pairs $(x,y)$ of real numbers that satisfy $ (x + y)^2 = (x + 1)(y - 1)$.
train