<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given four distinct positive real numbers a, b, c, d that satisfy (a^2012 - c^2012)(a^2012 - d^2012) = 2012 and (b^2012 - c^2012)(b^2012 - d^2012) = 2012, calculate the value of (ab)^2012 - (cd)^2012. Express your answer as an integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
-2012
Given four distinct positive real numbers a, b, c, d that satisfy (a^2012 - c^2012)(a^2012 - d^2012) = 2012 and (b^2012 - c^2012)(b^2012 - d^2012) = 2012, calculate the value of (ab)^2012 - (cd)^2012. Express your answer as an integer.
test