<|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
 In a square table consisting of 2015 rows and columns, positive numbers are arranged. The product of the numbers in each row and in each column is equal to 1, and the product of the numbers in any 1008 x 1008 square is equal to 2. What is the number in the center of the table? 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
16
In a square table consisting of 2015 rows and columns, positive numbers are arranged. The product of the numbers in each row and in each column is equal to 1, and the product of the numbers in any 1008 x 1008 square is equal to 2. What is the number in the center of the table?
test