<|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
 Consider a board on  $2013 \times 2013$  squares, what is the maximum number of chess knights that can be placed so that no  $2$  attack each other? 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
2026085
Consider a board on  $2013 \times 2013$  squares, what is the maximum number of chess knights that can be placed so that no  $2$  attack each other?
test