<|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
 Let  $E$  be a set of  $n$  points in the plane  $(n \geq 3)$  whose coordinates are integers such that any three points from  $E$  are vertices of a nondegenerate triangle whose centroid doesnt have both coordinates integers. Determine the maximal  $n.$  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
8
Let  $E$  be a set of  $n$  points in the plane  $(n \geq 3)$  whose coordinates are integers such that any three points from  $E$  are vertices of a nondegenerate triangle whose centroid doesnt have both coordinates integers. Determine the maximal  $n.$ 
test