<|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
 Among the coordinates  $(x,y)$   $(1\leq x,y\leq 101)$ , choose some points such that there does not exist  $4$  points which form a isoceles trapezium with its base parallel to either the  $x$  or  $y$  axis(including rectangles). Find the maximum number of coordinate points that can be chosen. 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
201
Among the coordinates  $(x,y)$   $(1\leq x,y\leq 101)$ , choose some points such that there does not exist  $4$  points which form a isoceles trapezium with its base parallel to either the  $x$  or  $y$  axis(including rectangles). Find the maximum number of coordinate points that can be chosen.
test