<|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
 A polynomial of the twentieth degree with integer coefficients is given. On the plane, all points with integer coordinates are marked, where the ordinates are not less than 0 and not more than 10. What is the maximum number of marked points that can lie on the graph of this polynomial? 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
20
A polynomial of the twentieth degree with integer coefficients is given. On the plane, all points with integer coordinates are marked, where the ordinates are not less than 0 and not more than 10. What is the maximum number of marked points that can lie on the graph of this polynomial?
test