<|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
 How many ways can one color the squares of a $6 \times 6$ grid red and blue such that the number of red squares in each row and column is exactly 2? 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
67950
How many ways can one color the squares of a $6 \times 6$ grid red and blue such that the number of red squares in each row and column is exactly 2?
test