While walking by a classroom, Linda sees two perfect squares written on a blackboard.  She notices that their difference is her favorite number, 99.  She also notices that there are exactly two other perfect squares between them.  What is the sum of the two perfect squares on the blackboard?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
While walking by a classroom, Linda sees two perfect squares written on a blackboard.  She notices that their difference is her favorite number, 99.  She also notices that there are exactly two other perfect squares between them.  What is the sum of the two perfect squares on the blackboard?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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While walking by a classroom, Linda sees two perfect squares written on a blackboard.  She notices that their difference is her favorite number, 99.  She also notices that there are exactly two other perfect squares between them.  What is the sum of the two perfect squares on the blackboard?
train