You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
矩形 R 被分割成 2016 个小矩形，其中每个小矩形的边均平行于矩形 R 的边。小矩形的顶点称为结点，一条在小矩形边上的线段，若其两个端点均为结点，且其内部不含其他结点，则称这条线段为"基本线段"。考虑所有的分割方式，设基本线段条数的最大值为 a，最小值为 b，求 a + b 的值。
user
10171
rule
矩形 R 被分割成 2016 个小矩形，其中每个小矩形的边均平行于矩形 R 的边。小矩形的顶点称为结点，一条在小矩形边上的线段，若其两个端点均为结点，且其内部不含其他结点，则称这条线段为"基本线段"。考虑所有的分割方式，设基本线段条数的最大值为 a，最小值为 b，求 a + b 的值。
train