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
一个凸 2011 边形 M 内部有 2011 个点，这 2011 个点和 M 的顶点中不存在三点共线。一种将所有点染为两种颜色之一的方式称为好的，如果可以在某些点之间连线段，使得：(1) 每条线段的两个端点同色；(2) 任意两条线段在 M 内不相交；(3) 任意同色的两个点之间存在一条由所连线段组成的通路。求所有好的染色方式的数目。原始答案的形式为(k \times m + 2) \times 2^n，请给出k + m + n的值。
user
6032
rule
一个凸 2011 边形 M 内部有 2011 个点，这 2011 个点和 M 的顶点中不存在三点共线。一种将所有点染为两种颜色之一的方式称为好的，如果可以在某些点之间连线段，使得：(1) 每条线段的两个端点同色；(2) 任意两条线段在 M 内不相交；(3) 任意同色的两个点之间存在一条由所连线段组成的通路。求所有好的染色方式的数目。原始答案的形式为(k \times m + 2) \times 2^n，请给出k + m + n的值。
train