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
设整数 n\geq2. 某天 n 个人组成了一个社团，每人向政府交 1 元注册费。接下来每天都发生如下事情：每一个前一天组建的社团都分裂成两个团体，其中含至少两人的团体组建成一个新社团，每个新社团的成员向政府交 1 元注册费，只有一名成员的团体不再组建新社团。上述过程直到不能继续进行下去为止。求政府总共收到的注册费的最大值和最小值。最大值的答案形如\frac{k}{2}n(n+1) + m，最小值的答案形如(\lceil\log_2n\rceil+p)n-q^{\lceil\log_2n\rceil}，请给出k+m+p+q的值。
user
3
rule
设整数 n\geq2. 某天 n 个人组成了一个社团，每人向政府交 1 元注册费。接下来每天都发生如下事情：每一个前一天组建的社团都分裂成两个团体，其中含至少两人的团体组建成一个新社团，每个新社团的成员向政府交 1 元注册费，只有一名成员的团体不再组建新社团。上述过程直到不能继续进行下去为止。求政府总共收到的注册费的最大值和最小值。最大值的答案形如\frac{k}{2}n(n+1) + m，最小值的答案形如(\lceil\log_2n\rceil+p)n-q^{\lceil\log_2n\rceil}，请给出k+m+p+q的值。
train