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"面包圈"是指从 (a+2)\times(b+2) 矩形的中间去掉 a\times b 矩形后得到的由 2a+2b+4 个单位方格构成的环，其中 a,b 是任意正整数.考虑无限大的方格表. 对每个偶数 n\geq8，一个"n-阶面包店"是指由有限个方格构成的集合 S，满足对任意一个由 n 个方格构成的面包圈 B，存在与 B 全等（可平移和旋转）的面包圈，其方格都属于 S. 用 f(n) 表示 n-阶面包店中方格数的最小可能值.求实数 \alpha，使得对任意充分大的偶数 n，均有\df{1}{100}<\df{f(n)}{n^\alpha}<100.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
user
5
rule
一个"面包圈"是指从 (a+2)\times(b+2) 矩形的中间去掉 a\times b 矩形后得到的由 2a+2b+4 个单位方格构成的环，其中 a,b 是任意正整数.考虑无限大的方格表. 对每个偶数 n\geq8，一个"n-阶面包店"是指由有限个方格构成的集合 S，满足对任意一个由 n 个方格构成的面包圈 B，存在与 B 全等（可平移和旋转）的面包圈，其方格都属于 S. 用 f(n) 表示 n-阶面包店中方格数的最小可能值.求实数 \alpha，使得对任意充分大的偶数 n，均有\df{1}{100}<\df{f(n)}{n^\alpha}<100.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
train