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
在正方体的每个面上随机填人 $1$,$2$, $\cdots, 6$ 中的一个数字(各个面上的数字互不相  同）。再对八个顶点进行编号，使得每个顶点的编号数为其相邻三个面上的数字之积。则八个顶点的编号数之和的最大值为_____.
user
343
rule
在正方体的每个面上随机填人 $1$,$2$, $\cdots, 6$ 中的一个数字(各个面上的数字互不相  同）。再对八个顶点进行编号，使得每个顶点的编号数为其相邻三个面上的数字之积。则八个顶点的编号数之和的最大值为_____.
train