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
给定整数 $n \geq 2$. 在 $n \times n$ 方格表的每个小方格中各填入一个不超过 $n$ 的正整数, 使得每一行填入的数从左至右不减, 每一列填入的数从上至下不减。若两个有公共边的小方格填入的数相同，则称这两个（无序的）小方格为一个"好对"。求好对个数的最小可能值。当 $n = 4$ 时，求最小可能的好对个数。
user
4
rule
给定整数 $n \geq 2$. 在 $n \times n$ 方格表的每个小方格中各填入一个不超过 $n$ 的正整数, 使得每一行填入的数从左至右不减, 每一列填入的数从上至下不减。若两个有公共边的小方格填入的数相同，则称这两个（无序的）小方格为一个"好对"。求好对个数的最小可能值。当 $n = 4$ 时，求最小可能的好对个数。
train