<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 An equilateral triangle with side length 3 is divided into nine triangular cells, as shown in the figure. Initially, zeros are written in these cells. In one move, you can choose two numbers located in adjacent cells and either add one to both or subtract one from both. Petya wants to make several moves so that after these moves, the cells contain, in some order, consecutive natural numbers $n, n+1, \ldots, n+8$. For which $n$ can he achieve this? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
2
An equilateral triangle with side length 3 is divided into nine triangular cells, as shown in the figure. Initially, zeros are written in these cells. In one move, you can choose two numbers located in adjacent cells and either add one to both or subtract one from both. Petya wants to make several moves so that after these moves, the cells contain, in some order, consecutive natural numbers $n, n+1, \ldots, n+8$. For which $n$ can he achieve this?
test