<|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
 It is known that in a past chess tournament, all players were matched into pairs in each round, and the loser was eliminated (there were no draws). It is known that the winner played 6 games. How many participants in the tournament won at least 2 more games than they lost? 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
8
It is known that in a past chess tournament, all players were matched into pairs in each round, and the loser was eliminated (there were no draws). It is known that the winner played 6 games. How many participants in the tournament won at least 2 more games than they lost?
test