<|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
 In the land of Chaina, people pay each other in the form of links from chains. Fiona, originating from Chaina, has an open chain with  $2018$  links. In order to pay for things, she decides to break up the chain by choosing a number of links and cutting them out one by one, each time creating  $2$  or  $3$  new chains. For example, if she cuts the  $1111$ th link out of her chain first, then she will have  $3$  chains, of lengths  $1110$ ,  $1$ , and  $907$ . What is the least number of links she needs to remove in order to be able to pay for anything costing from  $1$  to  $2018$  links using some combination of her chains? 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
10
In the land of Chaina, people pay each other in the form of links from chains. Fiona, originating from Chaina, has an open chain with  $2018$  links. In order to pay for things, she decides to break up the chain by choosing a number of links and cutting them out one by one, each time creating  $2$  or  $3$  new chains. For example, if she cuts the  $1111$ th link out of her chain first, then she will have  $3$  chains, of lengths  $1110$ ,  $1$ , and  $907$ . What is the least number of links she needs to remove in order to be able to pay for anything costing from  $1$  to  $2018$  links using some combination of her chains?
test